The use of potential field and seismological data to analyze the structure of the lithosphere beneath southern Africa Susan Jane Webb School of Geosciences, University of the Witwatersrand A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Doctor of Philosophy Johannesburg, 2009 Declaration I declare that this thesis is my own, unaided work. It is being submitted for the Degree of Doctor of Philosophy in the University of the Witwatersrand, Johannesburg. It has not been submitted before for any degree or examination in any other University. (Signature of Candidate) ____________day of ______________________ 200____ ii Abstract The Bouguer gravity anomaly of southern Africa ranges from low values of approximately -200 mGal in the Kaapvaal Craton to over 50 mGal in the Lebombo near the Mozambique border. Three major contributions to the long wavelength Bouguer gravity along a profile extending from Cape Town, South Africa to near Masvingo, Zimbabwe have been investigated: (1) large scale crustal features such as the Bushveld Complex and the Limpopo Belt (2) variations in the depth to the Mohorovi?i? discontinuity (Moho) and (3) upper mantle seismic velocity perturbations. Crustal thickness determinations from receiver function analysis from 82 sites were used to forward model the gravitational response due to Moho depth variations. These crustal thickness variations display little correlation with surface topography. The variations in the sharpness of phase weighted stacks of the receiver function results suggests regional varying density contrasts at the Moho correlating with geological terrain or crustal thickness. A change in crustal thickness of over 10 km results in a gravity anomaly amplitude at surface of ~120 mGal for a density contrast of 300 kg/m3 at the transition between the Namaqua Natal Mobile belt and the Kaapvaal craton, which is not observed in the measured gravity data. It appears probable that the ~350 km wide Bushveld Complex is connected laterally at depth within the crust. However, this dense layered mafic intrusion has a limited long wavelength gravity signal as it is compensated by significantly thickened underlying crust. iii iv The seismic velocity perturbations beneath southern Africa determined from delay time tomography were related to density variations and the gravitational response was calculated. If the seismic velocity perturbations are related to temperature (whereby fast velocities are related to cold, dense mantle), the amplitude of the resulting gravity anomaly is large (~60 mGal) and of the same sign as that due to the crustal thickness variations in the same region, resulting in impossibly large gravity values at the surface. However, if the mantle is depleted in the central keel and the seismic velocities are related to a ~1% density decrease due to composition variations, this then results in a ~60 mGal decrease in gravity. This negative gravity anomaly largely counterbalances the gravity anomaly due to the thinner crust and the combination very nearly fits the observed gravity data, including the classic observed high-low gravity signal at the edge of the craton. The depth extent of these mantle density variations cannot be well constrained by this modelling, but could be limited to the upper 150 km; below ~250 km the effect of the velocity perturbations on gravity at the surface is minimal. This thesis has shown that it is critical to incorporate measured crustal thicknesses and measured mantle velocity perturbations to accurately evaluate contributions to the gravity field. If crustal thicknesses are assumed based on topography, this may lead to incorrect conclusions about mantle composition and temperature. Acknowledgements The Kaapvaal Craton Project was one of the most exciting scientific projects I have been privileged to be involved in. It was made possible through a cooperative funding scheme involving the US National Science Foundation, the South African National Research Foundation and a generous group of cooperative mining companies: De Beers, Anglo American, RTZ, BHP, Goldfields. Eddie Kostlin ably recruited many companies to join the project. Rod Green made sure the stations were built and installed. The Council for Geoscience, especially Edgar Stettler, provided significant data and encouragement for this thesis. A full listing of Kaapvaal participants is available at: http://www.ciw.edu/kaapvaal. My thanks to all. A big thank you is extended to Maarten de Wit for getting things started at that most memorable of meetings in 1995 and for inviting me to be involved. Another big thank you to Tom Jordon, for inviting me to MIT for several extended visits and to the computer support people, graduate students and professors who all made me feel welcome and extended a warm helping hand with GMT, Matlab, and countless geophysical discussions, especially Eliza Richardson and Frederick Simons. Tim Grove and Ann Marie Riley opened their home to me and made me feel like family during my visits to Boston. The field work with Tim Grove was so full of adventures; it was always a surprise that the work was actually completed! Many thanks to everyone at the Carnegie Institution of Washington, one of the most amazing places to work in! So many people helped me while I was v vi there on a number of visits: thanks to: Sean Solomon, Mike Acerino, Sandy Keiser, Shaun Hardy, Alan Linde, Steve Shirey, Rick Carlson, Paul Silver, Suzanne van der Lee, Christel Tiberi (visitor), Matt Fouch, and John VanDecar for making me feel welcome. John VanDecar is especially thanked for making his gravity code available for this project and Matt Fouch for many late night discussions and the mantle tomography results. Kevin Burke hosted me during one of my visits to CIW and continues to inspire me during his many visits to Africa! My colleagues and friends in Africa are thanked for their continuous support throughout the project. Many thanks to: Peter Burkholder, Teresia Nguuri, Gordon Cooper, Spike McCarthy, Mike Jones, Marian Tredoux, Jane Gore, Mike Knoper and Paul Dirks. Teresia and Jane kindly provided me with their crustal thickness receiver function results. Gordon Cooper provided some superb software that was used in this project. David James has been a truly inspirational supervisor and has helped me ?back on the horse? every time it seemed impossible to keep going. His positive approach and genuine interest in my results helped so much. Dave and Jeri Thomson welcomed me into their home and made me feel like family! They truly made it possible for me to finish this thesis. Lew Ashwal, thank you so much for sharing your life and science with me. It has been a privilege to have the opportunity to work with all of you. Thanks to Colleen Carter, my Mom and Dad, who have been so supportive, even though I moved so far away. I love you, Dad. I miss you, Mom. Contents DECLARATION............................................................................................................................II ABSTRACT.................................................................................................................................. III ACKNOWLEDGEMENTS...........................................................................................................V LIST OF FIGURES ..................................................................................................................... IX LIST OF TABLES ................................................................................................................. XVIII LIST OF SYMBOLS AND NOMENCLATURE ....................................................................XIX 1 INTRODUCTION .................................................................................................................1 1.1 OUTLINE OF LITHOSPHERE FORMATION AND EVOLUTION ..............................................1 1.2 CONTINENTAL KEELS ...................................................................................................11 1.3 GEOPHYSICAL STUDIES OF CRATONIC REGIONS.............................................................18 1.4 THE KAAPVAAL CRATON..............................................................................................20 1.5 PURPOSE OF THIS STUDY AND OUTLINE OF THESIS ........................................................27 2 REGIONAL GEOLOGY AND GEOPHYSICS, DATASETS AND PREVIOUS STUDIES........................................................................................................................................32 2.1 OVERVIEW OF SOUTHERN AFRICAN GEOLOGY..............................................................32 2.1.1 Terrains and boundary features ..............................................................................38 2.2 REVIEW OF GEOPHYSICAL STUDIES OF THE LITHOSPHERE OF SOUTHERN AFRICA ........45 2.2.1 Upper crustal geophysical anomalies of southern Africa .......................................45 2.2.2 Regional Bouguer Gravity and Topographic Studies..............................................55 2.2.3 Deep Crustal studies ...............................................................................................59 2.2.4 Upper mantle studies...............................................................................................69 2.3 DATA SETS ...................................................................................................................71 2.3.1 Gravity Data............................................................................................................71 2.3.2 Magnetic Data.........................................................................................................74 2.3.3 Topographic Data ...................................................................................................74 2.3.4 Seismological Data: crustal thickness and delay time tomography results of the Southern African Seismic Experiment .....................................................................75 2.4 TECTONIC REGIONALIZATION OF SOUTHERN AFRICAN GEOLOGY.................................85 2.5 DISCUSSION ..................................................................................................................90 3 GRAVITY MODELING AND CRUSTAL THICKNESS OF SOUTHERN AFRICA.91 3.1 GRAVITY MODELING.....................................................................................................91 3.1.1 Two and two and a half dimensional Talwani methods...........................................93 3.1.2 Rectangular prism method (3D)..............................................................................95 3.1.3 Contour methods .....................................................................................................97 3.1.4 Facet method ...........................................................................................................99 3.1.5 Parker?s fast Fourier transform method ...............................................................100 3.1.6 Spherical prism .....................................................................................................103 3.2 ISOSTASY AND FLEXURE .............................................................................................107 3.3 COMBINED STUDIES OF GRAVITY, SEISMIC TOMOGRAPHY, AND OTHER GEOPHYSICAL DATA . ...................................................................................................................................112 3.3.1 Joint Inversion.......................................................................................................113 3.3.2 Isostasy and lithospheric buoyancy.......................................................................115 3.4 ANALYSIS OF SOUTHERN AFRICAN GRAVITY AND TOPOGRAPHY DATA .....................117 3.5 PREDICTED CRUSTAL THICKNESS OF SOUTHERN AFRICA BASED ON AIRY ISOSTATIC BALANCE .........................................................................................................................123 3.6 SEISMICALLY DETERMINED CRUSTAL THICKNESS OF SOUTHERN AFRICA....................125 3.7 MODELING OF GRAVITY DUE TO CRUSTAL THICKNESS VARIATIONS............................134 3.7.1 Forward modeling: 2.5D block model of profile B to B?......................................135 vii viii 3.7.2 Forward modeling: Parker?s FFT method...........................................................137 3.7.3 Forward modeling: 3D spherical prism method ..................................................140 3.7.4 Comparison between measured and modeled results............................................144 3.7.5 Discussion .............................................................................................................149 3.8 DENSITY CONTRAST AS A FUNCTION OF CRUSTAL THICKNESS AND GEOLOGICAL TERRAIN ...................................................................................................................................150 3.9 DISCUSSION ................................................................................................................159 4 GRAVITY MODELLING OF THE BUSHVELD COMPLEX ....................................164 4.1 WEBB ET AL. (2004) ...................................................................................................164 4.2 BUSHVELD COMPLEX..................................................................................................177 4.3 CONSTRAINTS ON GRAVITY MODELING OF THE BUSHVELD COMPLEX FROM EXISTING GEOPHYSICAL DATASETS .................................................................................................185 4.3.1 Initial geological model of the Bushveld Complex ................................................185 4.3.2 Prior gravity and resistivity modeling...................................................................186 4.3.3 Reflection seismic data..........................................................................................193 4.3.4 Seismic receiver function and crustal velocity models of the Kaapvaal Project ...201 4.3.5 Magnetic studies....................................................................................................201 4.4 GRAVITY MODELING OF A CONNECTED BUSHVELD COMPLEX ....................................204 4.4.1 Geological arguments for a connected Bushveld Complex ...................................210 4.4.2 Gravity Data..........................................................................................................212 4.4.3 Constrained Gravity Model...................................................................................212 4.4.4 Discussion of the constrained gravity model.........................................................214 4.5 SUMMARY...................................................................................................................215 5 INFLUENCE OF VELOCITY VARIATIONS IN THE UPPER MANTLE ON THE BOUGUER GRAVITY OF SOUTHERN AFRICA............................................................218 5.1 RELATIONSHIP BETWEEN DENSITY AND SEISMIC VELOCITY VARIATIONS (B) ..............219 5.2 ISOPYCNIC DISCUSSION AND THERMAL CONSIDERATIONS..........................................225 5.3 FORWARD MODELING .................................................................................................226 5.3.1 2.5 D Gravity Modeling.........................................................................................227 5.3.2 3D Gravity Modeling.............................................................................................229 5.4 COMBINED MODELING OF DATA SETS..........................................................................244 6 CONCLUSIONS AND FUTURE DIRECTIONS...........................................................254 6.1 MAJOR CONCLUSIONS OF THIS STUDY.........................................................................254 6.2 DISCUSSION AND DIRECTIONS FOR FUTURE RESEARCH..............................................261 7 REFERENCES ..................................................................................................................267 8 APPENDICES....................................................................................................................292 APPENDIX A ..............................................................................................................................292 APPENDIX B ..............................................................................................................................328 APPENDIX C ..............................................................................................................................337 APPENDIX D ..............................................................................................................................353 APPENDIX E ..............................................................................................................................358 List of Figures Figure 1.1 Generalized schematic cross section through the Earth illustrating the main types of plate boundaries. The creation of oceanic crust occurs at mid ocean ridges and it is destroyed at subduction zones. The creation, preservation and destruction of continental lithosphere are not as well understood. The Low Velocity Zone (LVZ) occurs at the lithosphere asthenosphere boundary beneath the oceanic crust and is at a depth of 50-100 km. Low seismic wave velocities, high seismic energy attenuation and high electrical conductivity, all of which are indicative of partial melting, characterize the oceanic LVZ (Condie, 1997). A distinctive LVZ is generally absent beneath continental crust (Freybourger et al., 2001), although the Lehmann discontinuity (the lower boundary of the LVZ) has been identified beneath some platform regions and may be due to a change from anisotropic to isotropic material within the tectosphere (Gaherty and Jordan, 1995; Grand and Helmburger, 1984). Diagram modified from Vigil (1999)...............................2 Figure 1.2 Map of the age of the ocean floor developed from magnetic stripes on the ocean floor and micro palaeontological dating of samples retrieved from the ocean floor. The youngest ages are at the ridges shown in red, oldest ages in deep blue are about 180 Ma. Image from http://www.ngdc.noaa.gov/mgg/fliers/96mgg04.html by Sclater et al. (1980). ............................................................................................................................................3 Figure 1.3 The flexure of the oceanic lithosphere due to an applied load such as a volcanic island. The elastic thickness is a measure of the thickness of an ideal elastic plate (pink) that behaves the same as the lithosphere (crust and uppermost mantle) beneath an applied load. In the oceans the elastic thickness increases with the age of the oceanic crust (Watts, 1978). (Image modified from: http://www.earth.ox.ac.uk/Research/marine/litho.htm and Watts, 1978) ...........................5 Figure 1.4 Map of ages of the continental crust that demonstrates a significantly more complex pattern for ages than that for the ocean floor as seen in Figure 1.2. Yellow are Meso - Cenozoic, light blue are Palaeozoic, purple are Palaeoproterozoic, light green are Mesoproterozoic, pink are Neoproterozoic, and orange are Archaean rocks. Oceans are shown in grey (0-20 Ma), medium blue (20-65 Ma) and dark blue (>65 Ma). The continental crust has undergone significantly more lateral deformation than has the oceanic crust, but its additional buoyancy helps to preserve the record of deformation in the rocks (Dewey, 1988). Image from: http://quake.wr.usgs.gov/research/structure/CrustalStructure/database/maps.html. ...........7 Figure 1.5 Model illustrating the formation of the earliest Archaean continents from the stacking of collision zones of oceanic crust and mantle. It is hypothesized that when these stacks are thick enough they partially melt to form granite. (Directly from Hart et al. (1997b), their Figure 1.) ....................................................................................................................9 Figure 1.6 Postulated growth curves for the continental crust after Ashwal (1989). The estimates vary from nearly steady state (F) to more gradual growth through time (H&R). Key: F- (Fyfe, 1978), A-(Armstrong, 1981), B-(Brown, 1979), R&S-(Reymer and Schubert, 1984), D&W-(Dewey and Windley, 1981), O?N-(O'Nions et al., 1979), Al-(All?gre, 1982), M&T-(McLennan and Taylor, 1982), N&D-(Nelson and DePaolo, 1985), P&A- (Patchett and Arndt, 1986), V&J-(Veizer and Jansen, 1979), H&R-(Hurley and Rand, 1969). ................................................................................................................................11 Figure 1.7 A generalized global distribution of exposed Archaean provinces (in black). Grey areas are regions that are presumed to be underlain by Archaean rocks by Martin (1994), Goodwin (1991) and Condie (1981). Diagram from Martin (1994). The numbers refer to the exposed Archaean regions as: 1-Baltic shield, 2-Scottish shield, 3-Ukrainian shield, 4-Anabar shield, 5-Baikal, Sayan and Yienisei fold belts, 6-Aldan shield, 7-Sino-Korean, Tarim and Yangtze Cratons, 8-Indian shield, 9-Litchfield, Rul Jungle and Nanambu complexes, 10-Pilbara block, 11-Yilgarn block, 12-Napier complex, 13-Kaapvaal Craton, 14-Zimbabwe Craton, 15-Zambian block, 16-Kasa? Craton, 17-Central Africa Craton, 18- Ethiopian block, 19-Chaillu Craton, 20-Cameroon N?tem complex, 21-Man shield, 22- Tuareg shield, 23-Reguibat shield, 24-Rio de la Plata and Luis Alves massifs, 25-S?o ix Francisco Craton, 26-Guapore Craton, 27-Guiana shield, 28-Wyoming province, 29- Superior province, 30-Kaminak group, 31-Committee Bay block, 32-Slave province, 33- Labrador shield, 34-Greenland shield. ..............................................................................13 Figure 1.8 A schematic diagram illustrating the isopycnic hypothesis. If there is an increase in seismic velocity, the change could be due to a decrease in temperature or an increase in Magnesium number (Mg#), where the Mg# is defined as: Mg/(Mg + Fe). It is impossible to determine the cause of the seismic velocity variation based only on seismic velocities. However, an increase in the Mg# will cause a significant decrease in the density, whereas a decrease in temperature will cause a significant increase in density. These density variations should be apparent in the gravity data, especially when comparing cratonic keels with oceanic lithosphere. .........................................................................................15 Figure 1.9 An illustration of the isopycnic hypothesis. The top diagram shows contours for shear velocities, demonstrating that the shear velocity beneath the Archaean craton is higher than the surrounding Phanerozoic region due to the presence of a thick keel of depleted mantle. The isopycnic hypothesis is illustrated in the bottom diagram, where densities of positions A and B are compared at standard conditions and at mantle conditions. Image modified from (Jordan, 1979a). ........................................................................................16 Figure 1.10 Summary diagram of Re-Os model ages obtained from kimberlite xenoliths. There is a distinctive change between on- and off-craton mantle ages. The Premier kimberlite results appear to have been significantly affected by the emplacement of the Bushveld Complex at 2.054 Ga. The light yellow is the known extent of the Kaapvaal-Zimbabwe Craton, and the flesh color is the extent of the Limpopo Belt. Diagram from Carlson et al. (2000)................................................................................................................................21 Figure 1.11 Some important geological features of southern Africa and tectonic boundaries. The mafic intrusives in green are: Bushveld Complex and the Molopo Farms Complex, both of which are ~2054 Ma in age, and are connected by a prominent linear feature known as the Tabazimbi Murchison Lineament (TML) (Buick et al., 2001; Walraven et al., 1990). The Great Dyke is ~2571 Ma (Wingate, 2000), and Trompsburg is ~1915 Ma (Maier et al., 2003)). The darker greens are greenstone belts in South Africa: Barberton, Amalia, Kraaipan, Madibe, Pietersburg, Giyani,and Murchison. The location of the Morokweng impact structure is shown in blue, althought the extent of this feature is poorly constrained and the Vredefort impact structure is located in the center of the Witwatersrand Basin. The edges of the cratons and many of the geological features are constrained by the gravity (Figure 1.14) and magnetic (Figure 1.15) data. Full reference list included with Figure 2.1. ............................................................................................22 Figure 1.12 Geological subdomains of the Kaapvaal Craton as defined by de Wit (1992) on the basis of a summary of age data, with southern African seismic experiment stations overlain. The Colesburg lineament has its southern extent between the Colesburg Terrain and the Southern Terrain. The northern extent of the Colesburg lineament is poorly defined on both magnetic and gravity data. In this case it has been drawn with very limited extent. The locations of the Kaapvaal Craton Project seismic stations are shown for reference; unfortunately the spacing between stations is too large to use the seismic data to accurately resolve the detailed subdomains in the Kaapvaal Craton.....................23 Figure 1.13 Broadband seismometer station locations of the southern African seismic experiment (SASE). See Figure 1.11 for geological details. The blue stations of the Kaapvaal Seismic Array (KSA ? circles) were deployed for the first year of the experiment and then transferred to the red station locations. The yellow stations were deployed for the full two year period. While the SAGEO stations (black triangles) provided improved coverage for locations of local events they were short period stations and not used for the teleseimic data analysis, although they provided useful data for comparison purposes (Webb et al., 2001). The GSN stations SUR, BOSA, LBTB, were incorporated in the KSA data set. The Kimberley Telemetered Array (KTA ? green squares) was deployed for a period of 6 months in the region around Kimberley. The German experiment in Namibia known as MAMBA deployed five seismometers in Namibia for a period of roughly a year. They also included an analysis of the GSN station TSUM in their project. ..........................................................................................................................................25 Figure 1.14 Compilation of Bouguer gravity data for southern Africa. Data were supplied by the Council for Geosciences from the SADC database. Compare with Figure 1.11 for the x locality of prominent geological features such as the Bushveld and Trompsburg Complexes. .......................................................................................................................29 Figure 1.15 Compilation of airborne magnetic data for southern Africa from the Council for Geosciences SADC database. Geological features such as the Colesburg lineament and the Vredefort impact structure are readily apparent. These data have been used to map the edges of the cratons and other prominent geological features that are partially covered by younger materials.........................................................................................................30 Figure 2.1 Broad geological domains of southern Africa in the region of the Southern African Seismic Experiment (SASE). The Kimberley block is the part of the Kaapvaal Craton west of the Colesburg Lineament, while the Witwatersrand block is the cratonic region east of the Colesburg Lineament. Compiled from: (de Wit et al., 1992; Hunter, 1975; Key and Ayres, 2000; Knoper, 1992; Pretorius et al., 1986; Reichardt, 1994; Stettler et al., 2000; von Biljon and Legg, 1983). Only the larger greenstone belts in South Africa are shown, as they are indicative of the large scale trends in the Craton. The greenstone belts of Zimbabwe are much more numerous and complicated and were left off of this map for clarity, as have the smaller greenstone belts in South Africa. The reader is referred to (Blenkinsop et al., 1997; de Wit and Ashwal, 1997b; Jelsma and Dirks, 2000; Jelsma and Dirks, 2002) for detailed discussion of southern African greenstone belts. ...33 Figure 2.2 Magnetic data of southern Africa from a grid of data provided by the Council for Geoscience. The magnetic data were used to help define the outline of the Kaapvaal and Zimbabwe Cratons and several prominent features such as the Bushveld Complex and the Witwatersrand Basin and Vredefort impact structure (Stettler et al., 2000). The geological outlines have been left off of this map to emphasize the data. ........................34 Figure 2.3 Gravity data of southern Africa from data provided by the Council for Geoscience. The gravity data have been used to help define the outline of the Kaapvaal and Zimbabwe Cratons and several prominent features such as the Bushveld Complex and the Witwatersrand Basin and Vredefort impact structure (Fourie et al., 2005). The geological outlines were left off to emphasize the data......................................................................35 Figure 2.4 Crustal domains as defined by de Wit (1992). The Colesburg Lineament starts in the south as the feature between domains 9 and 10. It is more difficult to trace northwards. Diagram modified from de Wit (1992). Ages compiled from (Brandl and de Wit, 1997; de Wit et al., 1992; Poujol et al., 2005; Schmitz et al., 2004)...........................................40 Figure 2.5. Locations of crustal thickness studies with relevant references excluding the results of the Southern African Seismic Experiment. The details of these results can be found in Table 2.1, this map simply demonstrates the locations of deep crustal studies. ...............61 Figure 2.6 Image of more reliable seismic crustal thickness estimates from studies from 1959- 2000. See Table 2.1 for details and Figure 2.5 for reference information. Due to complications and ambiguity of seismic results in the Limpopo Belt, these results were left off of this map. This map does not include any results from the Southern African Seismic Experiment. .........................................................................................................62 Figure 2.7 Bouguer gravity data station locations of South Africa, Botswana and Zimbabwe as of 2000, as compiled by the Council for Geoscience (South Africa). For imaging purposes data were gridded to a 1 km grid cell size. The data coverage is uneven as large amounts of data are collected along roadways. ...............................................................................73 Figure 2.8 Digital terrain model of southern Africa from GTOPO30 sun-shaded from the northwest. On land the data were gridded at a spacing of 1 km. Offshore data are from (Smith, 1997). Geologic terrains overlaid, as shown in Figure 2.1..................................75 Figure 2.9 Stations of the main Kaapvaal Seismic Array (KSA), a component of the Southern African Seismic Experiment. These stations include stations deployed as part of the Kaapvaal Project , plus 4 permanent stations shown as light blue squares (SUR, BOSA, LBTB and TSUM) of the global seismic network (GSN) that were included in the interpretation. Stations were serviced from four service centers shown as circles with a plus sign, at Cape Town, Kimberley, Johannesburg, and Mashvingo. Crustal thickness determinations were made at all of these sites. These stations were also used in the tomographic inversion for seismic velocity variations. ....................................................77 Figure 2.10 The components of station 47 of the Kaapvaal Seismic Stations. A. The field- hardened hard drive and data acquisition system inside the ?dog house?. B. The dog house with solar panels and GPS receiver, C. The interior of the dog house with the xi electric board and batteries. Note that the batteries are well away from the other electronic components to minimize corrosion due to battery fumes. D. The STS2 seismometer in the 50 gallon drum. The cable has no tension in it and the connecting pipe is isolated with spray foam........................................................................................78 Figure 2.11 The receiver function technique is based on the conversion of P-waves to S-waves at a boundary with a prominent seismic velocity contrast. Diagram provided by Ammon (1997) and used with permission. In the case of determining crustal thicknesses the boundary used is the Moho. The results that were used in this study only include the single P to S conversion (Nguuri et al., 2001) where results from waves from a variety of azimuths were averaged....................................................................................................81 Figure 2.12 Crustal thickness variations determined using the phasing depth method of receiver function analysis from Nguuri et al. (2001). .....................................................................82 Figure 2.13 The grid spacing used for the determination of seismic wave speeds. The same grid spacing of 1/2? by 1/2? lateral grid interval and 50 km vertical grid interval has been used in the gravity calculations. Diagram from Fouch et al. (2004). .......................................84 Figure 2.14 View of the world centered on the Kaapvaal Seismic Array showing the azimuthal distribution of events used in calculating the delay time tomography for P-waves on the left and S-waves on the right Diagram from Fouch et al. (2004)......................................85 Figure 2.15 Delay time tomography results shown for a slice at 150 km depth. Diagram from (Fouch et al., 2004). ..........................................................................................................86 Figure 2.16 Tectonic regionalization of southern Africa in the region of the Kaapvaal Project seismic experiment represented as 0.5? x 0.5? cells. The region labeled ?unknown? is known to be underlain by Archaean ages due to xenoliths and diamonds in kimberlites such as Orapa. However, some of this region may also include an extension of the Limpopo Belt (Ranganai et al., 2002). In the legend the squares are surrounding mobile belts and the circles are cratonic regions...........................................................................89 Figure 3.1 The geometry used in the development of the Talwani et al. (1959) algorithm for calculating the gravitational anomaly due to a 2D source. In the upper diagram the source is seen to extend to great distance in the y-direction. In the lower diagram the smooth outline of the cross section is replaced by an n-sided polygon, which is used for integration. Diagram modified from Blakely (1995). ......................................................94 Figure 3.2 The geometry of the rectangular prism method. The gravitational attraction at position P(x, y, z) due to the cubes can be calculated from repeated calls to a subroutine containing the analytic solution for a cube. Diagram modified from Blakely (1995).......96 Figure 3.3 Illustration of the geometry used in the stacks of lamina method. Thin lamina are used to build up the three dimensional source. For sources that are easily converted to contours, such as topography, these methods are ideal. Diagram modified from Blakely (1995)................................................................................................................................98 Figure 3.4 By using Gauss?s Law, a three dimensional body can be approximated as a series of faces (or facets) and the gravity of complex bodies calculated from accounting for each individual face by using an analytic expression. Diagram modified from Blakely (1995). ........................................................................................................................................100 Figure 3.5 Definition of terms for the Fourier transform determined for a point source at Q and measured at a position P. Figure modified from Blakely (1995). ..................................101 Figure 3.6 The geometry used for Parker?s Fast Fourier Transform method. The value of gravity due to the shaded surface which has a constant density contrast across it, is calculated at a position P(x,y,z). Diagram modified from Parker (1972). .............................................103 Figure 3.7 There exists no analytic solution for the calculation of the gravity field due to a spherical prism on the surface of a sphere and numerical methods would be unwieldy for the broad scale case being considered here. However, the gravity field can be approximated by using small spheres of the same volume and center of mass to approximate the small cubes and by ensuring that the sources are far enough away (Lees and VanDecar, 1991). Diagram modified from (Smith et al., 2001)..............................104 Figure 3.8 Geometry for determining the vertical component of gravity at position A on the surface of the sphere for a mass element located at B beneath the spherical surface. Diagram modified from Heiskanen and Meinesz (1958, pg 162). ..................................106 Figure 3.9 Geometry comparing the spherical prism and a sphere of the same volume. A sphere is used in the calculation which has the same volume and center as the spherical prism. The xii vertical component of gravity due to a mass element is calculated on another spherical surface some distance above the surface containing the sources at a point P. ................107 Figure 3.10 The principle of Airy isostatic balance: Equal columns have equal mass above a reference level called the isostatic compensation depth. Airy isostatic balance implies that there is zero horizontal strength and topography is perfectly compensated by a root of its mirror reflection. ........................................................................................................109 Figure 3.11 An illustration of Pratt isostatic balance for crustal blocks of varying density. Here the density varies laterally to produce topography with a constant depth of compensation. Diagram modified from Blakely (1995). ........................................................................110 Figure 3.12 Airy-Heiskanen local vs. Vening-Meinesz regional compensation models for a topographic load against a flat layered background model (modified from Watts (2001). ........................................................................................................................................111 Figure 3.13 Southern Africa Bouguer gravity data compilation. Data are from the Council for Geoscience, South Africa and have been gridded to 1 km. The overlay includes the tectonic regionalization and some important geological features, such as the Bushveld Complex and the Witwatersrand Basin...........................................................................118 Figure 3.14 Topography of southern Africa with seismic station locations of the Southern Africa Seismic Experiment overlain. Blue stations were moved after year 1 to the positions of the red stations. The yellow stations were left in place for the entire two year period. Refer to Figure 2.9 for station numbers. .........................................................................119 Figure 3.15 Plot of ~100,000 Bouguer gravity stations in the South African Council for Geosciences database plotted against elevation determined at the position of measurement. The colored lines plotted are for different density values that could be used in the Bouguer correction. The value of 2.67 gm/cm3 has been used for the correction in the database. The ?smear? of data at 0 m elevation is due to values along the coast where the crust is thinning resulting in large gravity values. Values above the line are under compensated and values below the line are overcompensated for the Bouguer density selected. The majority of values are under compensated indicating that the elevations are too large for the root, suggesting that the high elevations in southern Africa are supported by a mechanism other than crustal isostatic balance.......................................................120 Figure 3.16 Schematic comparison of overcompensated and undercompensated topography. The crustal density is given by ?c, the mantle density by ?m, and the Airy thickness by tc. ...121 Figure 3.17 Plot of Bouguer gravity vs. elevation for the 82 seismic stations in the Southern African Seismic Experiemnt (SASE) using an averaged value within a 20 km radius circle around each station for elevation and Bouguer gravity values. Stations have been color coded by geological terrain as defined in Chapter 2. Station 54 occurs at the base of the great escarpment. Station 58 is ~100 km further east from the escarpment...................122 Figure 3.18 Predicted crustal thickness as determined from a simple Airy analysis of the topography data. No flexure or regional compensation has been included. Color bar is the same bar as used in Figures 2.12 and 3.19. ...............................................................124 Figure 3.19 Crustal thickness map combining results of previous seismic surveys and the SASE. Previous results, shown as pink diamonds and summarized in Table 2.1, are in good agreement with the SASE results of Gore, 2005 and Nguuri, 2004 (Table 3.1). Same color scale as Figure 3.18................................................................................................128 Figure 3.20 A comparison of elevations (averaged for 20 km radius around each station) and seismically determined crustal thicknesses from the 82 seismic stations of the SASE reveals no clear linear trends and only weak clustering of tectonic regions. ..................129 Figure 3.21 Histogram of seismically determined crustal thickness values for the 82 seismic stations in the SASE experiment. The histogram is bimodal. Data are from Table 3.1.130 Figure 3.22 A comparison of seismically determined crustal thicknesses and Bouguer gravity both of which were averaged across an area with a radius 20 km around each of the 82 seismic stations from the SASE. This plot reveals no clear linear trends and only weak clustering of cratonic regions. Compare this with Figure 3.17. ......................................................131 Figure 3.23 A comparison of seismically determined crustal thicknesses and those predicted using Airy isostatic balance (both averaged for a radius of 20 km around each station). The measured crustal thicknesses show more variation than the predicted variations. The straight line with 45? slope indicates a 1:1 correspondence between predicted and measured. ........................................................................................................................132 xiii Figure 3.24 A 2.5D model of the gravity response calculated from variations in crustal thickness, along a profile from Cape Town (B) to northern Zimbabwe (B?). The solid black line shows the calculated gravity due to the crustal thickness variation and the dotted green stars are the observed Bouguer gravity data. Crustal thickness variations shown are relative to an average value of 41 km thickness along this profile and were obtained from the gridded crustal thickness values sampled at 50 km intervals. The blocks are of limited strike length, 50 km in and out of the page. ....................................................................136 Figure 3.25 Schematic block model of the background crustal model for the determination of gravity from the Moho. The crustal layer from 0-30 km depth has a constant density value in this model, the 20 km thick layer from 30-50 km depth is divided in the middle at the average crustal thickness. The bottom layer from 50-100 km depth is a constant mantle density. In this model the absolute values of density are unimportant as only density contrasts are modeled. ........................................................................................137 Figure 3.26 Schematic model of the 3D variations in the crustal thickness represented by blue and red blocks. Red blocks represent thinner than average crust and densities higher than the background crustal density; blue blocks represent thicker crust and lower than background mantle density. ............................................................................................138 Figure 3.27 Surface gravity field determined from variations in the crustal thickness from a density contrast of 300 kg/m3 using the 3D Parker FFT method.................................................139 Figure 3.28 Gravity calculated on a spherical surface determined from variations in the crustal thickness using a density contrast of 300 kg/m3 at the Moho and the spherical prism method. Line of profile is shown on the map view.......................................................141 Figure 3.29 Mapped difference between the Parker FFT and the spherical prism method. Below are the profiles for the Parker FFT (red) and spherical prism method (green) where the black line shows the point by point difference between the two. The agreement between the methods is excellent. .................................................................................................143 Figure 3.30 Bouguer gravity data of southern Africa smoothed to preserve long wavelengths and clipped to the region of the SASE stations. The black profile is from the smoothed observed Bouguer gravity which has been placed for comparison next to the red curve which is determined from the modeled 3D gravity using the spherical prism method with a density contrast of 300 g /cm3 as determined in Figure 3.28........................................145 Figure 3.31 Comparison between the 3D Parker FFT method (light blue), the 3D spherical prism method (dark blue) and the 2.5D profile calculation (red) for the same profile and density contrast (300 kg/m3). The observed (pink) and smoothed (purple) gravity are included along the same profile for comparison purposes.............................................................146 Figure 3.32 A comparison of the 3D spherical prism model calculated gravity due to variations at the Moho for a variety of constant density contrasts across the Moho. The color and vertical scales have been kept the same for comparison purposes. A) 100 kg/m3, B) 200 kg/m3 C) 350 kg/m3, D) 450 kg/m3. Figure 3.28 shows the response for 300 kg/m3. ...148 Figure 3.33 Schematic diagram summarizing the various density depth relationships that were used to calculate the 3D gravity. Number 2 results in the gravity map and profile shown in Figure 3.34A; 3 to 3.34B; 4 to 3.34C; and 5 to 3.34D................................................153 Figure 3.34 Summary of calculations for 3D gravity where the density contrast between the crust and mantle varies with depth according to Table 3.2 and Figure 3.33. Model 2 in Figure 3.33 and Table 3.2 corresponds to the gravity calculated in 3.34A; Model 3, to 3.34B; Model 4 to 3.34C and Model 5 to 3.34D. .......................................................................154 Figure 3.35 Geological terrain map developed with cells of 0.5? size used here to examine the relationship between regional surface geology and density contrast at the Moho. .........156 Figure 3.36 Summary of calculations for 3D gravity where the density contrast between the crust and mantle varies according to geological terrain boundaries as summarized in Table 3.3. The gravity resulting from model 2 is shown in Figure 3.36A; from model 3 in 3.36B; from model 4 in 3.36C and from model 5 in 3.36D........................................................158 Figure 4.1 Locality map of the Bushveld Complex within southern Africa. Outcrops of the mafic portions of the Bushveld Complex rocks are shown in dark green. The Molopo Farms Complex which is the same age as the Bushveld Complex is just to the west of the Bushveld Complex is shown in light green. The Trompsburg Complex and Losberg intrusions are younger and are located south of the BC are also in light green. .............178 xiv Figure 4.2 Basic regional geology of the Bushveld Complex (BC) showing the four main lobes (Western, Northern, Eastern and Bethel) and the Far Western Lobe. Dashed lines trace the inferred Rustenburg layered suite (RLS) subcrop based on gravity, magnetic and geology data (van der Merwe, 1978). The Rooiberg Group represents early crustal melt synchronous to the emplacement of the mafic rocks of the BC. The Rashoop Granophyre Suite and the Lebowa Granite Suite are late stage granites associated with the BC. In the interior of the BC there are fragments of Traansvaal floor rocks such as the Crocodile River fragment, Rooiberg fragment, Dennilton dome and Marble Hall fragment. Several alkaline intrusions (Pilanesberg, Pienaars River, and Spitskop) intruded long after the BC. There are also several kimberlites in and around the BC of various ages including Premier, Palmietgat and Maarsfontein. The BV-1 borehole in the Northern Lobe has been used to measure a significant number of susceptibility and density values discussed in Appendix A. Diagram modified from Vermaak and Von Gruenewaldt (1986).........179 Figure 4.3 Stratigraphy of the layered ultramafic ? mafic sequence of rocks of the Bushveld Complex Diagram from Eales and Cawthorn (1996)......................................................181 Figure 4.4 A lopolith model of the Bushveld Complex, as originally proposed by Hall (1932), illustrated here by du Toit (1954). Note that the lopolith is not shown as continuous but rather as disrupted by later intrusions and tectonic events. .............................................185 Figure 4.5 Cousins (1954) discarded a lopolith model for the Bushveld Complex (BC) because measured gravity values are reduced to background values in the center of the BC as illustrated here. The top diagram (a) shows the measured gravity over an east-west profile through the BC. The middle diagram (b) demonstrates that the calculated values for gravity are significantly elevated above background values in the central portion if a lopolith model is used. Cousins (1954) solved the discrepancy by postulating the existence of well separated intrusions as shown in (c). Note that no depth scale is presented and that the gravity effect of a massive lopolith on the deeper crust and upper mantle is not considered. Similar models were produced by Smit (1961) and Smit (1962). ........................................................................................................................................187 Figure 4.6. An example of the dipping sheet model for the Bushveld Complex based on the analysis of gravity data and resistivity data (Meyer and de Beer, 1987). Note the extreme vertical exaggeration in the model as the length of the profile is 400 km, and the vertical depth extent displayed is 15 km. .....................................................................................189 Figure 4.7 Example of deep DC resistivity soundings from Meyer & de Beer (1987). The data for site 85 has been reexamined in the model in Figure 4.8. Note that in this diagram no data points are present beyond AB/2 of 30,000 m. Also curves 119 and 85 have not yet flattened out indicating that the depth of penetration at these sites was insufficient. .....190 Figure 4.8 Forward model of resistivity sounding number 85 from Meyer & de Beer (1987) using values from their geo-electric stratigraphy. Only the first three layers define the curve and the second layer has an unrealistic thickness, also used by Meyer and de Beer (1987). This illustrates that the model is ambiguous in terms of determining the 3D geometry of the BC. ............................................................................................................................191 Figure 4.9 Simplified model of the relationship between the intrusive Bushveld Complex and the sedimentary rocks of the Transvaal sequence from Cawthorn (1998). The dip of the underlying Transvaal sediments is steeper than the intruding Bushveld Complex implying that the basin could have been actively subsiding just prior to the emplacement of the Bushveld Complex..........................................................................................................192 Figure 4.10 Map of resistivity sounding locations from Meyer & de Beer (1987). They conclude that region 2 is not underlain by conductive rocks. However, Bushveld Complex mafic rocks have been intersected in drill cores in 2 locations inside this zone at A and B (Cawthorn, pers. comm., 2003 and Walraven, 1987). ....................................................193 Figure 4.11 Map of the Bushveld Complex showing the location of published seismic lines labeled 1 through 5, details of which are discussed in the text. In the Far Western Lobe, lines Rz-254 and Rz-256 were published by Tinker et al. (2002)...................................195 Figure 4.12. Scanned images of published data from lines 1 and 2 shown in Figure 4.11 after Campbell (1990) and Maccelari et al. (1991a). The salient features discussed in the text are apparent. (1s TWT = ~3 km depth)..........................................................................196 Figure 4.13 Gravity data of the Bushveld Complex and surrounding regions, showing seismic stations of the Kaapvaal Craton Project. The outcrop of mafic rocks of the Bushveld xv Complex has been outlined; the gravity data clearly delineate the Bethal Lobe to the south covered by younger rocks. The gravity high ?tongue? that was investigated by seismic line 2 is highlighted by the arrow. Gravity data from the Council for Geoscience (Venter et al., 1999). ....................................................................................................................198 Figure 4.14 Scanned images of published data from lines 3 and 4. The salient features discussed in the text are apparent. Diagrams from Odgers and du Plessis (1993) and Odgers et al. (1993)..............................................................................................................................200 Figure 4.15 Magnetic data of the Bushveld Complex (BC) and surrounding region with locations of the seismic stations of the Kaapvaal Craton Project shown. The red line in the Northern Lobe shows the suggested western extent of the Nothern Lobe and the red line in the southern portions shows the extent of the Bethel Lobe. The bent red line to the east of the Bushveld Complex traces the main directions of dyke swarms to east of the BC. It appears that the BC may have affected the strength of the crust and deflected dykes around it. Black diamonds denote kimberlite localities and colored circles Kaapvaal Project seismic stations. Underlying color image is based on data from Stettler et al. (2000) and the overlying higher resolution black and white image is from Ayres et al. (1998)..............................................................................................................................203 Figure 4.16 Contoured crustal thickness data in km in the region of the Bushveld Complex with locations of the seismic stations of the Kaapvaal Craton Project shown. The crustal thicknesses from the stations along the profile have been projected to the profile in the panel beneath the image. Crustal thickness is measured from the surface to the Moho depth. The data clearly show a significant increase in crustal thickness beneath the Bushveld Complex (data from Nguuri et al., 2001). .......................................................207 Figure 4.17 Simplified model of the Bushveld Complex if no isostatic compensation by a crustal root zone at the Moho is considered. This illustrates the argument that Cousins (1959) used against a connected Bushveld Complex. Note the extreme vertical exaggeration.208 Figure 4.18 Simplified model of the Bouguer gravity data of the Bushveld Complex using a dipping sheet type model as used in Meyer and de Beer (1987). Again, note the extreme vertical exaggeration.......................................................................................................209 Figure 4.19 Simplified model of the Bouguer gravity data over the Bushveld Complex illustrating how crustal flexure due to the load of the Bushveld Complex can account for the observed gravity signal while still having a connected Bushveld Complex. ..................210 Figure 4.20 Bouguer gravity model for the Bushveld Complex from Webb et al. (2004). The dotted green line shows the observed data and the solid black line is the calculated result. This model has been constrained by the use of surface outcrop, measured density values, measured crustal thickness values and Vibroseis seismic data. However, details in the mid crust are unconstrained. Figure 4.17 covers the range from roughly 175 km to 550 km along a slightly different, but parallel, profile...........................................................213 Figure 4.21 Map showing the relationship between the Thabazimbi ? Murchison Lineament (TML), Bushveld Complex and the Molopo Farm Complex. There are several additional intrusions of Bushveld Complex age in Botswana that need to be considered in terms of the tectonic environment that produced such a large province of layered mafic complexes. Diagram from Cawthorn and Walraven (1998). .............................................................216 Figure 5.1 Radial model of IASPEI 91 P wave velocities and density values and Radslw which uses the IASPEI 91 values, but at 50 km intervals corresponding to the sizes of the tomographic cells. Radslw is equal to S0 in the equations above and samples the IASPEI values at 50 km intervals. Density and P wave values from IASPEI 91 (Kennett, 1991). ........................................................................................................................................221 Figure 5.2 Sample plot used to determine B value from a primitive spinel lherzolite of McDonough and Sun (1995) and a depleted spinel hartzburgite of James et al. (2004) where the seismic velocity and density have been calculated at 50 km depth and 450?C. Compare with the left hand side of Figure 1.8................................................................223 Figure 5.3. This diagram illustrates the maximum (pink) and minimum (blue) of density contrast values generated from the maximum and minimum slowness values from the tomographic output for each B value. The diagram is nearly symmetric, however, the maximum and minimum seismic velocity perturbations (and hence densities) in James et al. (2001) results are not exactly the same amplitude. For comparison Tiberi et al. (2001) xvi xvii uses B =5, ?? = 65 kg/m3. The light blue line is ?? = 34 kg/m3, which is ? 1% change in mantle density. ................................................................................................................224 Figure 5.4 Profile showing gravitational response due to density variations for a factor B = -2.4. This is based on composition variations and the reds are higher density whereas the blues are lower density. The variations below ~400 km contribute little to the signal. The solid black line is the calculated gravity and the green dotted line is the observed gravity along the profile B to B?. ..........................................................................................................228 Figure 5.5 Schematic background model for density variations. The density increases downwards in layers based on IASPEI. The blocks are 50 km in thickness. This schematic diagram does not show the curvature of the blocks, which is illustrated in Figure 3.9.................230 Figure 5.6 Schematic diagram showing density values determined from slowness values. In this diagram the crust has a constant density. The upper most mantle (depths < 50 km), which is poorly resolved using delay time tomography, is assigned the same density as is determined for the layer underneath which is the first layer of the tomographic model. 231 Figure 5.7 Slice through the P wave delay time tomography model from Cape Town (B) to Masvingo (B?) to a depth of 700 km showing velocity perturbations in percent (Fouch et al., 2004). This is the same profile as in Figures 5.4 and 3.13)......................................232 Figure 5.8 Map view of P wave delay time tomography values at a depth of 150 km showing velocity perturbations in percent (Fouch et al., 2004).....................................................233 Figure 5.9 Forward model of the gravity field resulting from the velocity variations determined from seismic travel time tomography using a temperature dependent value for B = 2.0 and calculating the response to a depth of 300 km. ...............................................................234 Figure 5.10 Forward model of the gravity field resulting from the velocity variations determined from P-wave delay time tomography using a compositionally dependent value for B = - 2.0 and calculating the response to a depth of 300 km. ..................................................236 Figure 5.11 Comparison of the gravity signal resulting from variations in the delay time tomography calculated (inclusively) to depths of: A) 150 km; B) 200 km; C) 300km ; and D) 400 km, all for B = -2.0. ............................................................................................238 Figure 5.12 Comparison of the gravity signal resulting from variations in the delay time tomography calculated for B values of A) -2.0, B) -3.0, C) -4.0, D) -5.0, to a depth of 300 km. ..................................................................................................................................241 Figure 5.13 Variations in gravity for a value of B = -2.4, which results from density variations of ~1% in the model. ...........................................................................................................243 Figure 5.14 Map of smoothed gravity data and profiles of the contribution from the Moho for a density contrast of 300 kg/m3and a mantle component using a value of B = -2.4. .........246 Figure 5.15 Map and profile comparing measured gravity (blue) and calculated gravity (black) from the combined Moho (red) and mantle (pink) components shown in Figure 5.14...247 Figure 5.16 Comparison of various gravity models using crustal models from Table 3.2 and which include the delay time tomography gravity contribution with a B value of -2.4. A) Density contrast from Zoback (see Table 3.2, Figure 3.34A). B) Density contrast from Fischer (see Table 3.2, Figure 3.34B). C) Moho density contrast from Table 3.2, model 4C. D) Moho density contrast from Table 3.2, model 5D. (Compare with Table 3.2 and Figures 3.33 and 3.34) ....................................................................................................249 Figure 5.17 Comparison of various gravity models using crustal models from Table 3.3 and which include the delay time tomography gravity contribution with a variety of B values. A) Regional geology model 4, with B = +4.0 B) Regional geology model 4, with B = -4.0. C) Regional geology model 5, with B = -2.4. D) Regional geology density model 6, with B = -2.4. (Compare with Table 3.3 and Figures 3.35 and 3.36)..............................250 Figure 5.18 Best fitting forward model using thick model 3, and a mantle factor of B = -2.4 (see Figure 5.16 B). ................................................................................................................252 List of tables Table 2.1 Summary of crustal thickness studies. Error estimates are based on estimates of similar studies where not specified in the cited study. This table does not include SASE results. ..........................................................................................................................................63 Table 3.1 Crustal thickness determinations from the Kaapvaal Project Southern African Seismic Experiment (SASE) as determined from receiver functions. Data are summarized from Gore (2005) and Nguuri (2004). Station locations are given in Figure 2.9....................126 Table 3.2 Summary of crustal models using density determined from thickness variations for 3D gravity calculation. The density for the interval is assigned to the spherical prisms at that depth. Models 1 to 5 are shown graphically in Figure 3.33. The letters A to D refer to the resulting gravity calculations shown in Figure 3.34. ......................................................152 Table 3.3 Summary of model density contrasts used to examine relationship between density contrasts assigned by geological terrains defined at the Moho and the resulting gravity anomaly. Details for models 1-5 are discussed in the text. ............................................157 xviii List of symbols and nomenclature SASE = Southern African Seismic Experiment KSA = Kaapvaal Seismic Array KTA = Kimberley Telemetered Array B = parameter relating density and seismic velocity F = Fourier transform gz = vertical component of gravity G = Gravitational constant k = wave number ? = spherical coordinate P = point at which gravity is calculated ? = density ? = spherical coordinate r = distance between source and point of calculation, also radial spherical coordinate S = slowness, inverse of velocity U = gravitational potential V = Volume of gravity source, seismic velocity x, y, z = Cartesian coordinates ?mn = gravitational attraction at a point m, due to a prism n R = Radius of the Earth xix 1 Introduction The Kaapvaal Craton Project was a multidisciplinary study which ran from 1996- 2002 and was initiated to investigate the formation, evolution and composition of the Kaapvaal Craton. The purpose of this thesis is to integrate the results from several different Kaapvaal project studies into a large scale gravity model that incorporates crustal thickness variations and seismic velocity variations in the mantle in an effort to provide constraints on models of formation. Because the velocity-density relationship in the mantle beneath the Kaapvaal Craton is dominated by compositional variations as opposed to more commonly assumed temperature variations, I briefly review the main differences between lithosphere formation in the oceanic and continental environments. 1.1 Outline of Lithosphere Formation and Evolution The levels of understanding of the thermal structure, age, composition and origin of the oceanic versus the continental lithosphere are vastly different. In spite of limited direct access due to the presence of oceans, the oceanic lithosphere has been well studied using geological, magnetic, palaeomagnetic, heat flow, gravity, bathymetry, seismological, micropalaeontological and geochemical data. This has resulted in a relatively well-constrained model of formation involving partial melting of the upper mantle due to adiabatic decompression at mid-ocean ridges (MOR) (e.g. Klein and Langmuir, 1987), and lithospheric destruction at subduction zones (Figure 1.1). The ages of mid-ocean ridge basalts (MORBs), determined by magnetostratigraphy based on magnetic field reversals and micro palaeontological studies of the first sediments deposited on the basalts, have been used to establish detailed age maps of the ocean floor 1 (Figure 1.2) (Sclater et al., 1981). Geochemical and seismic studies provide constraints on the mantle source compositions of basaltic rock and their hydrothermal reaction with seawater at the mid-ocean ridges (MORs) (Condie, 1997; Forsyth, 1996). Seismic studies using teleseismic, local seismic data, ocean bottom seismometers and reflection/refraction data have shown that the oceanic crust is between 5 and 10 km thick in most regions. Evidence from geochemistry and petrology suggest that melting near a MOR is limited to upper mantle depths beneath the ridge (Klein and Langmuir, 1987; Wyllie, 1988). The MELT experiment has substantiated that the region of melting beneath a MOR is broad and is apparently driven by viscous drag of the overlying plate (Melt Seismic Team, 1998). Figure 1.1 Generalized schematic cross section through the Earth illustrating the main types of plate boundaries. The creation of oceanic crust occurs at mid ocean ridges and it is destroyed at subduction zones. The creation, preservation and destruction of continental lithosphere are not as well understood. The Low Velocity Zone (LVZ) occurs at the lithosphere asthenosphere boundary beneath the oceanic crust and is at a depth of 50-100 km. Low seismic wave velocities, high seismic energy attenuation and high electrical conductivity, all of which are indicative of partial melting, characterize the oceanic LVZ (Condie, 1997). A distinctive LVZ is generally absent beneath continental crust (Freybourger et al., 2001), although the Lehmann discontinuity (the lower boundary of the LVZ) has been identified beneath some platform regions and may be due to a change from anisotropic to isotropic material within the tectosphere (Gaherty and Jordan, 1995; Grand and Helmburger, 1984). Diagram modified from Vigil (1999). 2 Figure 1.2 Map of the age of the ocean floor developed from magnetic stripes on the ocean floor and micro palaeontological dating of samples retrieved from the ocean floor. The youngest ages are at the ridges shown in red, oldest ages in deep blue are about 180 Ma. Image from http://www.ngdc.noaa.gov/mgg/fliers/96mgg04.html by Sclater et al. (1980). The thickness of the oceanic lithosphere, defined as the rigid outer layer of crust and upper most mantle capable of transmitting deviatoric (i.e. non hydrostatic) stresses (Elsasser, 1969), is measured seismically by the depth below which velocities of P and S waves decrease sharply. This velocity decrease, known as the Low Velocity Zone (LVZ), occurs at roughly 80 ? 120 km depths and appears beneath all oceanic regions studied to date (Figure 1.1) (Condie, 1997). As the oceanic crust moves away from mid-ocean ridges, it cools and becomes denser. The underlying melt-depleted mantle is also cooled by conduction and becomes firmly attached to the overlying crust, thickening with time. Eventually the lithosphere, comprising crust and uppermost mantle to the LVZ, becomes gravitationally unstable and sinks back into the mantle at subduction zones. The depth of the ocean is also dependent on the distance away from the mid-ocean ridge. For oceanic crust less than 70 Ma, depth to the oceanic basement varies as t1/2, where t is time, away 3 from the spreading centers (Sclater et al., 1980), although this relationship fails for regions older than about 70 Ma, beyond which lithospheric thickness appears to change little with age as the cooling from the top is balanced by heat added from below (Fowler, 2005; Nagihara et al., 1996; Stein and Stein, 1996). More detailed models of plate cooling, depth and thickness variations are summarized in Stein and Stein (1996) and Fowler (2005). The strength of the oceanic lithosphere to a load can be determined by examining the flexural response to a topographic load, such as a seamount or island chain, and determining an elastic thickness (Watts, 2001). The elastic thickness is a measure of the strength of the lithosphere when the lithosphere is approximated as an elastic plate (Figure 1.3) (Watts et al., 1980). The elastic thickness is determined from the correlation between free air gravity and topography. For short wavelength features (< 50-100 km lateral extent) the strength of the lithosphere will fully support the load and the lithosphere has a Bouguer response. For larger, longer wavelength features (>~1,000 km lateral extent) the load will be completely compensated; this is an example of local Airy isostatic balance. For loads of intermediate lateral extent between these extremes the response is flexural. The lithosphere will flex depending on its strength, and a corresponding elastic thickness can be determined. For the oceans, the elastic thickness is between 5 and 35 km, and correlates well with lithospheric age, indicating that the oceanic lithosphere gets stronger as it gets older (Watts et al., 1980). 4 Figure 1.3 The flexure of the oceanic lithosphere due to an applied load such as a volcanic island. The elastic thickness is a measure of the thickness of an ideal elastic plate (pink) that behaves the same as the lithosphere (crust and uppermost mantle) beneath an applied load. In the oceans the elastic thickness increases with the age of the oceanic crust (Watts, 1978). (Image modified from: http://www.earth.ox.ac.uk/Research/marine/litho.htm and Watts, 1978) Learning the history of oceanic lithosphere older than 180 Ma is more difficult owing to its lack of preservation. Ophiolite sequences up to several hundreds of m.y. old, represent variably preserved cross-sections of oceanic lithosphere (e.g. Christensen and Salisbury, 1975; Gass and Smewing, 1980), and indicate that the structure of oceanic crust in the past was similar to that which can be studied today. While Moores (2002) has suggested that ophiolites older than 1 Ga are thicker than younger ophiolites, the lack of complete and well preserved sections of old ophiolites has made this a difficult proposition to test. Thus, while there are exceptions, such as the Ontong-Java plateau (Neal et al., 1997) and other large oceanic igneous provinces, much of the oceanic lithosphere is well understood in terms of composition, vertical structure, age, strength, history and evolution using a model of mid ocean ridge spreading, formation through adiabatic decompression melting, conductive cooling and thickening, and finally destruction by subduction at oceanic trenches. 5 A similar level of understanding of the origin and evolution of the continental crust and lithosphere does not exist, despite its relatively greater accessibility and significantly longer temporal record (e.g. Ashwal, 1989; Carlson et al., 2005; de Wit, 1998). Multiple tectono-magmatic and metamorphic events have affected the continental crust and upper mantle for nearly the entirety of geologic time, making age mapping far more complex than in the oceanic crust (Figure 1.4) (Rudnick and Nyblade, 1999). The constituent rocks of the continents show far more diversity of composition and record more tectonic activity than those of the oceanic crust. Today, continental crust is formed by a variety of mechanisms, including the accretion of island arcs, intrusion of granites into existing continents and volcanism due to subduction, most of which can be understood in the framework of plate tectonics. Preserved continental crust represents nearly the entirety of Earth history, from the 3.96 Ga Acasta gneisses in the Slave Craton of Canada (Bowring et al., 1989) to rocks forming today, allowing direct studies to be made over a longer time period than for oceanic crust. However, the variability of preservation makes it difficult to determine with certainty if the same processes and conditions were dominant in the Archaean prior to 2.5 Ga. In fact, the presence of 250- 350 km thick low density, high seismic velocity keels observed beneath most Archaean cratons suggests that the higher temperatures in the Archaean made a significant difference in lithosphere formation (de Wit et al., 1992). 6 Figure 1.4 Map of ages of the continental crust that demonstrates a significantly more complex pattern for ages than that for the ocean floor as seen in Figure 1.2. Yellow are Meso - Cenozoic, light blue are Palaeozoic, purple are Palaeoproterozoic, light green are Mesoproterozoic, pink are Neoproterozoic, and orange are Archaean rocks. Oceans are shown in grey (0-20 Ma), medium blue (20-65 Ma) and dark blue (>65 Ma). The continental crust has undergone significantly more lateral deformation than has the oceanic crust, but its additional buoyancy helps to preserve the record of deformation in the rocks (Dewey, 1988). Image from: http://quake.wr.usgs.gov/research/structure/CrustalStructure/database/maps.html. There are several competing models for the formation of Archaean crust and their associated high seismic velocity mantle keels, including: a) ?instantaneous? formation from a mantle plume (including the effects of crustal under- and over-plating), b) conductive cooling, c) lateral accretion of oceanic terrains such as island arcs and/or submarine plateaus, including stacking of komatiite-rich crustal fragments and d) crust formation from the mantle wedge in a convergent margin (Albarede, 1998; Carlson et al., 1996; Carlson et al., 2005; de Wit et al., 1992; Hart et al., 1997b; Herzberg, 1999; Moser et al., 2001; Seng?r and Natal'in, 1996). The first two of these models, ?instantaneous? formation of continental crust and lithospheric mantle due to lower mantle plumes rising to the surface (Albarede, 1998), and conductive cooling and thickening of the lithosphere through time (Boyd, 1989; Chapman and Pollack, 1975), have largely been discarded due to results of diamond inclusion age studies (Richardson et al., 1993) and Re-Os studies of 7 mantle xenoliths (Irvine et al., 2001). These studies reveal mantle ages mainly similar to the surface rocks, but without the systematic depth layering implied by these models. Continental crustal formation and lithospheric thickening in the Archaean has been suggested to be due to the lateral accretion of island arcs and/or the collision of continental fragments (Figure 1.5) (Hart et al., 1997b). Modern analogues of this process are the collisions occurring in the western Pacific and the continent-continent collision occurring between India and Asia. Both provide modern examples of probable past mechanisms of crustal formation and collision (Seng?r and Natal'in, 1996). Neither, however, provides definitive insight into the formation of the depleted, low-density keels found beneath Archaean cratons. Thus while these collision models are attractive for explaining much of the surface geology, they imply the accumulation of significant amounts of eclogitic material in the mantle keel from the subducting plates that far exceed realistic estimates (Schulze, 1989). An alternative mechanism for the formation of low density - high seismic velocity keels found beneath Archaean crust is provided by slightly higher temperatures in the Archaean (Grove et al., 1999). These higher temperatures, combined with water-assisted melting of the mantle wedge above a subducting plate, provide an attractive alternative for the formation of highly depleted keels. The secular decrease in the Earth?s temperature offers an explanation of why ultra-depleted keels may not have formed since the Archaean (Carlson et al., 2005; Grove et al., 2002). 8 Figure 1.5 Model illustrating the formation of the earliest Archaean continents from the stacking of collision zones of oceanic crust and mantle. It is hypothesized that when these stacks are thick enough they partially melt to form granite. (Directly from Hart et al. (1997b), their Figure 1.) The strength of continental regions has been much more difficult to interpret and to relate to measured seismic velocity structure of the continents than it has in the oceans. Early isostatic studies of continental regions concentrated on mountains and demonstrated that to a large degree most mountain masses are isostatically compensated by significantly thickened crust, by means of Airy isostasy, which implies a weak crust for long wavelength loads (Heiskanen and Vening Meinesz, 1958; Watts, 2001). However, as more and better crustal thickness data have become available, Airy isostatic balance is less successful at explaining these data and studies of elastic thickness have ensued in an effort to determine the important controls on continental crustal strength and the response to loading (Watts, 2001), and references within). It is probable that large lateral (such as on-craton and off-craton) and vertical (such as upper crustal brittle vs. lower crustal ductile zones) changes in rheology occur, making the continental lithosphere a poor approximation of a thin elastic plate (Meissner, 1986; Watts, 2001). A comprehensive compilation of calculated lithospheric elastic thicknesses, ages of the plate and load, and 9 ages of tectonic event is given in Watts (2001). The values show great scatter, although foreland basins and the response of continental regions to ice sheet loads tend to have a higher elastic thickness than rifted regions. The large amount of scatter in the data indicates that the continental lithosphere is capable of both great strength and weakness, with little relationship to age or even recent tectonic environment. This is in stark contrast to the oceanic environment (Watts, 2001). As there are still regions of Archaean crust in existence today, the destruction of continental crust by weathering, erosion and subduction has been arguably inefficient, especially in comparison to the oceanic crust. Some researchers have argued for a steady- state model of continental volume, implying rapid growth of continents early in Earth?s history (Armstrong, 1981). However, most researchers argue for more gradual growth of the continents through time, although lack of preservation makes this a contentious issue (Ashwal, 1989). The possibility that there may be selective preservation of continental crust (Morgan, 1985) further compromises studies of temporal evolution of continental crust (Figure 1.6). Evidence from the well-dated Archaean Superior Province in Canada (Stott, 1997) indicates that the mechanisms of formation and destruction of both oceanic and continental lithosphere may have been similar since the inception of plate tectonics, perhaps as early as ~4 Ga (Bowring and Housh, 1995; Bowring et al., 1989; de Wit, 1998). Values of ?18O are as high as 7.4 in the Jack Hills zircons, implying that the early earth was cool and wet (Cavosie et al., 2005; Mojzsis et al., 2001). Trace elements in these zircons suggest that they formed near the Earth?s surface and that continental crust was forming at 4.4 Ga (Wilde et al., 2001). Further studies of the zonation in the zircons suggests that plate tectonic processes similar to those of today may have occurred as early as 4.2 Ga (Cavosie et al., 2005). However, these conclusions are tentative at best. 10 Figure 1.6 Postulated growth curves for the continental crust after Ashwal (1989). The estimates vary from nearly steady state (F) to more gradual growth through time (H&R). Key: F-(Fyfe, 1978), A- (Armstrong, 1981), B-(Brown, 1979), R&S-(Reymer and Schubert, 1984), D&W-(Dewey and Windley, 1981), O?N-(O'Nions et al., 1979), Al-(All?gre, 1982), M&T-(McLennan and Taylor, 1982), N&D-(Nelson and DePaolo, 1985), P&A-(Patchett and Arndt, 1986), V&J-(Veizer and Jansen, 1979), H&R-(Hurley and Rand, 1969). 1.2 Continental Keels Seismic studies of Archaean cratons -- stable regions of the Earth older than 2.5 Ga not affected by present-day plate boundary activity (Figure 1.7) -- show high P and S seismic velocities extending to depths of 250-350 km in the upper mantle (e.g. Godey et al., 2004; Grand, 1987; James et al., 2001; Lerner-Lam and Jordan, 1987; Rudnick and Nyblade, 1999; Schimmel et al., 2003; Simons et al., 1999; Sipkin and Jordan, 1975; Sipkin and Jordan, 1976; Sipkin and Jordan, 1980; van der Lee and Nolet, 1997; VanDecar et al., 1995). The presence of these seismically fast, but low density depleted keels was predicted and observed by Jordan (1975b) on the basis of density calculations of residue composition after melt extraction. These calculations were corroborated by 11 some of the earliest detailed studies of mantle xenoliths found in kimberlites and helped to form an explanation for the observation known as Clifford?s rule that diamond bearing kimberlites are found only in Archaean cratons (Clifford, 1970). These mantle keels provide a means for stabilizing and preserving the continental crust as the residual mantle is compositionally buoyant and has a very high viscosity (Jordan, 1975a; Jordan, 1975b; Jordan, 1978; Jordan, 1979a; Jordan, 1979b; Jordan, 1981a; Jordan, 1988). The depth extent of these keels is not precisely mapped, but they extend to depths of 250-350 km (James and Fouch, 2002). There are several lines of evidence that argue for coupling between the crust and mantle keel from the time of formation and through subsequent deformation episodes. First, there is a generally strong positive correlation between the age of mantle xenoliths and the age of overlying crust (Meisel et al., 2001) such that old Archaean crust is mostly underlain by Archaean mantle ages, and younger crust is underlain by mantle that gives young ages. Due to the extensive xenolith suite available for southern Africa, this relationship has been examined in detail and evidence is found for a variety of correlations between crustal features and mantle ages. These include correlations of Re-Os ages with: crustal terrain boundaries (Carlson and Moore, 2004; Griffin et al., 2004; Pearson et al., 2002); major igneous event ages (Carlson et al., 1999); the seismic velocity variations beneath the Kaapvaal Craton (Carlson et al., 1999); and diamond occurrences (Carlson et al., 2005; Shirey et al., 2002). The study of the ages of diamonds in these old cratonic regions demonstrates that diamonds at least as old as 3.2 Ga exist beneath the cratons (Richardson et al., 1993). This has been interpreted as implying that these regions of high P and S wave seismic velocities, but low density have remained attached to and moved coherently with the overlying Archaean cratonic crust (Shirey et al., 2001) throughout their history, and have not been subjected to widespread high temperatures that would take the keel out of the diamond stability field (150 ? 250 12 km). There are crustal regions where the crust-mantle age relationship breaks down, suggesting that tectonic forces can disrupt the coupling between crust and mantle (Carlson et al., 2005). Figure 1.7 A generalized global distribution of exposed Archaean provinces (in black). Grey areas are regions that are presumed to be underlain by Archaean rocks by Martin (1994), Goodwin (1991) and Condie (1981). Diagram from Martin (1994). The numbers refer to the exposed Archaean regions as: 1- Baltic shield, 2-Scottish shield, 3-Ukrainian shield, 4-Anabar shield, 5-Baikal, Sayan and Yienisei fold belts, 6-Aldan shield, 7-Sino-Korean, Tarim and Yangtze Cratons, 8-Indian shield, 9-Litchfield, Rul Jungle and Nanambu complexes, 10-Pilbara block, 11-Yilgarn block, 12-Napier complex, 13-Kaapvaal Craton, 14- Zimbabwe Craton, 15-Zambian block, 16-Kasa? Craton, 17-Central Africa Craton, 18-Ethiopian block, 19- Chaillu Craton, 20-Cameroon N?tem complex, 21-Man shield, 22-Tuareg shield, 23-Reguibat shield, 24- Rio de la Plata and Luis Alves massifs, 25-S?o Francisco Craton, 26-Guapore Craton, 27-Guiana shield, 28- Wyoming province, 29-Superior province, 30-Kaminak group, 31-Committee Bay block, 32-Slave province, 33-Labrador shield, 34-Greenland shield. In tomographic studies of mantle seismic structure, high seismic velocities are traditionally associated with cold, dense regions of the Earth. However, according to the tectosphere model of Jordan (Jordan, 1975a; Jordan, 1978; Jordan, 1988) the mantle keels underlying Archaean cratons are intrinsically buoyant due to extensive melt depletion that results in residual mantle keel of significantly reduced density (James et al., 2004; Jordan, 13 1979b). Thus the large seismic velocity difference observed between cratonic keels and oceanic mantle lithosphere is as much due to compositional variation in the keel as it is to higher temperatures in the oceanic lithosphere (Forte and Perry, 2000). The higher temperatures that produce lower density mantle beneath the oceanic crust are counterbalanced by a compositional difference of higher Mg# (where the Mg# = molar Mg/(Mg + Fe)), which lowers the density in the keels beneath the cratons to compensate for their lower temperatures (Figures 1.8 and 1.9). Thus, to a significant depth on a broad scale, at mantle conditions, the density beneath the oceans is the same as that beneath the cratons, an idea called the isopycnic (same density) hypothesis (Jordan, 1988). The fact that there is no well defined long wavelength signal in the geoid correlating with cratons is support for the isopycnic idea. In the oceans the tectosphere and the lithosphere essentially coincide with the depth of the LVZ at about 100 km. But beneath the continents, the kinematic or translational depth of the tectosphere is commonly significantly greater, possibly up to 250-350 km, (Jordan, 1975a). This is different from the dynamic behavior of the lithosphere (i.e. the response to an applied force) of about 100 km thickness traditionally accepted for the lithosphere (Figure 1.9) (Jordan, 1988; White, 1988). Thus keels found beneath the Archaean cratons are old and cool, but they are also chemically buoyant and rheologically strong. This can be explained if the composition of the keel is significantly depleted in a basaltic, and possibly even a komatiitic component, resulting in a high Mg# and a low density when compared with undepleted oceanic mantle (Jordan, 1975a; Jordan, 1978; Jordan, 1979a; Jordan, 1979b)). Thus keels have a significantly depleted composition (Boyd and McCallister, 1976; Jordan, 1975a). This depleted character is supported by trace element studies in diamonds (Hart et al., 1997b), and Re-Os data from eclogites (Shirey et al., 2001). 14 The strength of the keel is vitally important to the preservation of the keel and that of the overlying crust. Geodynamic models of circulation in the mantle have difficulty accounting for the preservation of Archaean, neutrally buoyant mantle keels over their 3 b.y. history due to the effects of erosion and lateral transport (Lenardic et al., 2000; Lenardic and Moresi, 1999; Moresi and Lenardic, 1997; Shapiro et al., 1999). More recent detailed analysis suggests that mantle keels may be slightly less dense than oceanic mantle at the same depth, significantly aiding preservation (James et al., 2004; Kelly et al., 2003; Poudjom Djomani et al., 2001). There is a suggestion that keels have a lower density in the detailed analysis of geoid data (Poudjom Djomani et al., 2001). Figure 1.8 A schematic diagram illustrating the isopycnic hypothesis. If there is an increase in seismic velocity, the change could be due to a decrease in temperature or an increase in Magnesium number (Mg#), where the Mg# is defined as: Mg/(Mg + Fe). It is impossible to determine the cause of the seismic velocity variation based only on seismic velocities. However, an increase in the Mg# will cause a significant decrease in the density, whereas a decrease in temperature will cause a significant increase in density. These density variations should be apparent in the gravity data, especially when comparing cratonic keels with oceanic lithosphere. 15 Figure 1.9 An illustration of the isopycnic hypothesis. The top diagram shows contours for shear velocities, demonstrating that the shear velocity beneath the Archaean craton is higher than the surrounding Phanerozoic region due to the presence of a thick keel of depleted mantle. The isopycnic hypothesis is illustrated in the bottom diagram, where densities of positions A and B are compared at standard conditions and at mantle conditions. Image modified from (Jordan, 1979a). 16 With the advent of higher resolution teleseismic studies, particularly from portable broadband seismic arrays, the detailed imaging of these seismically fast keels is now possible (Fischer and van der Hilst, 1999; James et al., 2001). Images from southern Africa (James and Fouch, 2002; James et al., 2001), Tanzania (Nyblade et al., 1996; Ritsema and van Heijst, 2000), North America (van der Lee and Nolet, 1997), Brazil (Schimmel et al., 2003; VanDecar et al., 1995) and Australia (Fischer and van der Hilst, 1999; Simons et al., 1999) show significantly more variation in detail than can be determined from broad scale global tomography studies (e.g. Grand et al., 1997). These internal keel variations correlate with differences in diamond inclusion compositions. Seismically faster portions of the mantle keel correlate with more peridotitic silicate diamond inclusions and older Sm-Nd ages (Shirey et al., 2002). Although there are modern examples of the formation of continental crust that are similar in size and character to early Proterozoic and Archaean cratonic regions (Stott, 1997), it appears that the creation and preservation of high velocity, low density cratonic mantle keels has not occurred since the Archaean (>2.5 Ga) (Jordan, 1978). Keels are characterized by: 1) overlying surface outcrops that locally host diamondiferous kimberlites (Clifford, 1970), 2) higher than global average seismic velocities in the uppermost mantle (Jordan, 1979b), and 3) lower than average heat flow values (Jones, 1988). Keels remain effectively coupled to the cratons during large scale lateral motions (Carlson et al., 2000; Carlson et al., 2005). The initial formation of cratonic keels and their ability to survive tectonic activity and possibly even plume interaction and their close coupling with Archaean surface geology are phenomena that are not well understood. 17 1.3 Geophysical studies of cratonic regions Surface studies of cratons have yielded important clues to their origin and evolution, but their three-dimensional configuration is best addressed with geophysics. Geophysical studies of the disparate Archaean cratons scattered throughout the world have not been comprehensive and often yield contradictory results, making it difficult to derive a consistent model of Archaean crustal formation (de Wit, 1998). To date, the most revealing results have come from studies of cratons in Canada, Brazil and Australia. Some of the more intensive investigations include studies of the Canadian cratons (Superior and Slave), where a wealth of age data has been combined with detailed geological mapping (Stott, 1997). These studies have benefited from good geologic exposures, extensive geophysical coverage (magnetic, gravity, magnetotelluric and reflection seismic), refraction seismic data of the Lithoprobe Project (Cook et al., 1999), and a few teleseismic studies (Bostock, 1997; Bostock, 1998; Bostock and Cassidy, 1997). Results from these studies have allowed a fairly detailed history of the Canadian Shield to be compiled, which can be summarized as the successive amalgamation of island arcs (Stott, 1997). Regrettably, direct knowledge of the chemistry of the lithosphere beneath the Canadian Shield is sparse although growing, because there are few kimberlite pipes that have yielded mantle xenoliths. This is changing rapidly as a result of the recent discovery and exploitation of kimberlites in the Slave Province of the Canadian Shield (Carlson et al., 1998; Gr?tter et al., 1998; Kopylova et al., 1998). Some researchers have argued that the currently available geological, seismic and xenolith data indicate that the pre-2.6 Ga geological development of the Slave Craton is difficult to link to the development of a cool, buoyant cratonic keel (Davis et al., 2001; Davis et al., 1994; Gr?tter et al., 1998). One explanation that has been suggested for the presence of diamonds with ultradeep (transition zone or possibly deeper) signatures is the possible 18 reworking of the lithosphere beneath the Slave Craton by a deep-seated mantle plume (Griffin et al., 1998). This remains a controversial topic and the focus of active research. The Brazilian Lithosphere Seismic Project (BLSP) recorded broadband teleseismic data in the southeastern region of the Brazilian shield (James et al., 1993). P and S wave delay time tomography revealed a keel of high seismic velocities beneath the S?o Francisco Craton to depths of ~300 km and a distinctive cylindrical column of low velocity perturbations (1.5% in P and 2% in S), which were interpreted to be a remnant signature of a fossil plume in the deeper upper mantle (VanDecar et al., 1995). A study of the topography, gravity and isostatic balance in the same region of Brazil shows that the S?o Francisco Craton is significantly elevated and undercompensated at the Moho, although the Bouguer gravity suggests that the crust is in Airy-type isostatic balance (Assump??o et al., 2002). The relationships between the gravity, topography and isostatic balance can be interpreted in two ways: either there are significantly lower densities in the mantle beneath these regions, or there are higher densities in the lower crust, possibly due to underplating (Assump??o et al., 2002). Assump??o et al. (2002) attributed the cause of the gravity anomaly to lower density mantle beneath the S?o Francisco Craton, although underplating beneath the Parana basin has been invoked by previous workers (Molina et al., 1989). Although there are ultra-deep diamonds found in Brazil (Hutchinson et al., 1998), there are few mantle and crustal xenoliths from this region to aid in the integration of the gravity and seismic results. Thus the effort to reconcile the gravity anomalies with seismic results remains an area of active research. The temporary broadband regional seismological study ?Skippy? and the more localized Kimba studies in Australia show clearly defined keels of high seismic velocities beneath the Archaean Pilbara and Yilgarn Cratons (van der Hilst et al., 1994). A receiver 19 function study used to determine crustal thickness shows that the thinnest crust is in the Archaean Yilgarn Craton and the thickest crust occurs in the Proterozoic rocks of central Australia (Clitheroe et al., 2000). The seismically determined crustal thicknesses agree closely with those determined from deep crustal xenoliths from kimberlites (Clitheroe et al., 2000). The lack of a well characterized mantle xenolith suite has hampered the investigation of the density and composition of the mantle beneath the Archaean regions of Australia, but the results to date are remarkably similar qualitatively to those reported for the Kaapvaal Craton as summarized below. 1.4 The Kaapvaal Craton The Kaapvaal Craton of southern Africa has fewer age data from surface outcrops than the Canadian or Australian cratons, which makes it difficult to understand its detailed geological history (Figures 1.10, 1.11, 1.12) (de Wit, 1998; de Wit et al., 1992). This is compounded by extensive cover of younger platform sequences, such as the Karoo and Transvaal Basins. The Kaapvaal Craton, however, does have an extensive and well studied suite of direct deep crustal and mantle samples available from xenoliths found in numerous kimberlites both on- and off-craton (e.g. Boyd et al., 1999; Sweeney and Winter, 1999 and references within) from which much of the geological history has been deduced (de Wit, 1998; de Wit et al., 1992; Moser et al., 2001; Pearson et al., 1995b; Shirey et al., 2002). These lower crustal and mantle xenoliths define regional changes in mantle composition, P-T conditions and thermal ages beneath the Kaapvaal and the surrounding areas as preserved at the time of kimberlite eruption (Menzies et al., 1999; Moser et al., 2001; Schmitz and Bowring, 2001a; Schmitz and Bowring, 2003). One of the more obvious differences between on- and off-craton mantle xenoliths is the Re/Os 20 model ages. The ages of off-craton xenoliths are younger than 2.5 Ga (Pearson et al., 1995) and on-craton ages are generally older than 2.5 Ga (Figure 1.10) (Irvine et al., 2001). Figure 1.10 Summary diagram of Re-Os model ages obtained from kimberlite xenoliths. There is a distinctive change between on- and off-craton mantle ages. The Premier kimberlite results appear to have been significantly affected by the emplacement of the Bushveld Complex at 2.054 Ga. The light yellow is the known extent of the Kaapvaal-Zimbabwe Craton, and the flesh color is the extent of the Limpopo Belt. Diagram from Carlson et al. (2000). 21 Figure 1.11 Some important geological features of southern Africa and tectonic boundaries. The mafic intrusives in green are: Bushveld Complex and the Molopo Farms Complex, both of which are ~2054 Ma in age, and are connected by a prominent linear feature known as the Tabazimbi Murchison Lineament (TML) (Buick et al., 2001; Walraven et al., 1990). The Great Dyke is ~2571 Ma (Wingate, 2000), and Trompsburg is ~1915 Ma (Maier et al., 2003)). The darker greens are greenstone belts in South Africa: Barberton, Amalia, Kraaipan, Madibe, Pietersburg, Giyani,and Murchison. The location of the Morokweng impact structure is shown in blue, althought the extent of this feature is poorly constrained and the Vredefort impact structure is located in the center of the Witwatersrand Basin. The edges of the cratons and many of the geological features are constrained by the gravity (Figure 1.14) and magnetic (Figure 1.15) data. Full reference list included with Figure 2.1. Extensive gravity and magnetic data sets exist for the entire southern African region. While several regional and local interpretations of the gravity and magnetic data have been published (Stettler et al., 1989; Stettler et al., 1999), no isostatic studies have been conducted since the 1960s (Hales and Gough, 1960; Hales and Gough, 1962) except for a regional study of the African plate as a whole (Hartley et al., 1996) and a recent recalculation of the isostatic gravity field of South Africa (Fourie et al., 2005). 22 Figure 1.12 Geological subdomains of the Kaapvaal Craton as defined by de Wit (1992) on the basis of a summary of age data, with southern African seismic experiment stations overlain. The Colesburg lineament has its southern extent between the Colesburg Terrain and the Southern Terrain. The northern extent of the Colesburg lineament is poorly defined on both magnetic and gravity data. In this case it has been drawn with very limited extent. The locations of the Kaapvaal Craton Project seismic stations are shown for reference; unfortunately the spacing between stations is too large to use the seismic data to accurately resolve the detailed subdomains in the Kaapvaal Craton. The wealth of geological, xenolith and geophysical data available for southern Africa was a major motivation behind the Kaapvaal Craton Project (Carlson et al., 1996), a multinational, multidisciplinary research program, formally titled ?The Anatomy of an Archaean Craton? (Carlson et al., 1996). The U.S. National Science Foundation (NSF) funded the U.S. part of this study in 1996 for a period of four years. In southern Africa, mining companies, government agencies and academic institutions contributed at nearly 23 the same funding level to ensure the success of the project (Carlson et al., 1996; James et al., 2000). The keystone of this project was the deployment of broadband seismometers loaned from the PASSCAL and Carnegie Institution of Washington instrument pools. The bulk of the seismic data were collected between April 1997 and June 1999 over a large swath of southern Africa stretching from Cape Town, South Africa to Masvingo, Zimbabwe (Figures 1.12 and 1.13). In the first year 56 broadband stations were deployed from Cape Town to Mashvingo. Of these 33 were deployed for the full two years as a backbone to the array (yellow dots in Figure 1.13), the other 23 stations were deployed for the first year (blue dots in Figure 1.13) and then moved to occupy an additional 23 stations in the second year (red dots in Figure 1.13). In addition to these 79 stations, an additional 3 Global Seismic Network (GSN) stations were incorporated in the experiment (stations at Sutherland, Boshof, and Lobotse). This array was known as the Kaapvaal Seismic Array (KSA) and was serviced from four centers at Cape Town, Kimberley, Johannesburg and Masvingo/Harare. In addition to the KSA, a tightly spaced telemetered array was installed in and around Kimberley, known as the Kimberley Telemetered Array (KTA). This array of three component broadband stations was installed in June 1997 for 6 months to examine, at high resolution, the transition between more and less diamondiferous regions in the Kimberley area. At the time of the experiment, this was the largest deployment of portable broadband seismometers in the world. In addition to the Kaapvaal arrays, the Council for Geoscience has a network of short period seismometers used in the national seismic network. During the period of the Kaapvaal Project, the GeoForschungZentrum (Potsdam, Germany) also conducted a similar, though much smaller scale, experiment in Namibia, installing five, three component broadband stations for a period of roughly a year (Figure 1.13) (Hanka et al., 2000). 24 Figure 1.13 Broadband seismometer station locations of the southern African seismic experiment (SASE). See Figure 1.11 for geological details. The blue stations of the Kaapvaal Seismic Array (KSA ? circles) were deployed for the first year of the experiment and then transferred to the red station locations. The yellow stations were deployed for the full two year period. While the SAGEO stations (black triangles) provided improved coverage for locations of local events they were short period stations and not used for the teleseimic data analysis, although they provided useful data for comparison purposes (Webb et al., 2001). The GSN stations SUR, BOSA, LBTB, were incorporated in the KSA data set. The Kimberley Telemetered Array (KTA ? green squares) was deployed for a period of 6 months in the region around Kimberley. The German experiment in Namibia known as MAMBA deployed five seismometers in Namibia for a period of roughly a year. They also included an analysis of the GSN station TSUM in their project. The Kaapvaal project was designed to address fundamental questions such as the nature of the relationship between the surface geology and the mantle keel, the geochemical process of differentiation that led to cold, buoyant, viscous keels attached firmly to the craton (Jordan, 1975a), and the geological processes responsible for their 25 formation and stabilization and preservation. One of the main objectives of the Kaapvaal project was to assess different models of craton formation and the relationship between the surface geology and the underlying mantle (Carlson et al., 1996). It was envisaged in the Kaapvaal Craton project proposal that the mantle and crustal signatures left behind by these processes could help to differentiate between the different models of crustal formation. The age distribution of diamond inclusions with depth has eliminated several models and details of mantle chemistry from garnet studies are defining chemical variations throughout the Kaapvaal (Gr?tter et al., 1998). The tectosphere was imaged to a depth of about 300 km using delay time tomographic inversion, confirming a thick (~300 km) keel beneath the Kaapvaal Craton (James et al., 2001). Detailed variations within the tomography have been resolved at the scale of 50-100 km. Bearing in mind that the resolution of the xenolith data set is completely different from the seismic anisotropy, there is reasonable consistency between the xenolith determined seismic velocities (James et al., 2004), mantle xenolith fabric studies (Ben-Ismail et al., 2001) and seismic anisotropy results (Silver et al., 2001). The model for formation of the tectosphere proposed by Pearson et al. (1995), i.e. the accretion of continental and/or oceanic arcs and their highly depleted upper mantle components, suggests a connection between surface geology and underlying upper mantle structure. This model has been summarized, expanded and refined with the integration of extensive mantle ages and chemical information by Carlson et al., (2005), although considerable controversy still exists about the formation and preservation of Archaean cratons. In their model, Carlson et al. (2005) propose that different ages of the crust are expected to be physically associated with distinctive mantle compositions and ages. At present the best constraints on the crustal accretion of the Kaapvaal Craton come from the ages of the various crustal blocks (de Wit et al., 1992) (Figure 1.12). Bearing in mind 26 that much of the craton is covered by younger sequences, the boundaries between the various blocks are uncertain. The ages progress from oldest to youngest, from east to west with a probable prominent suture at the Colesburg lineament (Figures 1.11 and 1.12) (de Wit, 1998; de Wit et al., 1992; Schmitz et al., 2001; Schmitz and Bowring, 2001b; Schmitz and Bowring, 2003; Schmitz et al., 2004). The block to the east of the Colesburg lineament is known as the Witwatersrand block and the block to the west as the Kimberley block. As these detailed subdivisions are uncertain, complexities should not be unexpected; for example the recently determined age of the Amalia greenstone belt at 2750.1 ? 4.6 Ma is significantly younger than was anticipated (Poujol et al., 2005). 1.5 Purpose of this study and outline of thesis The main purpose of this study has been to develop a more detailed understanding of the long wavelength contributions to the gravity field of southern Africa and the constraints that gravity data place on models of crustal formation, upper mantle composition and the isopycnic hypothesis. Large geological features such as the Bushveld Complex (BC), Trompsburg, Witwatersrand basin, and Vredefort impact structure have modified the craton and have made a significant contribution to variations in both the crustal gravity and magnetic fields at short wavelengths. Indeed, gravity and magnetic data have been used extensively in determining the boundaries and internal structure of the craton (Figures 1.11, 1.14 1.15). As a result of the comprehensive Kaapvaal project and earlier local studies, the Moho in southern Africa has been exceptionally well mapped (Nguuri, 2004; Nguuri et al., 2001). The contribution to the gravity field caused by variations in Moho topography and variations in seismic velocity in the upper mantle is therefore more readily determined than is commonly possible. The 27 models of the gravity field presented in this thesis have benefited from the extensive coverage of the Kaapvaal project, allowing for evaluating both crust and upper mantle contributions. The delay time tomography has revealed a distinct high seismic velocity keel beneath the Kaapvaal and Zimbabwe Cratons (James et al., 2001). This high velocity keel appears to be associated with depleted mantle material of relatively low density, which contributes to the gravity signal at long wavelengths. For this thesis I have modeled the contribution from the tomographic signal and assessed the contributions of both thermal and chemical variations, which has permitted an evaluation of the isopycnic hypothesis (James and Jordan, 2006-manuscript; Jordan, 1975a). The compositional and thermal effects are indistinguishable in an analysis of seismic velocity alone, as it is impossible to determine if an increase in velocity is due to an increase in Mg# (i.e. a change in chemical composition), a decrease in temperature, or some combination of the two. However, by incorporating an analysis of gravity, the subsequent decrease in gravity (due to lowered density) from an increased Mg# can be distinguished from the increase in density that accompanies a decrease in temperature. Thus the main objective of this thesis is to examine the isopycnic hypothesis in light of the available gravity, kimberlite xenolith data, detailed delay time tomographic (James et al., 2001) and crustal thickness results (Nguuri et al., 2001) from the Kaapvaal Craton Project. While other large-scale studies of cratonic regions have been conducted (Bostock and Cassidy, 1997; James et al., 1999; van der Hilst et al., 1994) there has never previously been enough detailed data to fully explore this hypothesis. 28 Figure 1.14 Compilation of Bouguer gravity data for southern Africa. Data were supplied by the Council for Geosciences from the SADC database. Compare with Figure 1.11 for the locality of prominent geological features such as the Bushveld and Trompsburg Complexes. 29 Figure 1.15 Compilation of airborne magnetic data for southern Africa from the Council for Geosciences SADC database. Geological features such as the Colesburg lineament and the Vredefort impact structure are readily apparent. These data have been used to map the edges of the cratons and other prominent geological features that are partially covered by younger materials. In Chapter 2, I have compiled the results of previous deep crustal studies in southern Africa, including published results of the Kaapvaal project. These studies provide a basis for assessing the contribution of the crustal thickness variations to the gravity field. Chapter 2 also presents the technical background for the various data sets that are used and a parameterization of known geology into different tectonic units for cross-comparisons between datasets (i.e. a comparison of tectonic regions with the 30 31 gravity, tomography and crustal thickness is presented in Chapter 5). In Chapter 3 I present an assessment of the isostatic balance of the southern African crust and calculate the contribution of the Moho variations to the gravity field. I have used forward gravity models of the crustal thickness variations for a variety of crust/mantle density contrasts as developed for a spherical Earth configuration. The contribution to the gravity field is modeled for both the predicted crustal thickness variations based on Airy isostasy and the measured variation determined from receiver function results (Nguuri et al., 2001). I have used both the Fourier method developed by (Parker, 1972) and a modified version of the spherical block modelling of Lees and VanDecar (1991) for the modeling, and then compared the results. The gravitational effect of the Bushveld Complex is examined in detail in Chapter 4, where new physical property data (Ashwal et al., 2005) and gravity modeling results incorporating newly determined crustal thicknesses beneath the Bushveld Complex are presented (Cawthorn et al., 1998a; Cawthorn and Webb, 2001; Nguuri et al., 2001; Webb et al., 2004). In Chapter 5, the contribution to the gravity field of the seismic velocity variations in the mantle is modeled and combined with the crustal results from Chapter 3. These results are evaluated in terms of the isopycnic hypothesis and examined in terms of the regional geology. Finally, in Chapter 6 the results are summarized and discussed in a global context. Five referred publication have resulted from work in this thesis: Ashwal et al., 2005; Cawthorn et al., 1998b; Cawthorn and Webb, 2001; Nguuri et al., 2001; Webb et al., 2004 and are included in the appendices or in Chapter 4. 2 Regional Geology and Geophysics, Datasets and Previous Studies There are several excellent reviews of the geology of the Kaapvaal and Zimbabwe Cratons and surrounding mobile belts (Blenkinsop et al., 1997; Brandl and de Wit, 1997; de Wit et al., 1992; Jelsma and Dirks, 2002; Schmitz et al., 2004; Tankard et al., 1982). Here I present a brief review of the geology in the region of the Southern African Seismic Experiment (SASE) with more of a geophysical perspective. In this chapter I briefly review: 1) the geological structure of southern Africa; 2) relevant geophysical studies of southern Africa; 3) the technical aspects of the data sets that were used; and 4) develop a tectonic regionalization of the geology. 2.1 Overview of Southern African geology The Kaapvaal Craton of southern Africa has some of the best exposed, oldest and most unaltered Archaean rocks in the world. It is primarily composed of granite- greenstone terrains formed between 3.64 and 2.7 Ga, and has a roughly circular shape covering an area of 1.2 x 106 km2 (Figure 2.1). The boundaries of the Kaapvaal Craton were determined from a combination of geochronology, geological and structural mapping and geophysical data ? mainly magnetic and gravity data (Brandl and de Wit, 1997; Corner, 1991; Corner, 2003; Corner et al., 1990). The eastern boundary of the Craton is taken as the Lebombo monocline, which comprises rhyolites and basalts formed during the breakup of Gondwana (Tankard et al., 1982). The Lebombo monocline shows up distinctly on both the gravity and magnetic images (Figure 2.2 and 2.3) (Corner, 1991). 32 Figure 2.1 Broad geological domains of southern Africa in the region of the Southern African Seismic Experiment (SASE). The Kimberley block is the part of the Kaapvaal Craton west of the Colesburg Lineament, while the Witwatersrand block is the cratonic region east of the Colesburg Lineament. Compiled from: (de Wit et al., 1992; Hunter, 1975; Key and Ayres, 2000; Knoper, 1992; Pretorius et al., 1986; Reichardt, 1994; Stettler et al., 2000; von Biljon and Legg, 1983). Only the larger greenstone belts in South Africa are shown, as they are indicative of the large scale trends in the Craton. The greenstone belts of Zimbabwe are much more numerous and complicated and were left off of this map for clarity, as have the smaller greenstone belts in South Africa. The reader is referred to (Blenkinsop et al., 1997; de Wit and Ashwal, 1997b; Jelsma and Dirks, 2000; Jelsma and Dirks, 2002) for detailed discussion of southern African greenstone belts. 33 Figure 2.2 Magnetic data of southern Africa from a grid of data provided by the Council for Geoscience. The magnetic data were used to help define the outline of the Kaapvaal and Zimbabwe Cratons and several prominent features such as the Bushveld Complex and the Witwatersrand Basin and Vredefort impact structure (Stettler et al., 2000). The geological outlines have been left off of this map to emphasize the data. The Namaqua-Natal Mobile Belt (NNMB) forms the southern to southwestern margin of the Kaapvaal Craton and the transition has many of the characteristic features typical of craton to off-craton boundary zones. 34 Figure 2.3 Gravity data of southern Africa from data provided by the Council for Geoscience. The gravity data have been used to help define the outline of the Kaapvaal and Zimbabwe Cratons and several prominent features such as the Bushveld Complex and the Witwatersrand Basin and Vredefort impact structure (Fourie et al., 2005). The geological outlines were left off to emphasize the data. The NNMB possesses higher heat flow compared to the Kaapvaal Craton (Jones, 1988) and possesses barren kimberlites, whereas those in the Kaapvaal Craton can be diamondiferous (Skinner et al., 1992). The crustal thickness changes abruptly from ~37 km to ~46 km over a distance of ~100 km (Nguuri et al., 2001; Stankiewicz et al., 2002). The seismic structure of the crust in the Kaapvaal Craton has only ~15 km of intermediate velocity rocks (lower crust), whereas the NNMB has a much thicker lower crust with a 35 smaller velocity contrast between the crust and mantle (Durrheim and Mooney, 1991; Green and Durrheim, 1990; Nguuri et al., 2001). Even mantle tomography shows a clear break from fast seismic velocities beneath the Craton, to relatively slow seismic velocities in the NNMB (Fouch et al., 2004; James et al., 2001). This boundary also shows up clearly on magnetic and gravity images (Figures 2.2 and 2.3) (Corner, 1991). The Middle Proterozoic Namaqua-Natal Mobile Belt (NNMB) (~1100 Ma) borders the southern edge of the Kaapvaal Craton for roughly 2,000 km and is attributed to a deeply eroded continental collision zone (Clifford et al., 2004; Schmitz and Bowring, 2004; Tankard et al., 1982; Thomas et al., 1994). The delay time seismic tomography results of the Kaapvaal Project show no evidence of a keel beneath the NNMB (Fouch et al., 2004; James et al., 2001), suggesting either that a keel never formed beneath the NNMB or that it was eroded during subsequent collision. The western margin of the Kaapvaal Craton is less well defined but is generally located at the strong magnetic signature of the Kalahari line (Carney et al., 1994; Corner, 1991; Reeves and Hutchins, 1975), although there is limited outcrop exposure in this region. The Kheis and associated Proterozoic fold and thrust belts to the west are considered to overlie the Kaapvaal Craton (e.g. de Wit et al., 1992); however, there has been insufficient geophysical coverage to indicate how far west the Craton may extend under this younger cover (Tinker et al., 2002). Although the aeromagnetic coverage and compilation of magnetic data for Namibia has improved dramatically (Eberle et al., 2002), additional geophysical data are needed to complement this in order to resolve such issues. The Kaapvaal Craton is generally accepted to be bounded in the north by the Palala shear zone/Zoetfontein fault, marking the southern edge of the Central Zone of the Limpopo Belt (Brandl and de Wit, 1997). This fault zone has been mapped as a ~10 km 36 wide vertical shear zone and has a strong positive aeromagnetic signature (Corner, 1991; von Biljon and Legg, 1983). However, some authors suggest that the exact location of the craton edge under the Central Zone is unclear (McCourt and Vearncombe, 1992); certainly the northwestern boundary of the Kaapvaal Craton is poorly constrained due to extensive Karoo age (Mesozoic) and Kalahari age (Recent) cover (McCourt et al., 2004). The Kaapvaal Craton was probably significantly larger than is currently preserved, as is suggested by seismic evidence (Tinker et al., 2002); it may even have been connected to the Pilbara Craton in Australia as suggested by palaeomagnetic data (Wingate, 1998). The Zimbabwe Craton, directly north of the Kaapvaal Craton, also has well exposed old, largely unaltered Archaean granite-greenstone terrains. The Zimbabwe Craton has an elliptical shape, covering an inferred area of 2.68 x 105 km2, of which ~1.77 x 105 km2 is exposed (Blenkinsop et al., 1997; Jelsma and Dirks, 2002). The ages in the Zimbabwe Craton are slightly younger than in the Kaapvaal Craton, the Zimbabwe Craton having formed between 3.5 and 2.6 Ga (Figure 2.1). The Zimbabwe Craton is also surrounded by mobile belts: to the north and northwest is the Magondi Mobile Belt, formed at 2.0-1.8 Ga (Blenkinsop et al., 1997; Jelsma and Dirks, 2002). The Zambezi Mobile Belt (1.0-0.5 Ga) encircles the northern and eastern extent of the Zimbabwe Craton and to the south, the Limpopo Belt (2.7 Ga and 2.0 Ga) separates the Zimbabwe Craton from the Kaapvaal Craton (Blenkinsop et al., 1997; Jelsma and Dirks, 2002). The outline of the Zimbabwe Craton is well defined on aeromagnetic and gravity images (Figures 2.2 and 2.3), although the south-western extension of the Zimbabwe Craton into Botswana is poorly known due to extensive cover of Phanerozoic sequences (Aldiss, 1991; McCourt et al., 2004). The Saldanian, on top of which lies the Cape Fold Belt (~ 37 0.28-0.19 Ga), represents a collision similar to the NNMB at about 0.6 Ga (Tankard et al., 1982; van der Beek et al., 2002). 2.1.1 Terrains and boundary features For the purposes of this study, two terrains within the Kaapvaal Craton have been adopted and are termed the Kimberley (<3.26 Ga) and Witwatersrand (3.7 -3.1 Ga) terrains (de Wit and Tinker, 2004; Tinker et al., 2002). The Kimberly terrain is essentially the western half of the craton and Witwatersrand terrain is the eastern half (Figure 2.4). They are separated by the Colesburg Lineament, a prominent north-south linear feature on both the magnetic and gravity data sets (Figures 2.1, 2.2, and 2.3). The Colesburg Lineament also marks a distinct change in regional trend direction between the Witwatersrand terrain, which has a clear ENE-WSW striking fabric defined by the Thabazimbi-Murchison Lineament, and the Murchison, Pietersburg and Giyani greenstone belts (Figure 2.4) (Brandl and de Wit, 1997; de Wit, 1998; de Wit et al., 1992; Good and de Wit, 1997). The Inyoka fault, which separates the northern and southern halves of the Barberton Greenstone Belt, also strikes in this direction (Figure 2.4) (Eglington and Armstrong, 2004). The Kimberley block on the western side of the Colesburg Lineament has a strong N-S fabric, as defined by the Amalia and Kraaipan Greenstone Belts (Figures 2.1, 2.2 and 2.3). The Witwatersrand and Kimberley terrains were welded together along the Colesburg Lineament at ~2.96-2.94 based on U-Pb zircon ages of coeval igneous granite emplacement events in the two terrains (de Wit et al., 1992; Mapeo et al., 2004; Poujol and Anhaeusser, 2001). However, the Amalia Greenstone Belt has recently been dated at ~2750 Ma, suggesting that the region is more compex than previously thought (Poujol et al., 2005). The northern boundaries of these 38 domains are not well defined. Some authors (e.g. Eglington and Armstrong, 2004) extend the Colesburg Lineament as far north as the Palala Shear Zone, and create a third major terrain to the north, whereas others (e.g. Cawthorn and Walraven, 1998; McCourt et al., 2004) extend the Thabazimbi-Murchison Lineament westward to the Kalahari Line, while others remain undecided (Figure 2.4) (de Wit and Tinker, 2004). Since the area is poorly exposed the correct configuration is unknown. The dip of the Colesburg Lineament is also contested: Schmitz et al. (2004) contend on the basis of surface geology and geochronology that it is westward-dipping; Doucour? and de Wit (2002) and Evans et al., (2004) have argued using different geophysical methods that is it eastward-dipping. Unfortunately, the deep seismic reflection data that cross the Colesburg Lineament do not provide an unequivocal answer (de Wit and Tinker, 2004). Surprisingly, four very different origins have been proposed for the Colesburg Lineament. These include: a) a major suture zone (Doucour? and de Wit, 2002; Schmitz et al., 2004); b) buried BIFs of an unknown greenstone belt south of Amalia (de Wit and Tinker, 2004); c) thin back thrusts of BIF-bearing shales of the lower Witwatersrand (Corner, 1991); d) east-dipping magnetite-rich mid-crustal basement granites, which were detected in shallow drill cores to the west (Corner et al., 1986; Drennan et al., 1990). This last idea, of an upwarping of an upper-lower crustal boundary, which Corner (1986) termed the Vredefort discontinuity, has been linked to a prominent negative magnetic anomaly in the Vredefort impact structure. 39 Figure 2.4 Crustal domains as defined by de Wit (1992). The Colesburg Lineament starts in the south as the feature between domains 9 and 10. It is more difficult to trace northwards. Diagram modified from de Wit (1992). Ages compiled from (Brandl and de Wit, 1997; de Wit et al., 1992; Poujol et al., 2005; Schmitz et al., 2004). However, recent work suggests that the magnetic anomalies of the Colesburg Lineament and Vredefort impact structure may have different causes; the Vredefort anomalies are possibly due to magnetization effects of the impact process itself, causing a pronounced remanent magnetization (Carporzen et al., 2005; Hart et al., 1995). In the gravity data, the Colesburg Lineament has a signature similar to a cratonic boundary, although it is more of a low-high-low sequence, rather than the classic low (older province), high (younger province) first documented in Canada by Gibb and Thomas (1976). In the magnetic data, the Colesburg Lineament is clearly defined at the southern 40 edge of the Kaapvaal Craton as a strong positive magnetic anomaly and then becomes a somewhat weaker negative magnetic anomaly northwards, where it finally dies out to the north near the Thabazimbi-Murchison Lineament (TML). In an effort to construct a plausible history of craton formation, de Wit et al. (1992) defined 12 smaller terrains within the Witwatersrand and Kimberley terrains based on age data, geology and aeromagnetic features (Figure 2.4). The old core of the Kaapvaal Craton is the Ancient Gneiss Complex of Swaziland (~3.64 Ga), which joined with the Barberton Greenstone Belt (~3.5-~3.07 Ga) (de Wit et al., 1992). From this nucleus the Kaapvaal Craton expanded southwards over a 200 m.y. period during which time the regions to the southeast as far south as the Nondweni Greenstone Belt and the Natal Terrain were amalgamated (Figure 2.4) (Brandl and de Wit, 1997; Carlson et al., 2000; Eglington and Armstrong, 2004). Evidence from mantle xenoliths brought up by kimberlites suggests that the keel started forming by 3.5 Ga and that diamonds were forming by 3.2 Ga (Gurney, 1990). By ~3.12 Ga, the Witwatersrand Terrain was sufficiently stable to support the formation of the Pongola and Witwatersrand Basins (Armstrong et al., 1991; de Wit and Tinker, 2004; Eglington and Armstrong, 2004). The Witwatersrand Terrain then collided with the previously formed Kimberley Terrain at ~2.8 Ga, based on the occurrence of Ventersdorp and Transvaal lithologies crossing the Colesburg Lineament and U-Pb zircon geochronology of coeval instrusives (de Wit and Tinker, 2004; Schmitz et al., 2004). The interior of the Archaean Zimbabwe Craton hosts twenty-six recognized greenstone belts in a complicated arrangement of tonalite-trondhjemite-granite (TTG) suites (Blenkinsop et al., 1997; Jelsma and Dirks, 2002; Kampunzu et al., 2003; McCourt et al., 2004). The greenstone belts are generally less linear than they are on the Kaapvaal Craton, although the edges commonly form part of a major craton-wide system of shear 41 zones with two dominant directions of NNE-SSW and WNW-ESE (Blenkinsop et al., 1997). It is interesting to note that these old fracture directions are significantly different from both the orientation of the Great Dyke and the seismic shear wave splitting results attributed to fossil upper mantle fabric (Silver et al., 2004). Two major crustal formation events were identified on the Zimbabwe Craton at 3.5- 3.3 Ga and 2.9-2.6 Ga (Percival et al., 1997; Wilson, 1990). These two events were broken down into four major subdivisions and presented as a greenstone belt lithostratigraphy for the Zimbabwe Craton (Blenkinsop et al., 1997). This stratigraphy is largely based on models developed from studies of the Belingwe Greenstone Belt (Blenkinsop et al., 1997). However, more recent work suggests that applying a lithostratigraphy to the whole craton may be misleading and that some of the Zimbabwe Greenstone Belts may have formed in very different tectonic environments from others (Jelsma and Dirks, 2002). For example, Jelsma and Dirks (2002) propose that the older eastern belts (such as the Belingwe, Filabusi, and Shangani Belts) formed in a rift environment, whereas the belts to the north and west of Zimbabwe (such as the Bulawayo, Midlands and Harare Belts) are examples of greenstone belt formation in a magmatic arc environment (Jelsma and Dirks, 2002). Jelsma and Dirks (2002) prefer to develop a model of crustal growth through progressive stacking of the various components due to westward thrusting. In this way they can accommodate a variety of formation environments for the greenstone belts such as rifts or arcs, and have developed a model for the formation of the Zimbabwe Craton that grows from west to east (Jelsma and Dirks, 2002). Progressive younging of granitoid activity from west to east has also been observed, but some of the dates are not as well constrained as others (Oberthur et al., 2003). 42 The ideas of diapiric uprising of granite and associated deformation (so called vertical tectonics) have also been much discussed in the literature of the Zimbabwe Craton (e.g. Jelsma and Dirks, 2000). Most geophysics shows, however, that: a) greenstone belts are shallow, and b) that granites generally form sheets, not teardrop- shaped diapirs (Am?glio and Vigneresse, 1997; Stettler et al., 1997). The ~550 km long Great Dyke is 2571 ? 9 Ma (Wilson and Armstrong, 2000; Wingate, 2000) and cuts across the entire Zimbabwe Craton in a NNE-SSW direction, indicating that the Zimbabwe Craton had formed a rigid craton by this time (Eglington and Armstrong, 2004; Jelsma and Dirks, 2002). Its intrusion into the northernmost Limpopo Belt means that at least the northern part of the Limpopo Belt and the Zimbabwe Craton were welded together by ~2.5 Ga, if not earlier. Historically there were two competing models for the formation of greenstone belts. The ?synclinal keel? model implies that the greenstone belts extend to tens of km in the crust and were formed by gravitational collapse perhaps aided by the diapiric uprise of spatially and temporally associated granitoid plutons (e.g. Anhaeusser, 1973; Glikson, 1970). More recently, geological, structural and geophysical data show that many, perhaps most, greenstone belts represent a complex collage of tectonically juxtaposed packages of supracrustal rocks (Stettler et al., 1997). This ?thin-skinned? model is supported by gravity, seismic and electrical studies, which show that most greenstone belts are <10 km thick, and some are as little as 1 km thick (e.g. de Wit and Ashwal, 1995; Stettler et al., 1997). Many greenstone belts in southern Africa have positive Bouguer gravity signatures of between 20-40 mGal, are electrically conductive and have a subdued radiometric response compared to the surrounding granitic terrains (Stettler et al., 1997). These belts, including the Kraaipan, Barberton, Murchison, Pietersburg, Giyani, Nondweni and Sutherland Belts, have had extensive geophysical data sets such as 43 seismic, radiometric, magnetic and resistivity collected over them. These data sets, in conjunction with the modeling of gravity data constrained by measured density values, have confirmed that greenstone belts extend at most to depths of 8-10 km (de Beer et al., 1988b; de Beer et al., 1984; Kleywegt et al., 1987; Stettler et al., 1997; Stettler et al., 1988). These shallow depths argue against the ?synclinal keel? model of formation, as summarized in (de Wit and Ashwal, 1997a). The Limpopo Belt to the north of the Kaapvaal Craton records a collision between the Kaapvaal and the Zimbabwe Cratons at ~2.7 Ga (Barton and van Reenen, 1992); however, younger ages at 2.0 Ga suggest a complex history that is not fully understood (Barton et al., 1994). The Limpopo Belt has been divided into 3 regions, the Northern Marginal Zone (NMZ), the Central Zone (CZ), and the Southern Marginal Zone (SMZ) (von Biljon and Legg, 1983). Both the SMZ and NMZ have been interpreted as being thrust on top of the Kaapvaal and Zimbabwe cratons, respectively, (van Reenen et al., 1987) and this interpretation is supported by the receiver function results of the Kaapvaal project (Nguuri et al., 2001). A reinterpretation of the gravity data indicates that the Limpopo Belt extends further to the west than has been previously mapped (Ranganai et al., 2002). Furthermore, crustal thickness results (Nguuri et al., 2001) suggest that the Limpopo Belt has significantly thicker crust than the surrounding cratons in opposition to previous gravity interpretations (Gwavava et al., 1992). The cover sequences in the region of the southern African seismic experiment will be presented in the next section as they are discussed in the context of relevant geophysical studies. 44 2.2 Review of Geophysical Studies of the lithosphere of southern Africa Southern Africa hosts a rich history of geophysical studies including small-scale exploration-type studies (da Costa, 1989), early studies of deep crustal structure (Hales and Sacks, 1959) to large-scale multinational projects (Carlson et al., 1996). The summary presented here focuses on southern African geophysical studies that were collected outside the context of the Kaapvaal Project. I have emphasized gravity and a variety of seismological studies that were useful in defining crustal thickness. In the first two sections (2.2.1 and 2.2.2) I will discuss geophysical studies of the upper crust of the Kaapvaal Craton including studies that have been conducted over the terrains surrounding of the Craton. This discussion excludes the Bushveld Complex, which is presented in detail in Chapter 4. In next section (2.2.3) I will cover studies of the deep crust, including a compilation of crustal thickness determinations. Finally in section 2.2.4, I will discuss the upper mantle studies that have been conducted in southern Africa. 2.2.1 Upper crustal geophysical anomalies of southern Africa Bouguer gravity anomalies of southern Africa range from lows around ?200 mGal to highs of over 50 mGal. Many prominent Bouguer anomalies can be ascribed to sources in the upper crust (Figure 2.3). A number of these upper crustal anomalies have been well-studied, in some cases complemented with other geophysical measurements including magnetics, radiometrics, and seismic reflection and refraction (Antoine et al., 1990; Corner et al., 1986; de Beer et al., 1984; Henkel and Reimold, 1998; Meyer and de Beer, 1987; Mushayandebvu, 1995; Odgers and du Plessis, 1993; Stettler et al., 1988; Stettler et al., 1999). 45 2.2.1.1 The Witwatersrand Basin and Vredefort Impact Structure The Witwatersrand Basin is generally regarded as a structural remnant of a much larger basin that developed as a foreland basin between ~3074 Ma and ~2714 Ma in the south-central portion of the Kaapvaal Craton (Burke et al., 1986; Robb et al., 1997) (Figure 2.1). Since the initial discovery of gold in the Witwatersrand Basin, geophysics has played an important role in delineating the size, shape and structural complexities of the basin. The historical summary by Roux (1967) explains how gravity and magnetics were used in the early years of exploration to outline the extent of the Witwatersrand Basin, which led to the discovery of the West Wits line and Welkom gold fields. These methods in particular were extremely successful due to the large density contrasts between the low density granites and the high density lower Witwatersrand argillaceous rocks and the highly magnetic shale horizons in the lower Witwatersrand Supergroup, which acted as marker beds in a constant stratigraphic sequence below the gold-bearing conglomerates (Roux, 1967). In the center of the Witwatersrand Basin is the Vredefort impact structure, a giant eroded crater formed by the impact of a bolide that hit the Earth at 2.02 Ga (Figures 2.1, 2.2 and 2.3) (e.g. Hart et al., 1991; Kamo et al., 1996; Moser, 1997). The original crater size has been estimated at 300 km diameter, making it the largest known impact structure on Earth (Therriault et al., 1993). The central location of the Vredefort impact structure within the Wiwatersrand basin has provided the opportunity for many combined studies of Vredefort and the Witwatersrand Basin. A structural map of the Witwatersrand Basin enhanced by the addition of integrated magnetic and gravity data interpretations was produced (Corner et al., 1986; Corner et al., 1990; Corner and Wilsher, 1989), based on the earlier map of Pretorius et al. (1986). This work identified the magnetic ?Vredefort discontinuity?, made several suggestions for extensions to the Witwatersrand Basin, and 46 provided a geophysical interpretation of the Vredefort impact structure. The broad scale three dimensional geometry and shape of the Witwatersrand basin has been fairly well constrained by mining and exploration activity, especially with advances in hard rock seismic techniques (e.g. Campbell, 1990; Coward et al., 1995). The 112 km long trans- Witwatersrand seismic reflection profile details the structure of the Witwatersrand basin and part of the Vredefort impact, although deeper reflectors of the lowermost crust and Moho are not apparent (Durrheim et al., 1991). This is most likely due to the high frequencies of the source signals that were used and the fractured nature of the crust (Durrheim et al., 1991). Extensive gravity data were collected over the central uplift of the Vredefort impact in an effort to delineate and evaluate the 30 mGal local gravity high located there (Stepto, 1990), following on earlier work by Mar? (1945). Stepto (1990) found that the gravity signal could be wholly accounted for with the upwelling of lower crustal rocks. A larger scale interpretation of the available Bouguer gravity and seismic data of the Witwatersrand basin and Vredefort impact structure by Henkel and Reimold (1998) demonstrates a possible model for the impact structure involving uplift of the Moho by 4 km; however, the lowermost crust and Moho boundary location remain unconstrained in this model. The ?Vredefort discontinuity? is a magnetic anomaly concentric with the center of Vredefort originally proposed by Corner et al. (1990) as a mid-crustal magnetite-rich layer. Modeling of this anomaly, based on physical property measurements and estimates of magnetic remanence demonstrates that the source could be in the upper crust (Henkel and Reimold, 2002). However, it is more likely to be caused by impact-related changes in magnetic properties (Carporzen et al., 2005; Cloete et al., 1999; Hart et al., 2001; Hart et al., 1995). 47 2.2.1.2 Trompsburg Layered Mafic Intrusion One of the most prominent Bouguer gravity anomalies in southern Africa is associated with the Trompsburg layered mafic intrusion, known only from geophysical studies and boreholes (Buchmann, 1960; Davies et al., 1970; Ortlepp, 1959). The Trompsburg intrusion has a circular Bouguer gravity anomaly of about 100 mGal that is centered near the town of Trompsburg in the Free State (Figures 2.1 and 2.3). This anomaly is produced by a layered mafic intrusion with a radius of about 25 km, as determined by drilling and modeling of gravity data, and is overlain by approximately 1000 m of Karoo sediments of lower Beaufort age (~250 Ma) (Buchmann, 1960; Tankard et al., 1982). A strong magnetic high of several hundred nT is coincident with the gravity anomaly. B.D. Maree first discovered this feature in 1942 while collecting gravity data for the Geological Survey of South Africa (Buchmann, 1960). Seven boreholes were drilled into the gravity anomaly in an attempt to establish its cause, and a lopolith-shaped layered mafic intrusion was conjectured. Rocks of similar composition to the Bushveld Complex were discovered at a depth of 1050 m below surface (Ortlepp, 1959), although none of the boreholes penetrated the entire sequence of the layered intrusion. However, one borehole helped define the margins of the intrusion by entering underlying basement rocks directly beneath Karoo cover. The Trompsburg intrusion was initially dated at 1372 ? 141 Ma using the Rb/Sr whole-rock isotopic method (Davies et al., 1970), but has been recently redated using U-Pb zircon methods at 1915 ? 5.6 Ma (Maier et al., 2003), an age still significantly different from the age of the Bushveld Complex at 2058 Ma (Buick et al., 2001). Thus, in spite of similarities of lithologies, they are unlikely to be genetically related due to this significant age difference. Recent three dimensional modeling of the gravity field, constrained by drilling and physical property measurements 48 of core samples, has suggested that the Trompsburg Complex could be as thick as 10 km, prompting interest from mining companies (Mar? and Cole, 2003). 2.2.1.3 Morokweng Impact Structure The Morokweng impact structure is located approximately 23?32?E and 26?20?S in the Northwest Province of South Africa and is largely covered by post-Cretaceous sand and sediments (Figures 2.1 and 2.3). It is known largely from its aeromagnetic signature and initially was thought to be an intrusive magmatic body of low density and high magnetic signature, such as a magnetite rich syenite, similar to the Pilanesberg, with a diameter of approximately 30 km (Corner et al., 1986; Stettler, 1987). More recently, the circular magnetic feature has been interpreted as an impact structure based on the geophysical signature and on the identification of shock features in borehole core samples. The age of this impact has been constrained to 145 ? 0.8 Ma (Hart et al., 1997a; Koeberl et al., 1997). The gravity signature of Morokweng is subtle due to the many lithologies in the impact region but the isopach map of cover thickness has a distinctive arcuate shape (Andreoli et al., 1994; Reimold et al., 1999). The diameter of the impact has been constrained to less than 80 km based on borehole intersections and geophysical modeling, but it still qualifies as one of the largest impact structures on Earth (Henkel et al., 2002; Reimold et al., 2002). 2.2.1.4 Matsap Group ? Northwest Cape Anomaly The dense rocks of the 1.8-2.0 Ga. Matsap Group on the western side of the Kaapvaal Craton are coincident with a prominent gravity high in the gravity map (Figure 2.3) (Meyer and Duvenhage, 1981; Tankard et al., 1982). This has been described as the 49 Northwest Cape Anomaly and is attributed to a substantial thickness of dense material at a depth of less than 20 km (Smit, 1962). The coincident magnetic anomaly argues for the dense iron ores of the Matsap Group, which cover the western boundary of the Kaapvaal Craton, as being the cause of both the Bouguer gravity and the magnetic anomalies (Smit, 1962). 2.2.1.5 Molopo Farms Complex, Botswana The Molopo Farms complex in southern Botswana is a large (12,000 km2) layered mafic intrusion of Bushveld Complex age (~2.06 Ga) with similar rocks and broadly similar stratigraphy as the Bushveld Complex (Gould et al., 1987). The Molopo Farms Complex has little surface exposure due to extensive cover by Kalahari beds up to 220 m thick and is known mainly from drilling and geophysical studies, especially gravity (Figures 2.1 and 2.3) (Du Plessis and Walraven, 1990; Gould et al., 1987; Gould et al., 1989; Kimbell et al., 1984; Reichardt, 1994). To date, no profitable ore reserves have been found. Gravity modeling, constrained by boreholes and density measurements, suggests that a large region of elevated Bouguer values is associated with the dense mafic and ultramafic intrusives of the Molopo Farms Complex (Kimbell et al., 1984). Although the authors speculate that the Molopo Farms Complex might be isostatically compensated, with a diameter of roughly 100 km it is more likely to be largely supported by the strength of the crust, similar to the Trompsburg intrusion (Watts, 2001). 2.2.1.6 The Great Dyke, Zimbabwe The ~2586 Ma (Mukasa et al., 1998) Great Dyke is a long (~550 km) tabular instrusion trending NNE, comprising layered mafic and ultramafic intrusive rocks, and is 50 between 4 and 11 km wide (Figure 2.1 and 2.3) (Wilson, 1996). It shows up clearly on the regional Bouguer gravity data as an anomaly of about +40 mGal. Modeling of the gravity data, constrained by density measurements and some drilling has resulted in a model of a vertically dipping dyke with a mantle-tapping deep structure assumed to be the dyke feeder (Podmore, 1970; Podmore and Wilson, 1987; Weiss, 1940; Wilson, 1996). Complementary analysis of the anisotropy of magnetic susceptibility (AMS) data and palaeomagnetic studies of the Great Dyke (McElhinny and Gough, 1963) and the satellite dykes show a strong remnant component to the magnetism (Bates and Mushayandebvu, 1995; Mushayandebvu, 1995; Mushayandebvu et al., 1994). The AMS study (Bates and Mushayandebvu, 1995) was able to show at least 3 distinct feeder sites to the satellite Umvimeela Dyke that are analogous with the 3-4 coalescent feeder zones identified from geological studies (Wilson, 1996). 2.2.1.7 Lebombo Anomaly A large positive Bouguer anomaly of over 90 mGal running north-south along the border between South Africa and Mozambique is associated with the exposure of basaltic Karoo age (183 ? 1 Ma) lavas (Duncan et al., 1997) of the geomorphological Lebombo Monocline (Smit, 1962) (Figure 2.1 and 2.3). This Karoo igneous event has traditionally been associated with Gondwana breakup (Tankard et al., 1982), but that interpretation is currently under scrutiny largely because it takes place ~20 m.y. before the breakup (Le Gall et al., 2002; Watkeys, 2002). From an interpretation of the Bouguer gravity data, the thickness of the lavas is estimated at 8 km, and dipping at 23? east (Smit, 1962). Palaeomagnetic poles have also been determined for many sites in the Karoo including the Lebombo, which records at least four reversals (Hargraves et al., 1997) however, their 51 exact correlation remains enigmatic due to the large number of reversals occurring at that time (Duncan et al., 1997). 2.2.1.8 Limpopo Belt The high grade granulite-gneiss terrain of the Limpopo Belt links the Archaean Zimbabwe Craton to the north and Kaapvaal Craton to the south in a structurally complex zone that is only partially exposed (e.g. Hofmann et al., 1998; Tankard et al., 1982). The Limpopo Belt is subdivided into the Northern Marginal Zone (NMZ), Central Zone (CZ) and the Southern Marginal Zone (SMZ) based on lithology, structural, metamorphic grade and ages (e.g. van Reenen et al., 1987). There are three dominant ages reported for the Limpopo Belt at ~3.1 Ga, ~2.65 Ga, and ~2.0 Ga. The ~2.65 Ga ages, which are mainly from the SMZ, have traditionally been interpreted as defining the collision between the Limpopo Belt and the Kaapvaal Craton. The ~2.0 Ga ages have been interpreted as representing a later magmatic event (e.g. Barton and van Reenen, 1992; Hofmann et al., 1998; Kreissig et al., 2001; McCourt and Armstrong, 1998; van Reenen et al., 1987). However, the large number of ~2.0 Ga ages from the Central Zone is interpreted by some workers as the age of collision, based largely on the lack of deformation in the CZ and NMZ at ~2.65 Ga (Barton et al., 1994; Chavagnac et al., 2001; Holzer et al., 1998; Kamber et al., 1995; Schaller et al., 1999). Thus the timing of the collisions between the Zimbabwe Craton, Limpopo Belt and Kaapvaal Craton remains unresolved (Kamber et al., 1995). Coward and Fairhead (1980) developed a model of the Limpopo Belt and surrounding Cratons using the Bouguer gravity data. Although this model was unconstrained by other geophysical data, they argued for overthrusting of the Kaapvaal 52 Craton onto the Zimbabwe Craton along the Umlali shear zone, a broad ductile shear zone in the northern part of the Limpopo Belt (Rollinson, 1993). This argument was based partly on the observed asymmetry of the gravity signature over the Limpopo Belt. Coward and Fairhead (1980) also argued for a Pratt isostatic mechanism to explain the long-wavelength isostatic gravity anomaly, due to the correlation between the positive isostatic anomalies and the exposed high-density granulites (Coward and Fairhead, 1980). In another study of the gravity signature of the Limpopo Belt, Emenike (1986) claimed that the gravity profile over the Limpopo Belt is distinctive and can be used to determine the location of the buried Limpopo Belt in regions of cover. He also argued that an averaged gravity profile over the region could be modeled to produce a ?type? anomaly. Using forward modeling he obtained a fairly thick crust of 39-41 km in the Limpopo Belt region and argued for large lateral density changes with dense crustal blocks of the CZ and SMZ extending from surface to the Moho, causing the gravity high. This was offered only as a suggestion due to the unconstrained nature of the gravity modeling. An order of magnitude error in the modeled gravity results due to confusion between gravity units and milligals (1 g.u. = 0.1 mGal) was pointed out by Kleywegt (1988), who suggested corrections to the gravity modeling of Emenike, and proposed that while the Emenike model is partially plausible, other models, including those suggested by himself, are equally plausible. These include the presence of high density lower crustal rocks of the SMZ that extend from the surface to depths of about 10 km depth. De Beer (1988) argued that the strong, positive, Airy-Heiskanen isostatic anomaly present in the Limpopo Belt is due to mass excess in the upper crust. This argument is supported by their analysis of the gravity data of the Palmietfontein and Entabeni granite plutons (Stettler et al., 1990). They suggested that the lack of an isostatic anomaly associated with the plutons, which are located within an extensive positive isostatic anomaly of the SMZ, indicates 53 that the source of the positive isostatic anomaly is in the upper crust (de Beer and Stettler, 1988; Stettler et al., 1990), as it is readily counterbalanced by the plutons. A different interpretation of the gravity data was made by using travel-time seismic refraction data to constrain results (Gwavava et al., 1996; Gwavava et al., 1992). They prefer a model of crustal thinning through the Limpopo Belt and modeled the significant increase in Bouguer anomalies in Mozambique as due to crustal thinning, attributing this to the breakup of Gondwana (Gwavava et al., 1996; Gwavava et al., 1992). They also included a study of the elastic thickness (Te) properties of the Limpopo Belt, surrounding cratons and the Mozambique basin, which showed significant differences between the Limpopo Belt, with a Te of 56 km and the Mozambique basin with a Te of 22 km. However, the Limpopo region is a mixed region of cratons and mobile belts that is likely to have rapidly spatially varying strength properties (Gwavava et al., 1996; Gwavava et al., 1992). A further study by de Beer and Stettler (1992), combining a variety of geophysical data suggests that the cause of the positive gravity anomalies in the SMZ and NMZ is due to the high-grade rocks in the upper crust. Nguuri et al. (2001) have shown that the crust in the CZ of the Limpopo Belt is about 50 km thick, although the receiver function results are not as well defined as they are on the Kaapvaal and Zimbabwe Cratons. They also showed that the NMZ and the SMZ have a more cratonic-type Moho signature in the receiver function results (Nguuri et al., 2001). The westward extent of the Limpopo Belt has been considered by Rangani et al. (2002), who used the upward continued Bouguer gravity data to extend the Limpopo Belt westwards and wrap around the southern tip of the Zimbabwe Craton. 54 2.2.1.9 Aghulus Plateau Graham and Hales (1965) published the results of a surface ship gravity study off the southern coast of South Africa and their interpretation of the unconstrained gravity data gave a crustal thickness of 34 km onshore and 21 km offshore (Figure 2.5). As a result of their study Graham and Hales (1965) speculate that the Agulhas Plateau may not be typically oceanic and by implication, is continental. This is one of the few gravity studies in southern Africa to consider the entire crustal thickness when modeling the results. A short (46 km), deep (12 s) seismic reflection profile was obtained perpendicular to the Graham and Hales (1965) study as part of an oil exploration program (Durrheim, 1987). This study suggested that the lack of reflections from the lower most crust implies the presence of Archaean crust (Durrheim, 1987). 2.2.2 Regional Bouguer Gravity and Topographic Studies Gravity data in South Africa have been collected and compiled since 1939, and continue to be curated by the Council for Geoscience in Pretoria. The first extensive publication of a compilation of gravity data by Hales and Gough (1962) presented Bouguer gravity data and calculated isostatic anomalies for a variety of Bouguer gravity crustal thicknesses. The main crustal features seen in this isostatic anomaly map are the Great Escarpment, Bushveld Complex, Trompsburg anomaly, northwest Cape anomaly and the Lebombo anomaly, all of which are discussed in Hales and Gough (1962). These features are all short-wavelength features (<250 km) and are clearly attributable to upper crustal sources. Additional crustal features such as the Witwatersrand Basin and the Vredefort impact structure can also be distinguished on the Bouguer gravity anomaly map. 55 The Bouguer gravity anomaly map of southern Africa has a strong gradient all along the coast due to the thinning of the continental crust as it approaches the ocean. This effect is absent on the isostatic anomaly map as the contribution from varying crustal thickness is removed. The Great Escarpment of southern Africa corresponds to a persistent zero contour on the isostatic anomaly map, with negative values on the seaward side (Hales and Gough, 1962). This has been attributed to erosion, flexure and active compensation of the Great Escarpment (Hales and Gough, 1959; King, 1955). Further work on flexure morphology by Ten Brink and Stern (1992) and on modelling the flexural isostatic response due to denudation by Gilchrist et al. (1994) and Gilchrist and Summerfield (1990) has suggested that escarpments can be long lived and may persist in the face of a variety of denudation rates and styles. Other authors, however, argue convincingly that the formation of the escarpment and the uplift of Africa is more recent arguing that otherwise erosion would have smoothed it out (Burke, 1996). Several regional studies of the Bouguer gravity of Africa have also contributed to the understanding of the very large scale structure of southern Africa. Bouguer gravity anomalies over all of Africa have been examined by Brown and Girdler (1980) in an effort to assess the cause of the ?great negative Bouguer anomaly? associated with the East African Rift system. They interpret a profile from southern to northern Africa, and attempt to define a ?standard African lithosphere? with a nominal thickness of 100 km based on a modified version of the AFRIC model (Gumper and Pomeroy, 1970). They also define an ?axis of maximum thinning?, which, north to south, extends along the East African Rift before bearing to the west at about 12?S through to Angola, suggesting, along with abundant seismicity, a possible extension to the East African Rift system (Brown and Girdler, 1980). This thinning is based on the assumption that the long- wavelength anomalies are due to variations in the thickness of the lithosphere and 56 assumes ??that the lower part of the lithosphere is denser than the underlying asthenosphere? (Brown and Girdler, 1980, p. 6444). This assumption is based on the conversion of velocities to densities following the Nafe-Drake curve (Brown and Girdler, 1980). One consequence of that assumption is that their models show significant lithosphere thinning beneath the Kaapvaal and Zimbabwe Cratons ? in contradiction to the low density, thick lithospheric keel proposed by Jordan (1975). Mushayandebvu and Doucour? (1994) analyzed regional Free Air gravity anomalies. These Free Air anomalies appear to agree well with topographic and known structural trends in most of southern Africa, the agreement breaks down in the regions of the Kaapvaal Craton and eastern Transvaal and may be due to deeper structures (Mushayandebvu and Doucour?, 1994). The long and intermediate wavelength geoid pattern of the African plate was studied by Doucour? and Antoine (1994), who subtracted the spherical harmonics of degree 2-10 from 2-30 to demonstrate that the intermediate wavelength geoid is strongly associated with recent geological structures such as sedimentary basins, whereas the longer-wavelength component has little correlation with geological or even continent- ocean boundaries (Doucour? and Antoine, 1994). The isostatic balance of Africa on a plate-wide basis has been considered by Hartley et al. (1996) using an admittance calculation. They concluded that the continent-wide admittance appears to show an elastic thickness (Te) that is wavelength-dependent and not strictly an Airy or even a simple flexure response. They obtain Te values of >100 km in old Archaean craton regions and the age of the lithosphere at the time of loading does not appear to correlate with the determined Te in a systematic fashion. In a more detailed study, Doucour? et al. (1996) determined the elastic thickness of the Kaapvaal Craton and the Namaqua-Natal Mobile Belt using a coherence calculation based on the method developed by Forsyth, 57 (1985). They found that the Te of the Kaapvaal Craton was 72 km, and that of the Namaqua-Natal region was 38-48 km, in rough agreement with the admittance results determined by Hartley et al. (1996). A new era of large-scale gravity studies has been ushered in with the advent of dedicated satellite gravity missions and the study of the global gravity field from previous satellite missions, whose results are expressed in a spherical harmonic expansion. Analysis of the global gravity field has outlined the broad structure of depleted mantle keels in southern Africa and elsewhere in the world (Kaban and Schwintzer, 2001; Kaban et al., 1999). These broad scale studies of the gravity, geoid and topography fields of southern Africa have highlighted the anomalous values beneath the Kaapvaal Craton, with varying interpretations (Kaban et al., 2003). Since the initial observation of Holmes (1944) that the elevation of southern Africa is anomalously high, the topography of southern Africa has been intensely studied. This observation has been interpreted by some as originating from a shallow mantle convection system resulting from Africa being stationary for the past 30 m.y. (Ashwal and Burke, 1989; Burke and Wilson, 1972; England and Houseman, 1984; McKenzie and Weiss, 1975). Additionally, lack of rainfall may contribute to the excess elevations, especially in southern Africa (Burke, 1996). However, this interpretation is difficult to reconcile with global and detailed tomographic studies (e.g. Fouch et al., 2004; Grand et al., 1997), which show no indication of partial melting in the upper mantle, especially beneath cratons, except possibly in the Tanzanian Craton (Nyblade et al., 1996; Ritsema et al., 1998). Another explanation of the excess elevation anomaly is that the elevations are due to dynamic topography resulting from a deep mantle source of the African ?superplume? (Lithgow-Bertelloni and Silver, 1998; Nyblade and Robinson, 1994). This large low velocity region sits directly beneath southern Africa just above the core-mantle 58 boundary (CMB). However, it is difficult to reconcile the great distance between the superplume at the CMB and the topographic uplift at the surface. A more recent explanation is that the general three-dimensional flow pattern in the mantle incorporating the superplume is the direct source of the uplift (Behn et al., 2004). Behn (2004) incorporated modeling of the flow patterns, incorporating densities based on velocities determined from seismic tomography and comparisons with shear wave splitting measurements. The best fitting model included the effects of subduction and upwelling from the superplume (Behn et al., 2004). 2.2.3 Deep Crustal studies There is a long heritage of seismological studies in southern Africa. In this section I have compiled early seismic studies that have crustal thickness results and information about the lithosphere. Seismicity studies in southern Africa have largely been driven by interest in events associated with the extensive Witwatersrand gold mines. As early as 1910 seismographs were used to record mine events. Subsequently seismic events were monitored on the mines but have also been used as sources to determine the structure of the upper lithosphere in many studies, starting with the demonstration by Gane et al. (1946) that observations of the mine events could be made at large distances from their source. A subsequent study by Willmore et al. (1952) used well located mine events as sources to study the crustal thickness of the western Transvaal using travel time methods. They found that the crustal thickness in the region was roughly 36 km at a point roughly half way along their profile (Figure 2.5 and Table 2.1). A similar study by Gane et al. (1956) on a significantly expanded scale examined crustal structure in profiles emanating from Johannesburg to the north, south, west and east, and confirmed typical 59 thicknesses for Archaean cratonic crust in these regions (~35 km). Expanding this work to the eastern Transvaal led Hales and Sacks (1959) to discuss evidence of an intermediate layer, suggesting that the crust actually consists of an upper and lower crustal layer. Among the more comprehensive crustal thickness seismic studies using travel times from the Witwatersrand mine tremors was that of Durrheim and Green (1992), using three component 1 Hz geophones (Figure 2.5). They demonstrated that the Kaapvaal Craton crust is thinner than the surrounding Proterozoic crust, a result that is consistent with that found for other Archaean cratons worldwide (Durrheim and Mooney, 1994). These early travel time studies helped establish an active research program in South Africa and contributed to defining crustal structure (Figure 2.6). 60 Figure 2.5. Locations of crustal thickness studies with relevant references excluding the results of the Southern African Seismic Experiment. The details of these results can be found in Table 2.1, this map simply demonstrates the locations of deep crustal studies. 61 Figure 2.6 Image of more reliable seismic crustal thickness estimates from studies from 1959-2000. See Table 2.1 for details and Figure 2.5 for reference information. Due to complications and ambiguity of seismic results in the Limpopo Belt, these results were left off of this map. This map does not include any results from the Southern African Seismic Experiment. 62 Table 2.1 Summary of crustal thickness studies. Error estimates are based on estimates of similar studies where not specified in the cited study. This table does not include SASE results. Longitude (Dec deg) Latitude (Dec deg) Crustal Thickness (km) Error Est. (km) Stn. ID Type of Study Reference Notes 24.8096 -27.0007 36 5 n/a Travel time Willmore, Hales and Gane (1952) 26.7172 -28.5674 35 5 n/a Travel time Gane et al. (1956) 29.9675 -26.627 37 5 8 Travel time Hales and Sacks (1959) 23.1972 -33.4464 34 5 n/a Seismic Refraction Graham and Hales (1965) 26.4456 -38.6862 21 5 n/a Seismic Refraction Graham and Hales (1965) 20.7788 -35.4685 32 5 B4 Seismic Refraction Hales and Nation (1972) 19.4296 -29.0674 28 5 ES1 EM Sounding Van Zijl (1978) 1 17.8836 -30.2413 35 5 ES2 EM Sounding Van Zijl (1978) 1 16.514 -21.8852 38 5 ES5 EM Sounding Van Zijl (1978) 1 33.1222 -18.731 40 5 ES6 EM Sounding Van Zijl (1978) 1 29.5498 -23.875 40 5 ES7 EM Sounding Van Zijl (1978) 1 31.5682 -20.655 40 5 ES8 EM Sounding Van Zijl (1978) 1 16.5335 -21.5315 45 5 8a Seismic Refraction Baier et al. (1983) 17.69 -21.9599 45 5 8b Seismic Refraction Baier et al. (1983) 18.05 -23.6182 49 5 8c Seismic Refraction Baier et al. (1983) 23.5361 -34.167 30 5 n/a Seismic Reflection Durrheim (1987) 30.6041 -21.5722 29? 5? 1 Travel time Stuart and Zengeni (1987) 2 30.8147 -20.9102 34? 5? 10 Travel time Stuart and Zengeni (1987) 2 30.713 -20.2028 40? 5? 20 Travel time Stuart and Zengeni (1987) 2 29.2812 -23.8048 41 5 ES38 EM Sounding De Beer and Stettler (1988) 1 29.4864 -23.8186 34 5 ES36 EM Sounding De Beer and Stettler (1988) 1 29.6368 -23.9245 36 5 ES34 EM Sounding De Beer and Stettler (1988) 1 29.7812 -23.9875 41 5 ES37 EM Sounding De Beer and Stettler (1988) 1 30.0572 -23.8957 39 5 ES32 EM Sounding De Beer and Stettler (1988) 1 19.2776 -29.2594 42 5 Witsan d Seismic Refraction Green and Durrheim (1990) 28.03 -26.175 42 5 BPI Spectral Ratio Muller (1990) 23.865 -29.115 34 5 DGL Spectral Ratio Muller (1990) 63 24.893 -28.377 37 5 WAR Spectral Ratio Muller (1990) 27.618 -24.626 42 5 SND Spectral Ratio Muller (1990) 27.101 -25.221 45 5 PIL Spectral Ratio Muller (1990) 26.272 -25.853 41 5 KLI Spectral Ratio Muller (1990) 21.742 -29.742 40 5 KEN Spectral Ratio Muller (1990) 28.294 -25.728 35 5 PRE Spectral Ratio Muller (1990) 3 26.534 -33.304 39 5 GRM Spectral Ratio Muller (1990) 21.3318 -23.7931 42 5 line 9492 Seismic Reflection Wright and Hall (1990) 21.0862 -22.8433 42 5 line 9493 Seismic Reflection Wright and Hall (1990) 20.9116 -22.8172 42 5 line 9494 Seismic Reflection Wright and Hall (1990) 20.7356 -23.4439 42 5 line 9499 Seismic Reflection Wright and Hall (1990) 26.7972 -26.606 38 5 n/a Seismic Reflection Durrheim et al. (1991) 27.6505 -26.9112 35 5 Stn 13 Seismic Refraction Durrheim and Green (1992) 27.4875 -26.5136 36 5 Stn 35 Seismic Refraction Durrheim and Green (1992) 29.2684 -23.1763 none n/a n/a Seismic Reflection Durrheim et al. (1992) 4 22.21625 -28.2214 39 5 n/a Seismic Reflection Stettler et al. (1999) -21.759 13.968 33 2 CAPN Receiver Functions Hanka et al. (2000) 5 -21.359 14.749 35 2 BRAN Receiver Functions Hanka et al. (2000) 5 -20.151 15.689 37 2 OUTN Receiver Functions Hanka et al. (2000) 5 -20.612 17.335 40 2 WATN Receiver Functions Hanka et al. (2000) 5 -23.435 18.743 46 2 LEON Receiver Functions Hanka et al. (2000) 5 -19.202 17.584 37 2 TSUM Receiver Functions Hanka et al. (2000) 5 1. At base of layer 3 2. Crustal thickness is only tentatively identified 3. Adjusted to account for underestimation of up to 9% due to down dip effects 4. Excellent summary paper, no new measurements 5. Information obtained with permission of author (Winifried Hanka: hanka@gfz-potsdam.de) from: ftp://ftp.gfz-potsdam.de/pub/home/st/hanka 64 2.2.3.1 Damara, Namaqualand, Witswatersrand and Limpopo seismic lines and studies Baier et al. (1983) collected three seismic refraction lines in the Damara Orogen in Namibia. The western section of the Damara profiles appears similar to the Namaqualand results of Green and Durrheim (1990), although the lower crust of the Damara Orogen seems to have higher velocities (6.87 -7.0 km/s) and thicker crust at 47 km (Baier et al., 1983; Green, 1983). A 290 km long seismic refraction line was shot across the Namaqualand metamorphic complex from Springbok to Kakamas in 1983 as part of a multidisciplinary study including gravity, magnetic, and geoelectical studies (Green and Durrheim, 1990). The purpose of the study was to determine the deep structure of the Namaqualand metamorphic complex. The Moho reflected phase, PmP, and travel time modeling were used to constrain the depth to the Moho at approximately 42 km, with lower crustal P wave velocities in the intermediate range (6.6-6.9 km/s). Green and Durrheim (1990) found no correlation between the ultra-deep Schlumberger electrical sounding results (Van Zijl, 1969) and their own seismic results (Green and Durrheim, 1990). This lack of correlation is important, as it highlights the difficulties of using electrical soundings to determine the Moho. Four deep seismic reflection lines were collected in the Nosop Basin in Botswana by Wright and Hall (1990), who published the results for the two way travel time survey between 3 and 15 seconds, and suggested that this region was probably underlain by the Kaapvaal Craton. This would extend the area of Kaapvaal Craton significantly to the west (Figure 2.5). Because of the economic importance of the Witwatersrand Basin, a deep seismic reflection profile across the Basin was commissioned as part of the National Geophysical Program (1987-1992) and was analyzed by Durrheim et al. (1991). This 112 km long, 16 s two-way travel time reflection seismic line ran from Ventersdorp, through 65 Potchefstroom to the centre of Vredefort, with the objective of examining the deep structure of the crust to provide clues to the formation of Wits Basin as a foreland basin (Burke et al., 1986) or thin spot (Durrheim et al., 1991). Unfortunately the seismic data in the eastern section of the line are difficult to interpret due to steep dips and extreme faulting associated with the Vredefort impact (Durrheim et al., 1991). A detailed seismic refraction study of Vredefort provides some constraints on the velocity structure but is too limited for deeper structure (Green and Chetty, 1990). This single seismic line was unable to provide conclusive evidence supporting a particular model of formation, given the evident complexity of deformation in the region (Durrheim et al., 1991). Stuart and Zengeni (1987) tackled the crustal thickness determinations for the Limpopo Belt region using travel times from both the Witwatersrand mining region to the south and the Kariba-Zambia region to the north. While this method should produce better results since it uses sources from both directions, the region is very complex. Stuart and Zengeni (1987) reported tentative crustal thickness results for the Limpopo Belt, indicating a thin crust of only 29 km. However, they recognized that the region is quite complex and that, as they only used first arrival data, their results were not conclusive (Stuart and Zengeni, 1987). The National Geophysics Program (1987-1992) also funded a 13 s two way travel time deep seismic reflection profile across the Southern Marginal and Central Zones of the Limpopo Belt. These data, published by Durrheim et al. (1992) did not resolve the Moho in the Limpopo Belt, although the authors provide a synthesis of other seismic, gravity and geoelectric studies pertaining to the Limpopo Belt in an attempt to estimate Moho depth (Durrheim et al., 1992). Unfortunately the parameters (fold, number of sweeps) used to collect the seismic reflection data were significantly less than are generally accepted, and this may have resulted in the poor depth resolution and penetration (Durrheim et al., 1992). An indication that the 66 tentatively identified seismic Moho at ~35 km in the Limpopo Belt (Stuart and Zengeni, 1987) may be misidentified comes from a study of the crustal xenoliths in the Venetia kimberlite (Barton and Pretorius, 1998), which suggests a petrologic Moho at a depth of ~58 km. Barton and Pretorius (1998) explain this by invoking a major d?collement zone at 10 km depth. An alternative explanation could be that the crust-mantle boundary is at a significantly deeper depth due to collision and thickening as is currently happening in the Himalayas. The deeper crust may have partially melted and subsequently the entire package has rebounded as the Limpopo Belt has been eroded (Treloar et al., 1992; van Reenen et al., 1987). However, the amount of rebound may be limited due to a decrease in crustal buoyancy with age due to metamorphic effects in the lower crust, resulting in higher densities (Fischer, 2002). An integrated study of the gravity, seismic and geoelectric data in the Limpopo Belt demonstrated that both the north and south edges of the Belt dip inwards leading to an interpretation of the Limpopo Belt as a pop-up structure (de Beer and Stettler, 1992). Also as part of the National Geophysical program, vibroseis refraction data were collected over 6 long traverses in South Africa. Unfortunately, interpretations from only four of these lines were published: the Bushveld Complex, Limpopo Belt, Witwatersrand Basin, and Kheiss lines (Figure 2.5). The Bushveld Complex line will be discussed further in Chapter 4 and the Witwatersrand Basin and Limpopo Belt lines have already been discussed. The Kheiss seismic line was collected along the road between Sishen to Upington and then to Keimoes through the Kheiss Belt. There are strongly reflecting westward dipping reflectors, suggesting that the Kaapvaal Craton was being consumed (Stettler et al., 1998a; Stettler et al., 1999). While the Moho is indistinct on this seismic line, it is estimated at a depth of 39 km (Stettler et al., 1998a; Stettler et al., 1999). 67 As part of the Kaapvaal project, Anglo American released sixteen lines of vibroseis data to the Cape Town group for interpretation. Eight of these lines were shallow lines, recorded to six seconds two way traveltime (TWT), which is a depth of ~17 km. The remaining eight lines were deep profiles, recorded to 16 seconds TWT and they imaged the Moho at depths between ~36-41 km (de Wit and Tinker, 2004). Two of the six second lines are located further east and north of the Council for Geoscience (COG) Kheis seismic line, and also show strongly westward-dipping reflectors similar to those seen on the COG line (Figure 2.5 ? Tinker and de Wit, 2002). Unfortunately as these are shallow lines, they do not contribute to the crustal thickness data, although they do show significant thickening of the volcano-sedimentary sequences to the west. One of these western lines has been analyzed for crustal strength at ~ 1.8 Ga, which showed low elastic strength. This result was attributed to a transient marginal tectonic effect (Tinker et al., 2004). The remaining shallow seismic lines demonstrate that the Venterdorp rifting event was a major rifting event with up to 50% extension (Tinker et al., 2002). Two of the sixteen second, deep seismic lines cross the Colesburg Lineament without any indication in the data of a major suture zone (de Wit and Tinker, 2004). However, the lines cross the Colesburg Lineament at the position where it becomes difficult to trace on the magnetic and gravity data (Figures 2.2 and 2.5). The Moho depths determined from these studies are compatible with previous results and have been left off of Figure 2.6 for clarity (de Wit and Tinker, 2004). 68 2.2.3.2 Converted Phases Studies Receiver function methods were applied to the data from the southern Africa seismic experiment (SASE) to image the Moho and deeper mantle discontinuities beneath the Kaapvaal Craton. The results of the 3-D Moho imaging across the broad region of southern Africa, as presented in Nguuri et al. (2001), are summarized in Chapter 3 where they are used in the determination of the gravity signal due to the Moho. Detailed studies of the Moho and crust in the region around Kimberley, South Africa reveals a relatively thin crust ~35 km thick, composed predominantly of felsic to intermediate composition rocks with a flat, sharp Moho (James et al., 2003; Niu and James, 2002). The joint GFZ- Namibian seismic experiments included 5 broadband seismic stations where crustal thicknesses were determined using receiver functions (Figures 2.5 and 2.6) (Hanka et al., 2000). This study covers a region of southern Africa to the northwest of the Kaapvaal Project study (Figure 2.5). The results from the Namibian study, where crustal thicknesses are determined by the same technique of receiver functions and are also corrected for moveout, are directly comparable with those of Nguuri et al. (2001). An early study of converted phases, which is similar in theory to receiver functions, was conducted at nine stations throughout the Kaapvaal Craton (Figures 2.5 and 2.6) (Muller, 1991). The results show thin crust on the Kaapvaal Craton (~35-40 km) and thicker crust off craton (~45 km). These results are compatible with the Kaapvaal Project results in spite of differences in techniques (Nguuri et al., 2001). 2.2.4 Upper mantle studies Several global tomographic studies have shown that the average seismic velocities beneath the region of southern Africa are significantly faster than under oceans (Grand et 69 al., 1997; Montagner and Tanimoto, 1991; Ritsema and van Heijst, 2000). Early surface wave studies of the southern African region were collected using a limited number of global seismic network (GSN) stations or small local seismometer arrays (Bloch et al., 1969; Cichowicz and Green, 1992; Ritsema and van Heijst, 2000). These studies tend to average out the response of separate geological regions. Several regional dispersion and waveform surface wave studies of southern Africa have produced models with a high velocity lid overlying an upper mantle low-velocity layer (Bloch et al., 1969; Cichowicz and Green, 1992; Qiu et al., 1996). However, models requiring significant low-velocity layers (< 4.5 km/s) are inconsistent with the mantle xenolith data (James et al., 2004; Qiu et al., 1996) and can be demonstrated to be the result of inverting anisotropic data using an isotropic model (Anderson and Dziewonski, 1982; Saltzer, 2002). Two phase-delay surface wave studies of inversions of Rayleigh- and Love-wave data from the Kaapvaal project demonstrate that there is strong anisotropy beneath the Kaapvaal Craton, although the two studies disagree on the location and depth extent of the anisotropic layer (Freybourger et al., 2001; Saltzer, 2002). These studies also clearly show increasing seismic velocities with depth and no indication of an upper mantle low velocity zone. In addition, preliminary work on interstation surface-wave dispersion using data from the Southern Africa Seismic Experiment (SASE) has been used to confirm fast S-wave velocities and variations in the uppermost mantle in southern Africa (Gore, 2005; Nguuri, 2004). A recent, more detailed and selective study by Larson et al. (2006) investigates the S-wave velocity structure beneath the undisturbed portion of the Kaapvaal Craton south of the Bushveld Complex using carefully selected two station paths. They observe a slight decrease in S-wave velocity with depth to 180 km (consistent with xenolith results), but the data preclude a major low velocity beneath the craton. The fact that the 70 velocity structure is consistent with mantle xenoliths implies that mantle velocities (and temperature) have not changed significantly in the last 80-90 m.y. 2.3 Data Sets In this study I have made extensive use of the receiver function and delay time tomography results of the Kaapvaal Project (Fouch et al., 2004; Nguuri et al., 2001) and the gravity, magnetic and topography data available for southern Africa. The magnetic, gravity and some topography data were made available by the Council for Geoscience, Pretoria. Additional topography data from GTOPO30 database of the USGS were also used (USGS, 1996). In this section I review, in detail, the collection, processing and coverage of these various data sets. 2.3.1 Gravity Data The Council for Geoscience of South Africa has collected and compiled gravity data since 1939 (e.g. Gordon-Welsh et al., 1986). Since 1994 the Council has undertaken the task of compiling geophysical data in the surrounding Southern African Development Community (SADC) region in an effort to provide a framework for broad scale mineral and water exploration (Stettler pers. comm., 2001). The SADC countries include: Angola, Botswana, DRC, Lesotho, Madagascar, Malawi, Mauritius, Mozambique, Namibia, South Africa, Swaziland, Tanzania, Zambia and Zimbabwe. It is this compiled database of Bouguer gravity data that has been mostly used in this project. The actual point data were also available for South Africa, Botswana and Zimbabwe and the station locations are shown in Figure 2.7. The data points have been gridded to 1 km for imaging 71 (Figure 2.3), although the original data have variable spacing and were often concentrated along roads. The largest error in the gravity surveys is due to inaccuracies in elevation determinations (Smit, 1961; Smit, 1962; Smit et al., 1962; Venter et al., 1999). In some of the older parts of the data sets, elevations were collected with barometers, resulting in poorly constrained elevations (Leaman, 1984), which can lead to errors of between 2-5 mGal in the gravity data, especially in these compiled data sets (Hales and Gough, 1960). For the purposes of this study, errors of this magnitude are relatively unimportant as I am interested in long wavelength features of several 10s to 100s of mGal. The SADC gridded Bouguer gravity anomalies were computed with a Bouguer density of 2.67 Mg/m3 and with theoretical gravity based on the International Gravity Standardization Net (IGSN) 1971 system of absolute gravity values (Darracott, 1973). Readings were obtained mostly using LaCoste and Romberg geodetic gravity meters with barometers and topocadestral maps for height determinations. 72 Figure 2.7 Bouguer gravity data station locations of South Africa, Botswana and Zimbabwe as of 2000, as compiled by the Council for Geoscience (South Africa). For imaging purposes data were gridded to a 1 km grid cell size. The data coverage is uneven as large amounts of data are collected along roadways. The detailed Bouguer gravity data used in this study reveal a wealth of information that correlates very closely with the surface geology at short wavelengths (less than ~100 km). Features that are readily apparent on the gravity image include: the Vredefort impact structure, the Bushveld Complex, and the Trompsburg Complex (Figures 2.3 and 1.14). The long wavelength features (>~100 km) correlate with large scale structures such as the edge of the Kaapvaal Craton (Figure 2.3). 73 2.3.2 Magnetic Data Beginning in the 1970s, the Council for Geoscience began collecting and compiling aeromagnetic data. The earliest surveys were flown using proton precession magnetometers, with a nominal 150 m flight height, 1 km flight line and 5 km tie line spacing. The mean aircraft speed used was 240 km/h, resulting in a ~50-100 m along-line sample interval. In the 1980s, the development of Cesium-vapor magnetometers meant that data could be collected with shorter cycle times, resulting in better along-line resolution. The Cs-vapor magnetometer was also used in the collection of aeromagnetic data in southern Africa. Similar programs of collecting aeromagnetic data throughout the SADC region have resulted in nearly complete aeromagnetic coverage of South Africa, Namibia, Botswana and Zimbabwe (SADC Geophysics and Seismology Working Group, 1998). There exists incomplete coverage, as yet, in Mozambique and Angola, although surveys are currently being conducted. The Council for Geoscience has compiled all of the magnetic data available in southern Africa as part of a government sponsored SADC agreement and has gridded the data at one km grid spacing (Stettler et al., 2000). Because the government data have very large line spacing (1 km), they are only used for large scale mapping, mainly for mapping the Kaapvaal Craton boundary, lithology identification and for defining important magnetic linear features, but not for quantitative calculated interpretations (Figure 2.2). 2.3.3 Topographic Data The primary source of the topographic data used in this study was GTOPO30, global elevations gridded at 30 seconds of arc, which is freely available on the internet (USGS, 1996). For imaging purposes the GTOPO30 data were gridded at 1 km (Figure 74 2.8). Where more direct comparisons with the gravity data are appropriate, the elevations determined at the same time as the gravity data were used. Figure 2.8 Digital terrain model of southern Africa from GTOPO30 sun-shaded from the northwest. On land the data were gridded at a spacing of 1 km. Offshore data are from (Smith, 1997). Geologic terrains overlaid, as shown in Figure 2.1. 2.3.4 Seismological Data: crustal thickness and delay time tomography results of the Southern African Seismic Experiment Although data from previous seismological studies have been briefly considered in this study, the main seismological input to this project has been from the Southern African Seismic Experiment (SASE) of the Kaapvaal Project, as these data provide a 75 consistent, high quality dataset. SASE, a centerpiece of the Kaapvaal Project, involved the deployment of 54 broadband seismometers at 82 sites throughout southern Africa (Figure 2.9). The dataloggers used were Refraction Technologies (REFTEK) Data Acquisition Systems (DAS) with 16 bit dual gain systems from the Carnegie Institution of Washington (CIW) and 24 bit systems from the Integrated Research Institute for Seismology (IRIS) Consortium. All stations recorded continuous data at 20 samples/sec and a few stations were set to trigger and record data from local events at 100 samples/sec for a period of minutes. All systems had a 1 or 2 Gigabyte hard drive that was swapped for an empty drive every 4 to 6 weeks. An internal Global Positioning System (GPS) clock was used to provide accurate absolute time that synchronized an internal clock every hour. The seismometers used were mainly Streckeisen STS2 three component broadband systems. The sensors were placed in a 50-gallon drum, buried to roughly 1 meter and mounted on a concrete plinth that had been poured on bedrock. At some sites an effort was made to decouple the drum from the bedrock plinth using fast drying foam, but it is unclear if this procedure significantly improved the data. In addition to the Streckeisen instruments, 4 broadband Guralp sensors were also deployed in the southern portion of the array. At most sites (except for Goetz Observatory, Bulawayo) station power was supplied by solar panels with deep discharge marine style batteries providing continuous power. The optimum characteristics for the seismic station sites were: One meter of overburden to solid bedrock, no ground water, minimal cultural noise, and a secure site. At the time of the deployment from April 1997 - April 1999, the Kaapvaal Seismic Array was the largest deployment of its kind (Figure 2.9). 76 Figure 2.9 Stations of the main Kaapvaal Seismic Array (KSA), a component of the Southern African Seismic Experiment. These stations include stations deployed as part of the Kaapvaal Project , plus 4 permanent stations shown as light blue squares (SUR, BOSA, LBTB and TSUM) of the global seismic network (GSN) that were included in the interpretation. Stations were serviced from four service centers shown as circles with a plus sign, at Cape Town, Kimberley, Johannesburg, and Mashvingo. Crustal thickness determinations were made at all of these sites. These stations were also used in the tomographic inversion for seismic velocity variations. Four different teams were formed, based on the locations of the data servicing centers at Masvingo/Harare, Wits (Johannesburg), Kimberley and Cape Town. These teams set off in mid 1996 to find appropriate sites and build stations (Figure 2.10). Professor Rod Green of Green?s Geophysics coordinated site selection and construction for the overall experiment. I was involved with siting and building of stations both in South Africa with the Wits group and in assisting the Zimbabwe group. 77 Figure 2.10 The components of station 47 of the Kaapvaal Seismic Stations. A. The field-hardened hard drive and data acquisition system inside the ?dog house?. B. The dog house with solar panels and GPS receiver, C. The interior of the dog house with the electric board and batteries. Note that the batteries are well away from the other electronic components to minimize corrosion due to battery fumes. D. The STS2 seismometer in the 50 gallon drum. The cable has no tension in it and the connecting pipe is isolated with spray foam. The first stations were deployed in Zimbabwe in April 1997 with the assistance of Rio Tinto Zimbabwe after successfully extracting the instruments from customs and 78 running a huddle test. The huddle test ensures that all instruments (seismometers, dataloggers, and GPSs) are collecting data properly by setting up all of the instruments together in one place and running them for at least a 24 hour period. Data from the test are then examined for any irregularities before the instruments are installed in their field sites. The next set of instruments was distributed to 3 teams following the Kimberley huddle test and deployed in mid to late April 1997. All stations were up and running within 14 days of the huddle test as all sites had been previously prepared. The sites were then all checked within 2 weeks to ensure that data were being properly collected. Team members for the Wits portion of the deployment included: Tom Jordan, Teresia Nguuri, Rebecca Saltzer, Sue Webb, Cedric Wright, Peter Burkholder and Mpho Nkwana. Other groups had similar numbers of people involved in deploying stations, the full list of which can be found at: http://www.dtm.ciw.edu/kaapvaal. During the course of this experiment, station 52 had to be removed due to security problems (solar panels stolen) and station 55 had to be moved due to commencement of mining operations at The Oaks kimberlite pipe (Figure 2.9). Station 69 was added late in the initial deployment as the originally selected site in Zimbabwe proved to be inaccessible (Figure 2.9). The data collection was managed from four service centers: Cape Town (UCT and Rod Green), Kimberley (De Beers), Johannesburg (Wits University), and Masvingo (RTZ, Univ. of Zimbabwe). These centers were responsible for gathering data from the stations every 4 to 6 weeks, downloading the data to tapes, doing a first pass quality control assessment of the data, which involved ensuring that the instrument was collecting data and making and sending duplicate data tapes to Carnegie Institution of Washington (CIW). From CIW, Randy Kuehnel ensured that all data were correctly formatted and were incorporated into the IRIS seismic data archive at the Data Management Center in Seattle, Washington. 79 In April 1998, 23 stations were moved from the western portion of the array to the eastern positions. The Wits group (now including Peter Burkholder and later Rhod McRae-Samuel) constructed an additional 8 stations for the redeployment. Stations 42, 43, 44, 48, 49, 53, 54, and 58 were installed in April and May 1998 using instruments initially deployed in Zimbabwe and Botswana (Figure 2.9). In addition, all stations from the initial deployment were given a ?super service?, fences were rebuilt, and instruments were dug up and checked for leveling, good electrical connections, water problems, and cleaned of termite infestations. A 3-year commitment of a major portion of my time (1996-1999) was made to help ensure the success of the seismic part of the field work component of the project. The collected seismic data have been archived at the IRIS data management center in Seattle, Washington and used in a variety of studies. The crustal thickness measurements used in this study to determine the contribution to the gravity signal due to variations in Moho topography were determined using phasing depth images based on the receiver function method developed by Ammon (1991) (Figure 2.11). This method measures the time difference between the direct P-wave arrival and the time for the arrival of the P-to-S Moho converted phase to determine the crustal thickness. The crustal thickness was calculated at 81 stations across the Kaapvaal Seismic Array using data from 35 recorded teleseismic events (Nguuri, 2004; Nguuri et al., 2001) (Figure 2.12). The error in the depth determinations is estimated at 2 km (Nguuri et al., 2001). 80 Figure 2.11 The receiver function technique is based on the conversion of P-waves to S-waves at a boundary with a prominent seismic velocity contrast. Diagram provided by Ammon (1997) and used with permission. In the case of determining crustal thicknesses the boundary used is the Moho. The results that were used in this study only include the single P to S conversion (Nguuri et al., 2001) where results from waves from a variety of azimuths were averaged. 81 Figure 2.12 Crustal thickness variations determined using the phasing depth method of receiver function analysis from Nguuri et al. (2001). The data used to assess the mantle contribution to the gravity signal were the velocity variations of the mantle underlying the Kaapvaal Seismic Array, which had been previously determined (Fouch et al., 2004; James and Fouch, 2002; James et al., 2001). A variety of density-velocity relationships were tested in the gravity calculations. The seismic velocity variations were determined from delay time tomography for both P and S waves (James et al., 2001). This method first calculates the relative arrival times for teleseismic P- and S-waves and core phases (VanDecar and Crosson, 1990). These relative delay times are then inverted to determine the velocity structure beneath the array in a grid of knots or nodes using the well known inversion technique of VanDecar (1991). The grid consists of nodes at 1/2? by 1/2? intervals and 50 km in thickness (Figure 2.13). 82 At each node the velocity variation relative to a background model is determined. In addition, for each node, the hitcount is determined. The hitcount measurement gives an indication of the confidence that can be placed on a particular node and depicts how many rays are in a particular cell. Hitcounts in the central portion of the array are typically 25- 100; the minimum acceptable number is five (Fouch et al., 2004; James et al., 2001). There was a good azimuthal distribution of earthquakes used (Figure 2.14). The P wave results were inverted from 8693 rays from 234 events (Figure 2.15) (Fouch et al., 2004; James et al., 2001). The three dimensional grid that is used for the tomography, has also been used in the gravity calculation (Figure 2.13). Details of the inversion and improvement to the tomographic inversion methods used can be found in Fouch et al. (2004). The crustal thickness results (Nguuri et al., 2001) and the delay time tomography results (Fouch et al., 2004; James et al., 2001) of the Kaapvaal Project are the data used as a basis for the gravity calculations in chapters 3 and 5, respectively. 83 Figure 2.13 The grid spacing used for the determination of seismic wave speeds. The same grid spacing of 1/2? by 1/2? lateral grid interval and 50 km vertical grid interval has been used in the gravity calculations. Diagram from Fouch et al. (2004). 84 Figure 2.14 View of the world centered on the Kaapvaal Seismic Array showing the azimuthal distribution of events used in calculating the delay time tomography for P-waves on the left and S-waves on the right Diagram from Fouch et al. (2004). 2.4 Tectonic Regionalization of southern African geology In order to investigate the relationship between global surface geology and the underlying mantle, various studies have developed a coarse geological grid, or regionalization, of the surface geology on scales that are comparable with seismic results. These grids assign one geological age to each grid cell. For global scale studies the geology may be gridded as coarsely as 5? x 5?. Global regionalizations of geology established, as long as 30 years ago, that variations in seismic-wave velocities in the upper mantle correlate with surface geological features of specific tectonic ages (Dziewonski, 1971; Kanamori, 1970; Toks?z and Anderson, 1966). 85 Figure 2.15 Delay time tomography results shown for a slice at 150 km depth. Diagram from (Fouch et al., 2004). These regionalizations have been refined both for the oceans (L?v?que, 1980; Okal, 1977; Wu, 1972) and for the continents (Jacob, 1972; Knopoff, 1972; Poupinet, 1979; Sipkin and Jordan, 1976). Although coarse, these regionalization grids provide a starting point for comparisons of seismic velocity structure with regional surface geology. Most efforts have used tectonic age (i.e. age of last deformation) to correlate surface 86 geology with seismic velocity variations (Chapman and Pollack, 1975; Sclater et al., 1980). In contrast, Jordan (1981b) developed a regionalization based on the behavior of the continental crust only during the Phanerozoic. All of these studies were limited by an absence of detailed quality weighted geologic input and the coarseness of the geological grid that was used (5? x 5?). Division into a 1? grid is on a finer scale than has generally been previously emphasized in other studies (Jordan, 1981; Mooney et al., 1998; Simons et al., 1999). The study by Simons et al. (1999) comparing surface wave tomographic data with crustal domains of Australia represents a more detailed investigation of the relationship between seismic velocity and geology at a variety of scales. Simons?s study found a broad scale correlation between seismic velocity and tectonic age, but also showed that seismic velocities in the Australian mantle lithosphere varied significantly in domains of similar crustal age implying variations in mantle lithosphere composition or temperature that were not simply correlated with surface geology. A global crustal database at 5? x 5? grid spacing has been developed by Mooney et al. (1998). This model incorporates a variety of information, including crustal thickness measurements, geology and sedimentary thickness and provides a basis for a variety of comparisons between the compiled features and global seismic velocity variations. Zoback and Mooney (2003) have used CRUST5.1 to evaluate lithospheric buoyancy, and their work supports a lithospheric thickness of 200-350 km. Unfortunately, these global studies do not have consistent distribution of high quality data as some regions of the Earth remain poorly studied. In this study the surface geology of the Kaapvaal Craton has been divided into blocks of 0.5? x 0.5? in the region that is well covered by seismic stations, in order to investigate relationships between the surface geology, crustal thickness, gravity data and the upper mantle seismic velocity variations. A block has been assigned to a particular 87 domain if more than half of the cell falls into that domain. A close spatial relationship exists between the prominent Bouguer gravity low, which essentially outlines the Kaapvaal Craton, and the high P and S seismic wave speeds revealed by the upper mantle tomography. Large scale tectonic crustal blocks and large mantle tapping structures (e.g. the Bushveld Complex) were selected as the geological features to be investigated. While the detailed crustal domains defined by de Wit (1992) are too small to use due to the large spacing of the seismic stations (~100 km), they were used as a guide in defining the domains that were investigated. The broad patterns of the tectonic subdivisions that make up the initial basis of this study are shown in Figure 2.16. The geological provinces shown are based on basement age, but I have also included the Bushveld Complex due to its large size (~350 x 350 km) and the fact that it is derived from mantle melting processes. In this case the Colesburg Lineament has been extended northwards to link with the Palala Shear Zone following Eglington and Armstrong's (2004) simplification of the map of de Wit et al. (1992). These divisions facilitate ready comparison with the geophysical data sets (gravity, crustal thickness, and tomography). While this grid is coarse compared with the state of geological knowledge of southern Africa, it provides a powerful basis for the comparison of the regional geology with the tomographic and crustal thickness results, which have a resolution of approximately 50 km, hence the selected regional geology grid cell size of 0.5?. This regionalization is used in Chapter 3 to investigate possible mean density variations between crustal blocks. 88 Figure 2.16 Tectonic regionalization of southern Africa in the region of the Kaapvaal Project seismic experiment represented as 0.5? x 0.5? cells. The region labeled ?unknown? is known to be underlain by Archaean ages due to xenoliths and diamonds in kimberlites such as Orapa. However, some of this region may also include an extension of the Limpopo Belt (Ranganai et al., 2002). In the legend the squares are surrounding mobile belts and the circles are cratonic regions. 89 90 2.5 Discussion The purpose of compiling crustal thickness data for this study is to examine the relationship between predicted crustal thickness, measured crustal thickness, gravity and topography. Durrheim and Mooney (1991), who compiled global crustal thickness data, noted the inverse relationship between age and thickness (old crust, thin; young crust, thick). A global compilation of crustal thickness has been compiled and released as a model ?CRUST 2.0? by Bassin et al. (2000), and is available to researchers at http://mahi.ucsd.edu/Gabi/rem.dir/crust/crust2.html, as part of the compilation for a Reference Earth Model (REM). This compilation represents a significant improvement over CRUST5.1 (Mooney et al., 1998). In general, crustal thickness data coverage for Africa is sparse, but with results from the Southern Africa Seismic Experiment (SASE), the detail available for southern Africa has increased dramatically. These new crustal thickness determinations from the SASE that were summarized in the previous section are generally consistent with previous observations. 3 Gravity modeling and crustal thickness of southern Africa In this chapter I start with a brief review of the principles of gravity modeling (3.1), isostasic balance and crustal flexure (3.2). I then apply these ideas to data acquired during the Southern African Seismology Experiment (SASE), a component of the Kaapvaal Project, and examine the relationships between predicted crustal thickness, measured crustal thickness, elevation, the geological terrain model developed in chapter 2 and the measured Bouguer gravity field for southern Africa (3.3 ? 3.6). I also develop a first order model of the gravity field that results from the seismically determined crustal thickness, first using a two dimensional program based on a Talwani algorithm and then using both the fast Fourier transform (FFT) method of Parker (1972) and code modified from Lees and VanDecar (1991) (3.7). Various density contrasts between the lower crust and upper mantle across the Moho are used in the modeling, and the results are compared with the smoothed Bouguer gravity field as measured on the Earth?s surface (3.8). 3.1 Gravity modeling The principles of forward gravity modeling, isostasy and flexure are well developed and only a brief outline of the main ideas is presented here. The reader is referred to the excellent books by Blakely (1995) and Watts (2001) for further details. In pre-computer times, modeling of gravity anomalies proceeded from the painstaking calculation of profiles from two dimensional sources comprising simple elongated shapes. These shapes are based on criteria for a two dimensional calculation developed by Nettleton (1940), where a two dimensional source is considered to have infinite strike length perpendicular to the data profile. The rectangular, two dimensional block formulation as 91 developed by Vening Meinesz et al. (1934) is a typical example. These results were then compared with measured values and then the input parameters (density, depth and shape) were modified until a solution was obtained that satisfied both the data and geological constraints (Grant and West, 1965). Alternatively, graphical computing tools, such as dot charts, standardized curves, and graticules were used to determine the source (Talwani et al., 1959). A breakthrough in the speed of calculation was made by Talwani et al. (1959) by approximating two dimensional bodies as having the cross sectional area of an n-sided polygon (Nettleton, 1971; Talwani et al., 1959). With the advent of more computer power, limiting strike length became a feasible possibility, and 2.5 dimensional models became popular (Cady, 1980). Early three dimensional potential field modeling utilized line integral methods (James et al., 1968; Talwani and Ewing, 1960), but these methods are limited by the necessity of closed contours outlining the bodies of interest. The application of the fast Fourier transform to geophysical problems made the calculation of potential field anomalies due to variable surfaces at depth feasible (Parker, 1972). Parker?s method can be extended to include variable densities on the source surface and calculation of the anomaly on a variable surface (Parker, 1972). More recently, fully three dimensional modeling methods using analytic solutions to simple shapes, facetted surfaces, or surfaces of varying density have become popular as computer resources have expanded. There are several commercially available packages that exist for three dimensional potential field modeling, although they are generally expensive and require additional three dimensional viewing packages (e.g. Jessell, 2002). Freely available 3D gravity modeling codes are available, but they lack sophisticated viewing software (e.g. gbox by Blakely, 1995). The purpose in the following section is to briefly review the theory for several modeling methods that were used in this project. The simplest of these methods is a 2.5D 92 package that uses the 2.5D Talwani et al. (1959) algorithm and was implemented in the program Gravgrid (Cooper, 2005). Another analytical method investigated builds up a 3D geometry from the repeated application of the analytic solution for a simple cube in the program gbox (Blakely, 1995). Using Gauss?s law, the gravity modeling algorithms for facet versions of multisided polyhedra have been developed and implemented by Tiberi (2003). Parker?s (1972) method has also been utilized and employs a fast Fourier transform to calculate the gravitational attraction due to a layer of material. Finally, I have developed a modification of Lees and VanDecar (1991) as an approximation for a spherical prism to calculate the gravity on a spherical surface due to the variations of the Moho and compared these results with those obtained using Parker?s (1972) FFT method. 3.1.1 Two and two and a half dimensional Talwani methods The Talwani et al. (1959) algorithm has been used in many commercial and public domain modeling programs (e.g. Blakely, 1995; Cooper, 2003; Saltus and Blakely, 1993) and is based on using two dimensional bodies, which are potential fields sources where at least one dimension can be thought of as extending to infinity, such as is the case with a dyke or fracture (Figure 3.1). The complete derivation of the appropriate equations is readily available (Blakely, 1995; Talwani et al., 1959). This two dimensional formulation allows the integration to be performed only over the cross section, which is further simplified by approximating the smooth outline as the summation of an n-sided polygon, where rn is the distance from a polygon corner (xn, zn) to the calculation point P, and ?n is the angle between the polygon corner and the calculation point (Figure 3.1). The resulting equation for the vertical component of gravity, gz, is: 93 ?? ??? ? ??+?= + + = ? )(log12 111 2 nnnnn N n n n z r r Gg ???? ?? (3.1) where: nnnn nn nn n zxzz xx ??? ?=? ?= + + and 1 1 (3.2) and G is the gravitational constant and ? ? is the density contrast (Blakely, 1995). Figure 3.1 The geometry used in the development of the Talwani et al. (1959) algorithm for calculating the gravitational anomaly due to a 2D source. In the upper diagram the source is seen to extend to great distance in the y-direction. In the lower diagram the smooth outline of the cross section is replaced by an n- sided polygon, which is used for integration. Diagram modified from Blakely (1995). 94 The FORTRAN subroutine ?gpoly? in Blakely (1995) provides the foundation for implementing the Talwani et al. (1959) algorithm. Another freely available program, Gravgrid (Cooper, 2005), was used in this work to produce a first approximation to the gravity field from the variations in the thickness of the Moho in southern Africa along a profile from Cape Town to Masvingo. It is important to note that the general formulation of this method requires the source to be 2D, although end corrections can be applied for sources of limited strike length, making it a 2.5D method (Cady, 1980; Rasmussen and Pedersen, 1979) it is by no means a three-dimensional modeling algorithm. 3.1.2 Rectangular prism method (3D) A straightforward method of determining the 3D gravitational effect of a complicated source is to use a solution for a known simple shape, such as a rectangular prism, and build up the complex source from the simple shape (Figure 3.2). The details of the derivation for this rectangular prism method are in Blakely (1995), Plouff (1976), and Smith et al. (2001). Here I provide a brief outline following Blakely (1995). The gravitational anomaly )(Pgv due to a point source of density ? , of volume v, located at P on the surface, a distance r away, is given by: ??=??= dvrrGUPg 2?)( ?v (3.3) where U is the gravitational potential and G is the gravitational constant. The analytic expression for more complex sources can be determined by evaluating the integral for the appropriate mass element and integrating, assuming a solution exists. 95 Figure 3.2 The geometry of the rectangular prism method. The gravitational attraction at position P(x, y, z) due to the cubes can be calculated from repeated calls to a subroutine containing the analytic solution for a cube. Diagram modified from Blakely (1995). For the case of a rectangular prism aligned with the Cartesian axes, which has a constant density ? , and is evaluated at the origin, the vertical component of gravity determined from equation (3.3) is: ? ? ? ++= 2 1 2 1 2 1 ''' )'''( ' 2/3222 z z y y x x z dzdydxzyx z Gg ? (3.4) which after integrating over the volume, results in the analytic solution: ??? ? ??? ? +?+?= ??? = = = )(log)(logarctan 2 1 2 1 2 1 iijkjjijki ijkk ji k i j k ijkz xRyyRxRz yx zGg ?? (3.5) where: kji ijkkjiijk zyxR )1()1()1( and 222 ???=++= ? (3.6) 96 and G is the gravitational constant. The vertical gravitational attraction gz is calculated at each point on the surface by applying equation 3.5 with the appropriate density and summing the results: ? = = N n mnnmg 1 ?? (3.7) where gm is the vertical attraction at the mth observational point, n? is the density of prism n and mn? is the gravitational attraction at point m due to prism n. Thus, each cube can have a different density in the configuration. This method is generally considered to be cumbersome as it makes an unnecessary number of calls to the subroutine for equation 3.5 to build up realistic source configurations and does not take advantage of geometries where two side-by-side prisms may have the same density and the boundary between them need not be calculated. However, in applications where the source can easily be configured as cubes or blocks and the density between the blocks generally varies, as in seismic tomography results, the application of this method makes sense. Preliminary calculations using this method in this study have demonstrated its utility. In this study I have applied a modification of this method using approximated spherical prisms with results calculated on a spherical surface (Section 3.16 below). 3.1.3 Contour methods These methods were only briefly considered in this study as it was difficult to obtain meaningful closed contours in the region of interest for the tomographic and crustal thickness results. However, a brief outline of the method is presented for 97 completeness sake. Details of the derivations can be found in Blakely (1995), James et al. (1968) and Talwani and Ewing (1960). In this method, a three dimensional source is sliced up into thin laminae (Figure 3.3) and the surface integral of each thin lamina is formulated. This integral is then converted into a line integral around the perimeter of the lamina. Next the line integral is transformed to a summation over straight line segments between the points of a polygon used to approximate the perimeter of the lamina in a similar fashion to the procedure used in the two dimensional modeling. Finally the lamina are stacked and integrated over the vertical dimension (Blakely, 1995). There are complications to these methods if the source is significantly concave, but these can be resolved using specialized integration techniques (James et al., 1968). Figure 3.3 Illustration of the geometry used in the stacks of lamina method. Thin lamina are used to build up the three dimensional source. For sources that are easily converted to contours, such as topography, these methods are ideal. Diagram modified from Blakely (1995). 98 For sources such as topography or bathymetry where contours are readily available and the density within the source does not vary, these methods are ideal, however preliminary calculations for the purposes of this study revealed that the Moho variations and tomographic results proved too variable to obtain meaningful closed contours, especially in the regions close to the edge of the study area. 3.1.4 Facet method Generally a three dimensional source can be defined as having a large volume with the same density, making the rectangular prism method an inefficient method of calculation as it does not take advantage of the fact that many of the shared faces will have the same density. For oddly shaped bodies, it may be difficult to construct appropriate contours suitable for use with the stack of lamina method. Another alternative method of calculating the three dimensional gravity of a source is to use the facet method, which may be more suitable to calculate for certain sources. This method approximates a smoothly varying three dimensional source using flat polygonal facets over the surface of a polyhedral body (Figure 3.4). The details of the derivation can be found in Barnett (1976), Blakely (1995) and Okabe (1979). Code for testing this method was provided by C. Tiberi (pers. comm., 2000). 99 Figure 3.4 By using Gauss?s Law, a three dimensional body can be approximated as a series of faces (or facets) and the gravity of complex bodies calculated from accounting for each individual face by using an analytic expression. Diagram modified from Blakely (1995). Due to the configuration of the seismic tomography cells (Figure 2.13), this method offers no advantages over the rectangular prism method, as the facets formed are simply the sides of each cell. Moreover, preliminary calculations demonstrated that the time taken for each calculation is as long as for the cube method, while the preparation time to determine the facets adds significantly to the calculation time. 3.1.5 Parker?s fast Fourier transform method Parker (1972) showed that a series of Fourier transforms could be used to calculate the gravitational anomaly due to an uneven layer of material. I have applied this method to the uneven Moho discontinuity using the implementation of ?grdfft? available in Generic Mapping Tools (GMT) (Wessel and Smith, 1991) and used the results to 100 compare with the simplified spherical prism method developed in the next section. Here I briefly review the theory following Parker (1972) and Blakely (1995). Since potential fields can be expressed mathematically in terms of ( )r1 the Fourier transform of ( )r1 forms the basis for their Fourier analysis. This transform can be expressed as: k e zzk )'( 0 2 ? =?? ??? ? ? r 1F (3.8) where r is the distance between the source and measuring position P(x,y,z), F denotes the Fourier transform, and k is the wave number (Figure 3.5). The Fourier transform of more complicated geometries can be derived using this simple expression. Figure 3.5 Definition of terms for the Fourier transform determined for a point source at Q and measured at a position P. Figure modified from Blakely (1995). 101 Parker (1972) has shown that both the magnetic and gravitational anomaly for an uneven layer can be calculated using an appropriate summation of Fourier transforms of the layer. The detailed derivation is available in Parker (1972) and Blakely (1995). The resulting expression for the gravity calculation is (Blakely, 1995; Parker, 1972): )]([ ! 2][ 21 1 )1( 0 nn n n zk z zzn k eGg ??= ?? = ? ? ?? FF (3.9) where the surfaces z1 and z2 confine the density ? which can be a function of position (x,y) (Figure 3.6). Thus, the Fourier transform of gravity can be determined from the sum of Fourier transforms of topography with variable density (Parker, 1972). As with all Fourier transform applications, the data must first be properly prepared by gridding on a regular grid and appropriate precautions taken to avoid edge effects. Note that the observation points lie in a plane that is everywhere above the material and that the observation plane must be at least as far away from the uppermost layer as the horizontal spacing between the data points (Parker, 1972). This powerful algorithm has been used to calculate the gravity field of a variety of sources, for example sedimentary basins (e.g. Jachens and Moring, 1990; Saltus, 1993) and has also been used to calculate the isostatic residual anomalies of the conterminous United States (Simpson et al., 1986). There are several programs which easily implement Parkers?s (1972) method, e.g. grdfft in GMT (Wessel and Smith, 1991). Blakely (1995) provides the subroutine mtopo for the magnetic case and Shin et al. (2005) have developed FW3DFFT.F for gravity calculations. In this thesis I have used the GMT implementation of Parker?s method to determine the gravity anomaly resulting from the Moho discontinuity that was determined using receiver functions. I compare these results with the results developed for the spherical prism method in the next section. 102 Figure 3.6 The geometry used for Parker?s Fast Fourier Transform method. The value of gravity due to the shaded surface which has a constant density contrast across it, is calculated at a position P(x,y,z). Diagram modified from Parker (1972). 3.1.6 Spherical prism In an effort to develop a method where the surface on which gravity is calculated is spherical, without the complications of localized spherical harmonics (Simons and Hager, 1997), I have used a spherical prism, also called a tesseroid (Heck and Seitz, 2007), as a unit volume (Figure 3.7). Although the region on the Earth?s surface in this study only spans ~2000 km and is not extensive enough to require a spherical consideration for gravity calculations, the method developed here could be applied to larger regions. The equation for the gravitational attraction g, at a point P, due to a spherical prism in spherical coordinates (r, ?,? ) bounded by meridians ?1 and ?2 is given by: 103 ??? ????? ?? ?? ?? ?? dddr rrrr rrr Grg rr rr pp p? ? ? = = = = = = ?+ ??= 2 1 2 1 2 1 )2/3(22 2 )cos2( cos)cos( ),,( (3.10) where )]cos(coscossinarccos[sin ppp ??????? ?+= (3.11) is the geocentric angle between the measuring point P and the mass element ?? dddr (Figure 3.7). Unfortunately no closed form solution has yet been found for equation 3.10 (Smith et al., 2001) and using numerical methods is more involved than needed for the first order calculations considered in this work . Figure 3.7 There on the surface of a exists no analytic solution for the calculation of the gravity field due to a spherical prism sphere and numerical methods would be unwieldy for the broad scale case being considered here. However, the gravity field can be approximated by using small spheres of the same volume and center of mass to approximate the small cubes and by ensuring that the sources are far enough away (Lees and VanDecar, 1991). Diagram modified from (Smith et al., 2001). To obtain an expression for the vertical component of gravity I follow Lees and VanDecar (1991) and have developed an expression due to a spherical source that has the some volume as the spherical prism. This has been developed in spherical coordinates 104 and calculated on the sphere?s surface. The expression for the gravitational attraction g, due to a source of mass M, density ?, radius R, volume V and a distance r away from the source is given by Telford (1990): 2 3 22 4 3 r RG r VG r MG g ??? === . (3.12) It is the vertical component of gravitational attract Figure 3.8, the vertical component of gravity due to a mass element B located at some ion that is needed. With reference to depth h below the surface, and calculated at position A is found from: h ? d ? cos)(sin ??= RR (3.13) the depth from the surface of the sphere to the ource, where R is the radius of the sphere, h is s ? is the angular distance between the source and the measurement point and d is the straight line distance between the source and the measurement point (Figure 3.8) (Heiskanen and Vening Meinesz, 1958). 105 Figure 3.8 Geometry for determining the vertical component of gravity at position A on the surface of the and Meinesz (1958, pg 162). sphere for a mass element located at B beneath the spherical surface. Diagram modified from Heiskanen However, to ensure that the volume of the sphere is the same as the spherical prism, the spherical prism volume is substituted for the spherical volume. The expression for the volume of the spherical prism is given by: [ ][ 3)(coscos 3 rrV ?+?+??=? ??? ]? (3.14) where ? and ? are longitude and colatitude, respectively (Figure 3.9). This approximation will only be valid for sources whose effect is calculated at a distance significantly larger than the radius of the source sphere. In this case the center points of all sources were at least 30 km away from the surface on which they were being calculated, which is at least four times greater than the radius of the approximating sphere. This method introduces errors for sources close to the calculation surface, but in 106 this case a comparison with Parker?s (1972) FFT method reveals very close agreement (section 3.8.2). Figure 3.9 Geometry comparing the spherical prism and a sphere of the same volume. A sphere is used in ume and center as the spherical prism. The vertical component of ated on another spherical surface some distance above the surface containing the sources at a point P. the calculation which has the same vol gravity due to a mass element is calcul 3.2 Isostasy and flexure The concept of isostatic balance has played an important role in the development of gravity studies since some of the earliest measurements of the Earth?s gravitational field in the Himalaya Mountains (Airy, 1855; Heiskanen and Vening Meinesz, 1958; Pratt, 1855; Watts, 2001). Early formulations of isostatic balance attributed compensation of large mountainous masses to either a thick crustal root as in Airy isostatic balance (Figure 3.10) (Airy, 1855); or to lateral variations in density as in Pratt 107 isostatic balance (Figure 3.11) (Pratt, 1855). These early models explained the data equally well and were hotly debated at the time, but as more data about the density of rocks and the surface geology became available, the Airy isostatic model won favor in mounta is theory was more precisely formulated by Heiskanen (1931) and was generally favored in re 3.10 this expression can be formulated as: Mass in column A = Mass in column B: (mass in normal thickness continental crust = mass of thickened continental crust) inous settings and Pratt isostatic balance appears to be more applicable in oceanic crust, where the density of basalt is a function of temperature (Watts, 2001). Isostatic balance is based on the concept that equal columns have equal mass above a reference level called the isostatic compensation level. In Airy isostatic balance, the lateral density is constant and the balance is achieved by balancing topography with thick crustal roots. Th Europe Watts (2001). Referring to Figu rthrt ccccmcc ????? ++=+ . (3.15) Here, ?c is the average density of the continental crust, ?m is the mantle density, tc is the thickness of the crust, r, is the extent of the root and h is the height above sea level. Rearranging this expression the thickness of the root r, can be expressed as a function of the elevation, h as follows: hr cm c ?? ? ?= (3.16) For a typical crustal density of 2800 kg/m3 and a mantle density of 3300 kg/m3 the root will extend into the mantle ~5.6 km for every kilometer of elevation above sea level. Similar expressions can be developed for examining freeboard by comparing columns in the ocean with crustal columns (Figure 3.10). Historically, in order to calculate 108 continental thickness, the crustal and mantle densities were kept fixed, and the total crustal thickness was determined from elevation by calculating the root thickness (Equation 3.16) and using an ?Airy? thickness corresponding to tc in Figure 3.10. owever, different values of the average crustal or mantle density can have a dramatic effect on the overall crustal thickness determined by Airy isostatic balance. H Figure 3.10 The principle of Airy isostatic balance: Equal columns have equal mass above a reference level cal strength y lateral variations in density (Figure 3.11), with each column being of led the isostatic compensation depth. Airy isostatic balance implies that there is zero horizontal and topography is perfectly compensated by a root of its mirror reflection. The Pratt model of isostatic compensation was more precisely formulated by Hayford (1909) in an effort to use the ideas of isostatic compensation for geodetic calculations (Watts, 2001). The Pratt ? Hayford model proposes that the base of the crust (or some other compensation level) is at a uniform depth and that topography is compensated b 109 equal mass. In the 1900s, this theory was more widely supported by US researchers (Watts, 2001). Figure 3.11 An illustration of Pratt isostatic balance for crustal blocks of varying density. Here the density varies la Blakely ( igure 3.12). These ideas were m re completely formulated and applied especially to oceanic settings by Watts (1978) and these studies have been summarized in Watts (2001). terally to produce topography with a constant depth of compensation. Diagram modified from 1995). Although the Airy isostatic model appeared to explain the results of many early gravity studies, as more gravity data became available, strict Airy isostatic appeared unlikely. This was especially true in regions of no recent tectonic activity, and Vening Meinesz (1931) developed the concept of regional lithospheric compensation, which involved perceiving the crust as being able to flex under a load (F o 110 Figure 3.12 Airy-Heiskanen local vs. Vening-Meinesz regional compensation models for a topographic load against a flat layered background model (modified from Watts (2001). The recognition of the importance of loads other than topography (such as intrusions at mid crustal levels) has led to the more general development of flexure studies due to loads anywhere within the lithosphere (Forsyth, 1985). Flexure studies, which were originally developed in the context of loads in the oceanic lithosphere, are generally limited by heterogeneity in strength, thickness and density in the continental setting. The lack of fully 3D layered formulations that take into account all of the complexities of varying rheology as a function of depth and lateral changes in structure limits the applicability of continental flexure studies. Flexure is usually studied using the admittance or coherence between the gravity and topography data. The mathematical limitations of these methods include size and shape of the windowing of the data and the inability to mathematically characterize the heterogeneous nature of the crust and mantle. While early measurements of continental crustal thickness in mountainous regions generally supported Airy-Heiskanen regional isostatic models, the continued compilation of crustal thickness measurements demonstrated that the Moho does not inversely reflect 111 the topography in many regions (Durrheim and Mooney, 1994; Fischer, 2002). In continents the lithosphere-asthenosphere boundary generally remains undefined seismically, and it is not clear how well this boundary corresponds to the isostatic compensation depth. Several workers have shown that in certain tectonic settings crustal thickness is not related to topography in a simply Airy isostatic balance in spite of indications from the comparison of gravity and topography that the region is in overall balance (Durrheim and Mooney, 1991; Fischer, 2002; Zoback and Mooney, 2003). Elastic thickness studies have indicated that large variations in crustal strength are present in the southern African region (Doucour? and de Wit, 2002; Doucour? et al., 1996). 3.3 Combined studies of gravity, seismic tomography, and other geophysical data Combining different geophysical data sets is a useful way of placing constraints on the resulting geological model and optimizing the use of often limited data, especially when investigating the deep crust and upper mantle. Gravity and seismic tomography data are complementary as gravity studies have better resolution at shallow depths whereas tomography data have better resolution at greater depths (Parsons et al., 2001). Several methodologies have been developed to combine gravity and seismic tomography data. The most straightforward approach is to ensure that the resulting seismic tomography model is consistent with the gravity data. This is generally performed by converting the seismic velocity perturbations to density contrast distribution data and determining the resulting gravity field using forward modeling. The resulting gravity model is then compared with known gravity data and inconsistent regions in the crust are highlighted where the velocity-density relationship that was used may need to be re- 112 evaluated. Examples of these studies are mainly from the crust and upper mantle and include studies by Achauer (1992), Brocher et al. (2001), Langenheim and Hauksson (2001), and Masson et al. (1998). These studies usually assume a simple temperature- dependent relationship between seismic velocity and density based on the idea that an increase in temperature causes a decrease in both density and seismic velocity. 3.3.1 Joint Inversion Another approach is to conduct a joint inversion of both gravity and seismic data. Lines et al. (1988) termed this ?cooperative inversion? and differentiated between simultaneous inversions and sequential inversions. An example of a simultaneous, joint inversion is the study conducted by Lees and VanDecar (1991). This study inverted gravity data with local earthquake travel time data to a depth of 40 km in the western Washington area. They used Birch?s law for the relationship between density and velocity (Birch, 1961). They were able to satisfy the gravity data with a minor effect on the misfit of the seismic data, although the gravity data only provided a weak constraint on the seismic solutions of the lowermost layers due to the differences in the resolutions of the two data sets (Lees and VanDecar, 1991). They concluded that Birch?s Law was satisfactory for the velocity?density relationship in this region and could be used to relate these independent data sets. Simultaneous joint inversion studies such as Lees and VanDecar (1991) are limited by the assumption of a constant linear relationship between density and seismic velocities. Sequential inversions, which treat the data sets separately, are more flexible in terms of their calculation techniques (different inversion schemes may be used for the two data sets) and of the relationship between density and seismic data. Typically the results 113 of one inversion are used as an initial constraint for the other inversion, so that the spatially varying, nonlinear velocity-density relationship, such as a spatially varying version of Gardner?s Rule (Gardner et al., 1974), can be accommodated (Lines et al., 1988; Parsons et al., 2001). Other examples of joint inversions for crustal and upper mantle structure include Strykowski (1992), Tiberi et al. (2003), Vernant et al. (2002) and Zeyen and Achauer (1997). Generally these studies have been interested in determining details of shallow crustal structure where the resolution of the seismic data is least, due to near vertical ray paths, and the resolution of gravity is greatest. However, Tiberi et al. (2003) were successful in investigating structures down to 200 km in the Baikal rift region. While joint inversion may be a plausible procedure for future studies, the number of unknowns in the full formulation that would need to be inverted (crustal thickness, Moho density contrast, delay times and the relationship between seismic velocity variations and density) makes this a poorly resolved problem. In addition, there is little available information on the seismic velocity structure of the crust and the crust is likely to be the main contributor to the gravity signal, thus the inversion for gravity would be significantly decoupled from the seismic inversion. One way around this would be to formulate the inclusion in the joint inversion of surface waves with gravity and delay time tomography. However even joint surface wave/delay time inversions have proven difficult to develop and the formulation of better techniques remains an active area of research. Thus, the approach taken in this work has been to investigate, through forward modeling, a variety of plausible density contrasts across the Moho using seismically determined crustal thicknesses with the purpose of determining reasonable contributions to the gravity signal at surface that are generally ignored. In Chapter 5, a variety of 114 density-velocity relationships in the uppermost mantle are used to determined plausible gravity contributions from the uppermost mantle using the same procedure developed here. 3.3.2 Isostasy and lithospheric buoyancy An alternative method of investigating seismic and gravity data is to consider the isostatic balance of a region. Traditionally, a graph of Bouguer gravity vs. elevation is plotted. A slope of ~8.9 m/mGal indicates the stations are in isostatic balance for a Bouguer density of 2670 kg/m3 (Nettleton, 1971); however, the method does not determine where the isostatic balance takes place ? at the crust mantle interface or deeper within the lithosphere. Measured crustal thicknesses determined from seismic experiments can then be compared with elevations at the same locations to determine if there is crustal isostatic balance. A compilation of global crustal thicknesses and elevations led Durrheim and Mooney (1994) to the observation that Archean cratonic regions have thinner-than- expected crust and the surrounding mobile belts are generally thicker. This was investigated in some detail by Assump??o et al., (2002) in South America using data which spanned the Archaean Sao Francisco craton, with thin crust, via the Brasiliano fold belt (700-500 Ma) to the Palaeozoic Parana basin, which are characterized by thick crust. Using receiver functions, they concluded that two mechanisms were responsible for these observations (Assump??o et al., 2002). The lithospheric mantle beneath the Archaean craton has a lower density due to depletion and the lower crust beneath the Parana basin is very dense due to basaltic underplating. These results are in line with the observations 115 compiled by Durrheim and Mooney (1994) and imply that many older stable regions are not in isostatic balance at the Moho, but at some level deeper in the lithosphere. Another approach to examining the lateral density variations in the lithosphere is to relate them to lateral differences in lithospheric potential gravitational energy, or lithospheric buoyancy (Lachenbruch and Morgan, 1990). The forces generated by these differences can be an important source of intraplate stress, for example elevated and thickened continental crust with a thin mantle lid tends to develop extensional forces (Zoback and Mooney, 2003). These studies demonstrate the importance of processes other than plate tectonics for developing stresses in the lithosphere. The classic cycle of mountain building, which results in thick crustal roots, followed by erosion and root rebound due to regional isostatic balance, may need to be modified as at least parts of the old crustal roots appear to be preserved in many cases (Fischer, 2002). These preserved roots have an increased density due to metamorphism while at their lowest point (>70 km). The density contrast between the root and the mantle is then significantly reduced (Fischer, 2002). Kaban et al. (2003) evaluated gravity data determined from satellites to assess the global significance of crustal thickness, mantle lithosphere composition and temperature. They note a dichotomy between the cratons of the northern and southern hemispheres: the northern hemisphere has positive residual gravity anomalies and negative residual topography, while the southern hemisphere cratons have negative mantle gravity anomalies and positive residual topography (Kaban et al., 2003). In the southern hemisphere, the largest anomalies are found in South Africa. They also find that temperature variations dominate compositional variations, with the caveat that the amount of compensation due to temperature or composition is probably depth dependent (Kaban 116 et al., 2003). These studies demonstrate the complex nature of isostatic balance and the variety of factors that contribute to vertical balances in the Earth?s lithosphere. 3.4 Analysis of Southern African Gravity and Topography data The southern African Bouguer gravity data that have been used in this study are shown in Figure 3.13 and are part of an ongoing compilation of data reduced using standard techniques (i.e. drift corrections including tidal and machine drift, latitude corrections, free air and Bouguer corrections) (Gordon-Welsh et al., 1986). No terrain or isostatic corrections have been made to the data due to the lack of detailed information about topography around each individual gravity measurement. The data in Figure 3.13 have been imaged from a grid cell size of 0.01? (approximately 1 km) and sun shaded from the northwest. Where data are very sparse, such as northern Namibia and Angola, the map has been masked. The geological terrain map as developed in Chapter 2 has been overlain on the gravity map along with outlines of important geological features such as the Bushveld Complex, the Molopo Farms Complex, the Witwatersrand Basin, the Great Dyke, South African greenstone belts and the Trompsburg Complex. 117 Figure 3.13 Southern Africa Bouguer gravity data compilation. Data are from the Council for Geoscience, South Africa and have been gridded to 1 km. The overlay includes the tectonic regionalization and some important geological features, such as the Bushveld Complex and the Witwatersrand Basin. The Kaapvaal Craton shows up as a prominent Bouguer gravity low, as does the majority of the Zimbabwe Craton. The Limpopo Mobile Belt is a prominent Bouguer gravity high separating the Kaapvaal and Zimbabwe Cratons. Ranganai et al. (2002) have proposed that the Limpopo belt extends significantly further west than shown here and wraps around the Zimbabwe craton as part of the Shase belt from their interpretation of the gravity data. The Colesburg magnetic lineament is also well defined as a gravity 118 anomaly. In fact in the northern portion of the Kaapvaal Cration it is better defined by its gravity signature than by its magnetic signature. The topography data associated with gravity data are also a useful data set (Figure 3.14). One way of evaluating the isostatic state of a region is to plot the Bouguer gravity values against the elevation for each station (Nettleton, 1971). If the region is in general isostatic balance, the plot will yield a straight line. Points above and below the line will indicate regions that are under or over compensated. This simple analysis only considers the response of the crust to the load of topography in the sense of Airy isostasy, but is a rapid and effective method for targeting regions for more careful scrutiny (Figure 3.15) Figure 3.14 Topography of southern Africa with seismic station locations of the Southern Africa Seismic Experiment overlain. Blue stations were moved after year 1 to the positions of the red stations. The yellow stations were left in place for the entire two year period. Refer to Figure 2.9 for station numbers. 119 Figure 3.15 Plot of ~100,000 Bouguer gravity stations in the South African Council for Geosciences database plotted against elevation determined at the position of measurement. The colored lines plotted are for different density values that could be used in the Bouguer correction. The value of 2.67 gm/cm3 has been used for the correction in the database. The ?smear? of data at 0 m elevation is due to values along the coast where the crust is thinning resulting in large gravity values. Values above the line are under compensated and values below the line are overcompensated for the Bouguer density selected. The majority of values are under compensated indicating that the elevations are too large for the root, suggesting that the high elevations in southern Africa are supported by a mechanism other than crustal isostatic balance. Figure 3.15 demonstrates that although there is considerable scatter within the southern African data set, the standard Bouguer density value of 2670 kg/m3 roughly corresponds in slope to the data and is therefore probably an appropriate value for most of 120 the data for the Bouguer correction. The scatter in the data can be discussed in terms of regions that are over- or under-compensated for a particular elevation (Figure 3.16). Figure 3.16 Schematic comparison of overcompensated and undercompensated topography. The crustal density is given by ?c, the mantle density by ?m, and the Airy thickness by tc. In order to investigate the relationship between gravity and elevation I have calculated the average value of the Bouguer gravity and elevation in a circular region with a radius of 20 km around each of the Kaapvaal seismic stations and plotted these against each other using the color coding of the geological terrain model defined in Chapter 2 (Figure 3.17). This plot has a strong linear trend, indicating that most of the locations of the seismic stations in the SASE appear to be in isostatic equilibrium, i.e. stations with lower elevations have higher (less negative) Bouguer anomalies. The stations in cratonic 121 regions, both on the Kaapvaal and Zimbabwe Cratons, all have high elevations and cluster along a linear trend. Figure 3.17 Plot of Bouguer gravity vs. elevation for the 82 seismic stations in the Southern African Seismic Experiemnt (SASE) using an averaged value within a 20 km radius circle around each station for elevation and Bouguer gravity values. Stations have been color coded by geological terrain as defined in Chapter 2. Station 54 occurs at the base of the great escarpment. Station 58 is ~100 km further east from the escarpment. There are a few station locations on the Kaapvaal Craton and the Namaqua Natal Mobile belt that fall well outside this linear trend. The Namaqua Natal Mobile belt 122 stations tend to have much higher gravity values than their elevations require, indicating that these locations are under-compensated ? i.e. that the crust may be thinner there or significantly denser at depth. The only two cratonic stations that plot away from the main cluster are stations 54 and 58. Station 58 differs from the other cratonic stations in that it is located at low elevation east of the Great Escarpment, but it falls on a linear trend indicating isostatic equilibrium. Station 54 occurs near the base of the Great Escarpment, and its Bouguer gravity signal may demonstrate that the effects of erosion are more rapid than associated uplift as it is significantly over-compensated. Station 54, in combination with station 58, can possibly be used to provide constraints on erosion and uplift rates associated with retreat of the Great Escarpment. 3.5 Predicted crustal thickness of southern Africa based on Airy isostatic balance In estimating crustal thickness across southern Africa one approach is to examine each seismic station and determine the crustal thickness based on elevation and Airy isostasy and compare that with crustal thickness results from receiver functions. Early studies of the gravity and elevation data of southern Africa suggested that the crustal thickness would follow classically developed isostatic responses and mirror the topography from the strong linear trend seen in Figures 3.15 and 3.17 (Smit et al., 1962). Various thicknesses were proposed for the intermediate layer, tc, (Figure 3.16) in developing early Airy isostatic balance calculations (Hales and Gough, 1962; Smit, 1962). The degree of regional compensation was not determined in these studies, although the idea is discussed (Smit, 1962). The procedure used here for predicting crustal thickness is to use standard mean densities of 2670 kg/m3 for the crust and 3300 123 kg/m3 for the mantle. Using these density values the thickness of the root, r, which should correlate with the topographic height h, is determined from equation 3.16. The value of tc has been selected as 35 km. The crustal thickness map resulting from this analysis is shown in Figure 3.18 and shows the maximum variation possible as Airy isostatic balance implies no strength in the crust. The effect of incorporating regional compensation or flexure would be to smooth out and lower the amplitude of the crustal thickness variations. Figure 3.18 Predicted crustal thickness as determined from a simple Airy analysis of the topography data. No flexure or regional compensation has been included. Color bar is the same bar as used in Figures 2.12 and 3.19. 124 3.6 Seismically determined crustal thickness of southern Africa Geophysical studies that have determined crustal thicknesses for locations in southern Africa were reviewed in Chapter 2 and compiled in Table 2.1 for studies other than the SASE. The crustal thickness results determined as part of SASE were from two studies (Gore, 2005; Nguuri, 2004) (Table 3.1). All of the various seismic data with well resolved Moho boundaries from Table 2.1 have been combined with the SASE receiver function results in Table 3.1 and are imaged in Figure 3.19. This combined crustal thickness plot illustrates several important features. The data determined prior to SASE (Table 2.1; Figures 2.5 and 2.6) agree well with the SASE results. The extreme thicknesses (~50 km) observed to the northwest of the Kaapvaal Craton in the middle of Namibia suggest that the Rehoboth region may not be cratonic. The observed distribution and variation in crustal thicknesses is significantly different than those predicted from topography alone, indicating that surface topography is a poor predictor of Moho topography (Figures 2.18 and 2.19). This may be true in Archaean cratons in general and may help explain why there are less than satisfactory results for many admittance and coherence studies in cratonic regions (Watts, 2001). To illustrate the lack of correlation, I have plotted elevations averaged across a 20 km radius circle around each seismic station versus measured crustal thickness; for consistency I have only used crustal thickness results from SASE stations (Figure 3.20). No clear linear trends can be observed in this plot, although the stations on craton (where the crust is thinner) are generally clustered at the higher elevations and the mobile belt stations show significantly more scatter. 125 Table 3.1 Crustal thickness determinations from the Kaapvaal Project Southern African Seismic Experiment (SASE) as determined from receiver functions. Data are summarized from Gore (2005) and Nguuri (2004). Station locations are given in Figure 2.9. Southern African Seismic Experiment Number Longitude Latitude Thickness Station ID 1 30.772 -19.467 35 SA78 2 31.318 -19.959 36 SA80 3 30.517 -20.021 35 SA79 4 29.846 -20.636 35 SA76 5 28.611 -20.142 37 SA72 6 30.919 -20.756 37 SA75 7 28.999 -20.860 38 SA77 8 19.246 -34.295 30 SA01 9 20.266 -33.735 36 SA02 10 21.335 -33.662 48 SA03 11 19.621 -32.851 45 SA04 12 21.535 -32.605 44 SA05 13 20.226 -31.978 47 SA07 14 22.072 -31.910 50 SA08 15 22.986 -30.922 48 SA09 16 23.914 -30.972 45 SA10 17 20.947 -29.965 42 SA11 18 22.253 -29.849 45 SA12 19 23.140 -29.979 35 SA13 20 24.023 -29.868 34 SA14 21 25.031 -29.902 38 SA15 22 22.195 -28.950 36 SA16 23 23.226 -28.932 36 SA17 24 24.306 -28.632 36 SA18 25 24.833 -28.906 36 SA19 26 26.195 -29.022 38 SA20 27 22.009 -27.966 35 SA22 28 23.405 -27.930 44 SA23 29 24.236 -27.883 38 SA24 30 25.126 -27.846 38 SA25 31 26.180 -27.545 40 SA26 32 27.294 -27.862 40 SA27 33 28.066 -27.898 38 SA28 34 23.035 -26.932 35 SA29 35 24.165 -27.071 35 SA30 36 25.021 -26.995 38 SA31 37 26.284 -26.865 40 SA32 38 27.179 -26.899 40 SA33 39 28.099 -26.813 38 SA34 40 29.088 -27.018 40 SA35 41 30.125 -26.877 37 SA36 42 23.721 -25.971 34 SA37 43 25.085 -25.933 38 SA38 126 Table 3.1 (cont.) 44 26.151 -25.895 42 SA39 45 27.149 -25.898 45 SA40 46 29.222 -25.787 43 SA42 47 30.066 -25.787 44 SA43 48 30.902 -26.032 40 SA44 49 26.164 -24.879 45 SA45 50 27.109 -24.838 44 SA46 51 28.162 -24.847 50 SA47 52 29.216 -24.895 45 SA48 53 30.309 -24.959 38 SA49 54 27.166 -23.872 43 SA50 55 28.157 -23.863 50 SA51 56 28.897 -23.798 42 SA52 57 29.333 -24.113 43 SA53 58 30.668 -23.729 38 SA54 59 28.298 -22.980 45 SA55 60 29.074 -23.006 45 SA56 61 30.020 -22.981 43 SA57 62 31.397 -23.518 45 SA58 63 25.256 -28.614 35 BOSA 64 24.464 -24.837 45 SA59 65 24.959 -23.852 45 SA60 66 24.022 -23.948 46 SA61 67 25.135 -24.851 45 SA62 68 26.082 -23.658 47 SA63 69 26.202 -22.969 41 SA64 70 27.221 -22.818 45 SA65 71 26.373 -21.900 50 SA66 72 27.274 -21.886 46 SA67 73 28.188 -21.950 48 SA68 74 29.266 -22.304 52 SA69 75 26.335 -21.088 55 SA70 76 27.140 -20.926 45 SA71 77 30.278 -21.854 48 SA73 78 30.936 -21.923 44 SA74 79 20.812 -32.380 47 SUR 80 21.268 -30.925 47 SA81 81 22.247 -30.977 50 SA82 82 25.597 -25.015 45 LBTB 127 Figure 3.19 Crustal thickness map combining results of previous seismic surveys and the SASE. Previous results, shown as pink diamonds and summarized in Table 2.1, are in good agreement with the SASE results of Gore, 2005 and Nguuri, 2004 (Table 3.1). Same color scale as Figure 3.18. The crust beneath the Limpopo Belt stations is significantly thicker than the generally low elevations would suggest. The Limpopo Belt underlies much of the drainage basin of the Limpopo River and is actively eroding. It appears that rebound expected from erosion in this region has not occurred, suggesting that either the crust is unusually strong in this region and resists rebound or that the crust is unusually dense in this region and there is no buoyancy contrast with the mantle as suggested by Fischer (2002). More detailed crustal thickness coverage is needed to expand gravity calculations further northwest and southeast of the present SASE coverage. 128 Figure 3.20 A comparison of elevations (averaged for 20 km radius around each station) and seismically determined crustal thicknesses from the 82 seismic stations of the SASE reveals no clear linear trends and only weak clustering of tectonic regions. 129 A histogram of the SASE receiver function crustal thickness values is bimodal (Figure 3.21). A comparison of Bouguer gravity values averaged across a circular area of 20 km radius around each SASE seismic station, with crustal thicknesses reveals clustering of the cratonic stations, which are mostly located at high elevations and much spread in the other stations (Figure 3.22). The lack of a strong linear trend, such as is observed in Figure 3.17, demonstrates that crustal thickness is not the dominant control on the resulting Bouguer gravity as expected. 0 2 4 6 8 10 12 14 16 29 34 39 44 49 Thickness (km) N um be r Figure 3.21 Histogram of seismically determined crustal thickness values for the 82 seismic stations in the SASE experiment. The histogram is bimodal. Data are from Table 3.1. 130 Figure 3.22 A comparison of seismically determined crustal thicknesses and Bouguer gravity both of which were averaged across an area with a radius 20 km around each of the 82 seismic stations from the SASE. This plot reveals no clear linear trends and only weak clustering of cratonic regions. Compare this with Figure 3.17. In southern Africa, a comparison between the predicted crustal thicknesses based on elevations and Airy isostasy with a density of 2670 kg/m3 with seismically determined crustal thicknesses (Figure 3.23) reveals that there is greater variation in the measured 131 crustal thicknesses than in the predicted crustal thicknesses, suggesting that the Moho boundary has preserved variations for a significant period of time, although possible effects of laterally varying density in the crust also cannot be ruled out. The time period over which Moho boundary has been preserved is certainly greater than the expected relaxation time for flexure, which is approximately 45,000 years (Watts, 2001), indicating that the crust is also quite strong. Figure 3.23 A comparison of seismically determined crustal thicknesses and those predicted using Airy isostatic balance (both averaged for a radius of 20 km around each station). The measured crustal thicknesses show more variation than the predicted variations. The straight line with 45? slope indicates a 1:1 correspondence between predicted and measured. 132 Similarly to Figure 3.20, Figure 3.23 (the plot of predicted vs. seismically determined crustal thickness) demonstrates that topography is not a good predictor of crustal thickness, especially in the mobile belt regions in southern Africa. The Archaean cratons vary between somewhat thinner to significantly thicker than predicted; the surrounding mobile belts are significantly thicker than predictions based on elevation. The range of predicted crustal thicknesses is significantly smaller, a consequence of the mostly smooth topography of southern Africa. The measured Moho beneath southern Africa, while comparatively smooth, has significantly more variation than is predicted from the topography, implying long term strength at the Moho, or variations in lower crustal density (Fischer, 2002) or variations in mantle density. One could argue that using a larger crustal density would produce greater variations in the predicted thicknesses; however, using Airy prediction is already an over-prediction as the crust is likely to be strong and the response is likely to be of lower amplitude (Figure 3.12). Although this type of analysis is straightforward, it illustrates important relationships more clearly than admittance and coherence analysis appear to do in old continental regions (Watts, 2001). An admittance analysis for determining the effective elastic thickness of southern Africa by Doucour? et al., (1996) obtained highly variable results. If a southern African excess elevation anomaly is removed (i.e. Doucour? et al., 1996 removed a mean of 500 m), the fit between predicted and measured crustal thickness is even worse, as the predicted crustal thicknesses would mostly be 3-5 km smaller than indicated on the plot (Figure 3.23). 133 3.7 Modeling of gravity due to crustal thickness variations The largest density contrast in the lithosphere is likely to be at the seismically- defined Moho, between the lowermost crust and the uppermost mantle. This is unlikely to be greater than 500 kg/m3 (Niu and James, 2002; Tiberi et al., 2001) and likely to be significantly smaller (300 kg/m3 or less) (Fischer, 2002; Zoback and Mooney, 2003). The lateral density distribution in the crust will obviously give a strong contribution to the gravity observed at surface; however, the interest here is to determine plausible contributions from crustal thickness variations and mantle density variations as inferred from seismic velocity variations. A fully 3D gravity model can be developed along the central profile labeled B to B? in Figure 3.13. Although the gravity is calculated at each point on a surface grid, it is only along the profile B-B? (Figure 3.13) that there is sufficient 3D information of both crustal thickness and mantle velocity variations to calculate the gravity field without undue distortion from edge effects. The histogram of crustal thickness is bimodal, with peaks at 38 and 45 km (Figure 3.21). The average crustal thickness is ~41 km and variations around this value have been used to determine the gravitational attraction due to variations in crustal thickness. First a 2.5D method is applied to model the variations along the central profile. The comparison of the 2.5D method with the 3D methods demonstrates the importance of including the 3D information. Two different three-dimensional methods have been applied to calculate the gravity field: the Parker FFT method and the approximate spherical prism method. As will be detailed below, these 3D methods are compared and the two curves are virtually identical along the central profile with the maximum difference never exceeding 10% of the value. Thus the 3D spherical prism method 134 developed here can also be applied to the mantle calculations using the nodes determined from the seismic tomography. 3.7.1 Forward modeling: 2.5D block model of profile B to B? The rapid 2D modeling algorithm for potential field anomalies used in this work has been developed by Cooper (2003) and is based on the Talwani et al. (1959) algorithm with limited strike length. The profile B-B?starts near Cape Town (19.25? E, -34.25? S) and extends into Zimbabwe (31.5? E, -18.5? S), a distance of 2130 km (Figure 3.13). Figure 3.24 shows the gravity and crustal thickness data extracted along this profile. The crustal thicknesses have been extracted from the gridded crustal thickness values at an interval of 50 km. They are displayed as blue representing thicker than average crust, and hence having a negative density contrast compared to the background mantle density values, and as red repersenting thinner than average crust and having a positive density contrast compared to background crustal density values. For this calculation a Moho density contrast of +300 kg/m3 to -300 kg/m3 is used, depending on whether the crust is thinner or thicker than average. The blocks extend in and out of the profile for 50 km and are perpendicular to the profile. In reality the density contrast of the Moho probably changes dramatically depending on the geological terrain, age or metamorphic environment (Zoback and Mooney, 2003). These effects will be examined further in the 3D modeling section below. The plotted Bouguer gravity data have been extracted from the gridded gravity data at an interval of 10 km. To facilitate comparisons between the curves, no regional gravity trend has been removed from the modeled result. 135 Figure 3.24 A 2.5D model of the gravity response calculated from variations in crustal thickness, along a profile from Cape Town (B) to northern Zimbabwe (B?). The solid black line shows the calculated gravity due to the crustal thickness variation and the dotted green stars are the observed Bouguer gravity data. Crustal thickness variations shown are relative to an average value of 41 km thickness along this profile and were obtained from the gridded crustal thickness values sampled at 50 km intervals. The blocks are of limited strike length, 50 km in and out of the page. Neither the shape nor the amplitude of the calculated anomaly due to the Moho thickness variations matches the observed data, although the amplitude variations of the calculated signal are of similar magnitude to the observed data. This indicates that there are significant long wavelength contributions to the gravity signal that are independent of the Moho topography. One source may be the effect of the three dimensional geometry of the Moho having a significant effect on the gravity calculated along the profile. To investigate this possibility, in the next section I have calculated the 3D gravity along the same profile due to all of the variations determined at the Moho. 136 3.7.2 Forward modeling: Parker?s FFT method The gravitational response due to the variations in the seismically determined Moho can be calculated using Parker?s FFT method (Parker, 1972) using the implementation of grdfft from GMT (Wessel and Smith, 1991). The interface that is modeled is the Moho. The background model, as shown in Figure 3.25, is crust in grey overlying mantle in light green, with the first set of mantle voxels set to background values. In these models no crustal density variations are considered as I am only investigating variations in crusal thickness and (in Chapter 5) upper mantle contributions to the gravity signal. The variations in crustal thickness are between 30 km and 50 km, with the average depth to the Moho shown in Figure 3.25 as ~41 km. Variations around this average are shown schematically in 3D in Figure 3.26, with thinner crust having a positive density contrast against background (red) and thicker crust having a negative density contrast compared to background (blue). Figure 3.25 Schematic block model of the background crustal model for the determination of gravity from the Moho. The crustal layer from 0-30 km depth has a constant density value in this model, the 20 km thick layer from 30-50 km depth is divided in the middle at the average crustal thickness. The bottom layer from 50-100 km depth is a constant mantle density. In this model the absolute values of density are unimportant as only density contrasts are modeled. 137 Figure 3.26 Schematic model of the 3D variations in the crustal thickness represented by blue and red blocks. Red blocks represent thinner than average crust and densities higher than the background crustal density; blue blocks represent thicker crust and lower than background mantle density. In the Parker FFT calculation the crustal thickness is represented as a surface that has been gridded to an interval of 0.25? (~28 km). This is to ensure that the gridding interval is smaller than the depth to the shallowest part of the interface (Parker, 1972). The data used are only from the SASE results to ensure a consistent data source (Nguuri et al., 2001). Outside of the region where there are data, the crustal thickness has been set to the average value of 41 km and smoothly splined to reduce edge effects. From various model tests it was found that significant effects (>1 mGal) from Moho topography variations and density contrasts of 200 to 800 kg/m3 extend out to distances of ~200 km. Thus the 3D gravity calculations are most valid along profile B-B? (Figure 3.27). 138 Figure 3.27 Surface gravity field determined from variations in the crustal thickness from a density contrast of 300 kg/m3 using the 3D Parker FFT method. 139 3.7.3 Forward modeling: 3D spherical prism method The next method used to calculate the gravity effect of crustal thickness variations was the spherical prism method developed in section 3.1.6, which was coded by modifying code from Lees and VanDecar (1991). This modified code is found in Appendix E. The radius of all spheres used in the calculation is less than 20 km, which is sufficiently far from the surface, relative to the depth to the sphere. The surface on which the calculations are determined is a spherical Earth surface. This is a modification of the method used by Lees and VanDecar (1991) and the code used, gravity_sue.f is reproduced in Appendix E. The present method was adopted for two reasons: first the ease of programming the calculation and second the ease of combining crustal thickness with the delay time tomographic results (Chapter 5). Gravity was calculated at intervals of 0.25? (~28 km) across the region and areas where no crustal thickness data are available have been masked (Figure 3.28). Outside of the region where there are data, the crustal thickness has been set to the average value of 41 km and smoothly splined to reduce edge effects. The results of the gravity calculation are shown in Figure 3.28. The same features as those produced by the FFT method (Figure 3.27) are also immediately apparent in Figure 3.28, notably the large increase in gravity as the edge of the craton is approached from the south and the large decrease in gravity northward toward and into the Bushveld Complex. 140 Figure 3.28 Gravity calculated on a spherical surface determined from variations in the crustal thickness using a density contrast of 300 kg/m3 at the Moho and the spherical prism method. Line of profile is shown on the map view. 141 The next objective is to quantify differences between the gravity field calculated using the spherical prism method vs. the Parker FFT method. Both methods were calculated at the same positions on the surface at a 0.25? interval and then subtracted. Due to edge effects, the most important determination is along the central profile. The difference between both methods has been calculated on a point by point basis along the profile (Figure 3.29). The agreement between the two methods is excellent and was tested for a variety of different density contrasts, with similar results. The differences are most pronounced near the ends of the profiles due to edge effects and variations in crustal thickness, possibly due to differences in smoothness between the Parker FFT method, which is a surface, and the spherical prism method, which uses discrete sources. 142 Figure 3.29 Mapped difference between the Parker FFT and the spherical prism method. Below are the profiles for the Parker FFT (red) and spherical prism method (green) where the black line shows the point by point difference between the two. The agreement between the methods is excellent. 143 3.7.4 Comparison between measured and modeled results In order to compare the modeling results with the measured gravity data, the latter have been smoothed using a space domain filter to ensure that the magnitudes of the longer wavelengths are preserved (Figure 3.30). In doing this it is assumed that the short wavelength features are all likely to be sourced in the crust and can therefore be ignored in this study. Figure 3.30 displays the map of the smoothed Bouguer gravity of southern Africa and underneath compares the profile of the smoothed Bouguer gravity (black) with the profile extracted from the modeled gravity based on variations in crustal thicknesses using the spherical prism method. A DC shift has been applied to the spherical prism calculation for comparison purposes, as this calculation is performed using density differences about a zero value. 144 Figure 3.30 Bouguer gravity data of southern Africa smoothed to preserve long wavelengths and clipped to the region of the SASE stations. The black profile is from the smoothed observed Bouguer gravity which has been placed for comparison next to the red curve which is determined from the modeled 3D gravity using the spherical prism method with a density contrast of 300 g /cm3 as determined in Figure 3.28. 145 The various models and data sets presented in Figures 3.24, 3.27, 3.28, and 3.30 are compared in Figure 3.31 along profile BB?. The two dimensional modeling (red curve) shows all of the same features as the three dimensional models do, but the magnitudes are significantly different, as emphasized by the difference curve (brown) between the 2D and 3Dfft curves. For comparison, the observed gravity and the smoothed gravity along the same profile are included. Figure 3.31 Comparison between the 3D Parker FFT method (light blue), the 3D spherical prism method (dark blue) and the 2.5D profile calculation (red) for the same profile and density contrast (300 kg/m3). The observed (pink) and smoothed (purple) gravity are included along the same profile for comparison purposes. To illustrate the effect of the density contrast across the Moho, calculations of 3D gravity due to variations in crustal thickness using the spherical prism method and using density contrasts ranging from 100 kg/m3 to 450 kg/m3 are shown in Figure 3.32. The magnitude of the gravity anomalies resulting from density contrasts between 350 and 450 kg/m3 appear too large to be applicable regionally, although large contrasts may occur 146 locally (Niu and James, 2002). The obvious lack of correlation between the modeled gravity fields and the observed gravity indicates that either the crust or the mantle contribution to the gravity signal must significantly modify the gravity signal due to variations in Moho depth. 147 Figure 3.32 A comparison of the 3D spherical prism model calculated gravity due to variations at the Moho for a variety of constant density contrasts across the Moho. The color and vertical scales have been kept the same for comparison purposes. A) 100 kg/m3, B) 200 kg/m3 C) 350 kg/m3, D) 450 kg/m3. Figure 3.28 shows the response for 300 kg/m3. 148 3.7.5 Discussion The modeling results show that the spherical prism method is a valid method to determine the 3D gravity along the profile BB?, as results are nearly identical to those obtained using the Parker FFT method. The 3D results represent a significant improvement over the 2D modeling methods. The 3D spherical prism method is easy to implement and has the advantage of being compatible with the delay time tomography results, which will be incorporated into the modeling in chapter 5. The Parker FFT method, as implemented in GMT, assumes a flat Earth, but for profiles even over distances of ~2,000 km this assumption appears to make little difference. The difference in the vertical component of gravity on a spherical Earth vs. a flat Earth is only 0.01 mGal, for a spherical source with a 10 km radius sphere and a density contrast of 300 kg/m3 positioned at 40 km depth and measured at 50 km away horizontally. This difference is due to the very slight change in the vertical component of gravity due to the Earth?s curvature. Since the spherical prism method is determined on a spherical surface, this may explain the slightly larger values calculated on the spherical surface. When comparing calculated gravity profiles with the measured profile (Figure 3.32) it is clear that the thin crust beneath the Kaapvaal and Zimbabwe cratons is characterized by positive contributions to the gravity signal that must be counterbalanced by negative contributions likely due to low densities in the mantle. The next section examines variations in the 3D gravity response by varying the density contrast as a function of crustal thickness or as a function of varying geological terrains as developed in Chapter 2 to determine if this imposes significant changes. 149 3.8 Density contrast as a function of crustal thickness and geological terrain The idea that thicker crust is denser than average continental crust was proposed in early arguments about isostatic balance as summarized in Watts (2001). Fischer (2002) and Zoback and Mooney (2003) have used buoyancy arguments to claim that the lower crust, especially in regions of older, previously tectonically active crust, is likely to be significantly more dense due to metamorphic effects where it remains thicker than average. Variations in density with depth due do variations in crustal thickness can be incorporated into the gravity calculation to determine the magnitude of the effect. A series of crustal density models from published and additional hypothetical density contrasts with depth are summarized in Table 3.2. The gravity for these density models is calculated using the program gravity_crustal_regional.f (Appendix E), which uses the spherical prism method, but incorporates density values based on thickness. The density contrast assigned to the spherical prism in the calculation is determined by the depth extent of that prism. The density contrasts used are summarized in Table 3.2, and can be used to determine the gravity values for crust up to 56 km thick, so will account for all observed thicknesses in the SASE region. Because the prisms used in the calculation are large compared to the density variation with depth, some detail is lost in the calculation; however, as a first order examination of the effect of increasing density with depth, this method can be used to examine the effect. Model 1 is the control model used for comparison with a constant density contrast of 300 kg/m3 between the crust and mantle as shown in Figure 3.28. Model 2 applies an empirical relationship for crustal density, ?c, developed by Zoback and Mooney (2003) and expressed as: 150 cc t319.72.2581 +=? 3.17 where tc is the crustal thickness (20 ? tc ? 50) and density of the crust is ?c. Zoback and Mooney (2003) use a density of 3300 kg/m3 for the oceanic asthenosphere and the density contrasts predicted by Zoback and Mooney (2003) are tabulated in Table 3.2, and shown graphically in Figure 3.33. While this mantle density is too large for a continental region, this example provides a useful upper bound end member. The resulting gravity anomaly is shown in Figure 3.34A. There are notable differences from the control (model 1, Table 3.2), shown in Figure 3.28, which has a constant density contrast of 300 kg/m3. As all density contrasts in model 2 (Zoback and Mooney, 2003) are larger than the control contrasts, the amplitude of the resulting gravity calculation is noticeably larger; however, the shape of the curve has not changed significantly. Model 3 follows the work of Fischer (2002) in which she argues for smaller density contrasts at the crust mantle boundary, especially for older, thicker, previously mountainous regions (e.g. old eroded mountain belts). This argument is based on a global compilation of mobile belts where thickness and age have been determined. She determines density contrasts at the crust mantle boundary which start at ~350 kg/m3 for the youngest age crustal sections through eroded mountain belts and she observes a decrease in the density contrast with increasing age of the crust to a limit of ~0 kg/m3. The slope of the density contrast line is steeper for this model than for Model 2 (Figure 3.33). This density contrast distribution results in a significantly reduced contribution to the gravity signal in regions of thicker crust (Figure 3.34 B). 151 Table 3.2 Summary of crustal models using density determined from thickness variations for 3D gravity calculation. The density for the interval is assigned to the spherical prisms at that depth. Models 1 to 5 are shown graphically in Figure 3.33. The letters A to D refer to the resulting gravity calculations shown in Figure 3.34. Model # Model 1 Model 2 (A) Model 3 (B) Model 4(C) Model 5 (D) Input # Depth Interval Starting at 0 (km) Constant Density contrast (kg/m3) (Fig. 3.28) Density contrast from Zoback & Mooney (2003) (kg/m3) Density Contrast from Fischer (2002) (kg/m3) Lower crust more dense than upper most mantle if thicker than 50 km (kg/m3) Up to 41 km thickness contrast = 300 kg//m3, thicker goes to zero linearly (kg/m3) 1 24 300 543 350 300 300 2 26 300 529 328 278 300 3 28 300 514 306 256 300 4 30 300 499 284 234 300 5 32 300 485 263 213 300 6 34 300 470 241 191 300 7 36 300 455 219 169 300 8 38 300 441 197 147 300 9 40 300 426 175 125 300 10 42 300 411 153 103 263 11 44 300 397 131 81 225 12 46 300 382 109 59 188 13 48 300 367 88 38 150 14 50 300 353 66 16 113 15 52 300 338 44 -6 75 16 54 300 324 22 -28 38 17 56 300 309 0 -50 0 152 Figure 3.33 Schematic diagram summarizing the various density depth relationships that were used to calculate the 3D gravity. Number 2 results in the gravity map and profile shown in Figure 3.34A; 3 to 3.34B; 4 to 3.34C; and 5 to 3.34D. By extending Fischer?s (2002) argument to thick crust, it is reasonable to consider a scenario where the lower most crust might be denser than the upper most mantle due to the formation of eclogite, such as might have occurred in the Limpopo Belt. This scenario is investigated in model 4, which results in a negligible gravity response from regions of thick crust, and a significant positive gravity response in regions of thin crust due to the presence of mantle at shallow depths (~40 mGal) (Figure 3.34C). Model 5 explores a scenario where crust up to a thickness of 41 km has a constant density contrast. For crust with a thickness between 41 ? 56 km the density contrast is assumed to reduce down to 0 following a linear trend. The constant density contrast for thinner crust is based on the assumption that crustal extension causes homogenization of the density contrast in the crust (Table 3.2 and Figure 3.33). The resulting gravity is shown in Figure 3.34D. 153 Figure 3.34 Summary of calculations for 3D gravity where the density contrast between the crust and mantle varies with depth according to Table 3.2 and Figure 3.33. Model 2 in Figure 3.33 and Table 3.2 corresponds to the gravity calculated in 3.34A; Model 3, to 3.34B; Model 4 to 3.34C and Model 5 to 3.34D. As an alternative to variation in density with depth, density contrasts at the Moho can be assigned based on regional surface geology. This assumes there is a connection 154 between the surface geology and the lowermost crust. Here the geological terrain map developed in chapter 2 is used to assign density contrasts across the Moho (Figures 3.35 and Table 3.3), and the resulting gravity values are calculated in the region of the SASE stations (Figure 3.36 A-D). An implicit assumption in this case is that the mapped geological terrain boundaries are vertical and can be related to the Moho, i.e. that the upper and lower crust have remained coupled since the upper crust formed. The program gravity_crustal_regional.f is also used for this calculation (Appendix E). A number of scenarios were explored and these are summarized in Table 3.3 and Figure 3.36 (A-D). The control Model 1 assumes a constant density contrast of 300 kg/m3 for all of the geological terrain (Figure 3.28). Model 2 (Figure 3.36A) examines the case where cratonic regions (Kaapvaal, Zimbabwe, and Okwa) all have a contrast of 300 kg/m3 and the surrounding mobile belts have a lower contrast of 50 ? 200 kg/m3 depending on the sharpness of the Moho as defined by the receiver functions in each area, with more diffuse receiver functions having a lower density contrast. The resulting profile (Figure 3.36A) has a slightly different shape than the thickness-dependent models shown in Figure 3.34A-D, especially in the regions of the Bushveld Complex and Limpopo Mobile Belt. Model 3 (Figure 3.36B) considers the possibility that the region identified as the Okwa belt has a density contrast of 50 kg/m3, which is the same as the Limpopo Belt, assuming that the Okwa Belt may actually be part of the Limpopo Belt extending into Botswana and wrapping around the end of the Zimbabwe craton as postulated by Rangani et al. (2002) and as suggested by the receiver function results (Nguuri et al., 2001). This change doesn?t really affect the profile (B-B?) much as the Okwa region is largely off to the side of the profile (Figure 3.36B), but it does significantly affect the gravity calculated in the Okwa region, raising it by a substantial amount. 155 Figure 3.35 Geological terrain map developed with cells of 0.5? size used here to examine the relationship between regional surface geology and density contrast at the Moho. 156 Table 3.3 Summary of model density contrasts used to examine relationship between density contrasts assigned by geological terrains defined at the Moho and the resulting gravity anomaly. Details for models 1-5 are discussed in the text. Model 1 2 3 4 5 Regionalized Geology Zone # Cntrl (kg/m3) Cratons high, mobile belts low (kg/m3) Okwa Low Contrast (kg/m3) Cape Fold Belt Low Contrast (kg/m3) Zim Craton Low Contrast (kg/m3) Kaapvaal, west of Colesburg 1 300 300 300 300 300 Kaapvaal, east of Colesburg 2 300 300 300 300 300 Zimbabwe Craton 3 300 300 300 300 200 Limpopo, NMZ 4 300 50 50 50 50 Limpopo, CZ 5 300 50 50 50 50 Limpopo, SMZ 6 300 50 50 50 50 Bushveld 7 300 50 50 50 50 Okwa 8 300 300 50 50 50 Namaqua Natal Mobile Belt 10 300 100 100 100 100 Cape Fold Belt 11 300 200 200 50 50 Outside of range 12 300 0 0 0 0 Model 4 explores a scenario in which the crust below the Cape Fold Belt has a density contrast of 50 kg/m3 with the mantle. The gravity determined from this model along the profile (B-B?) is significantly different in the southern section as shown in Figure 3.36C. 157 Figure 3.36 Summary of calculations for 3D gravity where the density contrast between the crust and mantle varies according to geological terrain boundaries as summarized in Table 3.3. The gravity resulting from model 2 is shown in Figure 3.36A; from model 3 in 3.36B; from model 4 in 3.36C and from model 5 in 3.36D. 158 Model 5 (Figure 3.36D) considers a slightly lower density contrast at the Moho (200 kg/m3) beneath the Zimbabwe craton as compared to the Kaapvaal Craton in an effort to reduce the difference in gravity values between the Limpopo Belt and the Zimbabwe Craton. (Figures 3.28 and 3.30 compare black (observed) and red (calculated) profiles). This section has demonstrated that varying density as a function of crustal thickness or across regional geological terrain boundaries significantly alters the amplitude of the resulting gravity contribution, but changes the shape of the anomaly only slightly. Regardless of the density relationship used, the density contrast across the Moho contributes a significant gravity signal that is in direct opposition to the observed gravity signal (e.g. Figure 3.30). The variation in receiver function intensity, whereby the signal is sharp on the cratons and more diffuse in the surrounding mobile belts and Bushveld Complex zone supports the premise that these regions have more mafic material in the lower crust. This idea is also supported by the consistently lower elevations of the Limpopo mobile belt, especially considering the overall uplift of the region, which indicates that the older Limpopo mobile belt may no longer be rebounding as suggested by Fischer (2002). 3.9 Discussion The goal of this chapter has been to develop a method to determine the contribution to the gravity signal on surface from variations in the crustal thickness determined along a profile central to the stations deployed during the SASE. This has been accomplished first by evaluating several methods including: 2D Talwani (Talwani et al., 1959), 3D cube and facet prisms (Blakely, 1995), 3D stacks of lamina (Blakely, 1995) and 3D 159 Parker FFT method (Blakely, 1995). While the Parker FFT method is straightforward to implement in the case of the Moho boundary, it is more difficult to use for examining the mantle where the density varies continuously. The implementation of the Parker FFT method used here is found in Generic Mapping Tools (Wessel and Smith, 1991). Finally a modification of the Lees and VanDecar (1991) algorithm was developed in this chapter, called the 3D spherical prism model, whereby the surface on which the calculations are determined is spherical. In this modified algorithm the sources are still spheres; they have been given the same volume and center point as the coincident spherical prisms. Spherical prisms cannot be used directly as the source as no analytic solution exists (Heck and Seitz, 2007; Smith et al., 2001) and numerical methods are unwieldy for the level of accuracy required. This chapter has shown that there is excellent agreement in the modeled gravity field along profile B-B? between the spherical prism method as implemented here and Parker?s FFT method. Although there is a strong linear trend present in the Bouguer gravity vs. elevation plots (Figures 3.15 and 3.17) that suggests the region is in isostatic balance, the scatter in the plot of Bouguer gravity and crustal thickness indicates no such linear relationship (Figure 3.22). There is also no correlation seen in the elevation vs. crustal thickness plot (Figure 3.20), although there is clustering by geological terrain in these two graphs. The cratonic regions generally have high elevations, thinner crust, and lower gravity values, whereas the mobile belts have generally lower elevations, thicker crust and higher gravity values. The lack of correlation between elevation and crustal thickness suggests that for the Kaapvaal region, isostatic balance is not achieved at the Moho and there must be a significant contribution from the mantle in a process that is modified over time. It also appears that a different isostatic balance is reached in different geological terrains as there is strong clustering in the data (Figures 3.20, 3.22, 3.23). Part of this effect may be due to 160 more effective weathering of mobile belts compared to cratons or lack of rebound from denser lower crust especially in the older Limpopo Mobile Belt (Fischer, 2002). The significant amount of variation preserved in the Moho topography compared to that predicted from the current elevations suggests that the crustal strength has increased over time to preserve these variations. The effect of the regional, large scale (~5,000 x 5,000 km) elevation anomaly known as the African Superswell (Nyblade and Robinson, 1994) will be to raise the elevations in the entire Superswell region by about 500 m. But because the superswell is such a broad scale anomaly, there is no reason to suspect that it will cause the thickness variations observed between on and off craton, at a lateral scale of ~800 km. The effect of the superswell should be a straightforward DC shift in the elevation values over the SASE region. It is clear that a significant contribution to the gravity signal from long wavelength crustal density variations or mantle keel density variations are needed to counterbalance the gravity signal generated from variations in crustal thickness in order to match the observed data. Large variations in crustal thickness, such as those encountered at the transition between the Namaqua Natal Mobile Belt and the Kaapvaal Craton lead to large amplitude variations in the computed gravity response. Computed gravity values range from ~160 mGals amplitude for a constant density contrast at the Moho of 440 kg/m3 (Niu and James, 2002), to 40 mGals amplitude for a constant density contrast of 100 kg/m3. The latter density contrast is unrealistically small in a normal cratonic setting where there is little evidence for mafic lower crust and a strong receiver function response (Nguuri et al., 2001), but might be more realistic in a mobile belt (Fischer, 2002). The mobile belts surrounding the Kaapvaal craton have different gravity, topography and Moho topography signatures than the craton itself. The deep crustal roots of the mobile belts, as well as their smaller density contrast (based on weaker receiver 161 functions) with the mantle, appear to play an important role in protecting the fragments of Archaean craton from disruption (Carlson et al., 2005). The crust is generally thicker and Bouguer gravity generally higher in the mobile belts. This suggests that the mobile belts have a higher average crustal density when compared to the cratons. A comparison of models examining variations in density contrast with crustal thickness compared to models examining density contrast varying with geological terrains reveals a distinctly different shape to the profile in the Bushveld and Limpopo regions as compared to normal cratonic areas underlain by thick mantle roots. These differences will be further investigated in chapter 5 when the gravity response obtained from the tomography results is combined with the gravity response due to variations in Moho depth. The models considered in this chapter demonstrate that the seismically determined variations of Moho topography can make a significant contribution to the long wavelength gravity signature observed at the surface. In addition, the density contrast across the Moho is a variable that is poorly constrained but important in determining the magnitude of the gravity signal. While receiver function studies indicate that the Moho is fairly sharp (~1-2 km) and has a fairly strong contrast (Gore, 2005; Nguuri, 2004), the contrast cannot be well quantified with these studies. However, Moho density contrasts have been more precisely estimated from local seismic studies in the Kimberley region where they are calculated to be relatively large (440 kg/m3) (Niu and James, 2002). Such large contrasts are unlikely to persist throughout the craton as a whole, because for a density contrast of 440 kg/m3 the amplitude of the gravity response due to variations in crustal thickness is a positive ~170 mGal, which is considered to be too large to be counterbalanced by reasonable mantle density variations as will be discussed in Chapter 5. All of the models presented here have a strong gravity anomaly at ~600 km along 162 163 profile (B-B?) reflecting the dramatic change in crustal thickness moving from the NNMB to the Kaapvaal Craton. However, in the observed gravity data (Figure 3.30), this anomaly is a subdued local peak of ~15 mGal at the NNMB ? Kaapvaal Craton boundary. Although it is possible that there is a strong lateral change in crustal density, it will be demonstrated in chapter 5 that the strong positive gravity anomaly due to thinner crust in the craton is largely counterbalanced by a depleted lower density mantle keel throughout this region. It is important to carefully consider the contribution of crustal thickness variations to the surface gravity as they are significant. Frequently, especially at the global scale, these crustal thickness variations are ignored, or are assumed to be isostatically compensated based on topography (e.g. Kaban et al., 2003). This can lead to underestimating the variation in density of the uppermost mantle. 4 Gravity modelling of the Bushveld Complex In Chapter 2 I summarized the major crustal Bouguer gravity anomalies of southern Africa in an effort to recognize the signature of these features in the broader analysis of the gravity data undertaken in this study. One major set of crustal anomalies, the anomalies that mark the location of the Bushveld Complex, warrants more extensive treatment due to its large lateral extent and its possible effect on the shape of the Moho as noted in Chapter 3. In Chapter 4 I present a re-assessment of the large-scale structure of the Bushveld Complex based on a reinterpretation of the Bouguer gravity data and extensive sets of new density determinations derived from the BV-1 borehole in the northern lobe of the Bushveld Complex and described in Appendix A (Ashwal et al., 2005). This reinterpretation of the gravity data, as published in Webb et al. (2004), is presented first in its published form and followed by a more extensive discussion of some salient points arising from the study. Since Webb et al. (2004) is presented as published, the formatting, table titles and figure captions are inconsistent in this section with the rest of this thesis. In total five published papers have resulted from work in this chapter. In addition to Ashwal et al. (2005), found in Appendix A and Webb et al. (2004) presented here, three additional papers (Cawthorn et al., 1998b; Cawthorn and Webb, 2001; Nguuri et al., 2001) have included work related to this chapter and are found in Appendices B, C, and D. 4.1 Webb et al. (2004) 164 Introduction The Bushveld Complex (~2.06 Ga) (e.g. Eglington and Armstrong, 2004) is the world?s largest known layered mafic intrusion extending >350 km in both north-south and east-west directions (Figure 1A). The large-scale three-dimensional structure of the Bushveld Complex has been a long-standing source of debate due to the limited amount of outcrop and lack of deep probing geophysical studies in the central region. It has previously been described as: a lopolith (Hall, 1932; du Toit, 1954), separate intrusions (Cousins, 1959; Sharpe et al., 1981), and separated dipping sheets (Biesheuvel, 1970; van der Merwe, 1976; Walraven and Darracott, 1976; Molyneux and Klinkert, 1978; Meyer and De Beer, 1987). The lopolith model was initially proposed based on geological evidence. However, the interpretation by Cousins (1959) of the first regional gravity data appeared to be a convincing refutation of the lopolith model. Cousins based his argument on the fact that the Bouguer gravity anomaly in the central part of the Bushveld Complex is similar to the background value outside of the Complex. If a lopolith were present, the Bouguer gravity value in the central portion should be elevated relative to the background value. A very brief mention of the possibility of a lopolith topology of the Bushveld Complex causing flexure in the crust was considered by Smit (1962), but was dismissed based on the strength of Cousin?s model. Sharpe et al. (1981) speculated on isostatic adjustment of the eastern compartment based on structural evidence, but the size Gravity modeling of Bushveld Complex connectivity supported by Southern African Seismic Experiment results Susan J. Webb and R. Grant Cawthorn School of Geosciences, Private Bag 3, University of the Witwatersrand, Wits, 2050, South Africa e-mail:webbs@geosciences.wits.ac.za and cawthorng@geosciences.wits.ac.za Teresia Nguuri School of Geosciences, Private Bag 3, University of the Witwatersrand, Wits, 2050, South Africa CTBTO, Preparatory Commission, Vienna International Centre, P.O. Box 1200, 1400 Vienna, Austria e-mail:teresia.nguuri@ctbto.org David James Carnegie Institution of Washington, Department of Terrestrial Magnetism, 5241 Broad Branch Rd. N.W., Washington, D.C., 20015 USA e-mail: james@dtm.ciw.edu ? 2004 Geological Society of South Africa ABSTRACT Recent gravity modelling of the Bushveld Complex indicates that the western and eastern limbs of the Bushveld Complex are connected at depth. The model predicts a downwarp in the Moho beneath the Bushveld Complex, ensuring observed Airy isostatic balance is achieved. By constraining a new Bouguer gravity model with published Vibroseis results, crustal thicknesses determined using the receiver function method, and seismic velocity modelling of the crust from the Southern African Seismic Experiment; we demonstrate that the connected model of the Bushveld Complex is consistent with all available data. Crustal thicknesses determined from receiver functions indicate that the depth to the Moho thickens from a value of ~35 to ~40km in the southern Kaapvaal craton to ~50km beneath the central region of the Bushveld Complex. This seismologically determined Moho varies significantly from that calculated from Airy isostatic balance based solely on topography as a load in this region. The corresponding crustal velocity model, determined from inverting the receiver function results for Bushveld Complex stations, also indicates a thick crust and delimits a ~6km thick high velocity zone in the upper 10km of crust attributed to the presence of the Bushveld Complex. Comparison of the seismic crustal model with drill core data on the mafic rocks of the Bushveld Complex suggests a correspondence between high seismic velocities and high densities in the upper crust. Both the gravity model and the seismological results imply a density contrast of about 0.30mg/m3 at the crust/mantle boundary beneath the Bushveld Complex. We also find that the Moho transition beneath the Bushveld Complex is significantly broader than that beneath the rest of the Kaapvaal craton, outside of the Limpopo Belt. By constraining the modelling of the gravity data with these seismological results, outcropping geology and published Vibroseis profiles, we show that the dense mafic units of the western and eastern Bushveld Complex can be interpreted as having originally been emplaced as a connected sheet (or series of connected sheets), which has subsequently been deformed and faulted. The seismological results of the Kaapvaal project support the interpretation of a connected Bushveld Complex. SUSAN J. WEBB, R. GRANT CAWTHORN, TERESIA NGUURI AND DAVID JAMES SOUTH AFRICAN JOURNAL OF GEOLOGY, 2004, VOLUME 107, PAGE 207-218 207 Figure 1. Geological sketch map and conventional dipping sheet model of the Bushveld Complex (after Meyer and de Beer, 1987). (A) The locations of published seismic lines discussed in the text are shown as thick black lines numbered 1 through 4. The locations of the seismic lines published by Tinker et al. (2002) are labelled as Rz254 and Rz256. The location of the Moloto borehole is shown as a green dot. This borehole intersected mafic rocks of the Bushveld Complex in a region where the resistivity measurements suggested mafic rocks were absent. (B) The widely accepted dipping sheet model of the Bushveld Complex. Here we have included the total thickness of the crust for comparison with our revised model in Figure 6. The profile was extracted from the gravity data shown in Figure 2B at ~25?S latitude. SOUTH AFRICAN JOURNAL OF GEOLOGY GRAVITY MODELLING OF BUSHVELD COMPLEX208 Figure 2. (A) Topography, (B) gravity and (C) crustal thickness maps of the region around the Bushveld Complex. The black line shows the outcrop of the Bushveld Complex mafic rocks. The station locations of the southern African Seismic Array are shown in each plot as dots: blue, year one; yellow, years 1&2; red, year two. The numbers by each dot are the station names. The permanent World Seismic Network (WSN) station at Lobotse is shown as a gold triangle labelled LBTB. The thick red line in each figure shows the location of the extracted profiles that are compared with the receiver function results in Figure 3. GMT was used to create this diagram (Wessel and Smith, 1991). (A) The topography of the Bushveld Complex region is mostly over 1,000m above sea level. The escarpment is the prominent feature to the east. (B) The Bouguer gravity map clearly outlines the western, eastern, northern and Bethel lobes of the Bushveld Complex, extending the area of the Bushveld Complex well beyond the region of mapped outcrop of the mafic units (solid lines). A profile has been extracted along the red line and is modelled in Figure 6. The black line, extending south-southeast from station SA47, traces the line of alkaline volcanic complexes. (C) The crustal thickness contour map derived from receiver function results for all stations around the Bushveld Complex, with a profile extracted along the red line (Figure 3D). This map shows the thickening of the crust beneath the Bushveld Complex. The crustal thickness determined for stations LBTB, 45, 46, 47, 48, and 49 have been projected to the profile line and used to constrain the 2.5D gravity model shown in Figure 6. SUSAN J. WEBB, R. GRANT CAWTHORN, TERESIA NGUURI AND DAVID JAMES SOUTH AFRICAN JOURNAL OF GEOLOGY 209 Figure 3. (A) Stacked receiver function results for a 7-station profile from west (top) to east (bottom) across the Bushveld Complex showing the P to S conversion at the Moho as the prominent, wide peak located between 38 and 50km depth for stations SA49 and SA47 respectively. The first (zero-depth) peak, partially truncated, is simply the coherence peak, or direct P-wave arrival. Subsequent peaks on the records are related to velocity discontinuities at depth. As seen from Figure 3A, two or more Ps signals sometimes occur, and the largest Ps is readily associated with the conversion from P to S wave at the Moho discontinuity. Station SA49 is more typical of a station on craton in a region undisturbed by the Bushveld Complex; the peak is narrower and has larger amplitude, indicating a sharper Moho boundary. The number of events in each stack is shown on the right hand side, as is the station name. (B) Topography profile extracted along the red line in Figure 2A. The topography profile bears little resemblance to the extracted Bouguer gravity profile in (C) or the crustal thickness profile (D). SOUTH AFRICAN JOURNAL OF GEOLOGY GRAVITY MODELLING OF BUSHVELD COMPLEX210 of the compartment, with a proposed extent of only 50km, is too small to produce isostatic compensation in a continental setting (e.g. Watts, 2001). A relevant example is provided by the ~1.9 Ga Trompsburg igneous intrusion (Maier et al., 2003) known only from drilling and gravity studies in the southern Kaapvaal craton (Ortlepp, 1959; Buchmann, 1960). It is ~50km in diameter and appears to be fully supported by the strength of the crust with a Bouguer gravity anomaly of nearly 150mGal. The magnitude of this gravity anomaly exceeds that of the Bushveld Complex. However, drilling has not yet confirmed its full thickness (Ortlepp, 1959; Buchmann, 1960). The idea of separate intrusive lobes of the Bushveld Complex as proposed by Cousins (1959) was modified to one of inward dipping sheets by Molyneux & Klinkert, (1978) and Du Plessis & Kleywegt (1987), based on observed dips of the lithologies around the Crocodile River fragment that were considered inconsistent with a separated lobes model (Figure 1B). This ?dipping-sheet model? of the Bushveld Complex has become accepted in the literature through additional interpretations of geophysical studies (Du Plessis and Kleywegt, 1987; Meyer and De Beer, 1987) and has been entrenched in textbooks (e.g. Tankard et al., 1982). This model for the western and eastern lobes has two inward-dipping sheets that extend a mere 50-100km towards each other from their surface expression implying a ?hole? in the centre of the Bushveld Complex (Figure 1B). The most recent version of this model is based on 2D forward modelling of gravity and resistivity data (Meyer and De Beer, 1987). All of the above- mentioned geophysical models extend only to depths of ~15km, and thus do not incorporate any possible compensation at the Moho. A re-examination of the geological evidence and new modelling of the Bouguer gravity data has led to the proposal that the western and eastern limbs of the Bushveld Complex were connected at depth (Cawthorn et al., 1998; Cawthorn and Webb, 2001), based on the argument that a continuous sheet of ~350km in diameter and up to 7km thick of mafic material placed in the crust would cause isostatic readjustment and depression of the Moho. Here we summarize a wide range of existing geological and geophysical constraints on Bushveld Complex topology and emphasize the importance of the newly determined crustal thicknesses found using receiver functions. We then present new crustal velocity models constrained by surface wave inversions that lend support to the model of a connected Bushveld Complex. By constraining the modelling of the Bouguer gravity data with these and other seismic results and extending the gravity modelling to Moho depths, a Bushveld Complex connected at depth provides the most robust, viable solution. Geological Evidence for Bushveld Complex Connectivity There are 6 unusual petrological observations briefly summarized here that apply to both the western and eastern limbs of the Bushveld Complex which support a geological argument for connectivity between these two limbs (Cawthorn et al., 1998; Cawthorn and Webb, 2001). These are unique characteristics that are common to the western and eastern lobes and place strong constraints on their geometry. These limbs, which at surface are separated by over 300km, both display; 1) four layers of Middle Group chromitites with plagioclase becoming a cumulus phase above the second layer. 2) A bifurcated and deformed footwall of the Upper Group 1 chromitite. 3) Economic grade of PGE mineralization of the Upper Group 2 chromitite. 4) A sharp break in the initial Sr isotopic ratio of the Merensky Reef that hosts economic grades of PGE?s. 5) All Zones have identical initial Sr isotopic ratios. 6) Similar thickness and grade of vanadium of the Main Magnetite Layer in the Upper Zone. These similar, but unusual, petrological characteristics are compelling evidence for connectivity. Previous Seismic and Resistivity Observations In addition to the Bouguer gravity studies already mentioned, there are 4 Vibroseis reflection seismic lines collected in the Bushveld Complex that have been published (Figure 1). Regrettably none of these lines crosses the entire extent of the Bushveld Complex, and only two of these lines penetrate into the interior of the Bushveld Complex. Line 1 is a 10km-long reflection seismic line collected at Union Section Rustenburg Platinum Mines. The seismic section was aimed at mapping the Main Zone ? Critical Zone contact within the area of the mine (Campbell, 1990), and was a successful ?proof of concept? application of reflection profiling used to confirm the existence of Bushveld Complex mafic rocks at depth along the length of the seismic line. Line 2 is a 20km-long reflection profile collected across a distinct gravity high that occurs in the granites of the western lobe of the Bushveld Complex (Figure 1 and 2B). It was hoped that economic horizons of the Bushveld Complex had been uplifted sufficiently to explain the known gravity high, and hence occur at mineable depths. The objective of the survey was to map the contact between the overlying granites and the Upper Zone of the Bushveld Complex. This discontinuity was easily resolved seismically and shown to occur ~1400m below the surface; making the region unattractive for mining (Campbell, 1990; Maccelari et al., 1991a; b). The seismic section shows the Lower and Critical Zones pinching out where the floor rocks are domed up, but the Upper and Main Zones maintain a substantial thickness in the region. Line 3 is a reflection seismic profile across the southwestern Bushveld Complex, extending for 50km from Sandpits just west of Pretoria, to the north at Swartdamstad (Figure 1). The purpose of the survey was to image details of the Rustenburg Layered Suite (RLS) and the underlying rocks of the Transvaal Supergroup. SUSAN J. WEBB, R. GRANT CAWTHORN, TERESIA NGUURI AND DAVID JAMES SOUTH AFRICAN JOURNAL OF GEOLOGY 211 The contact between the Transvaal Supergroup and the RLS was clearly imaged and is seen to dip at ~24? to the north in the southern part of the line, parallel to the Main and Upper Zone contacts. From about 25km to the northern terminus of the line, the signal is less clear. This is interpreted as being caused by reflections outside of the plane of the survey and/or the presence of a prominent anticline in the basement (Odgers et al., 1993b). As with line 2, the anticline appears to cause a pinching out of the lowermost layers of the Bushveld Complex, suggesting that the anticlines are either pre- existing features (Hartzer, 1995, and references therein) or were caused by the emplacement of the Bushveld Complex (Uken and Watkeys, 1997). This line also confirms the presence of the Main and Upper Zones along its entire length. Line 4 is a regional reflection seismic survey over the northeastern Bushveld Complex and Transvaal Supergroup (Figure 1) (Odgers and du Plessis, 1993a). The profile traverses the Molopo Dome shown in Figure 1 and clearly shows the Rustenburg Layered Suite rocks being disrupted by the dome structure, which could be interpreted as a large scale diapir as suggested by Uken and Watkeys (1997). Two recently published deep seismic reflection studies over the Far Western Lobe of the Bushveld Complex (Figure 1, lines Rz-254 and Rz-256) help constrain the maximum depth of the Transvaal Basin to ~7km in this region (Tinker et al., 2002). Unfortunately they do not resolve the thin near surface sills of the Bushveld Complex in the Far Western Lobe. Lines Rz-254 and Rz-256 also document clear evidence of extensive Ventersdorp-age rifting beneath the Transvaal Basin. There have been a significant number of deep direct current (DC) resistivity studies in and around the Bushveld Complex (Meyer and De Beer, 1987). These studies detected a strong conductor at depth beneath the granites in the western and eastern lobes of the Bushveld Complex, which was interpreted as due to the highly conductive Silverton shales of the Pretoria Group. However, if the geometric model based on geological dip data by Cawthorn (1998) is correct, the conductive Silverton shales could occur at greater depth (>10km) than the DC resistivity penetrated. Instead the observed conductor could be the Upper Zone magnetitites of the Bushveld Complex. In support of this alternative interpretation of the resistivity data, drilling results (Walraven, 1987) have confirmed the presence of RLS rocks at the Moloto borehole (Figure 1) where resistivity results have suggested they were absent. Data: Gravity and Rock Densities The Council for Geoscience of South Africa has been collecting and compiling gravity data since 1939 (Gordon-Welsh et al., 1986). This compiled database of Bouguer gravity anomalies (Figure 2B) was used in the present study (Venter et al., 1999). The data points were gridded to 1km, although the original data have variable spacing and were often concentrated along roads. Barometers, topocadastral maps and orthophotos were used to determine elevation. The largest error in the gravity data is due to inaccuracies in elevation determinations and leads to errors of about 2-5mGal in these compiled data sets (Hales and Gough, 1960). For the purposes of this project, errors larger than 5mGal would be of interest. The gridded Bouguer anomalies were reduced using an assumed density of 2.67mg/m3. Absolute gravity values are based on the International Gravity Standardization Net (IGSN) 1971 system of absolute gravity values (Darracott, 1974), measured Table 1. Physical properties used in modelling of the Bushveld Complex profile ( Mar? et al., 2002; Ashwal et al., 2003; James et al., 2004). The value for the Elandskraal alkaline volcanic complex was calculated from major element analyses (Frick and Walraven, 1985), however, only one analysis was suitably unaltered. Rock Type Density # of Samples Source Stormberg Group (basic and felsic volcanics) 2.74 ? 0.19 4 Mar? et al. (2002) Dwyka, Ecca and Beaufort (Karoo Supergroup clastic sedimentary rocks) 2.51 ? 0.89 36 Mar? et al. (2002) Waterberg Supergroup 2.63 ? 0.60 2 Mar? et al. (2002) Bushveld Complex Granite 2.65 ? 0.07 201 Ashwal et al. (2003) Bushveld Complex Mafic Rocks 3.02 ? 0.24 1997 Ashwal et al. (2003) Rooiberg Group 2.66 ? 0.30 5 Mar? et al. (2002) Transvaal Supergroup (Malmani and Black Reef) 2.80 ? 0.12 21 Mar? et al. (2002) Transvaal Supergroup (Pretoria Group) 2.72 ? 0.14 63 Mar? et al. (2002) Ventersdorp Lavas 2.83 ? 0.05 9 Mar? et al. (2002) Elandskraal Alkaline Volcanic Complex 2.78 * N/A Frick and Walraven (1985) Basement 2.70* N/A Mar? et al. (2002) Mantle 3.30* N/A James (2004) * No uncertainty available SOUTH AFRICAN JOURNAL OF GEOLOGY GRAVITY MODELLING OF BUSHVELD COMPLEX212 mostly with LaCoste and Romberg geodetic gravity meters. The Bouguer gravity data have been contoured and a profile across the Bushveld Complex suitable for modelling has been extracted from the 1km gridded regional data along latitude 24? 56?S, indicated in Figure 2B as a thick red line. The extracted profile is shown in Figure 3C. A linear regional trend in the Bouguer gravity data has been removed from the data. In order to graphically evaluate the extent of Airy isostatic balance in the Bushveld Complex, a plot of Bouguer gravity against elevation is shown in Figure 4 for all stations of the Southern African Seismic Experiment network. Two of the seven stations appear slightly undercompensated in terms of Airy compensation (Wollard, 1959), but there is no consistent significant anomaly for the Bushveld Complex stations. Density values used in the modelling of the Bouguer gravity data described below are compiled in Table 1 and are taken mainly from Mar? et al. (2002). These values are consistent with more extensive compiled physical property results of the Bushveld Complex from Cawthorn and Spies (2003) and Ashwal et al. (2003). Methods and Results Seismic Receiver Functions Thirty-five teleseismic earthquakes were processed to yield a comprehensive set of high-quality receiver functions for stations SA45, SA46, SA47, SA48, LBTB, and SA62 (Nguuri et al., 2001, and references therein for an overview of the method). Receiver functions were corrected for moveout (ray parameter), binned by station and stacked at depth intervals of 0.5km between 1km and 101km. The resulting spatial (phasing depth) spike series image shows the discontinuity structure beneath each station (Dueker and Sheehan, 1997; Dueker and Sheehan, 1998; Gurrola et al., 1994). The crustal and uppermost mantle model for the moveout Figure 4. Plot of elevations and Bouguer gravity values for all 82 stations of the Southern African Seismic Experiment (SASE) for a conventional analysis of Airy isostatic balance (after Wollard, 1959). The values plotted are an average of the values within a 25km diameter circle around each station in order to reduce local effects. Bushveld Complex stations are shown as black dots and labelled with their station names. The other SASE stations are shown in grey for comparison purposes. A reference line for conventional Airy isostatic compensation with a density of 2.67 mg/m3 is shown and indicates that most of the Bushveld Complex stations appear to be compensated with respect to topographic loads. SUSAN J. WEBB, R. GRANT CAWTHORN, TERESIA NGUURI AND DAVID JAMES SOUTH AFRICAN JOURNAL OF GEOLOGY 213 correction is based on previous refraction studies (Durrheim and Green, 1992), and includes an average P-wave velocity for the crust of 6.6km/sec, Poisson?s ratio of 0.27, and Moho depth of 45km (Nguuri et al., 2001). The phasing depth images for the Bushveld Complex profile are plotted in Figure 3A and are arranged from west to east (top to bottom) along the gravity modelling profile located in Figure 2B and extracted in Figure 3C for comparison. The Moho is at 43 to 50km depths beneath stations of the Bushveld Complex profile (Figure 3A). Station SA49, which was located on undisturbed Kaapvaal Craton, has a characteristically thin cratonic crust, with a depth to Moho of 38km (Nguuri et al., 2001). We estimate the relative depth uncertainty to be approximately ?3km, based on forward receiver function calculations over a range of velocity-depth models. If we assume that the average crustal P-wave velocity can vary by ?0.2km/sec based on the standard deviation of the global compilation of Christensen and Mooney (1995), then the estimated uncertainty for a 42km crustal thickness will be around ?1.0km. An additional uncertainty of 0.03 in the Vp/Vs ratio corresponds to uncertainties of ?1.6km in the crustal thickness. Thus a generous error estimate in the mean crustal thicknesses listed in Table 2 would be ? 3.0km. Crustal Velocity Structure In an effort to extract more information about the crustal structure beneath the Bushveld Complex stations we have used linearized time domain waveform inversion to model the crustal velocity structure (Owens et al., 1984; Ammon et al., 1990). The waveforms used to model the crustal structure have a dominant frequency content of 1 to 2 Hz which allows a resolution of features in the crust that are >3km thick (Cassidy, 1992). Receiver functions were stacked using a simple linear stack. The stacked receiver functions were then subsequently modelled to get a detailed structure of the crust in the region of the Bushveld Complex. Figure 5 compares the observed radial receiver functions, synthetic receiver functions and the crustal velocity models that were derived from the receiver functions for stations SA47 and SA32. Station SA32 is a typical Kaapvaal Craton station Figure 5. Crustal velocity models for seismic stations SA47 and SA32. (A) Seismic velocity model resulting from inversion of receiver functions for station SA47 in the Bushveld Complex (location shown in Figure 2). This station is typical of Bushveld Complex stations and clearly shows a high seismic velocity layer in the upper crust. (B) Seismic velocity model resulting from the inversion of receiver functions for station SA32 on the Kaapvaal Craton (location shown in Figure 1). This station is typical of stations on the Kaapvaal Craton away from the Bushveld Complex and shows no evidence of a thick, high velocity layer in the upper crust. SOUTH AFRICAN JOURNAL OF GEOLOGY GRAVITY MODELLING OF BUSHVELD COMPLEX214 away from the Bushveld Complex, whereas station SA47 lies roughly midway between the western and eastern lobes of the outcrop of the mafic rocks of the Bushveld Complex. There is a distinctive high-velocity zone roughly 6km thick that is apparent on the inversion of both P- and S-waves of the radial receiver function in Figure 5A. Beneath station SA48 in the Bushveld Complex we see a similar layer, with a P-wave velocity of 6.3 to 6.5km/s and a thickness of 6 to 8km. We do not see evidence for distinctive high velocity layers in other stations on the Kaapvaal Craton away from the Bushveld Complex that were analysed, such as station SA32 (Figure 5B). The stations in the Bushveld Complex also have a significantly thicker crust, than those outside of the Bushveld Complex. Bouguer Gravity Modelling From the Bouguer gravity profile highlighted in Figure 2B and plotted in Figure 3C, a 2.5D model of the Bouguer gravity profile has been constructed (Figure 6) that is expanded from Cawthorn and Webb (2001). The model is deliberately simplistic as little is known about the Bushveld Complex at depth, but reflects known large surface features such as the Crocodile River fragment. Surface geology has been used to constrain the model by fixing outcrop positions (Cawthorn and Webb, 2001) and receiver function results have been used to constrain Moho depths (Nguuri et al., 2001). The few seismic lines that are published are confined to the edges of the complex, but none show the termination of the entire sequence of mafic rocks that would be inconsistent with this model. The gravity model requires that dense material be present in the crust to counteract the effect of the thickened crust. We constrain this dense material to be located in the upper 10km based on the crustal velocity structure derived from the waveform inversion discussed above. This model thus supports the hypothesis that the Bushveld Complex is connected between its western and eastern limbs, as previously proposed (Cawthorn et al., 1998; Cawthorn and Webb, 2001). Present outcrops of the Bushveld Complex occur at an elevation of over 1,000m above mean sea level (Figure 2A). Based on simple Airy isostatic models, Figure 6. Model of the Bouguer gravity of the Bushveld Complex (expanded from Cawthorn and Webb, 2001), incorporating the additional constraints placed by crustal thickness results from receiver function analysis, Transvaal basin thickness from seismic lines published by Tinker et al., (2002), and the crustal velocity model beneath stations SA47 (Figure 5) and SA48. The density values used for the various rock types are summarised in Table 1. It should be noted that the vertical exaggeration of the gravity model is about 5:1, which greatly exaggerates the apparent dips. The indicated line of intrusives, discussed in the text, extends normal to the plane of the page and corresponds to the line on Figure 2B. SUSAN J. WEBB, R. GRANT CAWTHORN, TERESIA NGUURI AND DAVID JAMES SOUTH AFRICAN JOURNAL OF GEOLOGY 215 topographic data predict crustal thickness of ~38 to ~40km underneath the Bushveld Complex. On the contrary, the crust beneath the Bushveld Complex is comparatively thick (~50km) as determined by seismic receiver function methods. For instance, under station SA47, elevation data predict the crust to be ~38km thick based on Airy isostasy due to simple compensation of topography, but the crust here has been determined from seismic receiver functions to be 50 ? 2km thick (Table 2). This ~12km difference between the seismically determined crustal thickness and that predicted based on the observed Airy isostatic balance (Figure 4) requires the presence of a dense subsurface load. It is simplest to assume that this compensating mass comprises the mafic rocks of the Bushveld Complex. We do not expect significant density variations beyond those used here (Table 1) that might further affect the modelling at the scale being considered. As the modelling of the Bouguer gravity anomaly shows in Figure 6, the high-density mafic rocks of the Bushveld Complex provide the required dense mass in the crustal section to balance the seismically determined thickened crustal ?root? beneath the Complex. Discussion and Conclusion The crustal velocity model derived from the inversion of receiver functions for station SA47 is consistent with a ~6km-thick, high P- and S-wave velocity layer in the upper crust. A plausible conclusion is that this layer is due to the presence of mafic and ultramafic rocks of the Bushveld Complex with an average density of 3.0 mg/m3 (Table 1). The high velocity upper crustal layer has Vp velocities modelled in the range 6.3 to 6.8km/s; these values are consistent with seismic velocities determined for Bushveld Complex mafic rocks from prior Vibroseis reflection surveys (Davison and Chunnett, 1999; Odgers et al., 1993; Sargeant, 2001). The receiver function results show that the amplitude of the converted phase P to S is significantly smaller and its width is greater for stations directly adjacent to and across the Bushveld Complex. Figure 3 shows receiver function results for a 7-station profile across the Bushveld Complex, with a typical cratonic station for comparison (station 49). The most prominent P to S conversion corresponds to the Moho, although for one station, SA48, the result is somewhat ambiguous. We note that crustal thickness varies smoothly between the stations shown in Figure 2C. Station SA51 in the northern lobe is especially intriguing, it appears to be under-compensated from the plot of Bouguer gravity vs. elevation (Figure 4), but the crustal thickness of 50km would argue for overcompensation. This paradox can be resolved if dense Bushveld Complex mafic rocks of the northern lobe extend at least as far west as station SA51. The gravity model (Figure 6) incorporates several updates and constraints from the previously published model (Cawthorn and Webb, 2001). At a distance of 325km along the gravity profile, there is a 20mGal local gravity high (Figure 5). We now attribute at least part of this gravity high to a possible buried alkaline volcanic complex similar to the Elandskraal alkaline volcanic complex to the south (?25?15?S, 28?15?E) described by Frick and Walraven (1985) that is responsible for a similar peak in the gravity data to the south of the profile. If this interpretation is correct, then the local gravity high implies a north-northwest continuation of the zone of alkaline (syenite to nepheline syenite) intrusions defined by Frick and Walraven (1985) (line on Figure 2B). The gravity high is in line with the Elandskraal alkaline volcanic complex, Roodeplaat caldera, Leeuwfontein pluton and the Franspoort pluton to the southeast, and the zone shows up throughout the Bushveld Complex as a gravity high trending northwest to southeast. It seems unlikely however, that the entire 100km width of the gravity high can be attributed to the presence of these alkaline volcanic complexes and plutons as the magnetic and drilling data show them to extend only to about 20km in diameter. This is the Table 2. Moho depths as determined from crustal receiver functions for stations in a 7-station west to east profile through the Bushveld Complex. Based on an analysis of waveforms from three different azimuths (southwest, northeast and east), we observe slightly different thicknesses from these directions. We interpret this to indicate that the Moho dips up to 3.6? to the west beneath stations near the eastern edge of the Bushveld Complex (e.g. between stations SA48 and SA49). Station Name Lat. Long. Crustal thickness Width of Moho Poisson?s Northeast Southwest East (deg) (deg) in km (? 3km) (km) Ratio (km) (km) (km) computed from all azimuths (# of events) SA62 -24.8505 25.1350 45 (16) 2 0.21 44 43 44 LBTB -25.0151 25.5967 45 (20) 6 0.25 45 46 46 SA45 -24.8792 26.1644 44 (30) 6 0.26 45 45 50 SA46 -24.8382 27.1092 44 (30) 6 0.24 48 44 50 SA47 -27.8469 28.1618 50 (20) 6 0.32 53 50 48 SA48 -24.8948 29.2163 45 (10) 6 0.29 45 ND* 45 SA49 -24.9597 30.3091 38 (5) 6 0.23 40 40 38 *ND means No Data SOUTH AFRICAN JOURNAL OF GEOLOGY GRAVITY MODELLING OF BUSHVELD COMPLEX216 motivation for the gentle fold of the Bushveld Complex mafic rocks presented in the model of the gravity data (arrows, Figure 6). Such a structure easily accounts for the 100km width of the central gravity anomaly, the sharp peak at 330km being attributed to the covered volcanic complex. The axis of this gentle fold may be a weakened zone through which these younger igneous rocks could have intruded. The gravity profile runs roughly along the axis of the deepest extent of the Transvaal Basin as revealed in seismic lines Rz-254 and Rz-256. These seismic lines constrain the depth of the Transvaal Basin and reveal Ventersdorp Supergroup rocks underneath (Tinker et al., 2002). These Ventersdorp rocks have been modelled as a continuous layer in Figure 6 in an effort to simplify the complex 3D structure revealed by the seismic lines. Ventersdorp rocks have also been continued to just below the edge of the western lobe of the Bushveld Complex, but not through to the centre. It is unlikely that the Ventersdorp extends much farther east as suggested by Schmitz and Bowring (2003), because none of the seismic lines published to date (Lines 1, 2, 3, 4, in Figure 1) show evidence of underlying Ventersdorp rocks. However, these reflection profiles are not deep seismic sections and have not been processed to enhance features at the depth where Ventersdorp rocks might be expected, so this issue remains unresolved. Finally, if the Bouguer gravity model developed in Figure 6 is correct, the crust may be even thicker under the Bushveld Complex as the effect of the higher velocities in the crustal mafic material has not been included in the receiver function analysis at this point. Acknowledgements The Kaapvaal Craton Project has been one of the most rewarding and productive geoscience projects ever conducted in Africa. The project would not have been possible without the substantial funding from a large variety of sources including the South African National Research Foundation, US National Science Foundation, and a plethora of mining companies that have never before cooperated on such a grand scale (De Beers, Anglo American, RTZ, BHP, Goldfields). The Council for Geoscience, especially Edgar Stettler, have also willingly provided data and substantial support. The Carnegie Institution of Washington, and MIT have made it possible for SJW and TKN to make extended visits. Lew Ashwal and Mike Knoper are thanked for many discussions about the Bushveld Complex. A special word of thanks is extended to Maarten de Wit, who got the ball rolling with the most memorable meeting in 1995. Gordon Cooper is thanked for providing modelling software (http://www.wits.ac.za/science/geophysics/software.htm. The reviewers, Maarten de Wit and Moctar Doucour?, are gratefully acknowledged for their suggestions, which significantly improved this paper. References Ashwal, L.D., Webb, S.J., and Knoper, M.W. (2003). Cyclicity in layered intrusions as revealed by near-continuous geophysical and petrologic measurements in the Bushveld Complex, South Africa. EGS-AGU-EUG Joint Assembly, Volume 5: Nice, France, Geophysical Research Abstracts, 03223. 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Editorial handling: M. J. de Wit SOUTH AFRICAN JOURNAL OF GEOLOGY GRAVITY MODELLING OF BUSHVELD COMPLEX218 4.2 Bushveld Complex The ~2054 Ma (Buick et al., 2001; Scoates and Friedman, 2008; Walraven et al., 1990) Bushveld Complex (BC) is the world?s largest known layered mafic intrusion and covers an area of ~65,000 km2, the outcrop forming a rough four-leaf clover shape centered north of Pretoria (Figures 4.1 and 4.2). The BC is doubly valuable to Earth scientists as it is economically important not only for platinum group elements, but also for significant deposits of chromium, vanadium and large amounts of nickel, copper and iron ores, dimension stone and gold (e.g. Lee, 1996). The granitoids associated with the BC also contain significant deposits of tin and fluorite (Robb et al., 2000). The following is a brief summary of the main geological features of the BC based on several excellent summaries by Ashwal (1993), Eales and Cawthorn (1996), Tankard et al. (1982), von Gruenewaldt (1985) and references included therein. The BC was intruded into the sedimentary and volcanic rocks of the early Proterozoic Transvaal Supergroup (Figure 4.2). The Transvaal Supergroup overlies the Archaean basement of the Kaapvaal Craton and the outcrop of the Transvaal rocks around the BC indicates that the BC transgresses through the sequence (e.g. Vermaak and Von Gruenewaldt, 1986). If it is assumed that the strongly layered BC was emplaced horizontally, this implies that the rocks of the Transvaal basin were concave at the time of BC emplacement (Cawthorn and Walraven, 1998). 177 Figure 4.1 Locality map of the Bushveld Complex within southern Africa. Outcrops of the mafic portions of the Bushveld Complex rocks are shown in dark green. The Molopo Farms Complex which is the same age as the Bushveld Complex is just to the west of the Bushveld Complex is shown in light green. The Trompsburg Complex and Losberg intrusions are younger and are located south of the BC are also in light green. The densest units in the BC are the mafic igneous rocks of the Rustenburg Layered Suite, which are responsible for the positive gravity anomalies around the edge. They are usually divided, bottom to top, into five distinct stratigraphic zones: the Marginal, Lower, Critical, Main and Upper Zones (Figure 4.3). The Marginal Zone, which includes noritic rocks at the base of the BC, is interpreted as a chilled zone (Hatton and Sharpe, 1989) and appears mostly as dykes and sills intruding into the Transvaal rocks. The Marginal Zone rocks are thought to approximate the compositions of some of the parental melts (Hatton and Sharpe, 1989). 178 Figure 4.2 Basic regional geology of the Bushveld Complex (BC) showing the four main lobes (Western, Northern, Eastern and Bethel) and the Far Western Lobe. Dashed lines trace the inferred Rustenburg layered suite (RLS) subcrop based on gravity, magnetic and geology data (van der Merwe, 1978). The Rooiberg Group represents early crustal melt synchronous to the emplacement of the mafic rocks of the BC. The Rashoop Granophyre Suite and the Lebowa Granite Suite are late stage granites associated with the BC. In the interior of the BC there are fragments of Traansvaal floor rocks such as the Crocodile River fragment, Rooiberg fragment, Dennilton dome and Marble Hall fragment. Several alkaline intrusions (Pilanesberg, Pienaars River, and Spitskop) intruded long after the BC. There are also several kimberlites in and around the BC of various ages including Premier, Palmietgat and Maarsfontein. The BV-1 borehole in the Northern Lobe has been used to measure a significant number of susceptibility and density values discussed in Appendix A. Diagram modified from Vermaak and Von Gruenewaldt (1986). Ultramafic cumulate rocks comprising bronzitite, dunite and harzburgite dominate the Lower Zone. The bottom half of the strikingly layered Critical Zone consists of pyroxenitic ultramafic rocks with interspersed chromite layers. The Upper Critical Zone contains the world?s two largest platinum ore bodies: the Merensky Reef and the Upper Group 2 (UG2) chromitite inter-layered with plagioclase-bearing cumulate rocks (Eales and Cawthorn, 1996). The overlying Main Zone comprises relatively homogeneous 179 gabbro-noritic cumulate rocks. Finally, the Upper Zone is composed of magnetite- bearing gabbros and ferrodiorites with abundant magnetite and anorthosite layers (Figure 4.3). The details of these divisions differ between researchers; for example Kruger (1990) defines the Main Zone-Upper Zone boundary based on a shift in initial Sr isotopic composition due to a new influx of magma at the Pyroxenite Marker unit. In places, this unit is difficult to find in the field. Other workers Vermaak and Von Gruenewaldt (1986) use the readily identifiable field marker of the appearance of first cumulus magnetite as the boundary. Rocks of the Rooiberg Group (rhyolites and granophyres) form the roof of the BC and appear to be synchronous with the formation of the mafic phases (Hatton and Schweitzer, 1995). Above the topmost phase of mafic and ultramafic rocks, the Rashoop granophyre suite and the Lebowa granite suite were emplaced (Eales and Cawthorn, 1996). Domes and diapirs of floor rocks appear to be common in the BC and intrude the Western and Eastern Lobes, creating the well-known Crocodile River and Marble Hall fragments (Figure 4.2). The metamorphism of the floor rocks due to the emplacement of the BC and the subsequent density instabilities possibly created these features (Uken and Watkeys, 1997a). The four major lobes of the BC are the Western, Eastern, Northern (or Potgietersrus) and the Bethel Lobes (Figure 4.2). In addition there is a Far Western Lobe, which occurs to the west of the Western Lobe, but contains only thin sills of the BC. The Western Lobe, in spite of somewhat limited outcrop, is well studied due to extensive mining in the region. The Eastern Lobe has good exposure and new mines are currently opening. The Northern or Potgieterus Lobe is poorly exposed and, while similar to the Eastern and Western Lobes in overall sequence, has no well developed Merensky Reef. However, the platinum-rich Platreef, while somewhat similar to the Merensky Reef, appears at a different level in the stratigraphy and transgresses into the Lower Zone (van 180 der Merwe, 1976; van der Merwe, 1978). The Bethal Lobe is the most poorly studied, as younger rocks mostly cover it and it is known mainly from boreholes and its geophysical signature (Buchanan, 1975). Figure 4.3 Stratigraphy of the layered ultramafic ? mafic sequence of rocks of the Bushveld Complex Diagram from Eales and Cawthorn (1996). Given the size of the Bushveld Complex and the wealth of its mineral deposits, it is perhaps surprising that its overall geometry is rather poorly characterized and understood compared to other layered intrusions such as Stillwater, Skaergaard, Kiglapait, or Muskox, some of which are located in very remote terrain and are not as well mineralized (Ashwal, 1993). Most research on the BC has been carried out on samples from the Eastern Lobe, where surface exposure is relatively good, and the Western Lobe, where extensive mining activity allows access to underground exposures. A great deal of effort has gone into characterization of the well-known mineralized 181 horizons (Merensky Reef, UG-series chromitite layers, UZ magnetitites), but much of the vast thicknesses of magmatic cumulate rocks in the BC remains poorly studied. Perhaps most importantly, the origin of the BC remains a mystery; ?What tectonic or magmatic events led to the production of more than 1 million cubic kilometers of basaltic magma 2 billion years ago?? (pers. comm. L. D. Ashwal, 1999) There are at least five different proposed tectonic settings for the origin of the BC: 1) subduction zone (e.g. Hatton and Von Gruenewaldt, 1987); 2) plume (Hatton, 1995); 3) rift (Kruger and Corner, 1987); 4) back-arc (e.g. Willmore et al., 2002) and 5) meteorite impact (e.g. Hamilton, 1970; Rhodes, 1975). The impact origin has essentially been discounted, as there is little evidence beyond the obvious arcuate shape of the BC to support this model (Buchanan and Reimold, 1998; French, 1990; French and Hargraves, 1971). While the plume model most easily explains the large volume of BC rocks, it is difficult to reconcile a plume with several lines of evidence. Firstly, the very existence of the underlying Transvaal basin indicates that the region was a depression before the intrusion of the BC, not domed as would be expected with a hot, relative low density, rising plume (Eriksson et al., 2001; Knoper et al., 2002). Secondly, the NNW-SSE striking Rustenburg Fault zone (Figure 4.2) shows evidence of at least two strong compressive deformational events before the emplacement of the BC; a plume should result in extensional events in this area (Bumby et al., 1998). Thirdly, the presence of nearby diamondiferous kimberlites, such as Premier (1180 Ma) and Maarsfontein (600 Ma), and especially the centrally located Palmietgat (~100 Ma) kimberlite argue against a plume (Figure 4.2). A plume large enough to create the ~600,000 km3 of BC rocks should have destroyed the mantle lithosphere keel beneath this part of the Kaapvaal Craton, and irreparably altered the diamond stability field beneath the BC. Diamond inclusion studies from diamonds found in the Palmietgat kimberlite in the center of the 182 BC record a variety of ages, including 3 Ga, indicating that this region has never left the diamond stability field (Simelane, 2004; Simelane et al., 2004). Fourthly an analysis of the Cr budget suggests that large volumes of original magma are unaccounted for in the present extent of the BC (Cawthorn and Walraven, 1998), suggesting any plume generating BC magmas would have had an even larger extent than indicated by the present size of the BC. Nearby layered intrusions may be spatially associated to the BC, but a lack of accurate age dates makes it difficult to test the possibility that a plume track connects the Molopo Farms Complex (to the west of the BC) dated at 2044?24 Ma (Kruger, 1989; Reichardt, 1994), the BC dated at 2054.4?1.3 Ma (Scoates and Friedman, 2008), the Losberg intrusion to the south dated at 2041 ? 41 Ma (Coetzee and Kruger, 1989) and the Trompsburg feature much further south dated at 1915.2 ? 5.6 Ma (Maier et al., 2003) (Figure 4.1). Although some of the late granites appear to be akin chemically to rift-related granites (Kruger and Corner, 1987), a rift zone model for the emplacement of the BC is difficult to reconcile with the timing of docking of the Zimbabwe and the Kaapvaal cratons as recorded in the Limpopo Belt, with prominent ages at both 2.7 Ga (probably too old) and 2.0 Ga (probably too young) (Barton and van Reenen, 1992; Hofmann et al., 1998; van Reenen et al., 1987). Alternatively, in a subduction zone model it is not clearly explained why such a temporally restricted, large volume of magma would form within a craton underlain by thick, Archaean lithosphere, more so because the BC appears to be a unique event and subduction zones are ubiquitous. A terminal subduction zone that trapped hot, low viscosity fertile mantle (Billen and Gurnis, 2001) and the subsequent convective instability that could develop (Knoper et al., 2002) does offer one possible explanation. A subduction-accretion origin for the cratonic rocks underlying the BC has 183 also been proposed to explain the low ?13C values from the eclogitic Premier diamonds (Shirey et al., 2002). The results from the Kaapvaal seismic experiment (Nguuri et al., 2001) have shown that the crust is significantly thicker (up to 50 km total thickness) beneath the BC and that the seismic velocities in the upper mantle are slower by up to 2%, when compared with the upper mantle of the Kaapvaal Craton to the south of the BC. These results are crucial evidence that must be incorporated into any discussion of the genesis of the BC (Knoper et al., 2002). To derive at a better constrained tectonic model for the BC, more accurate isotopic age dates and palaeomagnetic studies are needed to firmly establish the sequence of events in the region, including the history of the preceding Transvaal basin and the other nearby igneous intrusions such as the Molopo Farms Complex. In addition, a better understanding of the overall geometry of the BC will obviously be an important constraint on theories of its origin. The location of feeder dykes and mechanism of emplacement of BC magma are also contested. Sharpe et al. (1981) suggested that gravity highs around the BC are indicative of feeder pipes. Viljoen (1999) argued for arcuate feeder dykes although the gravity modeling presented is only schematic. Cawthorn (pers. comm., 2005) suggests that the Steelpoort fault and the conjugate Crocodile River fault (Figure 4.2) may be the source feeders. In a detailed assessment of Landsat imagery Lee and Sharpe (1986) identified six lineament domains with distinctive patterns, any one of which might been important during emplacement of the BC. Alternatively, Good and de Wit (1997), Reichardt (1994) and Kruger (2005) note that the Thabazimbi-Murchison Lineament (TML) represents a viable feeder zone from which magmas could be emplaced (Figure 4.2). The close spatial relationship between the TML, the BC and the Molopo Farms 184 Complex (Figure 4.21) lends support to the TML as the primary feature along which emplacement was accommodated for both complexes (Cawthorn and Walraven, 1998). 4.3 Constraints on gravity modeling of the Bushveld Complex from existing geophysical datasets The purpose of this section is to review past models of BC geometry and to reexamine the geophysical arguments that led to a BC model of separated unconnected lobes. In the last section I have compiled available geophysical data related to the geometry of the BC. 4.3.1 Initial geological model of the Bushveld Complex Based largely on geological mapping in the eastern lobe, the BC was originally mapped and interpreted as a large-scale lopolith (Hall, 1932). This configuration was supported by du Toit (1954) and was the accepted model until the late 1950s (Figure 4.4). Figure 4.4 A lopolith model of the Bushveld Complex, as originally proposed by Hall (1932), illustrated here by du Toit (1954). Note that the lopolith is not shown as continuous but rather as disrupted by later intrusions and tectonic events. 185 4.3.2 Prior gravity and resistivity modeling An early compilation of Bouguer gravity anomalies over the BC was published by Hales and Gough (1950) that showed a strong Bouguer gravity high largely associated with outcrops of the BC. Cousins (1959) interpreted these data using simple forward models and concluded that the BC must consist of well separated, individual intrusions, an interpretation in disagreement with the accepted lopolith model (Figure 4.5). He argued convincingly that the gravity anomaly in the center of the BC was too small to admit the possibility that the Eastern and Western Lobes were connected by a continuous, thick, dense sheet at depth. He argued that a lopolith would result in a long wavelength Bouguer gravity signal in the central portion of the BC (Figure 4.5? middle panel). But because the Bouguer gravity in the center of the BC returns to a background value similar to that elsewhere in the Kaapvaal Craton, he contended that the Western and Eastern Lobes could not be connected. His geological model did not, however, consider the possibility of isostatic compensation of the considerable additional mass of the BC by flexure of the crust creating buoyancy through displacement of dense upper mantle material. A suggestion of crustal flexure due to the weight of a continuous lopolith form of the BC was briefly considered by Hales and Gough (1962), but this idea was dismissed without a proper evaluation on the strength of the gravity modeling presented by Cousins (1959) and his persuasive talks (Anhaeusser, 1997). In one form or another, the idea of a BC comprising lobes unconnected or separated at depth was the accepted model for the next ~40 years. 186 Figure 4.5 Cousins (1954) discarded a lopolith model for the Bushveld Complex (BC) because measured gravity values are reduced to background values in the center of the BC as illustrated here. The top diagram (a) shows the measured gravity over an east-west profile through the BC. The middle diagram (b) demonstrates that the calculated values for gravity are significantly elevated above background values in the central portion if a lopolith model is used. Cousins (1954) solved the discrepancy by postulating the existence of well separated intrusions as shown in (c). Note that no depth scale is presented and that the gravity effect of a massive lopolith on the deeper crust and upper mantle is not considered. Similar models were produced by Smit (1961) and Smit (1962). Additional interpretations of the BC gravity data as caused by separate anomalies unconnected at depth include trough-shaped synformal models (Smit, 1961) and dipping unconnected layers (Molyneux and Klinkert, 1978; Walraven and Darracott, 1976). 187 Due to the presence of large normal faults in the BC, Sharpe et al. (1981) proposed that the eastern lobe of the BC might have caused crustal flexure, although they give no analysis of crustal strength and applied load. In presenting their argument they assume a conical geometry of limited (less than 50 km) lateral extent for each lobe in the BC. However, a load of dense material of 50 km lateral extent above the Kaapvaal Cration is expected to be wholly supported by crustal strength (Mar? and Cole, 2003). A pertinent South African example in support of this is the ~1915 Ma (Maier et al., 2003) Trompsburg Complex; a layered mafic intrusion about 500 km to the south of the BC, which has a significant Bouguer gravity anomaly of ~100 mGal. Borehole constraints and Bouguer gravity modeling suggest a diameter for the Trompsburg Complex of about 50 km, with lithologies and mineralogies - and therefore density contrasts - similar to the BC. The observed gravity anomaly can be re-created faithfully with a model that does not invoke crustal flexure (Buchmann, 1960; Mar? and Cole, 2003), and there is no evidence of crustal thickening in the region (Nguuri et al., 2001). Thus, although Sharpe et al. (1981) have proposed crustal flexure to explain some of the prominent structural normal faults in the BC, they were considering a lateral extent of separated lobes of the BC that are too small to cause the crustal flexure discussed. The idea of separate intrusions of the BC was modified by Molyneux and Klinkert (1978) and du Plessis and Kleywegt (1987) to a model of inward dipping sheets due to dissatisfaction with the separate, discrete intrusion idea. This modification was motivated by the observed dips of the lithologies around the Crocodile River fragment (Figure 4.2), which are inconsistent for a model with separated lobes. A similar dipping sheet model was adopted by Meyer and de Beer (1987), who investigated the Bouguer gravity signal and the electrical properties of the deep crust beneath the BC using deep DC resistivity soundings (Figure 4.6 and 4.7). The resistivity data demonstrate that there is a conductive 188 body at depth below the BC, which they attribute to the underlying Transvaal sedimentary basin (Figure 4.7). However, the authors admit (Meyer and de Beer, 1987 p. 611), ??both (the Transvaal and BC) conductors have similar conductances (conductivity- thickness products)??, and they propose different resistivities may be enough to distinguish them. The Upper Zone BC rocks are highly conductive, but this type of survey at the depths under consideration would not resolve the difference between Upper Zone rocks and the Transvaal Silverton Shales (Figure 4.8). In addition, the structure of the floor of the BC is likely to be complex with an undulating floor punctuated by diapiric upwellings (Uken and Watkeys, 1997a), which will further complicate resistivity modeling, and disqualify simplified horizontal sheet models. Figure 4.6. An example of the dipping sheet model for the Bushveld Complex based on the analysis of gravity data and resistivity data (Meyer and de Beer, 1987). Note the extreme vertical exaggeration in the model as the length of the profile is 400 km, and the vertical depth extent displayed is 15 km. 189 Figure 4.7 Example of deep DC resistivity soundings from Meyer & de Beer (1987). The data for site 85 has been reexamined in the model in Figure 4.8. Note that in this diagram no data points are present beyond AB/2 of 30,000 m. Also curves 119 and 85 have not yet flattened out indicating that the depth of penetration at these sites was insufficient. Figure 4.8 represents a remodeled data set from station 85, digitized from Meyer and de Beer (1987) using their published model parameters. In order to match the LHS or shallowest side of the curve, it was necessary to add a shallow surface layer of 150 m of 2,000 ?.m resistivity. Only the first three layers influence the shape of the curve, which demonstrates that the results can only be used to state that there is a conductor beneath the granites. The giant adjustment factor invoked by Meyer and de Beer (1987) using a thickness of 20,000 m to account for anisotropy in the Upper Zone rocks makes it difficult to determine a realistic conductivity for this layer. 190 Figure 4.8 Forward model of resistivity sounding number 85 from Meyer & de Beer (1987) using values from their geo-electric stratigraphy. Only the first three layers define the curve and the second layer has an unrealistic thickness, also used by Meyer and de Beer (1987). This illustrates that the model is ambiguous in terms of determining the 3D geometry of the BC. The dip of the BC mafic rocks and those of the underlying Transvaal sequence varies, with the BC generally having a shallower dip (Button, 1976). This does not necessarily imply a period of uplift and removal of stratigraphy, but may simply mean that the layers pinch out as shown in Figure 4.9 (Cawthorn, 1998). This may also offer a different geometrical explanation for the resistivity results of Meyer and de Beer (1987), as even the highly conductive shales of the Transvaal sequence may be too deep in the center to be detected. The depths postulated in the center of the Bushveld Complex are poorly constrained and may vary from as shallow as 5 km to as deep as 15 km. The depth will be strongly affected by diapiric upwelling and compressional events. 191 Figure 4.9 Simplified model of the relationship between the intrusive Bushveld Complex and the sedimentary rocks of the Transvaal sequence from Cawthorn (1998). The dip of the underlying Transvaal sediments is steeper than the intruding Bushveld Complex implying that the basin could have been actively subsiding just prior to the emplacement of the Bushveld Complex. The summary of resistivity readings presented by Meyer and de Beer (1987) suggests that there are no conductive rocks beneath region 2 (Figure 4.10). However, at two localities within this region, mafic rocks of the BC have been encountered in boreholes, further confirming that resistivity soundings may not have penetrated deep enough in the central section (Figure 4.10). 192 Figure 4.10 Map of resistivity sounding locations from Meyer & de Beer (1987). They conclude that region 2 is not underlain by conductive rocks. However, Bushveld Complex mafic rocks have been intersected in drill cores in 2 locations inside this zone at A and B (Cawthorn, pers. comm., 2003 and Walraven, 1987). The identity of the covered body labeled (2) in the gravity model in Figure 4.6 as the source of the ~80 km wide gravity anomaly in the center of the profile is suspect. It has been identified as a post-BC alkaline complex (Meyer and de Beer, 1987), although these intrusives are generally of low density (e.g. Pilanesberg), altered and of much smaller size than the ~80 km wide body shown in the modeling (Frick and Walraven, 1985). Thus, the cause of this ~70 mGal Bouguer positive gravity anomaly in the central portion of the profile remains unresolved. 4.3.3 Reflection seismic data Although active source seismic data have been collected in the BC to depths of 10-15 km since the 1980s (Campbell, 1990), few data sets have been published. Figure 193 4.11 shows the location of seven seismic lines that have been published, four in the main body of the BC (labeled 1-4), two over the Far Western Lobe (Rz-254 and Rz-256) and one in the northern lobe (labeled 5) (Campbell, 1990; Maccelari et al., 1991a; Odgers and du Plessis, 1993; Odgers et al., 1991; Odgers et al., 1993; Tinker et al., 2002). These lines are close to the edges of the BC and do not penetrate the interior. Another published line from the Western Lobe near Pilanesberg is not precisely located, but is only a few km in length (Davison and Chunnett, 1999). There is also a Ph.D. study of seismic data from Northam Platinum mine (Sargeant, 2001), but again it is of limited extent. The line in the Northern Lobe (5) delineates the connection between the covered sections of the Northern Lobe (Stettler et al., 1998b). As these are the only published deep, active-source lines in the BC, they supply limited constraints on gravity modeling, but are important as the only 3- dimensional view of the BC. All seismic data sets clearly show the mafic rocks of the Rustenburg Layered Suite (RLS) along the extent of the seismic lines. 194 Figure 4.11 Map of the Bushveld Complex showing the location of published seismic lines labeled 1 through 5, details of which are discussed in the text. In the Far Western Lobe, lines Rz-254 and Rz-256 were published by Tinker et al. (2002). Line 1 is a 10 km long Vibroseis reflection line from the Union Section in Rustenberg Platinum mine. It was collected as a ?proof of concept? line to image the contact between the Main and Critical Zones near the mine. The line confirmed the existence of mafic rocks at depth along the length of the seismic line thus paving the way for more extensive use of the seismic method in the BC (Figure 4.12). In all of the seismic section diagrams one second of two-way travel time is approximately equal to three km depth. 195 Figure 4.12. Scanned images of published data from lines 1 and 2 shown in Figure 4.11 after Campbell (1990) and Maccelari et al. (1991a). The salient features discussed in the text are apparent. (1s TWT = ~3 km depth). 196 In the western BC, there is a prominent gravity high; a ?tongue? extending eastwards from the main part of the Western lobe (Figure 4.13). The objective of seismic line 2 was to test the possibility that this gravity high hosted uplifted Critical Zone rocks at shallow depth. The target was to map the contact between the overlying granites and the Upper Zone of the BC. This discontinuity was easily resolved on the seismic data and shown to occur at ~1400 m depth (Campbell, 1990; Maccelari et al., 1991a; Maccelari et al., 1991b); the associated Critical Zone proved too deep for mining. In addition to the target contact, the seismic line also clearly imaged the Lower and Critical Zones. These zones were interpreted as being pinched out where floor rocks were domed up, whilst the Upper and Main Zones maintain a substantial thickness in the region. Domes appear to be present on both seismic lines 2 and 3, although other authors have ascribed the apparent doming to reflections from features that are outside of the line of the 2D seismic section (Odgers et al., 1991). 197 Figure 4.13 Gravity data of the Bushveld Complex and surrounding regions, showing seismic stations of the Kaapvaal Craton Project. The outcrop of mafic rocks of the Bushveld Complex has been outlined; the gravity data clearly delineate the Bethal Lobe to the south covered by younger rocks. The gravity high ?tongue? that was investigated by seismic line 2 is highlighted by the arrow. Gravity data from the Council for Geoscience (Venter et al., 1999). 198 As part of the South African National Geophysical Program which finished in 1989, a research seismic reflection line was collected from Sandpits, just west of Pretoria, extending to the north for 50 km to Swartdamstand (Line 3, Figures 4.11 and 4.14). This line crossed the southwestern BC with the objective of imaging the details of the Rustenburg Layered Suite (RLS) and the underlying rocks of the Transvaal Supergroup. The contact between the Transvaal Supergroup and the RLS was clearly imaged and was seen to dip at ~24? north in the southern part of the line, in agreement with outcrop measurements. From about 25 km to the northern end of the line, the signal is less clear. This has been interpreted as being caused by reflections outside of the survey plane, and/or the presence of an anticline in the basement (Odgers et al., 1993). As with line 2, the anticline appears to be associated with a pinching out of the lowermost layers of the BC, suggesting that the anticlines are either preexisting features (Hartzer, 1995, and references therein), or were caused at the time of BC emplacement as a solid state, diapiric deformation response by the underlying Transvaal rocks (Uken and Watkeys, 1997b). Line 3 also confirms the presence of the Main and Upper Zones along its entire length. Lines 2 and 3 suggest that the BC flattens to a horizontal attitude in the upper crust towards the interior of the BC, although these lines do not extend far enough into the interior to confirm this geometry. Line 4 (Figure 4.11) is a regional reflection seismic survey over the northeastern BC and Transvaal Supergroup (Figures 4.14). The profile extends across the Malope Dome (Figure 4.11) and clearly shows the Rustenburg Layered Suite rocks being disrupted by the domal structure, which has been interpreted as a large scale diapir (Uken and Watkeys, 1997a). 199 Figure 4.14 Scanned images of published data from lines 3 and 4. The salient features discussed in the text are apparent. Diagrams from Odgers and du Plessis (1993) and Odgers et al. (1993). 200 Two recently-published deep seismic reflection studies over the Far Western Lobe of the BC (Figure 4.11, lines Rz-254 and Rz-256) help to constrain the maximum thickness of the Transvaal Basin to approximately ~7 km in this region (Tinker et al., 2002). Unfortunately these lines do not resolve the thin near surface sills of the BC in the Far Western Lobe that outcrop locally. These lines document evidence of extensive Ventersdorp age rifting beneath the Transvaal Basin. Ventersdorp lithologies are not apparent beneath the BC on any of the other lines. 4.3.4 Seismic receiver function and crustal velocity models of the Kaapvaal Project The crustal thicknesses determined from seismic receiver functions provide important constraints on the gravity modeling (Webb et al., 2004; Nguuri et al., 2001). The results of the receiver functions are detailed in section 2.3.4 and appendix D. In addition, the crustal velocity models provide additional evidence for high velocity rocks in the upper 10 km of crust beneath stations in the central BC detailed in section 4.1. 4.3.5 Magnetic studies Regional magnetic data of the BC are shown in Figure 4.15 along with the profile extracted along the same line as the gravity profile in Figure 4.13 (Stettler et al., 2000; (Ayres et al., 1998). Few magnetic interpretations of the large-scale structure of the BC have been published, largely due to inconsistencies in the palaeomagnetic data (Letts et al., 2005) and lack of attention to the demagnetization effect (Guo et al., 2001; Telford et al., 1990). There is a suggestion that there may be magnetic rocks in the center of the BC, as the central set of magnetic peaks mirrors the pattern of peaks along the outcrop of the Western and Eastern lobes. However, their amplitude is significantly lower as seen at 201 ~340 km along the profile in Figure 4.15, which may indicate a thinner Upper Zone, or that it is deeper. 202 Figure 4.15 Magnetic data of the Bushveld Complex (BC) and surrounding region with locations of the seismic stations of the Kaapvaal Craton Project shown. The red line in the Northern Lobe shows the suggested western extent of the Nothern Lobe and the red line in the southern portions shows the extent of the Bethel Lobe. The bent red line to the east of the Bushveld Complex traces the main directions of dyke swarms to east of the BC. It appears that the BC may have affected the strength of the crust and deflected dykes around it. Black diamonds denote kimberlite localities and colored circles Kaapvaal Project seismic stations. Underlying color image is based on data from Stettler et al. (2000) and the overlying higher resolution black and white image is from Ayres et al. (1998). 203 4.4 Gravity modeling of a connected Bushveld Complex An examination of published gravity models for the BC reveals that such models have generally considered a wide horizontal extent of the source (nearly 400 km), while the depth extent of the models is usually limited to the upper 15 km of the crust. This precludes any consideration of crustal flexure as discussed in section 4.3.2 for models presented by Meyers and de Beer (1987) (Figure 4.6) and du Plessis and Kleywegt (1987). Furthermore, none of the gravity studies published to date have considered the effects of crustal flexure and isostatic balance. In light of these limitations, a reevaluation of the Bouguer gravity data of the BC has been conducted. The three dimensional shape of the BC is poorly constrained. The Bethel Lobe is known mostly from gravity and magnetic data confirmed by a few boreholes (Figures 4.2 and 4.15). The westward extent of the Northern Lobe is entirely unknown (Figure 4.15). Even the lateral extent and possible connectivity of the Western and Eastern lobes are unknown as there is no unambiguous signal from any geophysical markers in the center, and magnetic data do not even provide definitive markers around the entire perimeter of the BC (Figure 4.15). An important consequence of a lopolith geometry for the BC is that it must include a significant amount of crustal flexure due to the weight of the BC and its large lateral extent. This was first predicted by Cawthorn et al. 1998 (Appendix B) and observed by Nguuri et al. 2001 (Appendix D). The average density of the rocks of the BC is also poorly constrained. Considering the size and extent of the BC few values for density have been published. Much of the data that have been published are summarized in Mar? et al. (2002). In addition, Cawthorn and Spies (2003) and Ashwal et al. (2005) (Appendix A) provide more detailed densities. Although the results of Ashwal et al. (2005) suggest the mean density is 3020 204 kg/m3, the core studied only includes the Upper Zone and half of the Main Zone of the Nothern Lobe. Because the densities are so poorly constrained a range of values can be used (3000 ? 3050 kg/m3) in creating a variety of plausible models for testing. The thickness in the interior of the BC is also unconstrained and has been varied between ~7-8 km thickness in several model iterations, the extremes derived from the western and eastern BC outcrop. A straightforward calculation of the BC Airy isostatic response can be made by considering a simplified BC. Using the statement of equal sized columns have equal mass: Tc ?c + u ?m = Tc ?c + TBC ?BC (4.1) where Tc is the thickness of the undisturbed crust, ?c is the density of the crust, ?m is the mantle density, ?BC is the density of the BC and TBC is the thickness of the BC. The thickness of the BC, TBC can be expressed as: TBC = h + u (4.2) where h is the amount of uplift and u is the thickness of the depression. Using: Density of mafic Bushveld Complex rocks ?BC: 3050 kg/m3 Mantle density ?m: 3300 kg/m3 Mean crustal density: 2700 kg/m3 Thickness of mafic Bushveld Complex rocks: 7 km The amount of uplift h is 0.53 km and the thickness of the depression is 6.47 km. This illustrative result will be modified if there is significant strength in the crust supporting the BC or if other density or thickness values are used. This exercise simply 205 demonstrates that the BC is a significant load on the crust, which at ~350 km lateral extent should cause crustal flexure (Cawthorn et al., 1998, Appendix B). As the published seismic lines do not penetrate the interior of the BC (Section 4.2.3) the only other available constraints on the interior of the BC are the crustal thicknesses determined during the Kaapvaal Project (Figure 4.16), Nguuri et al. (2001). Fortunately, as predicted by Cawthorn et al. (1998) (Appendix B), there is a large crustal thickness anomaly coincident with the center of the BC, which was discovered by Ngurri et al. (2001) Figure 4.16). Although the station spacing of the seismic stations was quite large (100 km) and only two stations show the BC crustal thickness anomaly, the depth solution is well constrained by at least 20 earthquakes. In addition, crustal velocity models derived from inversion of receiver functions suggest the presence of high velocity material in the upper 10 km of crust beneath these two stations (Section 4.1, pg 172). The presence of a 7 km thick high velocity layer due to mafic BC rocks would actually lead to an underestimation of the crustal thickness, so these crustal thickness values are likely to be minimum determinations. 206 Figure 4.16 Contoured crustal thickness data in km in the region of the Bushveld Complex with locations of the seismic stations of the Kaapvaal Craton Project shown. The crustal thicknesses from the stations along the profile have been projected to the profile in the panel beneath the image. Crustal thickness is measured from the surface to the Moho depth. The data clearly show a significant increase in crustal thickness beneath the Bushveld Complex (data from Nguuri et al., 2001). 207 In order to test the possibility of a connected BC, I constructed three simple models (Cawthorn et al., 1998, Appendix B). First I reproduced the results of Cousins (1959) using a simplified model of the BC as a lopolith without isostatic compensation at the Moho. Here I have used a BC density of 3050 kg/m3 and a slightly thinner central BC. As expected, this model produces a strong elevated gravity signal in the central section of the profile (Figure 4.17). Figure 4.17 Simplified model of the Bushveld Complex if no isostatic compensation by a crustal root zone at the Moho is considered. This illustrates the argument that Cousins (1959) used against a connected Bushveld Complex. Note the extreme vertical exaggeration. I then produced a simple model of separate dipping sheets underlying the eastern and western BC, as closely reproducing the results of (Meyer and de Beer, 1987) as possible. This simple model successfully returns to low Bouguer gravity values in the center of the profile (Figure 4.18). 208 Figure 4.18 Simplified model of the Bouguer gravity data of the Bushveld Complex using a dipping sheet type model as used in Meyer and de Beer (1987). Again, note the extreme vertical exaggeration. Finally, I modeled the BC as a continuous lopolith, but with a significant component of isostatic crustal compensation being allowed at the Moho. This resulted in an excellent fit of the data similar to the fit produced in Figure 4.18 that is geologically more plausible (Figure 4.19, Cawthorn et al., 1998a; Cawthorn and Webb, 2001; Webb et al., 2004). 209 Figure 4.19 Simplified model of the Bouguer gravity data over the Bushveld Complex illustrating how crustal flexure due to the load of the Bushveld Complex can account for the observed gravity signal while still having a connected Bushveld Complex. This model is a ?proof of concept? model to demonstrate that a continuous BC model gives a plausible fit to the gravity data. The model is isostatically balanced at the center and the Moho has been adjusted to obtain a reasonable fit. 4.4.1 Geological arguments for a connected Bushveld Complex Prior to the gravity modeling of Cousins (1959), the shape of the BC was thought to be a lopolith based on broad geological similarities, especially between the Western and Eastern Lobes (Figure 4.4). However, since most layered mafic intrusions have a broadly similar magmatic stratigraphy due to the principles of differentiation, it is the similarities in stratigraphy that are atypical of fractionation that need to be considered when comparing these widely separated lobes. Cawthorn and Webb (2001) (Appendix C) 210 summarize six unusual geological features that occur in the BC and that support a connection between the Western and Eastern Lobes. These are: 1) The sequence of chromitite layers of the Middle Group chromitite is nearly identical in the Western and Eastern Lobes. Each layer has a distinctive chemistry (Hatton and Von Gruenewaldt, 1987), but between these widely separated lobes the chemistry is very similar. Although the sequence of chromite-pyroxenite-norite- anorthosite is not unexpected in a layered intrusion, it would not be expected that the chemistry and sequence of these layers would be exactly duplicated if the lobes were intruded separately. 2) The footwall of the Upper Group (UG1) Chromitite is bifurcated and deformed and is the only chromitite layer of a total of thirteen in the BC to display such features. The classic site for viewing this is the Dwars River national monument locality in the Eastern Lobe, but the same feature is seen throughout the Western and Eastern Lobes at the same stratigraphic level. 3) The Upper Group (UG2) Chromitite has an economic grade of PGE mineralization and is the only chromitite in the world mined for PGEs (Lee, 1996). The grade is similar in the Western and Eastern Lobes. 4) The platiniferous Merensky Reef is a well-known source of PGEs. There is also a sudden and strong increase in the 87Sr/86Sr ratio from 0.7063 to 0.7076 at the base of the Merenksy Reef (Kruger and Marsh, 1982; Lee and Butcher, 1990). Again this change is observed in both the Western and Eastern Lobes at the same stratigraphic level. 5) The Upper Zone has identical initial Sr isotopic ratios for both the Western and Eastern Lobes (Kruger et al., 1987). 211 6) The vanadium grade and thickness of the main magnetite layer in the Upper Zone is similar in both the Western and Eastern Lobes (Cawthorn and Molyneux, 1986). The similarities of these unusual features occur over ~350 km lateral extent and through 7 km of magmatic stratigraphy from the Lower Zone through to the Upper Zone. This strongly supports the view that a single body of melt existed across the whole area of the body (Cawthorn and Webb, 2001) (Appendix C). 4.4.2 Gravity Data The Bouguer gravity data over the BC area as supplied by the Council for Geoscience are shown in Figure 4.13 (Venter et al., 1999). These data have been extracted from the larger data set used in Chapter 3. The four main Lobes of the BC clearly show as distinct gravity highs outlining the extent of the BC, even over the unexposed Bethal Lobe. The outcrop trace of the Rustenberg Layered Suite is shown in Figure 4.13, and demonstrates the close correlation between the maximum gravity values and the outcrop of the BC. A typical west to east profile has been extracted for modeling purposes (Figure 4.13). 4.4.3 Constrained Gravity Model A gravity model of the BC constrained by surface geology (Cawthorn and Webb, 2001), seismically determined crustal thicknesses (Nguuri et al., 2001), measured density values (Appendix A; Ashwal et al., 2005) and available reflection seismic data have been constructed with a continuous lopolith-type source to test the possibility that the weight of the BC causes a depressed Moho. This model assumes a ~7 km thick Rustenburg 212 Layered Suite with an average density of 3.02 gm/cm3 an average crustal density of 2.7 gm/cm3, and an upper mantle density of 3.30 gm/cm3 (Figure 4.20). Various gravity models have been constructed using an average value of density for the BC varying from 3.00 to 3.30 gm/cm3. These various models only require minor adjustments in the thickness of the BC to fit the observed gravity data. They all indicate that an Airy isostatic balance in the central region of the BC is possible, and a typical example is given in Figure 4.20. Since the average density, thickness in the center and depth in the center are unconstrained, the models demonstrate plausible configurations, but further geophysical work will need to be done in order to confirm these possibilities. Figure 4.20 Bouguer gravity model for the Bushveld Complex from Webb et al. (2004). The dotted green line shows the observed data and the solid black line is the calculated result. This model has been constrained by the use of surface outcrop, measured density values, measured crustal thickness values and Vibroseis seismic data. However, details in the mid crust are unconstrained. Figure 4.17 covers the range from roughly 175 km to 550 km along a slightly different, but parallel, profile. 213 4.4.4 Discussion of the constrained gravity model The constrained gravity model presented here (Webb et al., 2004; Figure 4.20) fits the available constraints and provides an acceptable match to the observed data that differs only in details that can be ascribed to variations in density of surface and near- surface geology. Approximately midway along the profile I have modeled a pronounced fold in the rocks of the BC. This fold accounts for the long wavelength (~80 km) central peak in the gravity signal (e.g. Figure 4.6). This response is not unlikely and could be due to large scale diapirism from deformation of the underlying Transvaal rocks (Engelbrecht, 1990; Harris et al., 2003; Uken and Watkeys, 1997a). I have also included an alkaline intrusion to account for the very sharp peak at the summit of this longer wavelength peak (Frick and Walraven, 1985). This has been attributed by Meyer and de Beer (1987) as post?BC alkaline complex. However, it is more likely to be an intrusion with a higher density. It is interesting to speculate on how close to surface the BC rocks could be at the crest of this fold as the signal is moderately strong (~40 mGal) and the subsurface geology is poorly known. The Palmietgat kimberlite crustal xenolith suite is currently being investigated in order to locate samples of the BC to confirm continuity of the complex in the central portion (Simelane, 2004; Simelane et al., 2004). The BC and the regions to the west are underlain both by thicker crust (Nguuri et al., 2001) and slower seismic mantle velocities (Fouch et al., 2004; James et al., 2001) as compared to the Archaean crust of the Kaapvaal Craton away from the BC. The Moho beneath the BC as found by Nguuri et al. (2001) has smaller amplitude receiver functions indicating the seismic velocity contrast at the boundary is not as large as beneath the remainder of the Kaapvaal Craton. This could be indicative of underplating resulting in a significant increase in density of the lower crust. Preliminary inversions of receiver functions for crustal structure suggest the presence of a 7 km thick higher than average 214 velocity section in the upper crust, which also supports the continuous BC model (Webb et al., 2004). The lack of constraints available for the interior of the BC makes more detailed modeling of the Bouguer gravity data a speculative exercise. However, any model of the BC must now take cognizance of the significantly thicker crust beneath the BC (Nguuri et al., 2001). 4.5 Summary Using density data from Appendix A and additional published density data, crustal thickness results from seismic receiver functions (Nguuri et al., 2001, Appendix D), Vibroseis data and surface geology (Cawthorn and Webb, 2001; Appendix C), I have been able to develop a gravity model of the BC in which the BC is connected at depth and which provides an acceptable fit to the observed data (Webb et al., 2004; Section 4.1). This model demonstrates that a lopolith-shaped BC connected from the Western to the Eastern Lobes is a plausible configuration that cannot be dismissed on the grounds of gravity data. By taking into account a probable flexure of the crust due to the load of the BC and a vertical displacement of crustal material to depths normally occupied by mantle, this model brings an acceptable fit between observed and calculated gravity anomaly values. Although this model is non unique, it demonstrates that this configuration is plausible. Variations in the seismic velocities in the mantle will also have some effect on the anomalies present at surface and will be considered in the next chapter. This work should be continued to include the other lobes of the BC, the Bethel Lobe to the south, and the Northern Lobe to the north. Traditionally the Northern Lobe has always been modeled as only extending ~50 ? 100 km inwards from its outcrop. However, the 215 presence of thick crust (station 51, Figure 4.16) and the Waterberg Basin, suggest that the western extent of the Northern Lobe may be significantly further west as suggested in Figure 4.2. Drillholes have largely confirmed the presence of BC in the entire Bethel Lobe, but the detailed structure remains obscure. Further work should investigate the extent of BC age intrusions, especially their extent into Botswana (Figure 4.21) (Cawthorn and Walraven, 1998; Mapeo et al., 2004) and the effect the intrusion of these mafic intrusive complexes has on the underlying mantle lithosphere (Chatu et al., 2003). Figure 4.21 Map showing the relationship between the Thabazimbi ? Murchison Lineament (TML), Bushveld Complex and the Molopo Farm Complex. There are several additional intrusions of Bushveld Complex age in Botswana that need to be considered in terms of the tectonic environment that produced such a large province of layered mafic complexes. Diagram from Cawthorn and Walraven (1998). Many of the ideas presented in this chapter can be easily tested using Vibroseis or even deployments of passive broadband seismometer arrays leading to better constraints on the tectonic origin of the BC. Confirmation of continuity imposes important constraints on the volume of material involved. Placing a seismic line across the BC as a whole would do much to resolve continuing ambiguity in the gravity data and may even 216 217 open up new targets for exploration. Follow-up scientific drilling would assist with positively identifying the various horizons discovered. It is rather exciting to consider that an ore body as large and valuable as the BC could be hidden beneath the surface, as yet undetected by gravity due to the masking effects of crustal flexure! 5 Influence of velocity variations in the upper mantle on the Bouguer gravity of southern Africa The detailed relationships in the Earth?s mantle between temperature, density and composition as determined from seismic tomography are poorly constrained. Traditionally, in early tomographic studies, seismic velocity variations were related solely to temperature variations (e.g. Grand et al., 1997), whereby fast regions are cold and hence denser, and slow regions hotter and less dense. In a global sense this is certainly a reasonable assumption. Integrated studies incorporating both temperature and composition, however, confirm that compositional variations may be equally important, or even, as in the case of the mantle keels beneath Archaean cratons, dominant (e.g. Carlson et al., 2005; James et al., 2001). Highly depleted cratonic keels with large magnesium numbers (Mg#), defined as molar Mg/(Mg+Fe), have higher velocities but lower densities than they would have if temperature were the dominant control on density. This idea was originally proposed by Jordan (1975a) and Jordan (1979b) in his tectosphere hypothesis, in which cold, but compositionally depleted (intrinsically less dense) cratonic keels have approximately the same density as the much hotter fertile (intrinsically more dense) mantle beneath the ocean basins. This ?isopycnic? hypothesis is an elegant explanation for the lack of a strong positive gravity signature associated with continents relative to oceans. Evidence from xenolith observations (James et al., 2004) suggests that a depleted peridotite is approximately 2% less dense at the same temperature as a fertile peridotite. Global scale tomographic studies have established a broad, high S-wave velocity (~4%) anomaly beneath southern Africa localized on the broader Kalahari Craton, comprising the Kaapvaal and Zimbabwe cratons and the enigmatic Rehoboth region (Ritsema and van Heijst, 2000). Beneath the Kaapvaal 218 Craton, the Southern African Seismic Experiment (SASE) revealed more subtle spatial variations in seismic velocity directly beneath the array. These vary by up to 2% within the array (James et al., 2001) and are most likely due primarily to variations in the amount of depletion in the mantle keels that resulted from extensive extraction of partial melt early in the Craton?s formation, as opposed to temperature variations that should be comparatively small (Carlson et al., 2005). This chapter will briefly review some of the relationships implicit between variations in mantle composition (as measured by Mg#), temperature, metasomatism, seismic velocity, and density (Sections 5.1 and 5.2). These relationships are used, then used in Section 5.3 to produce models of the gravity field of southern Africa due to contributions from the mantle as determined by the delay time tomography. Finally in Section 5.4, the mantle contributions are combined with the crustal thickness contributions from Chapter 3 and combined models are determined and discussed. 5.1 Relationship between density and seismic velocity variations (B) The relationship between seismic velocity variation, ?V, and the corresponding density variation, ??, is deceptively simple: ( ) ( ) ( )zyxzyxV ,, z y, x,B,, ??=? (5.1) where B is the proportionality constant. In the most general formulation B is allowed to vary spatially (x, y, z). While this equation appears straightforward, the seismic velocity variations are determined from slowness, which forms the output from the tomographic code that is used in the gravity calculation. The slowness, S, is defined as: pV S 1 = (5.2) 219 where Vp is the P wave velocity at a particular depth. [In this section I use P-wave velocity variations as they are relatively better constrained than those for S-waves.] The seismic velocity variation can be expressed in terms of the slowness S as: 01 10 0 0 01 0 1 % SS SS V V VV VVV ??? ? ??? ? ?=??? ? ??? ? ?=?=? (5.3) where V0 is the background velocity model, V1 is the total perturbed velocity, S0 is the radial slowness model, and S1 is given by 031 SSS D += (5.4) where S3D are the 3D slowness perturbations that are output by the tomography code. Equation 5.3 can be rewritten as: )()( 2003 3 2 003 030 SSS S SSS SSS V D D D D +? ?=+? ??=? (5.5) where the first term in the denominator is frequently dropped as it is significantly smaller than the other terms. It is this equation, in combination with equation 5.1, which is used to determine the densities used in the gravity calculation from the S3D slowness values output from the tomography inversion. The starting radial slowness model (radslw = S0) that is used in the tomographic inversion is based on the IASPEI 91 model (Figure 5.1) (Kennett, 1991)1. 1 It is important to note that the tomographic velocity perturbations are not referenced to IASPEI 91. The tomographic inversion itself is quite insensitive to the details, including absolute velocities, of the starting model. 220 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 0 100 200 300 400 500 600 Depth (km) V el o ci ty ( km /s ) 2.5 3 3.5 4 4.5 5 D en si ty ( g /c m 3 ) IASPEI 91 P wave Radslw Density (g/cm3) Figure 5.1 Radial model of IASPEI 91 P wave velocities and density values and Radslw which uses the IASPEI 91 values, but at 50 km intervals corresponding to the sizes of the tomographic cells. Radslw is equal to S0 in the equations above and samples the IASPEI values at 50 km intervals. Density and P wave values from IASPEI 91 (Kennett, 1991). An example of the relationship between the B value, seismic velocity variations and the resulting density is given by Tiberi et al. (2001) in her study of the Corinth rift. Tiberi et al. (2001) examined the linear relationship between density and velocity proposed by Henkel (1990) but the resulting density value contrasts were unrealistically high. In this case they used B = 5, which for a velocity perturbation of 4 percent, results in a density contrast of about 60 kg/m3, or a roughly 2 percent variation in density relative to IASPEI 91. This is determined by taking 4 percent of the Vp IASPEI value at 35 km giving: km/s3216.0)04.804.0(%4 =?=?=? pVV (5.6) then ?? can be found from 221 3kg/m64 5 3216.0 ==?=? B Vp? (5.7) the IASPEI 91 density at 35 km is ? = 3320 kg/m3 and the percentage is found from: %202.0 3320 (64) percentin velocity === . (5.8) This illustrative example is for the case where the velocity?density relationship is temperature dependent, a reasonable assumption in much non-cratonic mantle. A similar calculation for values pertinent to the Kaapvaal project can also be done. In this case a negative value of B is used to indicate a velocity ? density relationship that is dominated by compositional effects, where an increasing Mg# results in a lower density due to the removal of Fe and Al via partial melting from the mantle. These effects are illustrated in Figure 5.2 for two samples representative of fertile mantle (Mg#=89) and depleted mantle (Mg#=93.8). Here I have chosen samples with a wide separation of Mg# that are both in the spinel facies and thus garnet-free. The determination of density and P-wave seismic velocity is at 450? C and 50 km depth. There is enormous scatter in the results using samples of xenoliths, indicating the degree of heterogeneity present in the mantle (e.g. pink squares in Figure 5.2, harzburgites that represent the most highly depleted mantle residue of melt extraction.); however, using samples with well-separated Mg#s gives negative B values for a plot of density vs. seismic velocities. The magnitude of B is perhaps better determined from large-scale seismic studies, which suggest that density is reduced by ~1%. In a global study examining the competing effects of thermal and compositional density variations, Kaban (2003) conclude that depletion has an important effect in southern Africa and that the density is reduced by 1.1 to 1.5% compared to fertile mantle. The resolution of their study is limited by the resolution of their gravity 222 field derived from global degree/order 20 spherical harmonics of the free air gravity of EGM96 of approximately 1000 km wavelength. As I will justify below, a value of B = -2.4 is a reasonable choice in that a 1% change in velocity results in a 1% change in density (Figure 5.3). 8.04 8.06 8.08 8.10 8.12 8.14 8.16 8.18 8.20 8.22 8.24 3.290 3.295 3.300 3.305 3.310 3.315 3.320 3.325 3.330 3.335 3.340 3.345 Density (g/cm3) P w av e ve lo ci ty ( km /s ) Depleted spinel hartburgite PHN 5248 Mg# = 93.8 Spinel lherzolite McDonough and Sun (1995) Mg# = 89 B ? -3.7 Low Ca Hartzburgite James et al. (2004) Mg#s from 92.6 to 93.9 Figure 5.2 Sample plot used to determine B value from a primitive spinel lherzolite of McDonough and Sun (1995) and a depleted spinel hartzburgite of James et al. (2004) where the seismic velocity and density have been calculated at 50 km depth and 450?C. Compare with the left hand side of Figure 1.8. 223 Figure 5.3. This diagram illustrates the maximum (pink) and minimum (blue) of density contrast values generated from the maximum and minimum slowness values from the tomographic output for each B value. The diagram is nearly symmetric, however, the maximum and minimum seismic velocity perturbations (and hence densities) in James et al. (2001) results are not exactly the same amplitude. For comparison Tiberi et al. (2001) uses B =5, ?? = 65 kg/m3. The light blue line is ?? = 34 kg/m3, which is ? 1% change in mantle density. At large values of B, a given change in velocity results in a relatively small change in density. At smaller absolute values of B, changes in velocity produce proportionately larger changes in density. These effects are shown graphically in Figure 5.3. In a temperature dominated rift zone, relatively high values of B=5 (Tiberi et al., 2003) seem to produce plausible results, as the relative effect of temperature on seismic velocity may be large relative to its effect on density. In cratonic regions, on the other hand, the relatively smaller overall range of velocity variations (~2%) may reflect proportionately greater variation in compositionally-controlled density. An important additional factor in the present study, moreover, is the fact that velocity perturbations recovered from tomographic inversion are typically reduced in amplitude by approximately a factor of 224 two (pers. comm. D. E. James, 2005). This has also been shown in resolution tests (James et al., 2001, supplementary material) and is a well known effect of the seismic velocity inversion. In order to obtain a 1% variation in density in agreement with the xenolith studies, a value of B equal to -2.4 is used in converting the seismic velocities to density values (Figure 5.3). In practice, several B values were used to examine the amplitude of the resulting gravity signal. Since the tomographic velocity perturbations used here have a mean of zero within the volume being analyzed, the resulting gravity anomalies will also vary around a mean of zero. So even though some regions are slow or ?red? i.e. less depleted, they are really fast or ?blue? relative to a more global perspective (Ritsema and van Heijst, 2000). Thus it is valid for a first order test to use a constant B value for the limited region under consideration as the red regions in southern Africa primarily reflect less depletion relative to the blue regions. A similar conclusion was reached by Tiberi et al.(2003), who found in a joint inversion of gravity and seismic velocities that allowing the B factor to also vary in the inversion did not lead to realistic results, suggesting that B did not vary significantly laterally or vertically in the Baikal rift zone. 5.2 Isopycnic discussion and Thermal Considerations The fact that the SASE study does not extend offshore makes it impractical to assess the isopycnic hypothesis by comparing oceanic mantle density distributions with cratonic mantle density distributions. If we assume, however, that the isopycnic hypothesis is 100% correct, then there would be no contribution to variations in the observed gravity from the upper mantle variations in seismic velocities, as there would be a fine balance between the amount of depletion and the temperature of the mantle 225 resulting in a B value that varies significantly spatially to maintain a constant density. These two parameters (depletion and temperature) do not have a causative relationship, however, and subsequent tectonic or magmatic activity will disturb isopycnic balance locally, although globally the isopycnic balance between oceanic upper mantle and continental upper mantle should be maintained. The Bushveld Province may be a special case. In this region of extensive mafic material, there could be a subtle blanketing effect, which would result in higher temperatures being driven down into the mantle. It has been speculated, for example, that this increase in temperature may be as much as 30?C, due to differing thermal conductivities of mafic rocks in the crust, although more modeling is needed to confirm these results (Chatu et al., 2003). As any temperature effects due to Bushveld Complex emplacement (2.05 Ga) should have long ago dissipated, however, an alternative possibility, and perhaps more plausible, is that the broad, reduced velocity anomaly seen beneath the Bushveld Complex region is due to metasomatic effects that lower the Mg# and increase the density of the upper mantle. 5.3 Forward modeling In this section I have modeled the gravitational response due to the variations in density of the mantle based on the variations in seismic velocity from the base of the crust to depths up to 700 km. Only constant values of B were used; however, B is expected to vary with depth, changing from a negative value in the keel directly beneath the craton, to a positive value corresponding to a temperature dominated regime in the asthenosphere below ~300 km depth. B will also vary laterally and is likely to depend on the temperature at the time of cratonization reflecting the degree of depletion. However, little 226 information about actual spatial variations of B is known, so to examine the first order variations that can be attributed to composition effects, a spatially constant B value is used throughout this work. In spite of the greater 3D coverage of the delay time tomography, the gravity calculation is still strongly affected by edge effects, especially in the shallowest region where the sources are closest to the surface. Because of this effect, I am again considering only the profile up the middle of the seismic transect, although the calculated gravity values are also shown in map view on the 3D plots. The first step is to construct a 2D model to determine the magnitude of the response and assess whether or not the B values selected are appropriate. 5.3.1 2.5 D Gravity Modeling I construct a 2.5D forward gravity model with limited strike extent (i.e. the extent of the blocks perpendicular to the plane of the profile) of 100 km to examine the magnitude and variation of the gravity response due to compositional variations in the mantle for the selected profile slice. The program used is GRAVGRID (Cooper, 2005). Here I have taken the slowness values from the tomography along the same central profile used previously (e.g. Figure 3.13). From the slowness values I have calculated the appropriate density values following the calculation procedure described in equations 5.6- 5.8. Using a B value of -2.4 results in density variations ranging from -29 to +29 kg/m3 along this particular profile. These density perturbations are then imported into GRAVGRID and the gravity values are determined on the surface along the profile using a Talwani type algorithm (Figure 5.4). In this case the cells centers are the same as the tomographic knots and the centers of the squares are in the same position as the knots. In this program the strike length of the cells is fixed to 100 km, hence it is a two and a half 227 dimensional program, as the strike length (i.e. in and out of the page) is limited and not infinite. Figure 5.4 Profile showing gravitational response due to density variations for a factor B = -2.4. This is based on composition variations and the reds are higher density whereas the blues are lower density. The variations below ~400 km contribute little to the signal. The solid black line is the calculated gravity and the green dotted line is the observed gravity along the profile B to B?. The modeling demonstrates that even modest density contrast variations lead to substantial gravity anomalies of fairly short wavelength (200 km and greater) on surface. The amplitude of the modeled signal is ~ 140 mgal peak-to-trough, similar to the amplitude of the observed signal, although the shapes are distinctly different. The smoothness of the modeled profile is largely due to the depth of the sources and the large cell size. The measured gravity data shown as stars display the effect of near surface density variations that are expressed primarily in the short wavelength signals. 228 5.3.2 3D Gravity Modeling The value of B selected actually reflects a combination of both composition variations and temperature variations. The implication of using a single B value is that the temperature effects vary spatially in a similar manner to the compositional effects ? as implied by the isopycnic hypothesis. The negative value of B used in this work does imply, however, that overall the effect of composition dominates in the region of interest. Because the gravity computations are based on velocity perturbations rather than on absolute velocities, the estimated density contrasts are also relative. This means that the choice of background model is largely arbitrary. For the model proposed here, I have chosen the same IASPEI 91 model used for tomographic inversion as background model to represent a layered Earth with density contrast increasing downwards as shown schematically in Figure 5.5. The individual blocks are approximated as spheres using the same method developed in Chapter 3. The surface on which the calculations are determined is a spherical surface and the station spacing on the surface was 0.5? x 0.5? or smaller. The cell size for all calculations was 0.5? x 0.5? x 50 km or smaller. 229 Figure 5.5 Schematic background model for density variations. The density increases downwards in layers based on IASPEI. The blocks are 50 km in thickness. This schematic diagram does not show the curvature of the blocks, which is illustrated in Figure 3.9. The density contrasts used to determine the gravity are based on perturbations in the seismic tomography, which is relative to a floating background model with zero mean. Frechet derivatives for the tomographic inversion were based on IASPEI91, although for that inversion the choice of a starting model is not important (VanDecar, 1991). In terms of density this means that in each layer the variations are relative to a constant value in each layer, which is consistent with the background model (Figure 5.6). 230 Figure 5.6 Schematic diagram showing density values determined from slowness values. In this diagram the crust has a constant density. The upper most mantle (depths < 50 km), which is poorly resolved using delay time tomography, is assigned the same density as is determined for the layer underneath which is the first layer of the tomographic model. The central profile is again used as the definitive profile to minimize edge effects. The delay time tomography along the central profile indicates that the keel probably extends to depths of at least ~200-250 km, although downward smearing inherent in body wave tomography limits more precise determination (Figure 5.7) (Fouch et al., 2004). While this vertical smearing is unavoidable in the delay time tomography data for gravity models we are more interested in the lateral variations, since gravity has poor depth resolution. Moreover, effects on surface gravity of density variations below 300 km depth are minimal. The overall result is that the vertical smearing will have limited effect on the resulting gravity model. 231 Figure 5.7 Slice through the P wave delay time tomography model from Cape Town (B) to Masvingo (B?) to a depth of 700 km showing velocity perturbations in percent (Fouch et al., 2004). This is the same profile as in Figures 5.4 and 3.13) The gravity signal determined along the central profile will be the integrated effect of these density variations, not just directly beneath, but from the sides, as there are strong lateral variations in the seismic velocities perpendicular to the line of the profile (Figure 5.8). One of the most pronounced is the variation in velocity perturbation from west to east across the Kaapvaal Craton, whereby the keel thickens and velocity perturbations increase in intensity towards the center of the craton. 232 Figure 5.8 Map view of P wave delay time tomography values at a depth of 150 km showing velocity perturbations in percent (Fouch et al., 2004). In order to investigate the influence of the sign of B, I have first calculated gravity for a value of B = +2.0, indicating a temperature-dominated regime (Figure 5.9). 233 Figure 5.9 Forward model of the gravity field resulting from the velocity variations determined from seismic travel time tomography using a temperature dependent value for B = 2.0 and calculating the response to a depth of 300 km. This value of B corresponds to a 1% change in the velocity perturbations, resulting in a slightly more than 1% change in the density values. The positive B value implies that 234 negative velocity perturbations (red = hot) produce lower densities and positive velocity perturbations (blue = cold) produce higher density values. This results in a very large gravity anomaly (160 mGal peak-to-trough), with the wrong sign for counteracting the large positive anomaly due to thin crust directly under the Kaapvaal Craton of southern Africa determined in Chapter 3. Several positive B values have been tested, but clearly this simply changes the amplitude of the results. Except for very large B values (B > 5) the amplitude of the resulting gravity signal is significant and it is always in the opposite sense (~60 mGals peak-to-trough for B = 5.0). This test is a clear indication that the B value must be negative and compositionally-dominated in this region, a conclusion that is in accord with detailed xenolith studies (e.g. James et al., 2004). In the following discussion I examine the effects of negative B values. I start with calculating the gravity response for a value of B = -2.0, which has previously been shown is plausible on the basis of xenolith measurements. As expected, the resultant anomaly from that calculation is opposite in sign to that found for positive B as shown in Figure 5.10. 235 Figure 5.10 Forward model of the gravity field resulting from the velocity variations determined from P- wave delay time tomography using a compositionally dependent value for B = -2.0 and calculating the response to a depth of 300 km. 236 The resulting gravitational response is dominated by a large (~80 mGal) negative gravity anomaly that is roughly centered over the Kaapvaal Craton. This anomaly will largely cancel the large positive anomaly produced by the generally thin crust under the Kaapvaal Craton (Figure 3.28). Since the gravity calculation essentially integrates the contributions of the seismic response over the depth range considered, it is instructive to calculate the gravity response to different depths to determine the depth at which the contribution is minimal. Computations where integrations are to depths of 150, 200, 300 and 400, respectively, are shown for comparative purposes in Figure 5.11. Here I have calculated the gravitational response using the spherical prism method developed in Chapter 3. The crustal contribution of the Moho has not been included; this section only examines the gravity signal due to the seismic velocity variations in the mantle. The velocity variations included start just below the Moho, incorporating the Moho variations on the underside and continue to a specified depth. 237 Figure 5.11 Comparison of the gravity signal resulting from variations in the delay time tomography calculated (inclusively) to depths of: A) 150 km; B) 200 km; C) 300km ; and D) 400 km, all for B = -2.0. 238 The shape of the central gravity profile is already well defined with integration to 150 km depth (Figure 5.11 A). There is little variation in the detail of the profile shape as the contributions from deeper sections are added. However the amplitude of the signal increases significantly when contributions from depths down to 300 km are included (Figure 5.11 B and C). The gravity signal starts to decrease slightly as contributions from below 300 km are included (Figure 5.11 D), apparently due to moving out of the range of the keel (Figure 5.7). The change in sign of the seismic velocity perturbations is apparent from the profile (Figure 5.7) and the velocity perturbations decrease gradually below ~300 km. Note that the reduction of amplitude of the delay time anomaly in the tomographic inversion is partially offset by downward smearing of the tomographic results. Although the depth extent of the keel cannot be resolved with gravity modeling, significant contributions to the surface gravity values appear to die off at a depth of ~300 km. The seismic velocity variations contributing to the gravity signal may actually be at shallower depth and of greater amplitude due to vertical smearing in the seismic tomography solutions. Tightening up the solution and shallowing up the delay time anomalies would have the effect of increasing the amplitude of the gravity signal as the seismic velocity variations are brought closer to surface. However, this has been accounted for through the use of a smaller B value. Thus, these calculations can be thought of as minimum gravity anomalies for each configuration. Since the regime of the mantle is likely to change from composition-dominated to temperature-dominated beneath ~300 and ~400 km depth, it is unrealistic to consider contributions from below this depth in these calculations. Here I calculate to a depth of 300 km to ensure that all of the reliable keel contributions are included. 239 To assess the comparative effect on the gravity amplitudes of different B values, I have calculated the gravitational response for a wide range of B values of -2.0, -3.0, -4.0, and -5.0 all to a depth of 300 km (Figure 5.12). Again the spherical cube method developed in Chapter 3 has been used for the calculations. The percent change in density at 100 km depth for B=-2, is ~1.2%, for B=-3, is ~0.8%, for B=-4, is ~0.6% and for B=-5 is ~0.5% (Figure 5.3). 240 Figure 5.12 Comparison of the gravity signal resulting from variations in the delay time tomography calculated for B values of A) -2.0, B) -3.0, C) -4.0, D) -5.0, to a depth of 300 km. 241 The smallest B value above, B = -5.0, demonstrates that even for a small percent change in density (0.5%), there is still a significant change in the gravity values along the line of the profile from +35 to -35 mGal peak-to-trough. From assessments of xenoliths (James et al., 2004) and global studies (Kaban et al., 2003) the percent density variation due to composition is probably closer to 1%. Certainly the gravity anomalies produced for values of B significantly less negative than B = -2.0 (larger than 1%) are likely too large to be realistic (B = -1.5, min gravity = -120 mGal, max gravity +110 mGal, larger than the observed gravity variations on surface). In these calculations, no explicit consideration is made of thermal effects, thus the B values really represent a combination of chemical (depletion) effects and thermal effects. The Zimbabwe Craton has a significantly thinner, less seismically prominent keel in the tomographic inversion than the Kaapvaal Craton. This is also reflected as lower values in the calculated gravity anomaly due to the mantle contribution. It does appear that the Bouguer gravity in the Zimbabwe Craton is less negative than in the Kaapvaal Craton, suggesting that the keel may be thinner and slightly less depleted below the Kaapvaal Craton (Figures 3.13 and 3.17), although it is possible that the amplitude of the velocity perturbations may be damped or otherwise skewed by edge effects and by a significant decrease in ray density to the north (James and Fouch, 2002) A value of B = -2.4 results in density variations of ~1% throughout the model. This calculation is shown in Figure 5.13 as a realistic estimate of the contribution to the gravity at the surface from composition variations in the mantle. 242 Figure 5.13 Variations in gravity for a value of B = -2.4, which results from density variations of ~1% in the model. 243 The gravity effect due to the density variations determined from the body wave tomography provides a method of expressing the tomography in an integrated fashion. This helps to determine which regions have an overall stronger ?negative? effect from the keel, which may not necessarily be the thickest sections of the keel. By doing the gravity calculation in 3D the values along the profile up the center of the array are well determined. In Figure 5.13, there is a strong computed gravity low of ~-70 mGal associated with the Kaapvaal Craton, corresponding with the most intense delay time anomalies in the keel, although these are not the thickest sections of the keel. The magnitude and location of this gravity low corresponds very closely with the large gravity high produced from crustal thickness variations in Chapter 3. The combination of these data is considered in the next section. 5.4 Combined modeling of data sets In chapter 3 I presented the results of modeling the gravitational response due to variations in Moho topography. These results will now be combined with the gravity modeling results of the delay time tomography presented in the last section. In these combined calculations, I have added the responses first, as they are both calculated about a mean of zero using density contrasts. I have then adjusted the regional to be comparable with the observed data. Again it is the central profile where the results are most valid; the map results are provided only for comparative purposes. To clarify the components of the gravity field, I have first plotted the response from the Moho variations (in red) for a constant density contrast at the Moho of 300 kg/m3 and the gravitational response from the tomography for a constant value of B = -2.4 (pink) to 244 a depth of 300 km (Figure 5.14). These profiles are compared with the smoothed observed gravity data (dark green). This comparison emphasizes that the amplitude of both signals is large, but that they are mostly out of phase with each other. The loss of resolution (and hence amplitude) of the velocity perturbations in the Zimbabwe craton region (pers. comm. D.E. James, 2005) produces an elevated gravitational response in the pink curve in that region that is not well constrained by data. In any event, this elevated response determined from the delay time tomography towards B? is unable to compensate for the observed thin crust in the Zimbabwe craton (Figure 5.14). By adding the Moho contribution and the mantle contribution together, the combined gravitational response is determined (Figure 5.15). Here the blue curve is the observed gravity and black is the combined gravitational response as calculated from the red and pink curves in Figure 5.14. The image map of the calculated gravitational response is shown for reference. In this case the constant density contrast across the Moho results in a very strong decrease in gravity towards the northeast that dominates the calculated gravity signal. Even so, the shape of the observed gravity profile and the calculated profile of the combined effects is quite similar in the region from Cape Town to the Bushveld Complex. 245 Figure 5.14 Map of smoothed gravity data and profiles of the contribution from the Moho for a density contrast of 300 kg/m3and a mantle component using a value of B = -2.4. 246 Figure 5.15 Map and profile comparing measured gravity (blue) and calculated gravity (black) from the combined Moho (red) and mantle (pink) components shown in Figure 5.14. 247 The general match of shape is surprisingly good, considering that there is no contribution from the crust other than the density contrast at the Moho. It is likely that the Bushveld Complex region and the Limpopo belt have significantly higher mean crustal densities than average cratonic crust. In the case of the Bushveld, the intrusion has a significantly higher density; however, the profile selected only grazes the edge of the Bushveld Complex, so the effect is probably subdued. However, the profile crosses directly over the Limpopo Belt, which is likely to have a significantly higher mean density ? on surface it is mapped as having been metamorphosed to granulite grade (Van Reenan et al., 1990). As this is a forward modeling exercise, the gravitational response for various density contrast models across the Moho have been determined. First models are constructed using density varying with thickness (Figure 5.16) and then models are constructed where the density variations occur with tectonic region (Figure 5.17). In this section these have been combined with a variety of B value calculations (Figure 5.12) to determine the closest match with the observed data. Only a selection of these combined models is presented in Figures 5.16 and 5.17. 248 Figure 5.16 Comparison of various gravity models using crustal models from Table 3.2 and which include the delay time tomography gravity contribution with a B value of -2.4. A) Density contrast from Zoback (see Table 3.2, Figure 3.34A). B) Density contrast from Fischer (see Table 3.2, Figure 3.34B). C) Moho density contrast from Table 3.2, model 4C. D) Moho density contrast from Table 3.2, model 5D. (Compare with Table 3.2 and Figures 3.33 and 3.34) 249 Figure 5.17 Comparison of various gravity models using crustal models from Table 3.3 and which include the delay time tomography gravity contribution with a variety of B values. A) Regional geology model 4, with B = +4.0 B) Regional geology model 4, with B = -4.0. C) Regional geology model 5, with B = -2.4. D) Regional geology density model 6, with B = -2.4. (Compare with Table 3.3 and Figures 3.35 and 3.36) In general, the regionalized geology models for density contrast at the Moho combined with mantle density values derived using a factor of B near -2.4 give the best fit 250 to the observed gravity data. I did not extend this exercise further in an effort to obtain an exact fit to the data along the profile as the goal here is to determine plausible gravitational responses from the Moho and mantle seismic velocity variations to determine if these contributions could be significant at the surface on a regional scale. The edge of the craton (to the south Figure 5.18) shows up as a distinctive high-low pair in the long wavelength gravity signal consistent with the edge of the high velocity zone in the tomography. In both Figures 5.16abcd and 5.17abcd, the steady thickening of the crust towards the northeast along the profile has a dominant effect, causing a strong decrease in the gravitational response. This is largely counteracted by the mantle response, except towards the northern part of the profile, where the mantle response is significantly subdued. Figure 5.17a shows the combined response for a temperature-dominated mantle ? nothing along the profile is matched and the gravitational response is out of phase with the measured response. This clearly indicates that composition is significantly more important than temperature in this region. 251 Figure 5.18 Best fitting forward model using thick model 3, and a mantle factor of B = -2.4 (see Figure 5.16 B). 252 253 One implication of this work is that the amount of eclogite in the mantle in southern Africa should be quite low, as the gravity data suggests that the mantle density of the keel is ~1% less than the surrounding mantle (Carlson et al., 2005). The observed variations in the amplitude of seismic velocity perturbations in the keel and crustal thickness generally correlate with the thinnest crust hosting the thickest, most well defined keel. This may have some influence on topography on a regional scale, especially as regions erode and the balance is changed through time. It may be possible to account for topographic ?swells? and basins on a regional scale from Moho topography or from mantle tomography, although there is insufficient coverage in this study to test this idea. The study here does show clearly, however, that an evaluation of the large scale gravity field must include contributions from at least the uppermost mantle and that measured crustal thicknesses are commonly poorly correlated with topography or with Bouguer anomaly. This study suggests that the relative gravity high calculated from large crustal thickness variations (regionally at least) needs to include a significant component of low- density mantle keel to counteract the thinner crust commonly found beneath older cratonic regions. More detailed geotherm data could aid in constraining temperatures and their spatial distribution. The high velocity (low density) keel beneath the Kaapvaal craton corresponds laterally to the surface expression of the Archean rocks, whereas lower velocity (higher density) mantle is located beneath regions of Proterozoic and Phanerozoic crust. This observation is entirely consistent with observations from mantle xenoliths. A majority of the mantle contribution to the surface gravity comes from the uppermost 150 km in the mantle model, the region most likely to be rheologically stiff and tightly coupled to the overlying crust. 6 Conclusions and Future Directions 6.1 Major conclusions of this study Since Jordan?s (1975) paper defining the continental tectosphere, there has been much speculation and investigation of these proposed keels attached to Archean cratons. While the existence of the keels is no longer disputed, as they are clearly imaged as high velocity structures beneath almost all Archaean cratons even on global tomographic images (Grand, 2002), the depth extent and density are not well constrained. On a broad scale this thesis has demonstrated that at least in the Kaapvaal Craton, the generally thinner crust of the Archean cratonic regions is underlain by low density, seismically fast mantle keels. These keels act to compensate for the thinner crust and make the Bouguer gravity signal appear to indicate that the region is in classic Airy isostatic equilibrium. Thus the observed gravity data place important constraints on the seismological results. The gravity data disallow the possibility that the observed seismically fast keel is cold and dense. The specific conclusions drawn here follow from the discussions presented in the individual chapters. Chapter 3 has shown that although the Kaapvaal Craton appears to be in isostatic equilibrium from plots of elevation vs. gravity, the seismically determined crustal thicknesses are significantly different than would be predicted from Airy-type isostatic balance for realistic density contrasts at the Moho. The pattern of crustal thickness variations is highly inconsistent with predictions based on current topography. The seismically-determined crustal thicknesses (Nguuri, 2004; Nguuri et al., 2001) can be summarized as: thin in the undisturbed Kaapvaal and Zimbabwe cratons (~32-41 km thick); thick in the surrounding mobile belt regions, including the Limpopo Belt (~45-50 254 km) and thick in the northern and northwestern Kaapvaal craton region, broadly associated with Bushveld magmatism (> 45 km thick). Classic Airy isostatic balance obtained by inverting the topography to determine depth to Moho simply doesn?t apply to the Kaapvaal Craton and appears to be a feature common to Archaean Cratons (Zoback and Mooney, 2003). I have developed a new, basic methodology for modeling the Earth?s gravity field on a spherical surface that does not rely on spherical harmonic methods or FFTs. This method is based on well-developed forward modeling methods previously published, such as those implemented by Lees and VanDecar (1991) and Tiberi et al. (2005). Although this method uses the simplifying assumption of substituting a sphere for ease of computation in place of the analytically unsolved spherical prism, future directions of this work would involve calculating numerical solutions for the gravity response of the spherical prism. For the purposes of this work, however, the equivalent sphere approximation is quite adequate, given that the gravitating sources are sufficiently distant from the surface of calculation for which this approximation is valid. I have shown, specifically, that at the deep crustal and mantle length scales involved in this study, the method produces results that are in good agreement with Parker?s (1972) FFT method. As computational power increases, this method can be revisited with an eye to incorporating more crustal detail over large regions using numerical methods. It could also be implemented in continent-ocean boundary region studies, extending for large sections of individual plates. The relatively weak Moho signals seen on teleseismic receiver function records in areas of thicker crust indicate that these regions may have a more diffuse Moho, and that this may be attributed to a smaller density contrast or to a gradational discontinuity at the Moho (Nguuri et al., 2001). Although a simple plot of Bouguer gravity vs. topography 255 generally suggests Airy-type isostasy, in which it is assumed that elevated surface topography is balanced by compensating crustal roots, in fact the surface topography in the study area bears little relationship to the seismically determined Moho topography. This lack of relationship between topography and crustal thickness has been observed in other Archean regions (Assump??o et al., 2002; Fischer, 2002; Zoback and Mooney, 2003). The Bushveld Complex region also lacks a clear relationship between topography and crustal thickness, but this is more likely due to the presence of a continuous, high density Bushveld Complex, which acts as a load in the crust (Webb et al., 2004). The Limpopo region appears to have higher than average crustal densities, as the underlying low density mantle keel is uninterrupted and appears continuous with the Zimbabwe cratonic keel, contributing to a long wavelength gravity low. The low elevations of the Limpopo region suggest thin crust based on isostatic balance, but the receiver functions and surface wave analysis (Nguuri, 2004) suggest thick crust. One mechanism that has been suggested to account for this in the Limpopo region and elsewhere is the increased density of the lowermost crustal root, resulting in decreased crustal buoyancy (Fischer, 2002). This has the effect of increasing the average density in the region and may account for the apparent lack of isostatic rebound in the area. This proposal is consistent with the generally high metamorphic grade and the low elevations of the Limpopo Belt. Within the undisturbed craton around the Kimberley region, where the crust is thinner, Bouguer gravity values are low, indicating that a less dense or thicker, buoyant mantle keel may counteract the effect of the thinner crust. Thus, one important conclusion is that calculations of crustal thickness based on topography can lead to very incorrect crustal thickness estimates, which will in turn bias determinations of the density of mantle keels. Since the wavelengths of the resulting gravity signals due to crustal thickness variations and uppermost mantle density variations due to a low density keel are 256 very similar, it is difficult to separate and extract these signals from spectral analysis alone. As more crustal thickness determinations become available, it will be increasingly possible to distinguish regions where crustal isostatic balance is maintained at the Moho (Airy isostasy) from those where topography does not correlate with crustal thickness. The gravity model of the crustal thickness suggests that the region of the Bushveld Complex deserves more detailed scrutiny. This region has been examined in four published papers presented in the appendices and discussed in chapter 4. The first paper is a proof-of-concept paper presenting a gravity model, showing that the Bushveld Complex could be connected and that crustal flexure alone could account for isostatic equilibrium (Cawthorn et al., 1998a). The second paper presents a model constrained by geological mapping that predicts ~6 km of crustal flexure (Cawthorn and Webb, 2001). The third paper incorporates further constraints on crustal thickness as determined from receiver function measurements at Kaapvaal seismic stations (Webb et al., 2004). These results agree with the previously predicted ~6 km increase of crustal thickness. The fourth paper includes an extensive compilation of physical property data in a stratigraphic context that aid in determining density values that are appropriate for gravity modeling (Ashwal et al., 2005). This systematic study of the Bushveld Complex region demonstrates that a connected limb structure satisfies all of the available data. Obvious expansions of this work include the collection of seismic reflection data and other studies aimed at imaging the mafic layer in the crust. Unconstrained gravity models can always be made to fit the data, but a large part of the value of gravity modeling is investigating the effects of different sources as inferred from other kinds of studies. This is especially true where I have extended the gravity modeling into the upper mantle to include the gravity response due to the seismic velocity perturbations in the mantle keel. While the magnitude of the computed tomographic 257 velocity perturbations (which are smoothed and damped) is always going to be less than the actual velocity anomaly, this is accounted for by using larger B values than are suggested by mineral chemistry of xenolith samples, e.g. B = ?2.4 as opposed to ?4.0. The downward smearing of the tomographic perturbations has also affected the gravity calculation. While there is little that can be done about this, the effect will be small and will act to lower the amplitudes and increase the wavelengths of the gravity anomalies compared to what they should be. In short, the contributions to the gravity signal from the deepest (smeared) perturbations are small, and thus the effect on the gravity signal of the downward smearing appears to be minimal. The resulting combination of gravity signals from crustal thickness variations and mantle seismic perturbations obviously will not produce a match to the short-period observed gravity data, mainly because lateral density variations in the crust are unknown and therefore are not modeled. Most of the more important long-wavelength features, however, can be accounted for by a combination of laterally varying crustal thickness and changing upper mantle density structure. Thus, while the combined crustal thickness and tomography perturbation gravity model does not perfectly fit the observed data, they reproduce several prominent features and suggest regions in the crust that should be more closely examined for major lateral density changes. In the gravity analysis I have focused largely on a profile that extends SW-NE from Cape Town, South Africa, to beyond Masvingo in Zimbabwe. The profile has been extracted from the full 3D model to minimize edge effects. If we consider that profile, starting at Cape Town and moving NE, the first prominent long-wavelength feature seen is the steep rise in gravity values at the coast due to crustal thinning at the continental margin. The observed increase in gravity at the coast is also seen in the computed gravity model, in spite of the fact that the B value is assumed constant and negative in the 258 modeling, optimized to match cratonic seismic velocities to density (where density decreases as velocity increases). In reality the B value is almost certainly spatially variable, and would be less negative or even slightly positive closer to the continental margin. Thus, thermal effects of increasing temperature towards the oceanic lithosphere would make both mantle velocity and density lower (positive B). But the thinner crust makes gravity higher as high density mantle is closer to surface. If the mantle is slightly hotter, it will have a lower density, but since this is a relatively old plate boundary (180 Ma) this is unlikely to be a significant effect. This demonstrates vividly the effect that thinner crust will have on gravity as an isolated effect. Further NE along the profile, one of the more significant shorter-wavelength features is the ?hump? in the gravity signal across the boundary between the NNMB and the Kaapvaal Craton. This gravity feature can be modeled by taking into account the tradeoff between the dramatically thinner crust on the craton side and the compensating effect of the thick mantle keel with ~1% lower density, although the model is not very sensitive to the exact thickness. In general, the thinner crustal regions on the craton, such as around Kimberley, exhibit low Bouguer gravity anomalies that are the product largely of the thick low density mantle keels that underlie the craton. These seismically fast keels beneath the cratons are likely to be 1% less dense than primitive mantle at the same depth and temperature (James et al., 2004). It is this lower density that contributes to the gravity signature observed at surface and compensates for the thinner crust. This result, which comes from the gravity modeling, is also supported by comparison with actual mantle xenoliths (James et al., 2004). Continuing along the profile to the NE, observed gravity values remain low throughout much of the Kaapvaal Craton, and these lows are also reproduced in the modeled results. The model did not reproduce the small rise in gravity values observed in the central portion of the profile, but this feature probably has its source in the crust. 259 Where the profile crosses the Colesburg lineament, there is a small inflection, which is not reproduced in the model and may be due to crustal differences on either side. The Colesburg lineament remains enigmatic; age data and structural alignments strongly suggest that these are two distinct blocks, the Kimberley block to the west and the Witwatersrand block to the east (de Wit et al., 1992) However, the vibroseis reflection seismic line that crosses the Colesburg shows no clear indication of a major crustal break (de Wit and Tinker, 2003). Continuing to the northeast of the Colesburg lineament along the profile, the value of the observed gravity increases in the Bushveld Complex region. The longer wavelengths of this increase are reproduced in the modeled profile. In the model this is due to the slightly higher density of the mantle contribution from the lower seismic velocities beneath the Bushveld Complex. These changes in the seismic velocity are most likely due to metasomatism either at the time of emplacement of the Bushveld Complex, or at a later stage, such as during the Karoo event (Fouch et al., 2004). In the Limpopo region, the model doesn?t match the data. This model has thick crust (up to 50 km thick) in this region and a thick low density mantle keel. Although the crustal thicknesses used in this study (Nguuri, 2004) were determined from both crustal receiver functions and surface wave velocities, they were poorly resolved. Thus the Limpopo belt could have thinner crust, as other workers have suggested based on xenolith data from the Venetia kimberlite (Barton and Pretorius, 1998). An alternative explanation is that the entire crust in this region is thick, but substantially denser than the surrounding cratonic crust. This is consistent with the observation that the central zone of the Limpopo Belt is at granulite facies metamorphic grade (Van Reenan et al., 1990) and that the elevation is substantially lower in the Limpopo Belt (Fischer, 2002). Finally the gravity in the Zimbabwe Craton is significantly lower than what is modeled. This could be due to either significantly lower crustal densities than in the Kaapvaal craton, or more likely, due 260 to edge effects in the seismic tomography inversion leading to a poorly resolved mantle keel (Fouch and James, pers. com., 2005). Thus a substantial portion of the long wavelength gravity signal of the gravity profile from Cape Town, South Africa to Masvingo, Zimbabwe, can be accounted for by variations in crustal thickness and the counterbalancing effect of density variations due to changes in composition in the mantle keel beneath the craton. These effects are of very similar wavelength and would be difficult to separate independently based on wavelength alone. As in many other cratonic regions, the observed crustal thicknesses are poorly correlated with elevation, implying that classic Airy isostatic balance is not maintained at the Moho and attempts to determine crustal thickness from elevation will be unsuccessful. 6.2 Discussion and Directions for Future Research The methodology for computing combined crustal and mantle contributions to the gravity field that was developed in Chapters 3 and 5 and applied to the region of the Kaapvaal array can be expanded to other regions where crustal thicknesses are determined. The method may be particularly useful for identifying regions in the Earth?s crust that justify scrutiny for further investigation. To refine the method so that shallow shorter wavelength features can be better resolved, the next obvious step is to include numerical methods in the calculation of the gravity response of the spherical prisms. The first step is to determine how many terms of the expansions would be necessary to obtain accurate results. The method could then be used with confidence in modeling the crustal contributions to the surface in a spherical geometry over a large area. Numerical methods were not employed in this work, due partly to the obvious limitations of computational power, but more to the fact that the scale of the experiment and the features being 261 modeled did not require high resolution numerical modeling. Near-surface contributions, for example, would need to be accounted for with an increasingly finer grid, for which supporting crustal information is not available at present. However, for more detailed studies in which higher resolution seismic data are available, the method has the definite advantage that it would allow for the computation of fairly small-scale structures in a spherical geometry without the complications and limitations of using spherical harmonics. The isostatic balance across the region has been evaluated, and in Chapter 3 it was noted that station 58, which is close to Mozambique, but off of the escarpment, appears to be isostatically balanced (i.e. it falls on the trend in Figure 3.17), whereas station 54 (at the foot of the escarpment) falls well off the isostatic trend. The crustal thickness of SA58 is 45 km, whereas for SA54 is 38 km. Station 58 sits on the edge of the Kaapvaal Craton, close to the Lebombo monocline and the large amplitude gravity anomaly stretching into Mozambique. This gravity anomaly has traditionally been assigned to the breakup of Gondwana and the thinning of the Mozambique crust. The gravity anomaly is closely associated with the terminus of a number of large dyke swarms. It will be important to determine crustal thickness values in Mozambique to determine if there is extensive underplating in the region or thinning due to breakup. Station SA58 appears to be in isostatic balance, so if the crust is thick here due to underplating, the underlying mantle could be hotter and less dense than cratonic mantle and the mantle densties in this region more dominated by temperature effects than composition effects. Underplating is also consistent with the low values of topography in the region: if the crust is underplated, and therefore dense, it will not rebound further in response to erosion. A study of the detailed response of these stations and further work extending into Mozambique may 262 reveal important clues to the details of the Gondwana breakup and the extent of the Kaapvaal craton keel to the east. The gravity signal can be thought of as having two components, dynamic and static. Here I have only considered static contributions due to seismically determined thickness variations occurring at the Moho and mapping seismic velocity perturbations to density variations. The fact that the topography is elevated over a significant (i.e. ~5,000 x ~5000 km) (Nyblade and Robinson, 1994) region suggests that the dynamic effects causing southern Africa to be high are of much longer wavelength than this study addresses. In this study, the effect can be treated as a broader regional signal, essentially producing a DC shift in the gravity signal in the limited region of the SASE seismic stations. However, the effect of dynamic influences cannot be ignored in terms of the larger picture of African plate dynamics and is another obvious area for future investigations. Unfortunately, the isopycnic hypothesis cannot be fully evaluated in this study as the tomographic and crustal thickness data do not continue off shore. Recent studies of the Bushveld Complex have generated an enormous amount of data that have not been fully analyzed. The large database of physical properties used to aid in the determination of density used in the development of the gravity models, has not been fully examined. Work has commenced on the wavelet and spectral analysis of both the susceptibility and density data of the Bellevue core data (Webb et al., 2007). Additional density and susceptibility data are available for the Moordkopjie borehole located ~10 km east of the Bellevue hole. These data add a further ~1700 m to the density and susceptibility data from borehole logging instruments. Unfortunately there is a gap of up to 400 m in the stratigraphic context between the Bellevue and the Mordkopjie borehole (Knoper and von Gruenewaldt, 1996). 263 The model of a connected Bushveld Complex as proposed in this thesis, should be tested using seismic techniques. Ideally, a vibroseis survey should be run, although a broadband seismic experiment with a very dense array could also address this question effectively. From these data a seismically-constrained 3D gravity and magnetic model of the entire Bushveld Complex could be developed, which could be used to assess the economic potential of the central region. In another study by Letts (2007), palaeomagnetic data have been reconciled with the age data and a consistent palaeopole for the Bushveld Complex has been determined. This work identified several reversals in the Earth?s magnetic field that are recorded in the Bushveld Complex that should be examined in more detail. In a real sense, geophysical investigations of the Bushveld Complex are still in their infancy. The large-scale results of examining the gravity response due to variations at the Moho and changes in mantle density due to velocity perturbations can assist greatly in examining the long wavelength gravity field for anomalous regions in general. Such regions, similar perhaps to the Bushveld Complex, could easily be hidden from view under surficial cover and by the guise of apparent isostatic compensation. Bearing the economic importance of the Bushveld Complex in mind, it may be considered worthwhile to examine the gravity field at Bushveld scales as more definitive crustal thickness and upper mantle tomography results become available. This thesis has shown that a mantle keel approximatly 1% less dense than the surrounding less depleted mantle results in a gravity model consistent with the observed data. The anomalous ?blue blob? located at ~300 km depth beneath the NNMB along the B-B? profile is more likely to be low-density depleted mantle material rather than cold, dense mantle material related to subduction, based on preliminary gravity modeling. While we may speculate that this is evidence of keel disruption, the feature requires considerably more investigation before anything definitive can be said. 264 The discrepancies between the gravity model of the Moho and mantle compared with the data, clearly show two very anomalous areas: the Bushveld Complex and the Limpopo Belt. Due to the shorter wavelength of these anomalies, the source of the discrepancy between the modeled and calculated gravity most likely resides in the crust. The crustal contribution of the Bushveld Complex has been modeled in Chapter 4 and incorporating a crustal component in the Limpopo would go a long way towards accounting for the discrepancy in the gravity signal in this region. The simplest explanation for the discrepancy in the Limpopo region is an increase in the average density of the crust and its thick root, consistent with the arguments made by Fischer (2002). The discrepancy in the modeling of gravity in the Limpopo region appears to be due to higher-than-average crustal densities in the lowermost crust, perhaps due to eclogites or mafic granulites in the lowermost crust that were formed when the lower crust was at depths in excess of 75 km during the active phase of craton-to-craton collision (Fischer, 2002). This idea warrants further testing as it has important implications for plate tectonics at that time. In addition, the Limpopo Belt region appears to be eroding at a faster rate than the surrounding cratons, as is observed by the noticeably lower topography. Whether lowered elevation is due to reduced buoyancy because of higher density lower crust and consequential lack of rebound as Africa has been uplifted, or because of more fracturing and faulting that enhances erosion in the region is unresolved. A more detailed study of the uplift of the region and the changes in the river patterns would help to better understand this system. 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Lithospheric buoyancy and continental intraplate stresses. Int. Geol. Rev., 45: 95-118. 8 Appendices Appendix A This appendix presents Ashwal, Webb and Knoper (2005) in its published format. Consequently, the formatting, layout, figure numbering and table titles do not follow the rest of the thesis. My contribution to this paper has been significant; I initiated the physical property data collection, contributed substantially to the collection of the density and susceptibility data and supervised the acquisition and compilation of all the density and susceptibility measurements. In addition I made several of the diagrams and contributed a significant portion of the text. 292 Introduction: Bushveld Facts and Figures There is a vast literature on the Bushveld Complex (see review papers by von Gruenewaldt et al., 1985; Eales and Cawthorn, 1996), and with very good reason. It is widely recognised as the world?s largest mafic layered intrusion, and is the world?s largest repository of Magmatic stratigraphy in the Bushveld Northern Lobe: continuous geophysical and mineralogical data from the 2950 m Bellevue drillcore Lewis D. Ashwal School of Geosciences, University of the Witwatersrand, Private Bag 3, WITS, 2050, RSA. e-mail: ashwall@geosciences.wits.ac.za Susan J. Webb School of Geosciences, University of the Witwatersrand, Private Bag 3, WITS, 2050, RSA. e-mail: webbs@geosciences.wits.ac.za Michael W. Knoper Department of Geology, University of Johannesburg, P.O. Box 524, Auckland Park, 2006, RSA. e-mail: knoper@gmail.com 2005 Geological Society of South Africa ABSTRACT We present a large database of geophysical, petrological and mineralogical measurements for the ~3000 m Bellevue borehole through the entire Upper Zone (UZ) and about half of the Main Zone (MZ) of the Northern Lobe of the Bushveld Complex, South Africa. Magnetic susceptibilty readings were taken every 2 cm (n = 109,360) and densities were measured on average every 1.7 m (n = 2252). Petrographic data and microprobe analyses (n = 14,160) were obtained for plagioclase, mafic silicates, Fe-Ti oxides, amphibole and biotite in 502 samples throughout the entire sequence of layered mafic cumulates. The Bellevue UZ, as marked by the first appearance of cumulus magnetite, is ~1190 m thick (corrected for mean dip of 17.5?), which is less than UZ thicknesses in the Eastern and Western Lobes. A prominent 4 m thick pyroxenite horizon occurs ~390 m below the UZ-MZ boundary, but we show on the basis of mineralogy that this horizon cannot be correlated with the well known Pyroxenite Marker (PM) of the Eastern and Western Bushveld Complex. If the PM is indeed absent in the Northern Lobe, then a substantial portion, perhaps 500 m of the uppermost MZ may be missing; possible causes include non-deposition (e.g. due to syn-magmatic upwarping or diapirism) or removal (e.g. due to emplacement of UZ magmas). The Bellevue drillcore penetrated only about half of the MZ (total dip-corrected thickness ~1270 m), and the lowermost ~200 m contains unusual olivine-bearing (or troctolitic) horizons that are atypical of MZ rocks elsewhere in the Bushveld Complex. These troctolites have mineral compositions as primitive as those of the upper Critical Zone (CZ), suggesting that they might represent a sliver of CZ rocks dismembered by intrusion of MZ magmas. Alternatively, they may represent an intrusive sill of syn- or post-Bushveld age, or merely a mineralogically unusual horizon in otherwise typical MZ lithologies. Mineral compositions show broad normal fractionation upwards, with plagioclase An7821, opx (and inverted pigeonite) En 8026, cpx Mg 8627, olivine Fo 7874 (in the lowermost troctolitic horizon) and Fo 5906 (in the UZ olivine ferrodiorites). There are, however, numerous prominent reversals and discontinuities in mineral compositions, some of which are likely related to magma additions. The extensive dataset of mineral compositions allows the estimation of a new fractionation trend for the Bushveld Complex. On an En-An diagram, the Bushveld trend is shifted toward more An-rich plagioclase at equivalent Mg# of coexisting pyroxenes relative to those for Kiglapait or Skaergaard. This is attributed to the relative paucity in Bushveld of augite, which has a high fractionating power for Ca/Na in evolving liquids. Magnetic susceptibility data clearly reveal the presence of the UZ-MZ boundary. MZ cumulates have susceptibilty values <0.05 SI units, and generally <0.02 SI units. Above the UZ-MZ boundary, susceptibilty varies enormously, from anorthosites (<0.1 SI units) to magnetitites (to almost 5 SI units), and there is excellent correlation between susceptibility and lithology, in many cases to a resolution of <5 to 10 cm. Anorthositic rocks, especially in the MZ, commonly show higher susceptibilty than surrounding polyphase cumulates, due to intercumulus and/or dust-like inclusions of magnetite. Density data reveal surprising cyclicity in the Main Zone on the scale of 50 to 200 m, with progressively increasing density upwards in individual layered units, reflecting gradual increase in modal colour index from 0 to 10% to 50 to 60%. In some cases the upward density increases are correlated with broad reversals in chemical fractionation trends (e.g. upward increases in Mg# of pyroxenes), arguing against simple fractionation. We suggest that such layers may represent blending zones in which dense liquids and/or crystals from new magma additions drain downwards into the existing cumulate pile. MZ cumulates, therefore, may have been constructed by successive, compositionally different magmatic influxes, implying the existence of a sub-Bushveld magmatic staging chamber. LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY, 2005, VOLUME 108 PAGE 199-232 199 magmatic ore deposits (e.g. Lee, 1996). Known exposures of the Bushveld Complex (Figure 1) are typically divided into 4 to 5 ?Limbs? or ?Lobes?; these have been interpreted as discrete magmatic bodies (Cousins, 1959; Meyer and De Beer, 1987), but recent re-interpretation of the regional gravity signature, taking into account crustal flexure, allows the possibility that at least the Eastern and Western Limbs might be continuous at depth (Cawthorn et al., 1998; Cawthorn and Webb, 2001: Webb et al., 2004). The total areal extent of Bushveld rocks has been estimated at about 65,000 km2, and with an average thickness of 6 km for the layered mafic cumulate rocks, the Bushveld Complex must have formed from a volume of basaltic magma of nearly 400,000 km3, and perhaps as much as 1,000,000 km3 if large volumes of volcanic rocks (now eroded) escaped to the surface as theorized by Cawthorn and Walraven (1998). In either case, this is comparable in size to many of the world?s so-called Large Igneous Provinces (e.g. Mahoney and Coffin, 1997). The Bushveld Complex was intruded into Palaeoproterozoic (~2.5 to 2.06 Ga) supracrustal rocks of the Transvaal Supergroup, which include quartzite, dolomite, banded ironstone, basalt and rhyolite. Emplacement of the mafic cumulate rocks, referred to as the Rustenburg Layered Suite, must have taken place after 2060 ? 2 Ma, the age of granophyric sills intruded into Rooiberg Group rhyolites (uppermost Transvaal Supergroup, Walraven, 1997), and before 2054 ? 2 Ma, the age of crosscutting granitoids (Lebowa Suite, Walraven and Hattingh, 1993). The most precisely constrained age for Bushveld emplacement comes from U-Pb isotopic analyses of titanite in a retrogressed calc- silicate xenolith (Buick et al., 2001). This age of 2058.9 ? 0.8 Ma is interpreted as the time of hydrothermal circulation associated with the late magmatic crystallization and cooling of the layered mafic rocks. Thermal modeling indicates that crystallization of the entire Bushveld Complex, including the numerous successive injections of magma, took place in about 200,000 years (Cawthorn and Walraven, 1998). The Rustenburg Layered Suite has been divided into five stratigraphic zones, mainly based on data from the Eastern and Western Lobes (SACS, 1980; Eales and Cawthorn, 1996), although the criteria for distinguishing these are not universally agreed upon (e.g. Kruger, Figure 1. Geological map of the Bushveld Complex showing the locations of the various Lobes, the position of the Bellevue (BV-1) borehole and the region of the detailed map of the Northern Lobe given in Figure 2. SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE200 SOUTH AFRICAN JOURNAL OF GEOLOGY LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER Figure 2. Geological map of the Northern Lobe of the Bushveld Complex, modified from van der Merwe (1978). The position of the Bellevue (BV-1) and Moordkopje (MO-1) boreholes are indicated. 1990). The Marginal Zone (up to 800 m thick), at the base of the Complex, consists of medium-grained, heterogeneous but generally unlayered noritic rocks, interpreted as composite sills or cumulates rather than chilled parental magmas (Cawthorn et al., 1981). The Lower Zone (800 ? 1700 m thick) consists dominantly of ultramafic cumulates including orthopyroxenite, dunite and harzburgite in cyclic units ranging from cm to tens of m in thickness (e.g. Cameron, 1978). The base of the overlying Critical Zone (CZ) is taken by most workers as the horizon at which there is a distinct increase in post- cumulus plagioclase in orthopyroxenite; the first chromitite layers appear about 25 m above this horizon (Cameron, 1980). The Critical Zone is further divided into a pyroxenitic lower CZ (500 to 800 m thick) and a noritic to anorthositic upper CZ (520 to 1000 m thick). The lower CZ contains some of the world?s largest chromite deposits, and the upper CZ is host to two of the world?s largest PGE ore deposits- the UG2 chromitite and the Merensky Reef. The base of the overlying Main Zone (MZ, 2200 to 3100 m thick) is generally taken as the top of the Giant Mottled Anorthosite, which occurs about 45 to 90 m above the Merensky Reef. The Main Zone represents a sequence of relatively homogeneous norite, gabbro, gabbronorite and anorthosite, generally lacking olivine or chromite (Mitchell, 1990). The base of the Upper Zone (UZ, 2000 ? 3000 m thick) is generally taken at the appearance of cumulus magnetite (e.g. Eales and Cawthorn, 1996), but some workers prefer the MZ- UZ boundary to be represented by the Pyroxenite Marker horizon, some 600 to 700 m below this, where significant changes in petrologic and isotopic signatures have been recognized (e.g. Kruger, 1990; Kruger et al., 1987). Upper Zone rocks are prominently layered, with varying amounts of cumulus plagioclase, magnetite, olivine and pyroxene. Cumulus apatite appears high in the sequence, and the uppermost fractionated rocks are fayalite and/or hornblende-bearing ferrodiorites, some of which contain intercumulus quartz and/or K-feldspar (e.g. Molyneux, 1974). The Northern (Potgietersrus or Mokopane) Lobe The Northern (or Potgietersrus, or Mokopane) Lobe of the Bushveld Complex is exposed over a strike length of about 110 km, from about 30 km southwest of the town of Mokopane (formerly Potgietersrus), to about 25 km north of Gilead (Figure 2). The total areal extent of layered mafic cumulate rocks in the Northern Lobe was estimated at 7275 km2 by van der Merwe (1978). Most workers also include as part of the Northern Lobe a ~320 km2 exposure of layered mafic rocks north of Villa Nora (Figure 1). South of Mokopane, the layered rocks strike northeast and dip 15 to 27? west. To the north, the strikes change to northwest and eventually to due north, with westward dips of 10 to 45?. Van der Merwe (1976) reports gradual decreases of dips from the bottom upward in the layered sequence. In the Villa Nora area, mafic cumulate rocks strike dominantly east-west and dip gently southward. An important feature of the Northern Lobe is the transgressive nature of the mafic cumulate sequence across successively older basement rocks toward the north, a point recognized by Hall (1932). South of Mokopane, the basal rocks of the Bushveld Complex abut against quartzites of the Magaliesburg Formation, near the top of the Transvaal Supergroup. Northward from Mokopane, the Bushveld rocks rest upon successively older strata of the Pretoria Group, followed by the banded iron formations and dolomites of the Chuniespoort Group, and eventually onto Archaean granitic basement rocks (van der Merwe, 1976; Cawthorn et al., 1985). Additionally, the stratigraphy of the Complex itself is apparently transgressive with respect to the bottom contact. South of Mokopane, ultramafic rocks of the Lower Zone abut against Transvaal basement, whereas to the north, the basal Bushveld rocks constitute those higher in the stratigraphic sequence, principally Main Zone lithologies. Only about 400 m of Critical Zone rocks (norite, pyroxenite, anorthosite and chromitite) is present south of Mokopane, and the entire Critical Zone is thought to wedge out to the north (van der Merwe, 1976). The Platreef, the major mineralized horizon in the Northern Lobe, occurs along about 30 km of strike length at the contact between the layered mafic rocks and either granitic or metasedimentary basement rocks (Lee, 1996). This horizon bears some similarities to the Merensky Reef, but the mineralized zone is much thicker (Gain and Mostert, 1982). The Bellevue (BV-1) Drillcore Despite the wealth of data on rocks, minerals and ores of the Bushveld Complex, most information comes from the Eastern Lobe, where surface exposures are good, and the Western Lobe, where there is widespread mining activity. In addition, there have been extensive studies of the relatively thin mineralized horizons, such as the Merensky Reef, UG-series chromitite layers and UZ magnetitites, but comparatively lesser work has been carried out on the vast majority of intervening Bushveld lithologies. In this study we report an extensive dataset of near-continuous geophysical and petrological information, for a ~2950 m drillcore in the Northern Lobe of the Bushveld Complex. The deep stratigraphic borehole on the farm Bellevue (Figures 1 and 2, Latitude = 23?55?34.669? south; Longitude = 28?45?20.327? east; Elevation ~980 m) was motivated in the late 1980s by Professor G. von Gruenewaldt, then of the Institute for Geological Research on the Bushveld Complex at the University of Pretoria. Drilling to a depth of 2949.5 m was carried out over a period of 10 months, and completed in late 1991. The BV-1 borehole is collared in Bushveld roof granites (80 m), and penetrates through the entire Upper Zone (1492 m vertical depth) and about half of the Main Zone (1374 m). A detailed core log was prepared by Knoper and von Gruenewaldt (1996), which is available on-line. The entirety of the BV-1 drillcore, less those LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY 201 portions sampled (at least 1/4 core has been retained throughout), is housed and curated at the Council for Geoscience National Core Library in Donkerhoek, near Pretoria. The drillcore is generally in very good condition, with few intervals of missing or broken core (Figure 3). The Bellevue (BV-1) deep stratigraphic borehole represents an ideal target for detailed measurements of geophysical, petrological and mineralogical properties, which can be made in stratigraphic context for nearly 3000 m of Bushveld magmatic rocks. Recognizing the paucity of geophysical measurements for Bushveld rocks, especially in stratigraphic context, we recovered all extant magnetic susceptibilty data for the BV-1 borehole (acquired in 1991 by the Council for Geoscience), and supplemented this with additional detailed measurements of density and magnetic susceptibility (MS). The results are relevant to establishing an improved understanding of magmatic processes in layered mafic intrusions, as well as to regional and local geophysical modeling. We also carried out petrographic studies and determination of mineral compositions in closely spaced samples throughout the drillcore. We report here the large database of geophysical and mineralogical information, which is essentially complete; other measurements are still in progress (e.g. bulk-rock geochemistry, radiogenic and stable isotopes). Results from the Bellevue drillcore may represent the most comprehensive set of measurements, in stratigraphic context, for any layered intrusion. Borehole Stratigraphy and Lithologies A lithological log of the Bellevue drillcore, based on the data of Knoper and von Gruenewaldt (1996) is presented in Figure 4. The uppermost 83.55 m of the Bellevue drillcore is composed of granitic roof rocks, which are very likely part of the suite of intrusive granitoids that immediately post-dates the emplacement of the Bushveld Complex. In addition to the roof rocks, granitoids occur sporadically throughout the drillcore, and occur as veins as thin as 2 cm, to sills or intrusive bodies up to 56 m thick. Granitoids constitute just over 10 % of the total drillcore lithologies. Also intrusive into the Bushveld cumulate rocks, near the top of the sequence is a prominent dolerite sill or dyke 72.17 m thick (depth = 161.97 m) with distinctive chilled margins on both the top and bottom contacts. A thinner (5.46 m thick) dolerite is present about 28 m below this (depth = 262.3 m). Van der Merwe (1978) mapped a significant body of ?diabase? for a distance of about 75 km, sub- parallel to the upper contact of the Bushveld rocks; the dolerites present in the upper part of the Bellevue drillcore could be equivalent to these rocks. Van der Merwe (1978) considered these doleritic rocks to be of Waterberg age (ca. 1.6 to 1.9 Ga), although no geochronology has yet been carried out. Dolerites constitute about 2.5 % of Bellevue rocks. Xenoliths of metasedimentary rocks, presumably derived from the underlying Transvaal Supergroup are present sporadically throughout the Bellevue drillcore, representing about 2 % of Bellevue rocks. Most prominent are a 24.6 m thick, distinctly cross-bedded feldspathic quartzite (depth = 116.5 m) and a 3.4 m thick calc-silicate xenolith with abundant coarse-grained sulfides (depth = 272.21 m). The Bushveld Complex Upper Zone in the Bellevue drillcore is ~1188 m thick (corrected for mean dip of 17.5?). The uppermost rocks are magnetite-rich olivine ferrodiorites, representing the most fractionated of Bushveld lithologies. Most abundant are magnetite gabbro (41.1 %) and olivine ferrodiorite (21.4 %), with lesser gabbro/norite, plagioclase-magnetite cumulates, magnetitite and pyroxenite. The Upper Zone in the Bellevue core contains 32 discrete layers of magnetitite or magnetite-enriched rock (>20% opaque minerals), ranging in thickness between 7 cm and 13 m; these were correlated with the 20 magnetitite layers identified in the Northern Lobe by van der Merwe (1978) based on field studies. Most prominent are the uppermost massive magnetite layer, which is 13 m thick (depth = 590.75), and a 10.6 m layer with variable magnetite content (20-50%) whose base (depth = 1523.45) is about 42 m above the UZ-MZ boundary. It is worthwhile noting that the V2O3 content (discussed below) of the lowermost magnetitites in the Bellevue drillcore is comparable or exceeds that currently being mined in the eastern Bushveld Complex. Upper Zone anorthosite (>90% plagioclase) horizons range in thickness between 5 cm and 29 m (average = 4.0 m). Anorthositic rocks are especially abundant in a 110 m thick zone at depth = 1170 to 1180 m, about 400 m above the UZ-MZ boundary. The UZ-MZ boundary is readily apparent as a distinct change in magnetite content at depth = 1575.8 m. Over 1370 m of Main Zone rocks are present. Based on surface geology, we estimate that drilling penetrated SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE202 Figure 3. The upper third of the Bellevue drillcore as laid out at the Council for Geoscience National Core Library in Donkerhoek. Ashwal and Webb are shown making detailed magnetic susceptibilty measurements. Note the good condition of the drillcore. LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY 203 Figure 4. Lithological log of the Bellevue borehole, adapted from the data of Knoper and von Gruenewaldt (1996). The colour key to lithologies is used in this and subsequent figures. only about half of the MZ (total dip-corrected thickness = 1269 m). The most abundant lithologies are gabbronoritic rocks (59.9%, including gabbros and norites), with lesser anorthosite (15.5%), leucogabbro/ leuconorite (9.7%) and an assortment of other mafic cumulates. There are two pyroxene-rich (up to 80 to 90 % total pyroxenes) horizons at depth = 1971.8 m (1.88 m thick) and at depth = 2806.8 m (2.3 m thick). The upper pyroxene-rich horizon occurs at an appropriate stratigraphic level to be considered as a candidate for the Pyroxenite Marker unit of the Eastern and Western Lobes (e.g. Cawthorn et al., 1991), although evidence is presented below that this is not the case. Anorthositic layers in the Main Zone range between 10 cm and 31.6 m thick (average = 3.75 m). The bottom 204.4 m of the Bellevue drillcore constitutes part of a distinctive and unusual olivine-bearing or troctolitic horizon that was mapped for about 35 km of strike length in the Northern Lobe by van der Merwe (1978); this troctolitic unit, along with other rocks of the Main Zone, appears to be transgressed by Upper Zone lithologies in the region between latitudes 23?50? south and 23?40? south (Figure 2). Olivine does not occur in MZ rocks of the Eastern and Western Lobes (Eales and Cawthorn, 1996). Data Collection All data for this paper can be found as supplemental data on the GeoScience World website at the following address: http://sajg.geoscienceworld.org. The data is stored in a number of files, as follows: Table 1. Sample Log and Summary of Mineral Compositions Table 2. Visually Estimated Modal Abundances Table 3. Microprobe Data - Plagioclase Table 4. Microprobe Data - Low-Ca Pyroxene Table 5. Microprobe Data - Clinopyroxene Table 6. Microprobe Data - Olivine Table 7. Microprobe Data - Magnetite Table 8. Microprobe Data - Ilmenite Table 9. Microprobe Data - Biotite Table 10. Microprobe Data - Amphibole Table 11. Magnetic Susceptibility Data Table 12. Density Data Magnetic susceptibility Magnetic susceptibility (MS) data for the lowermost 1969 m of the BV-1 drillcore (depth = 980.2 to 2949.5 m) were acquired over a 12-month period in 1991 by Annabel Graham and Timothy Molea of the Council for Geoscience (CGS). Their measurements were made approximately every 2 cm, using a Fiskars Geoinstruments TH-15 susceptibility meter; readings were recorded by hand into 14 notebooks, and subsequently the data were entered into digital files. These data, a total of 70,696 individual measurements, were kindly provided to us by the CGS, and we compiled them into a single database. Recognizing the value of these results, and the valiant efforts of two dedicated individuals, we completed the magnetic susceptibility measurements for the uppermost 980 m of the BV-1 drillcore, during an 8-month period (August, 2000 to April, 2001). We were fortunately provided access to the same TH-15 instrument by CGS staff, although readings were digitally recorded in a PC rather than manually transcribed. Measurements were also made every 2 cm, and depths were carefully measured and recorded at least every 0.5 m. Depths were also recorded for intervals where measurements could not be made due to missing and extensively broken core; these appear as gaps up to 502 cm in the plotted data. Because the Bellevue drillcore has been extensively sampled since 1991, we applied a simple correction to magnetic susceptibility measurements for sampled intervals, based on the volume of drillcore remaining (at least 1/4 core is always retained; measurements before and after sampling confirm our correction factor). Three different core diameters are represented in the BV-1 borehole: diameter = 8 cm (depth = 0 to 136.8 m), diameter = 6.5 cm (depth = 136.8 to 600.9 m) and diameter = 5.5 cm (depth = 600.9 to 2949.5 m). SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE204 Figure 5. Magnetic susceptibility measurements for two intervals in the Bellevue drillcore. The plots compare data taken in 1991 by staff of the Council for Geoscience with results acquired in this study. The magnetic susceptibility measurements are remarkably similar; the principal source of uncertainties comes from depths determined from driller?s marks (maximum = 12 cm). The intervals shown here represent lithologies with both high and low magnetic susceptibility. LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY 205 Figure 6. Magnetic susceptibilty measurements for a 10 m interval of the Bellevue drillcore across the UZ-MZ boundary, comparing data taken in 1991 by staff of the Council for Geoscience with results acquired in 2001 by Wits University students. The results show the integrity of measurements made both before and after removal of variable volumes of core for sampling purposes. Unfortunately, we were unable to acquire magnetic susceptibility data for the uppermost 136.8 m of 8 cm diameter core, because in this interval the drillcore has been haphazardly sawn into pieces of widely differing sizes, presumably to facilitate storage in standard core trays; in any case, drillcore of this diameter is larger than the 7.5 cm diameter opening in the sensor of the TH-15 instrument. Magnetic susceptibility readings for the 464.1 m interval of 6.5 cm diameter core were reduced by 28.4 %, to account for the volume difference between 6.5 and 5.5 cm diameter core. Due to the lack of information about core size or volume standardization for the Fiskars TH-15 instrument, we calibrated the instrument by re-measurement of 16 core samples (5 to 6 cm long, representing a large range in susceptibility values) using a volume susceptibility meter at the Geological Survey of Norway, Trondheim. A linear relationship was found between the Fiskars instrument results and the volume susceptibility meter results. This result was confirmed by re-measurement of several core samples using the volume susceptibility meter at the Council for Geoscience, Pretoria. Based on this, all Fiskars results were multiplied by a factor of 11.8 to give the final volume magnetic susceptibility data. To check the reproducibility of magnetic susceptibility data collected in 1991, we re-measured three sections of drillcore, representing intervals of between 1 and 9 m. The results show a remarkable agreement, both in terms of magnitude of magnetic susceptibility and profile shape (Figures 5 and 6). Comparison of measurements made both before and after sampling (Figure 6) shows that the volume correction described above for intervals of partial core produces accurate results. The major error comes from depth measurements, which are linearly extrapolated between driller?s marks inscribed at 0.5 m intervals; we estimate the maximum error in recorded depths to be ? 12 cm, and typically is better than ? 5 cm. The final combined dataset includes about 110,000 magnetic susceptibility and depth measurements for 2812 m of drillcore. The magnetic susceptibilty data can be found in two MS-Excel files (11.9 and 1.0 MB) stored as Table 11 at the Journal Website. Density To complement this dataset, we have made 2252 (plus many replicates) density measurements for the BV-1 drillcore, at depth intervals of 1 to 1.5 m (average = 1.7 m), using core lengths of 8 to 25 cm (average = 13.3 cm). Measurements were made with two electronic balances, using Archimedes Principle. Several samples were left to soak in water overnight to check for possible porosity; no significant difference in density measurements was observed. The precision of the density measurements was determined by 10 replicate measurements for each of 3 samples ranging in density between 2.73 and 4.55 g/cm3. The results, with 1 uncertainties, are as follows: anorthosite BV-1934.92 ( = 2.733 ? 0.0016 g/cm3), melagabbro BV-1657.93 ( = 3.154 ? 0.0010 g/cm3), magnetitite BV-849.53 ( = 4.556 ? 0.0031 g/cm3). Accordingly, we consider the maximum uncertainty of our density measurements to be ? 0.005 g/cm3. Petrography Samples for petrographic, chemical and microprobe analyses were taken at intervals at least every 10 m throughout the Bellevue drillcore. For horizons of particular interest, such as distinctive pyroxene- and olivine-rich units, continuous samples were taken. Polished thin sections were prepared for all samples (n = 479), and visually estimated modal abundances (given in Table 2) were determined for most of these (n = 430). Rock names were assigned using the IUGS classification schemes (Streckeisen, 1976). Mineral Chemistry Most of the electron microprobe data reported here are energy-dispersive analyses obtained at the Department of Geology, Rand Afrikaans University (now the University of Johannesburg), using a Cameca Camebax instrument to which an EXL2 energy dispersive system (EDS) has been added. Operating conditions for most analyses were as follows: acceleration potential = 15 kV, absorbed current = 10 na (measured on brass). Beam diameter was enlarged to 10 to 30 m for most analyses to avoid Na volatilization (in feldspars) and to re- integrate finely exsolved pyroxene compositions. For coarsely exsolved inverted pigeonites, the samples were moved under a broadened electron beam during analysis times, in attempts to re-integrate primary SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE206 Figure 7. Comparison of electron microprobe data for pyroxenes determined at RAU (energy-dispersive analyses) and at the Carnegie Institution of Washington (Geophysical Laboratory, wavelength-dispersive analyses). The results demonstrate the accuracy of the energy-dispersive analyses (which represent the bulk of our dataset), at least for the major element oxides. LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY 207 Figure 8. Visually estimated petrographic modes for 430 samples from the Bellevue drillcore, plotted against depth. SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE208 Figure 9. Summary diagram showing lithology, magnetic susceptibility, density and mineral composition data for the entire Bellevue drillcore. The positions of the Upper Zone ? Main Zone boundary (UZ-MZ) and the pyroxenite horizon are shown. Arguments are presented in the text that the pyroxenite horizon cannot be correlated with the well known Pyroxenite Marker interval in the Eastern and Western Lobes. Detailed data plots for 1000 m intervals are presented in Figure 10. LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY 209 magmatic pigeonite compositions. This was only partially successful, and generally, resulting pigeonite compositions are less calcic than the likely original magmatic compositions. A set of natural silicate standards was used, and element calculations were performed using a ZAF correction program. For a few samples, wavelength-dispersive (WDS) microprobe analyses were also obtained using a JEOL Superprobe housed at the Geophysical Laboratory, Carnegie Institution of Washington. These results confirm the precision of the energy-dispersive analyses (Tables 4 and 5; Figure 7). Another approach of re-integrating magmatic pigeonite compositions was attempted for a few samples by combining WDS spot analyses of host and lamellar phases in the proportions calculated digitally from SEM images of large, coarsely exsolved grains. This method yielded better results, but a WDS instrument with SEM capability was not available for most of the data collection period. A total of 14,160 individual spot analyses were obtained for 435 samples throughout the Bellevue drillcore, and include data for plagioclase (n = 4485), olivine (n = 920), low-Ca pyroxene (orthopyroxene and/or inverted pigeonite, n = 2831), clinopyroxene (n = 3102), amphibole (n = 524), biotite (n = 854), magnetite (n = 1166) and ilmenite (n = 278). For most samples, a minimum of ten spot analyses was obtained for each mineral phase, from several grains in each thin section. Aberrant analyses (e.g. resulting from alteration) were discarded, and a mean composition was computed for each mineral analysed in each sample. These mean compositions are given in a series of tables stored in files at the Journal website. (Tables 3 to 10). Results Data Presentation Estimated modal abundances of minerals in Bushveld Complex lithologies (Table 2) are plotted vs. depth in Figure 8. Physical property and mineral composition data are plotted vs. depth in a series of diagrams in Figures 9 and 10, along with a lithological log derived primarily from Knoper and von Gruenewaldt (1996). The colour scheme used to distinguish rock types is given in Figure 4. More detailed summary plots of the magnetic susceptibility, density and mineral composition (An content of plagioclase, Mg# of mafic silicates) are given in a series of diagrams representing depth intervals of 1000 m (Figure 10). Modal Abundances and Petrography Bushveld Complex lithologies in the Bellevue drillcore are dominantly composed of plagioclase and low-Ca pyroxene (orthopyroxene and/or inverted pigeonite), with lesser high-Ca pyroxene (augite). Colour index (volume % mafic silicates + Fe-Ti oxides) varies from 0 to 100, but averages 41 for UZ lithologies and 37 for MZ rocks (Table 2). The modal abundance of Fe-Ti oxides (magnetite and/or ilmenite) increases dramatically from <1 % at the UZ-MZ boundary and rises from a few percent to 15 % over an interval of about 3 m; above this interval Fe-Ti oxides constitute a major constituent of most UZ rocks. Oxide minerals (dominantly magnetite) are present in minute quantities in some MZ lithologies, particularly the anorthosites, where they form interstitial (intercumulus) phases of up to a few percent. A very few samples contain minor sulphides (Barnes et al., 2004). Mg-rich olivine (Mg# = 74.3 to 78.5, average = 76.8) occurs in the lowermost troctolitic horizon (minimum thickness = 204 m), is absent above depth = 2745.11 m, but reappears in UZ rocks at depth = 1002.50 m, as Fe-rich olivine (Mg# = 6.1 to 58.7). Accessory phases include biotite, amphibole, quartz, apatite and K-feldspar, which are especially abundant in intercumulus magmatic patches in UZ rocks. Secondary alteration of plagioclase to sericite or epidote, of pyroxenes to amphiboles and of olivine to serpentine + magnetite is variable throughout the drillcore, but most rocks are quite free of alteration effects. Low-Ca pyroxene in most Bellevue rocks is orthopyroxene, but inverted pigeonite is present, with or without coexisting orthopyroxene in a depth interval of ~1640 m thick (529.07 m to 2175.20 m). Inverted pigeonite is characterized either by coarse exsolution lamellae of augite parallel to the ?fossil? (001) crystallographic direction in (now) host orthopyroxene, but in many rocks such grains are accompanied or replaced by orthopyroxenes that contain irregular ?blobs? of variably coarse augite, presumably formed by coalescence of coarse augite exsolution lamellae during protracted cooling. In some samples, original inverted pigeonite has been reconstituted by external ?granule? exsolution or recrystallization into coexisting lower-Ca orthopyroxene and augite. This renders identification of original pigeonitic pyroxene difficult in some cases. Gabbroic and Anorthositic Rocks The vast majority of the rocks in the Bellevue drillcore are gabbroic (including gabbros, norites, gabbronorites) to leucogabbroic to anorthositic cumulates, with colour index ranging from 0 to ~60. The stratigraphic distribution of these lithologies on various scales is important to the understanding of the origin of magmatic layering in the Bushveld Complex, and in layered intrusions in general. In the Bellevue drillcore, there are relatively few examples where mineral distributions could be ascribed to gravitational crystal sorting, to produce, for example, a modally graded sequence from basal pyroxene-rich rocks upward to plagioclase-rich ones. One possible example occurs in the depth interval ~400 to 600 m, where basal pyroxene- and magnetite-rich cumulates seem to grade progressively upward, with decreasing colour index, into thin anorthositic horizons (Figure 10a). Far more common is cyclicity on the scale of 50 to 200 m, in which a gradual upward increase in colour index is correlated with upward increases in density (Ashwal et al., 2003, Figure 10c); these cycles are also associated SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE210 Figure 10. Lithology, magnetic susceptibility, density and mineral composition data for Bellevue drillcore intervals (a) 0 to 1000 m, (b) 1000 to 2000 m and (c) 2000 to 3000 m. Significant features are discussed in the text. Note the changes in scales between the three diagrams. LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY 211 Figure 10. continued SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE212 Figure 10. continued LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY 213 with reversals in chemical fractionation trends as discussed below. Most gabbroic rocks are characterized by tabular to blocky plagioclase crystals, commonly with weak alignment parallel to the larger scale layering or lamination present in Northern Lobe cumulate rocks. Far fewer gabbroic rocks have randomly oriented plagioclase crystals. Grain size of plagioclase tablets typically averages 5 to 6 mm, but there is a tendency for more leucocratic rocks to show larger grain size; some leucogabbroic to anorthositic rocks contain plagioclase crystals up to 2 cm across (e.g. BV-1102.19). In many cases, especially in the more leucocratic rocks, tabular plagioclase crystals form an interlocking network with dominantly straight to curved grain boundaries at ~120?. Patchy to irregular zoning is common; very few rocks show oscillatory zoning of plagioclase (e.g. BV-1028.04). Plagioclase in many samples contains fine, dust-like or randomly oriented needle-like inclusions (e.g. BV- 1960.56) of Fe-Ti oxides, imparting a dark colour to the rocks macroscopically. Calcic myrmekite (vermicular intergrowths of quartz + calcic plagioclase) is a very common constituent of Bellevue gabbroic rocks, constituting up to 5 modal % of some rocks, and generally occurs as subrounded to subangular to plumose aggregates, commonly at plagioclase grain boundaries, but also as patches within grains. Similar myrmekitic phases were documented in Bushveld rocks by von Gruenewaldt (1979). In some cases, calcic myrmekite is clearly associated with late-magmatic biotite, with which it is intergrown in a few samples. These myrmekites often appear texturally as replacement products of plagioclase, and Dymek and Schiffries (1987) proposed an origin by corrosive reaction between primary plagioclase and magmatically derived, high-temperature aqueous fluid. Pyroxenes in gabbroic rocks (orthopyroxene ? inverted pigeonite ? augite) occur as irregular grains and aggregates of grains, typically positioned between tabular plagioclase crystals. In many cases it is difficult to distinguish between cumulus and post- cumulus/interstitial pyroxenes, although some rocks contain large (several mm), euhedral, cumulus pyroxenes (e.g. BV-2675.50). Poikilitic texture is present in some rocks, with large oikocrysts of orthopyroxene (e.g. BV-1970.30) or inverted pigeonite (e.g. BV-1572.14) up to 3 cm across, enclosing randomly oriented or weakly aligned plagioclase laths. Although Fe-Ti oxides are present in major proportions only above the UZ-MZ boundary (depth = 1575.80 m), where they become cumulus phases, minor oxide minerals (<5 modal %) occur in MZ gabbroic rocks, particularly the anorthosites (Figure 8). For example, the anorthosite BV-2115.00 contains ~4 % Fe-Ti oxides, which occur as irregular patches up to 5 mm across, interstitial to plagioclase laths. Magnetic susceptibility data (discussed below) show that many anorthositic rocks have higher values than surrounding mafic cumulates. This could be interpreted to indicate that anorthositic rocks contain a larger proportion of trapped residual liquid, from which Fe-Ti oxides eventually crystallize. Sulphides (dominantly chalcopyrite and pyrrhotite) are uncommon in the Bellevue drillcore, but are present sporadically in a few samples. One exception occurs in quartz leucogabbro BV-1520.33, in which sulphides (pyrrhotite > chalcopyrite > pentlandite) constitute ~3 modal %. This sample is unusually rich in platinum group elements, possibly of economic grade (Barnes et al., 2004). Pyroxenitic Rocks There are two prominent pyroxene-enriched horizons in the Bellevue drillcore. The lower occurrence is a ~1.3 m thick zone (depth = 2807.97 m to 2809.26 m), within the troctolitic horizon, and is dominated by olivine-bearing orthopyroxenite, with 0 to 20 % olivine, 50 to 75 % orthopyroxene and 3 to 40 % clinopyroxene (Table 2, Figure 8). This unit consists of large (up to 5 to 6 mm), euhedral to subhedral orthopyroxene crystals with lesser cumulus olivines. Augite occurs either as smaller cumulus crystals, or as large poikilitic grains that surround orthopyroxene and olivine. Plagioclase is invariably interstitial, and red-brown biotite occurs as late-magmatic patches (in some cases up to 2 mm across) between the cumulus phases. The upper occurrence is a ~4.2 m thick zone (depth = 1969.27 m to 1973.50 m), nearly 400 m below the UZ- MZ boundary, and is dominated by melanorite with up to 80 % inverted pigeonite (a few samples contain orthopyroxene instead of inverted pigeonite); augite is minor in these rocks (0 to 15%) (Table 2, Figure 8). Texturally, this unit is characterized by large (up to 2 to 3 cm), irregular, poikilitic inverted pigeonite crystals that partially or totally enclose plagioclases, which vary from lath-shaped to irregular grains. In some cases the enclosed plagioclase laths are aligned parallel to the overall layering direction. Minor augite occurs as irregular grains enclosed by inverted pigeonite. This horizon is at approximately the correct stratigraphic level (Knoper and von Gruenewaldt, 1992) to represent a candidate for the distinctive Pyroxenite Marker horizon, which is widespread in the Eastern and Western Lobes. However, several lines of mineralogical evidence suggest that this is not the case. In the Eastern and Western Lobes, the Pyroxenite Marker is dominated by orthopyroxene (von Gruenewaldt, 1973; Molyneux, 1974; Klemm et al., 1985b; Cawthorn et al., 1991; Nex et al., 2002), whereas the Bellevue horizon contains mainly inverted pigeonite. In addition, the Pyroxenite Marker unit occurs at an upward transition from inverted pigeonite to orthopyroxene, whereas the Bellevue pyroxenite horizon occurs at a boundary between underlying orthopyroxene + inverted pigeonite to overlying inverted pigeonite (Table 2, Figure 11). There is no reversal in Mg# associated with the Bellevue pyroxenite horizon. It appears that the Pyroxenite Marker horizon senso stricto is absent from the Bellevue borehole, and possibly from the Northern Lobe entirely. Troctolitic Rocks The distinctive troctolitic unit at the bottom of the Bellevue drillcore is dominated by olivine-norite, gabbro and gabbronorite, with lesser leucocratic varieties and pyroxenite (discussed above). The average colour index of the entire unit is 50, and the average olivine content is 21.1 modal %. Olivine content declines irregularly upward, and is complemented by a gradual upward increase in orthopyroxene (Table 2, Figure 8). Irregular olivine (variably serpentinized) and orthopyroxene up to 8 mm across are clearly cumulus phases, whereas lesser augite mainly occurs as small intercumulus grains. In some specimens thin rims of orthopyroxene partially or totally surround olivine. Plagioclase occurs as adcumulus intergrowths; in some cases weakly aligned or random laths can be discerned. Late magmatic red-brown biotite is present in a few samples. Upper Zone Rocks The cumulate rocks in the UZ become increasingly chemically and mineralogically fractionated upward after the first appearance of cumulus magnetite at depth = 1575.8 m. Biotite, amphibole and quartz are present sporadically throughout the UZ, and generally increase in abundance upward (Figure 8). In many UZ rocks, these phases clearly represent crystallization products from trapped (H2O-bearing) residual magma, inasmuch as they occur in angular patches between euhedral plagioclase crystals. Cumulus apatite appears at depth = 1362.30 m, and occurs as euhedral crystals up to 1-2 mm long. Fe-rich olivine re-appears at depth = 1002.50 m, and becomes a major rock-forming mineral thereafter upwards. There is a major increase in magmatic quartz at depth = 417.90 m, and K-feldspar appears as a discrete phase at depth = 318.26 m. Above 328 m, ilmenite joins magnetite as a discrete Fe-Ti oxide SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE214 Figure 11. Broad-scale stratigraphy of the Bellevue borehole compared to other stratigraphic data for sections elsewhere in the Bushveld Complex, including the Northern, Western and Eastern Lobes. The sections are normalized at the UZ-MZ boundary, taken as the first appearance of cumulus magnetite. Orthopyroxene-bearing cumulate rocks are shown in blue; those with inverted pigeonite in yellow. Note that the Pyroxenite Marker (PM) unit (red lines) of the Western and Eastern Lobes is marked by a transition from underlying inverted pigeonite to overlying orthopyroxene. This differs from the Bellevue pyroxenite horizon (depth = 1975 m), for which the transition is reversed. LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY 215 phase. Zircon has been observed in thin sections of 4 samples (BV-311.16, 269.25, 106.21 and 105.23); in sample BV-269.25, zircon occurs as large euhedral crystals up to 2 mm long. The rocks of the upper part of the Bellevue drillcore include some of the most fractionated rocks of the Bushveld Complex. The uppermost olivine ferrodiorites are characterized by highly zoned, tabular, weakly aligned plagioclase crystals, abundant clusters of titanomagnetite and ilmenite, cumulus olivine, augite and/or orthopyroxene, and interstitial patches containing late-magmatic quartz, biotite, amphiboles and K-feldspar. Amphiboles are commonly highly zoned as displayed by continuous colour variations in shades of green and blue-green. In some UZ rocks (e.g. BV-871.58, 882.05, 901.54, 920.83), Fe-rich olivine has broken down to form complex symplectic intergrowths of orthopyroxene + magnetite. Similar features were documented in UZ rocks from elsewhere in the Northern Lobe by Nienaber- Roberts (1986), and were suggested by Goode (1974) and Carstens (1958) to represent late magmatic or subsolidus oxidation of olivine. Magnetite-rich Rocks Most of the oxide in the magnetitite layers is titanomagnetite, with a few % of granular ilmenite, probably resulting from oxy-exsolution. A small amount (1 to 2 %) of sulphide minerals (chalcopyrite + pyrrhotite) are present in many of the magnetitites, occurring as droplets within the oxides. The proportion of sulphides decreases upwards from the basal magnetitite layer (depth = 1561.7 m) to the uppermost layer (depth = 590.75 m). A thin nelsonite layer occurs at depth ~305 m, and is composed of about 60% Fe-Ti oxides (dominantly ilmenite), ~30% euhedral apatite crystals ~0.5 mm across and minor pyroxene, amphibole and biotite (Barnes et al., 2004). Magnetic Susceptibility The complete dataset of magnetic susceptibility measurements is shown on a linear scale in Figure 9. The magnetic susceptibility data for the Bellevue drillcore represents a near-continuous profile relating almost entirely to a single parameter- the modal percentage of magnetite in the rocks. Other magnetic minerals, including sulphides such as pyrrhotite are present in minor amounts in a very few samples, but are essentially absent in the vast bulk of the lithologies. Although the composition of magnetites varies throughout the drillcore, as shown below (principally in terms of Ti and V content), there is evidently little or no change in magnetic susceptibilty of magnetite with increased amounts of chemical substituents (Clark and Emerson, 1991; Clark, 1997). We assume, therefore, that there is likely to be a linear relationship between magnetic susceptibilty and magnetite content in Bellevue rocks. Based on values in the literature, measured magnetic susceptibility for titanomagnetite ranges from 1 to 50 SI units, depending mainly upon grain size (Clark, 1997; Clark and Emerson, 1991). On the broad scale, the magnetic susceptibility (MS) data clearly reveal the position of the Main Zone ? Upper Zone boundary, which was determined visually at a depth of 1575.80 m, by the first appearance of cumulus magnetite (Knoper and von Gruenewaldt, 1996). Below this depth, Main Zone cumulate rocks invariably have magnetic susceptibility <0.05 SI units, and generally <0.02 SI units. The most magnetic rocks of the Main Zone are thin (<1 to 5 m) granitic sills, which yield MS values up to nearly 0.7 SI units, although a second type of granitoid, with very low MS values, may be magnetite-free. Above the MZ-UZ boundary, MS values vary enormously, from anorthositic horizons with MS <0.1 SI units, to magnetitites with MS values of nearly 5 SI units. On the fine scale, there is excellent correlation between our measured MS and lithological diversity (as determined by core-logging), in many cases to a resolution of ?5 to 10 cm. Detailed analysis and interpretation will require petrographic and petrologic studies, but the following points are noteworthy. Anorthositic rocks, especially those of the MZ, commonly (but not invariably) show higher susceptibility than surrounding polyphase cumulates, and in many cases there appears to be a correlation between plagioclase content and MS. This may be caused by small amounts of intercumulus magnetite and/or sub-micron sized dust-like magnetite inclusions in unaltered, magmatic plagioclase. In some cases, however, anorthositic horizons are magnetically dead, and individual layers ?0.5 m thick can be identified. UZ anorthositic rocks are generally magnetically lower than adjacent gabbros or leucogabbros, possibly because cumulus or post-cumulus magnetite content correlates with lithological colour index. Profiles across some (but not all) of the magnetitite horizons reveal a progressive, upward decline in MS in the immediately underlying horizon (on the scale of a few tens of metres), regardless of rock type. This may suggest that magnetitite layers may have formed by drawing chemical constituents from both below, as well as from above their present stratigraphic level. Gradual increases or decreases in MS are present within otherwise uniform-appearing horizons, over scales from 0.5 to 25 m, in both the MZ and UZ. These gradational changes may reflect subtle, continuous variations in modal mineralogy, and/or trapped liquid components. In the lowermost 150 m of the BV-1 drillcore (depth = 2810 to 2950 m) a distinctive troctolitic unit occurs, in which MS values are quite variable, but generally significantly higher than those in the overlying MZ gabbroic rocks. The magnetic signature of the troctolitic rocks probably reflects the variable production of secondary magnetite during olivine alteration. Density The upper part of the BV-1 drillcore contains several granitic intrusions, varying in thickness from a few cm to over 80 m. The uppermost granitic intrusive (depth = 0 to 83.55 m) shows nearly uniform density of 2.617 ? 0.008 g/cm3 (n = 76) (Figure 10a); an underlying granitic sill 56.15 m thick (depth = 358.3 to 414.45 m) has similar mean density ( = 2.626 ? 0.034 g/cm3, n = 24), but shows a slight density decrease upwards, from 2.63 to 2.60 g/cm3, possibly reflecting minor settling of mafic silicates and/or Fe-Ti oxides. A dolerite sill (presumably of Waterberg age) 72.17 m thick (depth = 161.97 to 234.14 m) shows uniform density of 2.993 ? 0.019 g/cm3 (n = 14). Xenoliths in the upper part of the drillcore include feldspathic quartzite (24.6 m thick, depth = 116.5 to 141.1 m) with  = 2.719 ? 0.09 g/cm3 (n = 15), and a 32.44 m calc-silicate xenolith (depth = 272.21 to 304.65 m), which has variable density (2.759 to 3.304 g/cm3, average = 2.962 ? 0.16 g/cm3), caused by highly variable mineralogy, including sporadic sulfide concentrations. Cumulate rocks of the Upper Zone show extremely variable densities, controlled, obviously, by modal proportions, and most significantly, magnetite content. The uppermost and thickest (13.03 m) magnetitite layer (depth = 590.7 to 603.78 m) varies in density from 3.509 to 4.495 g/cm3, reflecting variable silicate content and compositional impurities (pure magnetite = 5.20 g/cm3). Typical gabbroic rocks of the Upper Zone, dominated SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE216 Figure 12. Magnetic susceptibility (MS) vs. density for Bushveld cumulate rocks and granitoids from the Bellevue drillcore. Note log scale on y-axis; this provides better resolution, especially for low MS samples. Data for dolerites and xenolith lithologies have been omitted for clarity. LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY 217 by olivine-magnetite gabbros and diorites, show two striking intervals in which density declines progressively upwards from ~3.4-3.5 to <3 g/cm3. The uppermost of these intervals (depth ~420 to 500 m) consists of basal olivine-magnetite gabbro that varies in colour index upwards, and is dominated by anorthositic rocks near the top. The lower interval (depth ~650 to 750 m) is dominated by olivine- and/or magnetite gabbros, but also contains thin layers of pyroxenite, gabbroic and granitic pegmatoids and xenolithic zones. A possible third interval showing a similar density decline occurs in the uppermost mafic cumulate rocks (depth ~85 to 250 m), although the relationships here are obscured by the presence of abundant xenoliths and later intrusives. Values for density and corresponding magnetic susceptibilty are plotted on a semi-log diagram in Figure 12. A log scale is used for MS so as to resolve better the differences between and among rock types. For example, the large variability in MS and relatively constant density for granitoids is apparent, and the two populations discussed above can be discerned, although there is considerable scatter. Anorthositic rocks also show over three orders of magnitude variation in MS. Mafic cumulate rocks (gabbro, norite, troctolite, etc.) generally show a smaller variation in MS. The most prominent feature of Figure 12, however, is the correlation of MS and density amongst magnetite- bearing gabbroic rocks from the UZ, where the modal percentage of magnetite becomes a significant component of the rocks (~10% magnetite in magnetite gabbros and norites corresponds to density ~2.9 to 3.1 g/cm3 and MS ~10-1?1 SI units). The scatter amongst these rocks, however, is explicable mainly in terms of the variable mineralogy (plagioclase, pyroxene, olivine, magnetite) contributing to the rock densities. Mineral Compositions Plagioclase Mean An content of plagioclase in individual samples generally declines upwards, from about An76-78 at the bottom of the drillcore, to An36.8 (depth = 84.07 m), reflecting the overall effects of fractionation in the Bushveld stratigraphy. There are, however, long intervals of several hundred m, over which plagioclase composition remains relatively constant (e.g. depth = 894 to 1322 m, An56.3 ? 1.3 molar %; depth = 1607 to 1939 m, An54.6 ? 1.4 molar %, depth 2820 to 2949 m, An76.1 ? 0.8 molar %). The most calcic plagioclases (An77-78), which occur in the troctolitic rocks at the bottom of the Bellevue drillcore, are comparable to the most An-rich cumulus plagioclases in any of the cumulate rocks of the Bushveld Complex. The mean within-sample variation in An content remains relatively constant at about 1.5 molar %, except at the very top of the UZ, where plagioclases are highly zoned, showing up to 8.5 molar % variation in composition (BV-84.07) (Figure 10a; Table 3). Despite the overall upward decline in An content, there are numerous compositional reversals, both gradual and abrupt. Some, but not all of these compositional shifts are correlated with shifts in compositions of mafic silicates, as discussed below. A gradual reversal of ~7.8 molar % An occurs (from An46.2 to An54.0) over a ~100 m interval between depths ~740 m and ~640 m. This is correlated with a reversal in Mg# of olivine and pyroxenes. Density uniformly declines over this interval (Figure 10a). There is a sharp reversal of ~6.3 molar % (from An55.6 to An61.9) between depths of 1535 and 1523 m, or about 40 m above the UZ-MZ boundary (Figure 10a, Table 3). There is no obvious corresponding shift in compositions of mafic silicates associated with this reversal. Associated with the olivine-bearing pyroxenite horizon at depth ~2808 m is a shift in plagioclase composition toward less An-rich plagioclases; olivine gabbros below the pyroxenites contain plagioclases of ~An77-78, whereas those above the pyroxenites are more Ab-rich, at ~An72-73. The pyroxenites in this interval contain only intercumulus plagioclase, with more Ab- rich mean compositions (An69.8-71.7), and larger within- sample variations (up to 4 molar %) relative to surrounding gabbroic rocks, reflecting crystallization from trapped residual liquids (Figure 10c, Table 3). Figure 13. Depth vs. weight % K2O in plagioclase as measured by microprobe for 438 samples from the Bellevue drillcore. Note the general upward increase in K2O to the UZ-MZ boundary, followed by a reversal to lower K2O, and the larger scattering of data points for the Upper Zone. However, there is no prominent reversal in plagioclase composition at the pyroxene-rich interval at depth = 1969 to 1973 m, as would be expected if this horizon correlates with the Pyroxenite Marker of the Eastern and Western Lobes. A shift in plagioclase composition from An43-44 to An45-47 occurs in UZ magnetite norites above a 56 m thick granitic intrusive at depth = 358 to 414 m, but the intervening granite prevents a detailed assessment of the nature of this compositional shift. After a ~40 m interval of normal fractionation to An44.4 (depth = 311.16 m), there is a dramatic shift toward calcic plagioclase (to An54.4) within ~1.5 m of the overlying 32.4 m thick calc-silicate xenolith at depth = 272 to 304 m. This is very likely due to magmatic assimilation effects that raised the effective Ca/Na ratio of resident magma in the vicinity of the xenolith. Minor elements in plagioclase as measured by microprobe are unremarkable except for K2O content. The entire measured range in K2O in Bellevue plagioclase is 0.03 to 0.51 weight % (mean = 0.26 ? 0.10 weight %). There is a general trend of increasing K2O upward until the UZ-MZ boundary, followed by a reversal to lower K2O, although the data show considerable scatter in the UZ (Figure 13). This reversal may be associated with the appearance of magmatic biotite at depth ~1520 m, but may also be related to the shift toward higher An content at 1523 to 1535 m, as discussed above. Mafic Silicates Compositions of olivines and pyroxenes are plotted on a pyroxene quadrilateral diagram in Figure 14, and span an enormous range in Mg#. Olivine compositions in both olivine-bearing horizons (the lower MZ troctolitic unit and the UZ olivine ferrodiorites) are homogeneous within individual samples. The mean compositional variation of olivine within 96 individual samples is 0.35 molar % Fo (0.12 to 1.75 molar % Fo). In the troctolitic horizon at the base of the Bellevue drillcore, olivine decreases irregularly in Fo content upward from ~Fo77-78 (depth = 2.949 m) to ~Fo75 (depth = 2745.11 m). There is a slight reversal of ~1.75 molar % to more Fo- rich compositions between depth = 2860 m and 2880 m. The ~1.3 m thick olivine-bearing pyroxenite horizon starts with a shift to lower Fo content at depth = 2809.26 m, such that the underlying olivine gabbro contains olivine of Fo77.5, whereas the overlying olivine orthopyroxenite contains Fo74.8. This pyroxenite unit is characterized by slight upward increase in Fo content (to Fo76-77). Olivine is absent above depth = 2745.11 m, but re- appears as Fo58.7 at depth = 1002.50 m in UZ olivine- bearing norites and ferrodiorites. Upward from this depth there is an irregular decline in Fo content of olivines to Fo6.1 in the uppermost ferrodiorite at depth = 84.07 m. This is comparable to the most Fe-rich olivine composition reported elsewhere in UZ Bushveld rocks. There is a prominent reversal of ~12 molar % Fo at depth ~680 m, which also correlates with reversals in plagioclase and pyroxene compositions. Here, olivine of Fo32.0 at depth = 689.49 m shifts to more Mg-rich compositions of Fo37.4 at depth = 671.08 m; Fo content increases upward to Fo43.6, above which a normal Fe-enrichment trend is present. Microprobe analyses of minor element substituents in Bellevue olivines are not considered sufficiently precise to consider compositional relations, with the exception of MnO. Olivine in MZ troctolitic rocks has relatively uniform MnO = 0.23 ? 0.04 weight % (n = 44), whereas UZ olivines increase in MnO from 0.28 weight % (BV-1002.50) to 1.63 weight % (BV-90.27). Low-Ca pyroxenes (including orthopyroxene and inverted pigeonite) are also compositionally homogeneous within individual samples (range of variation in Mg# = 0.16 ? 2.12, mean = 0.58 ? 0.32). Much of the higher within-sample variability in Mg# comes from inverted pigeonite analyses that vary modestly in Wo content (molar Ca/[Ca+Mg+Fe]) due to variable incorporation of host and lamellar phases in the microprobe beam. Clinopyroxenes show slightly higher variability in Mg# (range in Mg# = 0.04 ? 3.80, mean = 1.07 ? 0.50); again, larger within-sample variability is due to Wo variations, in part caused by differential incorporation of fine low-Ca pyroxene exsolutions. Both pyroxenes show an overall decline in Mg# upward, although there are several reversals and discontinuities, as discussed below. With very few exceptions, the mafic silicates constituting individual specimens partition Fe and Mg such that Mg# increases in the sequence olivine ? low Ca pyroxene ? high-Ca pyroxene (Figures 9 and 10). In some specimens, only one pyroxene is present, and in many of such cases, the composition of the single pyroxene (e.g. in terms of Mg#) plots off the main variation trend defined by surrounding samples. Likewise, the pyroxenes in some anorthositic rocks are intercumulus, and their compositions tend to fall off the main variation trend, typically to unusually low Mg#. At depth ~900 m, there is a dramatic change in slope of the depth vs. Mg# fractionation trends for all mafic silicates (Figure 9). Similar relations have been documented in other layered mafic intrusions such as Skaergaard, and are explicable in terms of fractionation after the addition of (Fe-rich) olivine to the crystallizing assemblage. This is discussed further below. A prominent reversal in Mg# of pyroxenes occurs over a ~100 m interval at depth = 2000 to 2100 m (Figure 10c). At depth ~2125 m, low-Ca pyroxene (mainly orthopyroxene) attains Mg# ~54-56 after an underlying interval of normal Fe-enrichment. Between depth = 2125 m and 2100 m Mg# remains fairly constant, but then passes upward into a ~60 m interval in which Mg# of both pyroxenes increases (opx to Mg# = 62.9, cpx to Mg# = 68.7). A similar, but smaller reversal occurs below this one, at depth = 2160 m to 2200 m (Figure 10c). Plagioclase composition remains approximately SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE218 LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY 219 Figure 14. Pyroxene quadrilateral diagram showing mean compositions of pyroxenes and olivines from Bellevue rocks. Different colour data points are used to distinguish mafic silicate assemblages. constant through both of these reversals in pyroxene composition. However, both reversals are associated with upward increases in bulk rock density, as discussed by Ashwal et al. (2003) and illustrated in Figure 10c. An abrupt upward shift toward more Mg-rich pyroxene compositions (from ~ Mg# 60 to 65) occurs in association with the melanorite horizon at depth ~1974 m. Above the shift, there is a weak decline in Mg# upward, over the span of ~10 m, back to Mg# ~60. There is no associated shift in plagioclase compositions. These compositional relations are different from those observed in the Pyroxenite Marker interval in the Eastern and Western Lobes, where plagioclase shifts to markedly more calcic compositions, with a corresponding increase of Mg# in pyroxene, followed by a continued upward increase in Mg# over several hundred meters (Eales and Cawthorn, 1996; Mitchell, 1990). The UZ-MZ boundary, as defined by the first appearance of cumulus magnetite, is not associated with any major shift in pyroxene compositions. Rather, there SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE220 Figure 15. Compositions of Bellevue Fe-Ti oxides vs. depth, showing (a) weight % V2O3 in magnetite and (b) molar % hematite in ilmenite (determined stoichiometrically). Magnetitites near the UZ-MZ boundary contain V2O3 as high as or higher than those actively being mined in the Eastern Lobe. Ilmenites show a general decline in molar % hematite above the UZ-MZ boundary, although there is considerable scatter. LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY 221 is an irregular reverse fractionation trend of upward increasing Mg# for ~40 m above and below the boundary. As discussed above, a shift to more calcic plagioclase compositions occurs about 50 m above the UZ-MZ boundary. A broad reversal in Mg# upward for both olivines and pyroxenes occurs between depth = 600 ? 700 m. This is associated with a corresponding reversal in An content of plagioclase, although there is a slight offset in the actual depth at which the reversals in An and Mg# occur. The peak of this reversal (i.e. the maximum Mg# attained for olivine and both pyroxenes) occurs at depth = 618.53 m, which is about 26 m above the associated peak in An content (depth = 644.8 m), and about 16 m below a prominent zone of magnetite-rich rocks that starts at depth ~602 m. Pyroxene compositions in a zone of about 14 m below the calc-silicate xenolith (depth = 304.65 to 318.26 m) are unusually Mg-rich, and disrupt the overall upward Fe-enrichment trend. A likely explanation involves partial assimilation of calc-silicate components into the Bushveld magma at this zone. Fe-Ti Oxides Magnetite compositions show a marked decline in V2O3 content from ~2.6 weight % at the UZ-MZ boundary, upwards to <0.1 wt% V2O3 at the uppermost contact of the layered mafic rocks with granite (Figure 15). There is a dramatic decline in V2O3 content at depth ~850 m. The overall pattern is similar to depth versus V2O3 patterns from elsewhere in the Bushveld Complex (e.g. Klemm et al., 1985b), although the maximum V2O3 values in Bellevue magnetites slightly exceed those, for example at Roossenekal (Klemm, et al., 1985b). Other minor substituents in magnetite (Al2O3, Cr2O3) show similar, but more scattered patterns to those of V2O3, with values declining from ~4 weight % (Al2O3) and ~1 weight % (Cr2O3) upwards from the UZ-MZ boundary. Below the UZ-MZ boundary, intercumulus magnetite is generally depleted in minor substituents (e.g. V2O3 <2 weight %; Figure 15). Ilmenite is a minor modal constituent of most UZ Bellevue rocks below depth ~320 m. Fe2O3 content, expressed as molar % Hematite component (calculated assuming ideal stoichiometry) declines irregularly upward from ~8 to 9 molar % at the UZ-MZ boundary, to <1 molar % at depth ~300 to 400 m (Figure 15). The uppermost olivine ferrodiorites at depth <100 m contain ilmenites with slightly higher Fe2O3 (~1.5 to 3.5 molar % Hematite). Intercumulus ilmenites below the UZ-MZ boundary generally have <5 molar % Hematite component. Amphibole Amphiboles are present in variable modal abundances throughout the cumulate rocks of the Bellevue drillcore, and occur as intercumulus, late magmatic phases (especially in UZ rocks), as thin rims on pyroxenes, and as fine-grained replacement products after pyroxenes. Although a comprehensive study of amphibole compositions has not been carried out, there are no obvious compositional differences between texturally magmatic amphiboles and those occurring as secondary replacement products of primary pyroxenes. This may suggest that even the texturally secondary amphiboles may be late magmatic or deuteric crystallization products. Amphiboles show a wide variation in Mg# throughout the Bellevue drillcore, from Mg# ~80 in the lowermost troctolitic horizons, to Mg# ~20 in UZ ferrodiorites. These compositions, therefore, correspond roughly to Mg# of coexisting pyroxenes in individual samples. Chlorine contents are uniformly low in the lower parts of the drillcore (<0.5 weight % Cl), but at about 400 m above the UZ-MZ boundary, Cl content is markedly higher, reaching a maximum of 2 to 3 weight % in the depth interval ~900 to 1100 m (Figure 16). Above this interval, Cl content of amphibole first declines to <0.5 weight %, and then gradually increases to ~1 to 1.5 weight % in the uppermost olivine Figure 16. Weight % Cl in biotite (filled symbols) and amphibole (open symbols) vs. depth. Note the zone of halogen enrichment at depth = 900 to 1100m. ferrodiorites (Figure 16). There is a broad correlation between Cl content of amphibole and Mg# such that the most Cl-rich amphiboles have the lowest Mg# (Figure 17a). Some UZ samples, especially olivine ferrodiorites, contain amphiboles with enormous variations in Cl content, and individual amphibole spot analyses in such samples again show negative correlations with Mg# (Figure 17a). These zoned amphiboles may represent the effects of crystallization from fractionating trapped magmatic liquids and/or interactions with halogen-rich hydrothermal fluids. Biotite Biotite shows similar petrographic and compositional features to amphiboles in Bellevue cumulate rocks. As with amphiboles, there is an upward decrease in Mg#, but biotites show an irregular upward increase in K2O that is less apparent in the amphibole data. Biotites occurring in the troctolitic rocks (i.e. below depth ~2500 m) are slightly enriched in Cr2O3 and slightly depleted in Al2O3, TiO2 and MnO relative to those of the UZ. Biotites in the UZ show scattered values, with no apparent compositional trends. In terms of Cl content, biotites show very similar relationships to amphiboles, in terms of depth and correlations with Mg# (Figure 17). En-An Relations Our data allow the assessment of fractionation relationships for the Bushveld Complex, based on mineral compositions. En-An relations are shown in Figures 18 and 19, and can be used to discuss fractionation of Bellevue and other Bushveld cumulate rocks, and comparison with those from other layered mafic intrusions. The following points are significant. The troctolitic zone at the bottom of the Bellevue drillcore contains plagioclase and mafic silicate compositions similar to those of the Upper Critical Zone in the Eastern and Western Lobes of the Complex (Figure 19a). The Bellevue troctolitic rocks, therefore, are among the most primitive plagioclase-bearing rocks in the Bushveld Complex. Bellevue Main Zone rocks from above the troctolitic horizon show a high density of data points at An52-65 and En53-68, with a sparse group of points trending toward the more primitive field of troctolitic compositions (Figure 18). We can presume that the apparent gap would be filled by lower MZ rocks from horizons below the bottom of the Bellevue drillcore. Indeed, data for lower MZ rocks from the Northwestern part of the Western Lobe (Mitchell, 1990) plot in the region between the compositions for the Bellevue troctolitic rocks and the large cluster of Bellevue MZ points (Figure 19a). For Bellevue UZ rocks, compositions of coexisting plagioclase and orthopyroxene form an array that overlaps the large clustering of data points for the Bellevue MZ, and extends to more fractionated compositions, reaching about An42 and En25 (Figures 18 and 19a). The field for Bellevue UZ plagioclase and olivine is displaced to about 10 molar% lower Mg# for equivalent An content relative to the plagioclase ? low-Ca pyroxene field (Figure 18a; see also Figures 9 and 10). The most fractionated end of this array reaches An36 and Fo7 (Figure 18a). Results for the Bellevue rocks represent the most comprehensive available dataset of UZ mineral compositions for the Bushveld Complex. In some cases, compositions of intercumulus pyroxenes in anorthositic rocks are displaced to lower Mg# relative to polyphase cumulates, presumably reflecting compositional homogenization after crystall- ization from trapped liquid components (Figure 18). Similarly, intercumulus plagioclases in some pyroxenitic rocks are displaced to lower An content. These effects are minor, and do not have a major affect upon fractionation curves discussed below. The Bellevue microprobe data allow a new set of fractionation trends to be established for the Bushveld Complex (Figure 19). Separate fractionation trends are plotted for plagioclase ? low-Ca pyroxene, and plagioclase ? olivine. Although there is considerable scatter for Bellevue data points, as is typical of other mafic layered intrusions such as Skaergaard (McBirney, SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE222 Figure 17. Weight % Cl vs Mg# for (a) amphibole and (b) biotite, showing that Fe-rich samples are halogen-enriched. The large variations in Cl at high Fe/(Fe+Mg) for many of the data points represent highly zoned amphibole and biotite in fractionated rocks of the Upper Zone. LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY 223 Figure 18. En-An diagrams for coexisting plagioclase and mafic silicates from the Bellevue borehole. The diagram in (a) shows data for plagioclase coexisting with low-Ca pyroxene and olivine, whereas (b) shows data for plagioclase and clinopyroxene. Colours are used to distinguish rock types. SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE224 Figure 19. En-An diagrams for the Bushveld Complex (Bellevue data) compared with results for other mafic layered intrusions. In (a), Bellevue data are shown as separate fields for the troctolitic horizon, Upper Main Zone and Upper Zone. Also shown are results for Upper Critical Zone norites, Upper Critical Zone anorthosites (data from Maier and Eales, 1997), and Lower Main Zone gabbroic rocks (Mitchell, 1990). Note the overlap of Bellevue troctolitic rocks with Upper Critical Zone norites. In (b), a generalized fractionation path for the Bushveld Complex is compared with those for Kiglapait (Morse, 1996), Skaergaard (McBirney, 1989; 1996) and Stillwater (Raedeke, 1982). Note the divergence of fractionation paths, especially at low An and Mg#. Also note the similarity of ?vertical? trends for Bushveld and Stillwater anorthosites. LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY 225 1989), Kiglapait (Morse, 1996) and Stillwater (Raedeke, 1982), fractionation trends can be drawn through the densest clustering of data points. Changes in slope on these trends generally reflect changes to the crystallizing mineral assemblages, and highlight the appearance of new liquidus phases. Olivine, for example, has a higher fractionating power than pyroxene in terms of Mg# because of higher MgO and FeO content, resulting in steeper slopes in fractionation trends on En-An diagrams. The prominent inflection in the Bellevue fractionation trend at about An55 and Mg# = 60 is caused by the addition of olivine to the crystallizing mineral assemblage of plagioclase + low-Ca pyroxene + clinopyroxene. The small segment of shallow fractionation slope in the uppermost UZ of the Bellevue drillcore (An36-43, Mg# = 7-10) is caused in part by an increase in the fractionation efficiency of plagioclase, which results in a rapid decline in An content, possibly due to apatite and K-feldspar removal during the final crystallization of the Bellevue UZ magma chamber. The shallow fractionation trend at high An and En (An70-80, En = 75-80) represents mineral compositions for the Upper Critical Zone (Eastern and Western Lobes, Cameron, 1982; Eales et al., 1988), as well as for the Bellevue troctolitic zone. The parallel trend for olivine ? plagioclase compositions is from the Bellevue troctolitic zone. These segments are characterized by little Mg# fractionation amongst mafic silicates, with slightly larger evolution of An content in plagioclase. Such fractionation slopes are typical for the initial, primitive stages of differentiation in other layered intrusions such as Kiglapait and Stillwater (Figure 19b). The new fractionation trends for Bushveld are displaced toward higher An and Mg# relative to the Kiglapait intrusion of Labrador (Morse, 1996) and the Skaergaard Complex of East Greenland (McBirney, 1989) (Figure 19b). Aside from this, the fractionation trend for Kiglapait is remarkably similar to Bushveld in terms of shape and slopes. Skaergaard seems to lack the early, shallow fractionation segments that are apparent in Bushveld, Kiglapait and Stillwater. The Stillwater gabbronorites closely match the trends for the Bushveld Critical Zone (and troctolitic horizons) and parts of the Main Zone, but the highly fractionated rocks like those of the Bushveld Upper Zone are evidently absent at Stillwater. Discussion Stratigraphic Relations Absence of a Pyroxenite Marker Horizon Mineralogical evidence was presented above (inverted pigeonite instead of orthopyroxene, inappropriate compositional trends for An and Mg#) that the 4.2 m thick pyroxenite horizon at depth = 1969 to 1973 m in the Bellevue borehole cannot be equated with the well known Pyroxenite Marker unit of the Eastern and Western Lobes. Pyroxenitic units are known to occur sporadically throughout the Main Zone at numerous intervals below the Pyroxenite Marker (e.g. Nex et al., 1998), and possibly the Bellevue horizon could be correlated with one of these, although many of these layers are not laterally persistent, wedging out on various scales. The absence of a Pyroxenite Marker unit in the Bellevue drillcore, and possibly in the Northern Lobe in general, demands explanation. It is apparent that the uppermost Main Zone sequence, from at least the level of the Pyroxenite Marker to the top of the Main Zone is absent in the Bellevue drillcore. Such stratigraphic ?gaps? have been discussed in terms of faulting, folding, non-deposition and intrusion (e.g. Viljoen et al., 1986). Most of the faults mapped in the Northern Lobe are northeast to southwest trending normal faults (van der Merwe, 1978), and no layer-parallel faults, as would be necessary to explain the absence of stratigraphic units, have been identified. Folding of layered rocks cannot account for gaps in vertical stratigraphic sequences, as discussed by Wilson et al. (1994). A region of non- deposition, caused for example, by active upwarping or diapirism (e.g. Uken and Watkeys, 1997) of floor rocks during crystallization, could account for the missing Upper Main Zone rocks. This possibility is difficult to evaluate without detailed seismic profiles or a number of deep boreholes that penetrate into basement rocks. There is, however, no evidence from surface geology for the presence of such upwarps or basement diapirs. We consider the most likely explanation to be a magmatic transgression of Upper Zone magmas over Main Zone cumulates. In this model, the uppermost Main Zone sequences, including the Pyroxenite Marker unit, representing perhaps up to 500 m of previously formed cumulate rocks, were effectively removed by emplacement of Upper Zone magmas. The missing stratigraphic units may have been physically displaced upwards, or more likely, were thermally eroded and possibly dissolved into the intruding magmas. A similar explanation was offered by Wilson et al. (1994) to explain the absence of uppermost Main Zone and lowermost Upper Zone horizons in the ?Northern Gap? area of the Western Lobe. In support of this model, we call attention to several examples of transgressive relationships between Upper Zone and Main Zone stratigraphic units, as recognized by Hall (1932) and van der Merwe (1976; 1978). The most prominent of these occurs at about latitude 23?50? south, where Upper Zone units crosscut northeastward across the entire Main Zone, and come to directly overlie Archaean basement at about latitude 23?40? south (Figure 2). Another transgression occurs at about latitude 24?05? south, where Upper Zone rocks cut through Main Zone units almost to the level of the troctolitic horizon (Figure 2). Magmatic removal of uppermost Main Zone rocks would account, in part, for the attenuated total thickness of Main Zone cumulates in the Northern Lobe, a point noted previously (e.g. van der Merwe, 1976; 1978). Origin of the Northern Lobe Troctolite Horizon Olivine is not known to be present in the cumulate rocks of the Main Zone (e.g. Eales and Cawthorn, 1996; Nex et al., 1998). This calls into question the origin of the unusual >200 m thick troctolitic horizon at the base of the Bellevue borehole. Thin layers of troctolite or olivine-bearing norite have been reported from the Upper Critical Zone in the Western Bushveld Complex (e.g. Maier and Eales, 1997). These occur as horizons between 3 cm and 30 m thick, between the UG2 chromitite layer and the Merensky Reef, and in some cases are associated with thin harzburgitic units referred to as ?Pseudoreefs? (e.g. Viljoen et al., 1986). We consider it significant that compositions of coexisting plagioclase, orthopyroxene and olivine in these Upper Critical Zone troctolitic rocks overlap with those of the Bellevue troctolitic horizon (Figure 19a). This raises the possibility that the Bellevue troctolitic horizon is correlative in some way with lithologies of the Upper Critical Zone, and it is unfortunate that the Bellevue drillcore did not penetrate through this horizon. The mapping and surface sampling in the Northern Lobe by van der Merwe (1976; 1978) reveals that below the troctolitic horizon and above the Platreef, there is a ~300 m thick sequence of norites and gabbros, with four pyroxenite layers. Not much is known about this interval beyond the cursory petrographic work of van der Merwe (1978), who does not mention the presence of olivine or chromite in these rocks. A few optically-determined mineral compositions indicate the presence of plagioclase (An70-80) and orthopyroxene (En66-80) that are more primitive than those of the Lower Main Zone in the northern part of the Western Lobe, as determined by Mitchell (1990). It seems unlikely, however, that the entire stratigraphic package from the Bellevue troctolitic horizon downward as far as the Platreef, is representative of the Upper Critical Zone. If, on the other hand, the regions between the troctolitic horizon and the Platreef are to be correlated with Main Zone lithologies, as suggested by van der Merwe (1976; 1978), then Northern Lobe troctolitic rocks may represent a sliver of Critical Zone dismembered by the intrusion of Main Zone magmas, although it must be kept in mind that known Critical Zone troctolitic rocks are far thinner than the >200 m thick Bellevue troctolitic horizon. A detailed examination of the rocks below the Northern Lobe troctolites seems critical to this issue; an ideal study target would be the Moordkopje drillcore (MO-1, Figure 2), which would effectively extend the stratigraphic sampling from the bottom of the Bellevue drillcore, down to the Platreef. Alternatively, the Bellevue troctolitic horizon might represent an intrusive entity, such as a sill, into Main Zone cumulate rocks. A roughly conformable geometry would be indicated by the map pattern of this horizon (Figure 2), although intrusive relations are not apparent in the drillcore at the top of the horizon. Olivine-bearing sills have been reported, mainly as intrusives into floor rocks, but also as components of the complex Marginal Zone (e.g. Sharpe, 1981); the role of cumulate processes in the origin of many of these rocks was discussed by Cawthorn et al. (1981). However, most of these sills seem to pre-date the formation of the majority of Bushveld cumulate rocks. Detailed isotopic studies of the Bellevue troctolites will be useful in possible correlations with known syn-Bushveld intrusives, or in determining if they might represent a substantially younger magmatic intrusive event. Another possibility is that the Bellevue troctolites merely represent a mineralogically unusual horizon in otherwise typical Main Zone lithologies. This would be consistent with the apparent lack of discontinuities in mineral compositions, at least at the top of the troctolitic horizon (Figure 10c). The bottom contact remains to be investigated. Isotopic studies, specifically focusing on mineral separates, will help to evaluate this and other possibilities. Magmatic Processes Cyclicities Reversals in cryptic variation trends of mineral compositions (chiefly An and Mg# of plagioclase and pyroxene, respectively) are commonly attributed to influxes of new magma into a resident magma chamber. A well known example occurs at the Pyroxenite Marker unit (Eastern and Western Lobes), where distinct reversals in An content of plagioclase and Mg# of pyroxenes (e.g. Cawthorn et al., 1991) are correlated with a change in mineralogy (inverted pigeonite to orthopyroxene, e.g. von Gruenewaldt, 1973), a Sr isotopic shift (e.g. Sharpe, 1985), and changes in trace element abundances and ratios (e.g. Mitchell, 1990; Nex et al., 2002). For the Bellevue drillcore, numerous reversals in mineral compositions have been documented above; in some cases the shifts in An content of plagioclase and Mg# of pyroxenes are correlated, but in other cases they are not. Whether or not these reversals all represent new magma additions await isotopic and trace element analyses of Bellevue whole rocks and minerals. A new type of cyclicity is revealed by the density data for the Bellevue drillcore, particularly in the Main Zone, where at least eight cycles of upward increasing density are apparent on scales ranging between 50 to 200 m (Figures 9 and 10). These cycles reflect gradual increases in modal colour index (C.I.) from anorthositic rocks (C.I. = 0 to 10) to gabbronorites (C.I. = 50 to 60). In some cases the upward density increases are correlated with broad reversals in chemical fractionation trends (e.g. upward increases in Mg# of pyroxenes), arguing against simple fractionation. Ashwal et al. (2003) have argued that such layers may represent blending zones in which dense liquids and/or crystals from new magma additions drain downwards into the existing cumulate pile. This model implies that a significant fraction of the polyphase cumulate rocks in the Bushveld Complex, and in layered intrusions in general, may be composed of mixtures of crystals from chemically and/or isotopically distinct magmas. This is becoming increasingly apparent by the dramatic isotopic SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE226 LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY 227 disequilibrium effects between minerals (e.g. plagioclase and pyroxene) in individual cumulate rocks (e.g. Mkaza, 2001; Prevec et al., 2005). Fractionation vs. Magma Replenishment The detailed dataset of mineral compositions acquired for the Bellevue drillcore allow an assessment of the mechanisms of compositional change amongst Bushveld cumulate rocks, at least for the Main and Upper Zones. Obviously, closed-system fractional crystallization cannot be the sole mechanism, given the mineralogical record of compositional reversals, and the isotopic evidence for crustal contamination (as yet documented chiefly in the Eastern and Western Lobes). If the density cycles observed in the Main Zone (above the troctolitic horizon) are due to magma replenishment, as suggested by Ashwal et al. (2003), then this would imply that a substantial thickness of cumulate rocks, on the order of 1000 m, may have been constructed by successive magmatic influxes. This would constitute an important result, inasmuch as the Main Zone is perceived by some Bushveld workers, on the basis of isotopic data, as representing a single magma influx (e.g. Kruger, 1994). Based on the thicknesses of the density cycles, each of these influxes would have been between 50 and 200 m thick. Given that the Bellevue drillcore records an overall upward fractionation trend of decreasing An content of plagioclase and Mg# of pyroxenes over the depth interval 2745 to 1575 m (Figure 9), this would suggest the existence of a sub-Bushveld magmatic staging chamber that fed progressively variably fractionated magmas into the presently-exposed Bushveld Complex. The relative compositions of successive magma influxes would have controlled the degree to which compositional shifts in cumulus mineral compositions and density occurred. Successive inputs of compositionally similar magmas could possibly account for the minimal mineral fractionation in the upper Main Zone, especially between depths of 1575 and 1975 m in the Bellevue drillcore (Figures 9 and 10b). The evolution of mineral compositions in Upper Zone cumulates cannot as easily be reconciled with magma addition processes. Many magnetite-rich horizons are clearly associated with reversals in Mg# values of pyroxenes and olivines. A good example occurs at the UZ-MZ boundary, where the first appearance of cumulus magnetite is associated with a broad zone of upward-increasing Mg# in low- and high- Ca pyroxene (Figure 10b). Magnetite crystallization, which may be induced by progressive or transient increases in fO2 (e.g. ?oxygen spikes? of Morse, 1980), obviously increased the Mg# of resident magma, causing the precipitation of unusually magnesian pyroxenes (and in some cases olivines). Other examples occur at depth 580 to 680 m, where a thick (~13 m) magnetite- rich horizon occurs at ~600 m (Figure 10a), and at depth ~1400 m (several magnetite-rich horizons 0.4 to 1.6 m thick) (Figure 10b). The magnitude of the shift in Mg# of mafic silicates clearly relates to the thickness of magnetite-rich layers. Broad reversals in plagioclase composition are also associated with several of the magnetitite-associated shifts in Mg# of mafic silicates. The most prominent example occurs over a 100 m interval at depth = 640 to 740 m (Figure 10a), where a broad reversal of about 8 molar % An (An46 to An54) takes place above a zone of normal fractionation. Another example associated with the first major magnetite horizon occurs about 20 m above the MZ-UZ boundary, where a shift of about 6 molar % An (An56 to An62) takes place. The reason for reversals in An content associated with these horizons is not immediately apparent. One possibility is that magnetite crystallization may suppress the precipitation of a Ca-rich phase such as clinopyroxene, thereby increasing the Ca/Na of resident magmas. Experimental phase equilibrium studies would be needed to confirm this. Of relevance to this is the observation of Morse and Ross (2004) that in the Kiglapait intrusion, the addition of titanomagnetite to the crystallizing assemblage of augite + olivine + plagioclase results in a Ca-enrichment trend in fractionating liquids. The broad, rather than abrupt shapes of these reversals in plagioclase and pyroxene compositions, and their variable positions relative to the magnetite layers suggest that if their origins are linked, then some process other than simple crystal settling by gravitation may be involved. One possibility is a variant of in-situ crystallization (e.g. Campbell, 1978; McBirney and Noyes, 1979), in which magnetitite layers form within the resident magma chamber, perhaps near the cumulate-magma interface. The magnetite layers might form dominantly by adcumulus growth, drawing the necessary constituents from both above and below their sites of formation. This would have resulted in increases in Mg/Fe (and perhaps Ca/Na, as discussed above) in surrounding magmas, ultimately resulting in reversal in mafic silicate and plagioclase compositions. Some of the Bellevue magnetitite layers, however, do show evidence for an origin dominantly involving conventional crystal settling, as has been well documented elsewhere in the Bushveld Complex (e.g. Eales and Cawthorn, 1996; McCarthy et al., 1985). A good example occurs over the depth interval ~1380 to 1390 m, where a ~3 m thick magnetite-rich layer overlain by leucogabbronorite and anorthosite is associated with a gradual upward decline in magnetic susceptibility (Figure 10b). Over a depth interval of at least 300 m (depth ~1000 to 1300 m), there is a sequence of gabbronorites, leucogabbronorites and anorthosites in which mineral compositions are surprisingly uniform (Figures 9 and 10b). This interval consists of ~140 m of relatively uniform oxide-bearing gabbronorite (colour index ~50), overlain by ~200 m of plagioclase-rich cumulates dominated by anorthosites and leucogabbronorites (colour index ~10 to 20), with a few thin magnetitite layers. Plagioclase compositions over this interval show little variation (mean = An56.5 ? 1.3, range = An54.4-59.8, n = 38). Pyroxene compositions are less uniform (mean Mg# opx = 57.8 ? 5.3), but show no discernable fractionation trends or clear reversals. One possible explanation is that this thick interval was constructed by multiple magmatic replenishment episodes, each with essentially constant An and Mg#. If, however, these thick horizons are related by crystal sorting processes (e.g. gravitational settling), then chemical fractionation must somehow have been prevented or effectively minimized. An explanation for this is not immediately apparent, although B.D. Marsh and colleagues have discussed mafic intrusive bodies of substantial thickness (100 to 500 m) that show no significant effects of crystal fractionation; such bodies may owe their origin to emplacement and relatively rapid cooling of phenocryst- free or phenocryst-poor magmas (Marsh, 1992; Hort et al., 1993). However, there is nothing remarkable about the grain size of the rocks in this interval of Bushveld rocks that would suggest rapid cooling. The origin of these horizons, therefore, remains somewhat of a problem. At depth ~1000 m in the Bellevue drillcore, olivine of intermediate composition (Fo58.65) became a liquidus phase. Its crystallization had a profound effect upon the fractionation rate of the mafic silicate assemblage, which shows marked iron enrichment upward from this depth. This can be seen as a dramatic change in slope in the depth vs. Mg# diagram for olivines and pyroxenes in the uppermost Upper Zone (Figure 9). The most fractionated olivine ferrodiorite at the top of the Upper Zone (depth = 84.07 m) contains fayalite (Fo6.08) and Fe- rich clinopyroxene (Mg# = 27.30). Fe-rich ortho- pyroxene is absent in the olivine ferrodiorites above depth = 157 m, but reaches Mg# = 27.03 just below this depth (Figure 10a). Compositional fractionation of plagioclase in the Upper Zone also increases in the Upper Zone, especially above depth ~900 m, although there are at least two reversals that moderate the decrease in An content. Plagioclase in the uppermost olivine gabbro (depth = 84.07 m) is highly zoned, with compositions of An17.84-43.99 (mean = An36.82). Feldspar compositions more sodic than this occur in the uppermost fractionates of both Skaergaard (An26) and Kiglapait (An11), as discussed below; it is not certain if the final differentiates of the Bushveld Upper Zone, as present in the Bellevue drillcore, may have been removed by intrusive granites, although no mineral compositions more evolved than those presented here have been yet recognized elsewhere in the Bushveld Complex (e.g. Eales and Cawthorn, 1996). The reason for the increased fractionation in An content at depth ~900 is not immediately clear, but may be related to an increase in augite crystallization, which has substantial fractionating power for Na/Ca in basaltic magmas (Morse, 1979a). Other Ca-rich minerals like apatite may also play a role, but in Bellevue, although apatite appears as a liquidus phase at depth ~1100 m, it only becomes an important phase at depths above ~600 m. A new fractionation trend for the Bushveld Complex The extensive Bellevue drillcore dataset of new mineral compositions for the Upper Zone and Main Zone allow the construction of a new fractionation trend for the Bushveld Complex, in terms of plagioclase and mafic silicates. The Bellevue data are shown on En-An diagrams in Figures 18 and 19. Because the Bellevue section terminates in the middle of the Main Zone, mineral compositions for the lower Main Zone (Mitchell, 1990) and Upper Critical Zone (Maier and Eales, 1997) are also shown in Figure 19a. These compositions, from the Eastern and Western Lobes, are similar to those determined by earlier workers, including Eales et al. (1988) and Cameron (1982). Data for ultramafic rocks (e.g. from the Lower and Critical Zones) are not shown because where present, plagioclase is intercumulus, and does not reflect liquidus mineral compositions. However, data for Upper Critical Zone anorthosites (Maier and Eales, 1997) are shown, mainly for comparison to Stillwater anorthosites, to be discussed below. Not surprisingly, the most primitive mineral compositions are to be found in rocks of the lower stratigraphic horizons, and become progressively more fractionated upwards. Amongst those rocks containing both cumulus plagioclase and mafic silicates, the most primitive compositions occur in norites of the Upper Critical Zone, with values of An80 + En83. For comparison, the highest values of Mg# measured for mafic silicates in the Bushveld Complex occur in harzburgites of the Lower Zone, which contain orthopyroxenes up to En89 and olivines up to Fo87, with no cumulus plagioclase (Cameron, 1978). On the En-An diagram, most ultramafic rocks from the Lower and Critical Zones would plot in a horizontal-trending field from An80 to An40, at En80-85 (see Maier and Eales, 1997); the large range in plagioclase compositions is due to their crystallization from trapped intercumulus liquids. Compositions of coexisting plagioclase and mafic silicates for Bellevue rocks are shown in Figure 19a as fields for the troctolitic horizon, (upper) Main Zone and Upper Zone. Separate fields are distinguished for coexisting plagioclase + low-Ca pyroxene and plagioclase + olivine; the latter fields are displaced to slightly lower Mg#, owing to the Fe-Mg fractionation between olivine and low-Ca pyroxene. It is significant that the lowermost Bellevue rocks, in the so-called troctolite horizon, contain mineral compositions nearly as primitive as those in the Upper Critical Zone. These compositions are distinctly more primitive than those determined by Mitchell (1990) for the lower Main Zone (Figure 18a). This has been discussed above as indicating, amongst other possibilities, that the troctolite horizon might represent a sliver of Upper Critical Zone lithologies that was dismembered by the intrusion of Main Zone magmas. Upper Main Zone rocks in the Bellevue drillcore (plag + low-Ca pyroxene) plot as an irregular field extending from that of the troctolite horizon toward SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE228 LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY 229 more fractionated compositions, reaching about An52 and En53 (Figure 19a). The scattering of data points is typical of layered intrusions (see below), and is probably caused by a variety of cumulus, intercumulus and subsolidus effects; the differences in Mg# caused by orthopyroxene vs. inverted pigeonite is not significant. The field for Bellevue Upper Zone plag + low-Ca pyroxene overlaps that for the upper Main Zone, and extends in a steeper array to about An45 and En25 (Figure 19a). Parallel to and partly overlapping this array is the field for Upper Zone plag + olivine, which is on average displaced to about five molar % lower Mg#. Low-Ca pyroxene is not present in the uppermost Upper Zone rocks, and the plag + olivine array extends to the limit of Bushveld fractionation, at about An35 and Fo07 (Figure 19a). Inflections in fractionation trends, as marked by clear changes in slope on plots such as the En-An diagram generally indicate changes in crystallizing mineral assemblages, or sudden shifts in their compositions. In the case of the Bellevue results, there is a marked increase in slope at about An55 and En58 (Figures 18 and 19). This corresponds to the appearance of intermediate olivine in the crystallizing assemblage in about the middle of the Upper Zone (depth ~1000 m). Olivine has a higher fractionating power for Mg# than pyroxene because of its relatively higher MgO content, and this accounts for its ability to instantaneously steepen fractionation trends on En-An diagrams. A similar inflection in the fractionation trend of the Skaergaard intrusion occurs after the re-appearance of olivine at the base of the Upper Zone (McBirney, 1996), as discussed below (Figure 19b). Another inflection in the Bellevue data occurs at about An42 and Mg# = 11, where there the slope of the fractionation trend becomes shallow (Figure 19). This occurs in the uppermost 75 m of the Bellevue Upper Zone (depth ~157 m), and corresponds to the cessation of orthopyroxene crystallization, which allows a rapid decline of An content in plagioclase due to the powerful effect of augite to remove Ca from the remaining melt. Similar inflections in fractionation trends amongst the latest differentiates are apparent at Skaergaard (due to the appearance of Fe- rich calcic clinopyroxene referred to as ?ferrowollastonite?, McBirney, 1989; 1996) and at Kiglapait (Morse, 1979b). Comparison of Bushveld fractionation trend to other layered intrusions An approximation of the newly determined Bushveld fractionation trend is compared to those from several other layered mafic intrusions in Figure 19b. Of course there is considerable scatter connected to these trends, but it is instructive to compare the general shapes and positions of trends between different layered intrusions. An interesting observation is that most fractionation trends (or their hypothetical extensions) seem to converge at about An75-80 and Mg# = 80 (Figure 19b). This includes data for Bushveld, Skaergaard and Kiglapait; gabbronorites of the Stillwater Complex, however, are slightly more primitive, extending to An85 and En85 (Figure 19b). This similarity in ?starting? compositions probably merely reflects the dominant liquidus compositions that crystallize from basaltic magmas, broadly defined, at least at a stage when plagioclase and mafic silicates co-precipitate. Thereafter, the fractionation trends diverge, depending upon the detailed crystallization history. As discussed above, olivine is the most potent fractionating agent for Mg#, and augite for Ca/(Ca+Na) or An. Kiglapait, for example, consists of cumulate rocks dominated by olivine and augite (+ plagioclase), with no orthopyroxene (only traces as rims on olivine, Morse, 1979b)- its fractionation paths are shifted to the left relative to those of other intrusions, and its most extreme differentiates are Mg- free at An11 (Figure 19b). Similarly, Skaergaard mafic silicates are dominated by olivine and augite, with lesser inverted pigeonite (McBirney, 1996), and its paths are positioned between those for Kiglapait and Bushveld, and extend to Mg-free residua at An27. The fractionation paths for Bushveld, to the right of Skaergaard, and its apparent inability to fractionate beyond An37 and Mg# = 11 (Figure 19b) could be attributed to the relative abundance in Bushveld of low-Ca pyroxene (orthopyroxene and inverted pigeonite). Although not emergent from the Bellevue data, it is worth noting that the vertical trend of variable En at relatively constant An among upper Critical Zone anorthosites (Maier and Eales, 1997) resembles a similar trend for Stillwater anorthosites (c.f. Figures 19a and 19b). This has been interpreted by Raedeke (1982) and Raedeke and McCallum (1980) in terms of crystallization of variable amounts of liquid trapped between cumulus plagioclase crystals in anorthositic mushes- the abundance of plagioclase buffered the An content to nearly constant values, whereas larger variations in Mg# of mafic silicates resulted from differences in percentages of trapped intercumulus liquid and cumulus mafic minerals. Bushveld anorthosites probably formed by a similar process, even though they are far thinner (maximum 75 m thick) than Stillwater?s AN I (350 m) and AN II (750 m) (McCallum et al., 1980), a point noted by Ashwal (1993, page 245). The thick Stillwater anorthosites were proposed by Czamanske and Bohlen (1990) to represent the emplacement of plagioclase-rich mushes into evolving magma chambers. This idea is tenable for Bushveld, and is worth testing. Summary We provide the first dataset of petrological, mineralogical and geophysical measurements on a near-continuous basis for Upper and Main Zone cumulate rocks from the Northern (Potgietersrus or Mokopane) Lobe of the Bushveld Complex. Data were taken from the Bellevue drillcore, a ~3000 m deep stratigraphic borehole, and include >14,000 electron microprobe analyses (plagioclase, mafic silicates, amphibole, biotite, Fe-Ti oxides) in >500 samples, nearly 110,000 magnetic susceptibilty measurements (taken every 2 cm), and >2200 density measurements (taken every ~1.7 m). These results may represent the most extensive and comprehensive dataset of such measurements, in stratigraphic context, for any layered intrusion. The Upper Zone in the Bellevue drillcore, as marked by the appearance of cumulus magnetite, is ~1190 m thick, which is less than Upper Zone thicknesses in the Western (~1700 m) or Eastern (~2000 m) Lobes. This is underlain by ~1269 m of Main Zone lithologies, although the lowermost ~200 m of the Bellevue drillcore is composed of olivine-bearing (or troctolitic) rocks that are not present amongst Main Zone lithologies elsewhere in the Bushveld Complex. We estimate based on surface geology that Main Zone rocks continue for at least another 1.3 km below the base of the Bellevue drillcore. Mineral compositions show broad normal fraction- ation trends upwards, with plagioclase (An78  21), low-Ca pyroxene (En80  26), augite (Mg# 86  27), olivine (in the lower troctolitic horizon = Mg# 78  74) and Fe-rich olivine (in the Upper Zone = Mg# 59  06). There are, however, many prominent reversals and discontinuities in mineral composition trends. The extensive dataset of mineral compositions allows the establishment of a new fractionation trend for the Bushveld Complex, which is presented here in terms of an En-An diagram. There are clear inflections in this fractionation trend that can be linked to changes in liquidus mineral assemblages. The new Bushveld fractionation trend is shifted toward more An-rich plagioclase compositions (at equivalent Mg#) relative to those for Kiglapait or Skaergaard. This may be explicable in terms of the relative paucity in Bushveld rocks of augite, which has a high fractionating power for Ca/Na. Bushveld fractionates, therefore, are prevented from attaining low-An plagioclases due to the lesser degree of prior augite crystallization. The most fractionated Bushveld rocks in the Bellevue drillcore contain An37 and Fo11. Although a prominent ~4 m thick pyroxenitic horizon occurs ~388 m below the first appearance of cumulus magnetite, mineralogical data suggest that this layer cannot be equated with the well known Pyroxenite Marker horizon of the Eastern and Western Lobes. The Bellevue pyroxenite represents an upwards transition from orthopyroxene to pigeonite, rather than the reverse for the typical Pyroxenite Marker. Moreover, the Bellevue pyroxenite is not associated with marked reversals in plagioclase and pyroxene compositions that typify the classical Pyroxenite Marker horizon. This may suggest that a substantial portion, perhaps up to 500 m of the uppermost Main Zone (including the Pyroxenite Marker), is missing from the Northern Lobe. There are several possible explanations for this, perhaps the most likely of which involves thermal and/or mechanical erosion of the uppermost Main Zone by the emplacement of Upper Zone magmas, a model invoked by others for the Northern Gap area of the Western Bushveld Complex. Since olivine is not typical of Main Zone cumulates in the Bushveld Complex, this calls into question the origin of the ~200 m thick troctolitic horizon at the base of the Bellevue drillcore. This horizon has been mapped at surface over a strike length of ~30 km. The primitive nature of mineral compositions in this horizon (An70-80, En80-83, Fo75-78) are more akin to Critical Zone rocks, suggesting that the Northern Lobe troctolitic horizon might represent a sliver of Critical Zone rocks dismembered by the intrusion of Main Zone magmas. This may have important implications for mineral prospecting. Alternatively, the troctolitic horizon might represent a syn- or post-Bushveld sill, or merely a mineralogically unusual horizon in otherwise typical MZ rocks. Main Zone cumulate rocks have magnetic susceptibility values <~0.003 SI units, and are generally <~0.0005 SI units. Above the MZ-UZ boundary, magnetic susceptibility varies enormously, from anorthosites (<~0.001 SI units) to magnetitites (to 0.4 SI units), and there is excellent correlation between magnetic susceptibility and lithology, in many cases to a resolution of <5 to 10 cm. Anorthositic rocks, especially in the Main Zone, commonly show higher magnetic susceptibility than surrounding polyphase cumulates, due to intercumulus and/or dust-like inclusions of magnetite. Density data in the Main Zone reveal a surprising cyclicity on the scale of 50 to 200 m, with progressively increasing density upwards in individual layered units, reflecting gradual increase in modal colour index from 1 to 10 % to 50 to 60 %. In some cases, the upward density increases are correlated with broad reversals in chemical fractionation trends (e.g. upward increases in Mg# of pyroxenes), arguing against simple fractionation. Such layers may represent blending zones in which dense liquids and/or crystals from new magma additions drain downwards into the existing cumulate pile. This model implies that many Bushveld polyphase cumulate rocks may be composed of mixtures of crystals from chemically distinct magmas, a hypothesis that can be tested isotopically. A substantial thickness of Main Zone cumulates, therefore, may have been constructed by successive magmatic influxes on the order of 50 to 200 m thick. This would suggest the existence of a sub- Bushveld magmatic staging chamber that fed variably fractionated magmas into the presently-exposed Bushveld Complex. Upper Zone rocks cannot as easily be explained by magma addition processes, and the diversity of cumulate rocks there may be dominated or solely formed by internal magma chamber processes such as crystal settling and/or in situ growth with attendant fractionation. Whether or not the Upper Zone represents fractionation in a closed magmatic system awaits further data, notably isotopic studies. SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE230 LEWIS D. ASHWAL, SUSAN J. WEBB AND MICHAEL W. KNOPER SOUTH AFRICAN JOURNAL OF GEOLOGY 231 Acknowledgements We thank Council for Geoscience staff for providing magnetic susceptibility data (Edgar Stettler, Annabel Graham, Timothy Molea), loan of equipment (Manfred Hauger and Leone Mar?), and displaying of the Bellevue drillcore (Martin Kohler). Tony Morse, Chris Hatton and Suzanne McEnroe provided valuable critical comments on the manuscript. We are especially grateful to Grant Cawthorn for his insightful comments. We also thank Paul Nex for helpful discussions and for comments on a version of this paper. The following students assisted with density measurements: J. Adams, K. Boerst, N. de Koker, M. Le Grange, E. Kgaswane, L. Mdluli and B. Powell. A great deal of the microprobe data were expertly collected by Gabisile Violet Simelane and Nico de Koker. We thank Chris Hadidiacos and Rick Carlson of the Carnegie Institution of Washington (Geophysical Laboratory) for assistance with wavelength-dispersive microprobe analyses. Prof. Trond Torsvik (Geological Survey of Norway) kindly measured volume susceptibilty for several samples. 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Australian Society of Exploration Geophysicists, 15th Geophysical Conference and Exhibition, Brisbane, Australia, published on CD. Webb, S.J., Nguuri, T., Cawthorn, R.G., and James, D. (2004). Gravity modelling of Bushveld Complex connectivity supported by southern African seismic experiment result. South African Journal of Geology, 107, 207-218 Wilson, J.R., Cawthorn, R.G., Kruger, F.J. and Grundvig, S. (1994). Intrusive origin for the unconformable Upper Zone in the Northern Gap, western Bushveld Complex. South African Journal of Geology, 97, 462-472. Editorial handling: J. M. Barton Jr. SOUTH AFRICAN JOURNAL OF GEOLOGY MAGMATIC STRATIGRAPHY IN THE BUSHVELD NORTHERN LOBE232 Appendix B This appendix presents Cawthorn, Cooper and Webb (1998) in its published format. Consequently, the formatting, layout, figure numbering and table titles do not follow the rest of the thesis. This paper is a proof-of-concept paper and it is the first to examine crustal flexure and isostatic response due to the load of the Bushveld Complex. My contribution to this paper has been significant; I prepared the gravity models that show that it is possible to have a laterally connected Bushveld Complex if the crust has flexed under the load. This simple model paved the way for more detailed models presented in later papers. Our prediction of an increase in crustal thickness of 6 km due to flexure is surprisingly close to that found from receiver functions (Nguuri et al., 2001). 328 Appendix C This appendix presents Cawthorn and Webb, (2001) in its published format. Consequently, the formatting, layout, figure numbering and table titles do not follow the rest of the thesis. This paper examines the geological evidence for a connected Bushveld and presents a model of the gravity field that is constrained by surface geological outcrop and existing published seismic lines. My contribution to this paper has been substantial as I constructed the geophysical model and contributed much of the text. 337 Connectivity between the western and eastern limbs of the Bushveld Complex R.G. Cawthorn*, S.J. Webb Departments of Geology and Geophysics, University of the Witwatersrand, Private Bag 3, P.O. Wits 2050, Johannesburg, South Africa Received 18 January 2000; accepted 4 October 2000 Abstract The mafic layered rocks of the Bushveld Complex are 6?8 km thick and crop out over an area of 65,000 km2. Previous interpretations of the Bouguer gravity anomalies suggested that the intrusion consisted of two totally separate bodies. However, the mafic sequences in these arcuate western and eastern limbs are remarkably similar, with at least six petrologically distinctive layers and sequences being recognisable in both limbs. Such similarity of sequences in two totally discrete bodies 200?300 km apart is petrologically implausible, and it is suggested that they formed within a single lopolithic intrusion. All previous Bouguer gravity models failed to consider the isostatic response of the crust to emplacement of this huge mass of mafic magma. Isostatic adjustment as a result of this intrusion would have caused the base of the crust to be depressed by as much as 6 km. With this revised whole crustal model, it becomes possible to construct a gravity model, consistent with observed data, which includes a 6 km-thick sequence of mafic rocks connecting the western and eastern limbs of the Bushveld Complex. The exact depth at which the mafic rocks of the Bushveld Complex lie in the centre of the structure cannot be constrained by the gravity data. Such a first-order model is an approximation, because there have been subsequent deformation and structural readjustments in the crust, some of them probably related to the emplacement of the Bushveld Complex. Specifically, the observed geometry of the rocks around the Crocodile River, Dennilton, Marble Hall and Malope Domes suggests that major upwarping of the crust occurred on a variety of scales, triggered by emplacement of the Bushveld Complex. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Bushveld Complex; gravity; isostasy; stratigraphic correlation 1. Introduction The mafic rocks of the Bushveld Complex crop out in four geographically discrete areas in South Africa, with a further body totally hidden under younger sedi- mentary cover (Fig. 1). Several studies on different parts of the complex, using different minerals, and using different age-dating techniques give ages of about 2060 Ma (Walraven, 1997). It was intruded into the intercratonic sedimentary rocks of the Trans- vaal Supergroup deposited from over 2550?2060 Ma ago (Nelson et al., 1999), and has undergone minimal deformation or alteration subsequently. The western limb describes a semicircular arc from Thabazimbi through Rustenburg to Pretoria, and the eastern limb can be described as the mirror image from north of Burgersfort to Belfast (Fig. 1). The layering of these rocks dips centripetally at between 10 and 208. The Tectonophysics 330 (2001) 195?209 0040-1951/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S0040-1951(00)00227-4 www.elsevier.com/locate/tecto * Corresponding author. Tel.: 127-11-717-6557; fax: 127-11- 339-1697. E-mail address: 065rgc@cosmos.wits.ac.za (R.G. Cawthorn). other limbs, the northern or Potgietersrus limb, the far western limb, and the completely covered southeast- ern or Bethal limb, are not discussed in detail here. The roof rocks consist of either metamorphosed sedi- mentary and volcanic rocks of the Transvaal Super- group, or the Bushveld Granite, which was emplaced immediately after the mafic rocks (Walraven et al., 1990). The stratigraphic successions in the eastern and western limbs have numerous similarities (Fig. 2), whereas the other limbs display more differ- ences than similarities (Eales and Cawthorn, 1996). The similarities between the eastern and western limbs are remarkable, and until 1959 it was assumed that these two bodies were physically connected at depth underneath the Bushveld Granite and younger sedimentary rocks in the centre of the complex (Hall, 1932). However, as a result of a regional gravity inter- pretation, it was argued that, since there was no posi- tive gravity anomaly present in this central area (Pienaars River?Warmbaths area in Fig. 1), the mafic rocks were not continuous at depth (Cousins, 1959). Subsequent, more detailed gravity interpreta- tions have tended to perpetuate this hypothesis that the eastern and western limbs are inward-dipping sheets that get thinner towards the centre and terminate at depth (Molyneux and Klinkert, 1978; Meyer and De Beer, 1987; Du Plessis and Kleywegt, 1987). The Council for Geoscience, South Africa, has recently produced a gravity map of South Africa, and the Bouguer gravity anomaly of the area underlain by the Bushveld Complex is shown in Fig. 3. The purpose of this paper is to report on the strati- graphic and petrological reasons why continuity between the two limbs is suggested. Then the assump- tions made in the previous gravity models are re- examined, and finally it is suggested that the gravity data are, in fact, consistent with continuity at depth between the two major limbs. R.G. Cawthorn, S.J. Webb / Tectonophysics 330 (2001) 195?209196 Fig. 1. Simplified geology of the Bushveld Complex (after Eales and Cawthorn, 1996), showing outcrops of the northern, eastern, western and far western limbs, and the position of the unexposed southeastern limb. 2. Petrological similarities The general similarity between the eastern and western limbs is apparent in Fig. 2. In the column showing the profiles in the eastern and western limbs, dashed lines across the entire column width indicate that specific layers are identifiable in both limbs, whereas the dashed lines that terminate in the middle of the column indicate that identical layers have not been unequivocally correlated in both limbs. Layers recognised in both limbs include most of the chromitite layers and the platiniferous Merensky Reef of the Critical Zone, the Pyroxenite Marker of the Main Zone, and the Main Magnetitite Layer of the Upper Zone (Eales and Cawthorn, 1996). The principles of differentiation and phase diagrams predict that a similar sequence of cumulate rocks should form from similar magma bodies, with- out them having to be physically connected. Hence, it is the occurrence of atypical sequences, which are not the normal consequence of magma fractionation, that must be identified and correlated to substantiate connectivity between two sections. Six such examples occur in the eastern and western limbs. 2.1. Middle Group chromitites The Critical Zone of the Bushveld Complex is well- known for its spectacular cyclic layering from ultra- mafic to leucocratic, often with a chromitite layer at the base (Eales and Cawthorn, 1996). Magmatic fractionation of a single magma of appropriate composition could produce a sequence of chromi- tite?pyroxenite?norite?anorthosite. However, repeti- tive chromitite layering probably requires some additional process, generally attributed to magma addition. In the two limbs, there is a nearly identical and complex sequence of numerous, closely-spaced, chromitite layers (Fig. 4). These layers have been designated the Middle Group chromitites 1?4 (MG1?4). Many of the layers are composite, and indi- vidually are named MG4a and MG4b, for example. Each chromitite layer has a distinct chemical compo- sition (Hatton and von Gruenewaldt, 1987), and there is a strong compositional similarity between the comparable layers in each limb, but marked differ- ences exist between successive layers (Fig. 4). In both limbs the MG2 layer is intimately associated with the first appearance of cumulus plagioclase in the entire sequence (Fig. 2). 2.2. Upper Group 1 chromitite The Upper Group 1 chromitite layer is distinctive because it splits into numerous thin layers and rejoins, enclosing lenses of anorthosite. There is also evidence of brecciation and deformation of chromitite, and re- intrusive relationships between anorthosite and chro- mitite (Lee, 1981). The famous Dwars River locality in the eastern limb displays these features, but similar features are seen throughout the eastern and western R.G. Cawthorn, S.J. Webb / Tectonophysics 330 (2001) 195?209 197 Fig. 2. Simplified vertical sections through the eastern and western limbs, showing maximum thicknesses and main marker horizons. Where the latter occur in both limbs, a dashed line from the west to east side of the column is shown. If they are not convincingly correlatable in both limbs, a short dashed line is used. LG, MG and UG refer to the Lower, Middle and Upper Groups of chromi- tites. Numbers 1?21 refer to the numbering scheme for the magne- titite layers (after Eales and Cawthorn, 1996). limbs wherever the Upper Group 1 chromitite layer is exposed. No other chromitite layer in the Bushveld Complex, of which there are 13, displays these features. 2.3. Upper Group 2 chromitite This layer of chromitite is unique in that it is the only chromitite layer in the world mined for its plati- num-group element (PGE) content (Lee, 1996). Although mining only occurs in the western limb at present, this is a consequence of lack of infrastructure in the east, not lower grade, and equally high PGE contents are known from the eastern limb (Gain, 1985; Vermaak, 1995). 2.4. Merensky Reef This layer is well-known as a major source of PGE. Apart from its PGE, geochemically it is remarkable, because there is a sudden increase in the initial 87Sr/86Sr ratio from 0.7063 to 0.7076 at the base of the reef in both eastern and western limbs (Kruger and Marsh, 1982; Lee and Butcher, 1990). The reef R.G. Cawthorn, S.J. Webb / Tectonophysics 330 (2001) 195?209198 Fig. 3. Gravity map of the Bushveld Complex, covering the area shown in Fig. 1. The image was produced using GMT (Wessel and Smith, 1995) from a subset of the South African gravity data base, and reproduced here by courtesy of Dr Edgar Stettler, of the Geophysical Division of the Council for Geoscience, South Africa. The outline of the outcrop of the mafic rocks of the Bushveld Complex is shown. The profile line shown in Fig. 9 is indicated. defines the base of the Merensky Cyclic Unit, which is overlain by the Bastard Cyclic Unit in both limbs. These two cyclic units are the last two and the thin- nest of all the cyclic units in the Critical Zone, further emphasizing the similarities between the two limbs. 2.5. Main Zone/Upper Zone transition Towards the top of the Main Zone in both limbs, there occurs a major reversal in mineral composi- tions, and a change in the initial 87Sr/86Sr ratio (von Gruenewaldt, 1973; Sharpe, 1985; Cawthorn et al., 1991), which have been attributed to addition of magma. Magma addition in itself is not unique, but what is remarkable is that above this level samples from the upper part of the Main Zone and the entire Upper Zone from both the eastern and western limbs plot on identical isochrons, yielding the same initial 87Sr/86Sr ratio (Kruger et al., 1987). As these rocks are believed to have formed from magma that is the product of mixing of several magmas residual to the lower parts of the Main Zone and new magma, an identical ratio in both limbs, occurring at the same stratigraphic horizon, at a level where the magma had evolved to yield similar mineral compositions suggests connectivity. 2.6. Main magnetitite layer The base of the Upper Zone is defined as the lowest level at which cumulus magnetite first appears. A short distance above this level in both limbs there is a 2 m-thick layer of magnetitite. This layer contains 1.0% vanadium, for which it is mined in both limbs (Cawthorn and Molyneux, 1986). These six, highly distinctive, and atypical layers and sequences require unusual magmatic processes, and all of these sequences (chromitites, Merensky Reef, pyroxenite marker, magnetitite) have been attributed to the addition of magma into a partially crystallised magma chamber. Magma addition is an unpredictable and erratic event. For such an event to occur synchronously in two disparate magma cham- bers 200?300 km apart (Fig. 1) seems unlikely. For addition to have occurred repeatedly (at least six times to produce unambiguously identical rock sequences) must be considered highly implausible. For example, there are no reported examples of sepa- rate volcanic centres, over 200 km apart, which display matching eruption sequences either tempora- rily or geochemically. Every volcano has its own unique evolutionary sequence. It seems more logical therefore to assume that the western and east- ern limbs were connected and part of one magma R.G. Cawthorn, S.J. Webb / Tectonophysics 330 (2001) 195?209 199 Fig. 4. Comparison between the Middle Group chromitite sequences, and Cr2O3 and Al2O3 contents of the chromite layers in the eastern (vertical profile A) and western (profile B) limbs (data from Hatton and Von Gruenewaldt, 1987). Black shading ? chromitite; narrow spaced vertical lines ? pyroxenite; broadly spaced vertical lines ? norite; no shading ? anorthosite. chamber, rather than to suggest that these special processes could have repeatedly occurred at identical levels in totally separate bodies. 3. Petrological differences The previous discussion might suggest that the eastern and western limbs are identical. There are, indeed, certain differences. However, it should be stressed that there are also lateral differences even within each limb, which may represent gradual or abrupt facies changes. For example, all of the Middle Group chromitite layers change abruptly in absolute thickness on either side of the Steelpoort lineament (Fig. 1) in the eastern limb (Hatton and von Gruene- waldt, 1987), but each layer continues across the lineament. The thickness of the Merensky Reef increases from 20 cm to more than 7 m quite abruptly between Rustenburg and Brits in the western limb (Viljoen, 1994). The 1 m-thick layer of pyroxenite in the Main Zone, called the Pyroxe- nite Marker, is not present in the eastern part of the western limb or the southern part of the eastern limb, but the mineral compositional reversal persists in those areas (Klemm et al., 1985). In the eastern limb, the Lower and Critical Zone sequences are overstepped and disappear towards the south from Burgersfort to Stoffberg. The same diminution occurs from Rustenburg to Pretoria in the west (Fig. 1). Hence, whereas stratigraphic differences do occur, they occur as frequently within a single limb as between the limbs. 4. Geological complexities Petrologically, there are several similarities between the sequences in the eastern and western limbs, supporting the concept of continuity at least from the Critical Zone upwards. However, there are geological features that appear to contradict this model. For example, the western limb thins when traced eastward towards Pretoria (Fig. 1) suggesting it does not join with the eastern limb. However, at Moloto (Fig. 1) a vertical section of at least 300 m of olivine?apatite?magnetite-bearing rocks, analo- gous to Upper Zone rocks, has been intersected in bore core (Walraven, 1987). Further to the southeast, at Cullinan, the Premier diamondiferous kimberlite pipe cuts through a thinned Main Zone sequence (Bartlett, 1994), but no Upper Zone was developed. Even further south, 25 km southwest of Balmoral, Martini (1998) reported a small outcrop of Upper Zone material. Hence, there is considerable evidence for at least intermittent development of mafic rocks of the Bushveld Complex between the western and east- ern limbs to the east of Pretoria. Evidence for connectivity between the two limbs further north is more limited. However, outcrop of Upper Zone material is reported immediately west of the Marble Hall Dome (Hartzer, 1995), and 40 km east of Thabazimbi, at Rhenosterhoekspruit (Fig. 1), over 1200 m of layered magnetite gabbro has been reported (Eales and Cawthorn, 1996). These observations suggest that at least the Upper Zone had a substantial thickness in the centre of the two limbs. R.G. Cawthorn, S.J. Webb / Tectonophysics 330 (2001) 195?209200 Fig. 5. Schematic north?south section across both eastern (Olifants River to Belfast) and western (Union Section to Pretoria) limbs of the Bushveld Complex, shown in Fig. 1. Slight differences exist between such sections through each limb, but the principle of southward attenuation of the Lower and Critical Zones is emphasised. To the east of Brits and to the south of Roossenekal, Lower and Critical Zone rocks are missing, and only Main and Upper Zones are developed. In contrast, the thickest development of the Lower Zone rocks (as summarised by Eales and Cawthorn, 1996) is to be found in the Western limb south of Thabazimbi, at Union Section platinum mine, and in the Olifants River Trough in the eastern limb (Fig. 1). A schematic cross-section of the eastern and western limbs from north to south is shown in Fig. 5. These observations may be interpreted to suggest that the early stages of magmatism were focused in a long east?west chamber towards the north, and that intrusion of subsequent magmas became more extensive southwards. The parallelism between the thick ultramafic sequence and the Thabazimbi?Murchison lineament (Fig. 1) suggests that the latter had some control on the evolu- tion of the magma chamber. The original southern margin of the intrusion may have been controlled by the anticlinal axis of Archaean basement rocks running east?west through Johannesburg (Fig. 1). Downsag- ging in, or emplacement of, the magma chamber may have been more active initially in the north producing the Lower Zone, with the subsidence moving south- wards producing a thicker Upper Zone sequence in the south. With this model the facies changes would occur in parallel in both limbs of a single magma cham- ber from north to south, rather than between isolated limbs developing in the east and west. The above discussion indicates that physical connectivity of the magma chambers between eastern and western limbs appears far more likely than infer- ring that repeated and simultaneous magma addition occurred in two separate chambers over 200 km apart. R.G. Cawthorn, S.J. Webb / Tectonophysics 330 (2001) 195?209 201 Fig. 6. Isostatic implications for the double dipping sheet model for the Bushveld Complex. (a) Currently inferred section through the Bushveld Complex and Transvaal Supergroup, the inward-dipping geometry being attributed to isostatic response to emplacement of the Bushveld Complex (from Meyer and De Beer, 1987). (b) Schematic model of how the Bushveld may have originally been emplaced according to the model involving two inward-dipping, wedge-shaped sheets, which assumes no connection between eastern and western limbs. (c) Result of readjustment of Fig. 6b if the mass of these two wedges had been adequate to cause subsidence. Note that the result would have been outward ? not inward-dipping sheets. 5. Isostatic response There have been several qualitative allusions to isostatic adjustment of the crust due to the emplace- ment of the Bushveld Complex. Typically, it is suggested that the centripetal dips observed around the Bushveld Complex and the underlying Transvaal Supergroup sedimentary rocks result from crustal flexure in response to the load of each individual limb of the Bushveld Complex. Sharpe and Snyman (1980) suggested that each limb was discrete. They described the eastern limb as the result of coalescence of three bodies producing an elliptical body 50 km from west to east and 200 km from north to south. They concluded that the westward dip of these rocks resulted from continued subsidence within the basin of the Transvaal Supergroup. In other models for the western (Walraven and Darracott, 1976) and eastern (Molyneux and Klinkert, 1978) limbs, they are inferred to be inward-dipping wedges less than 100 km across that do not connect beneath the centre of the Bushveld. There are two problems associated with these inter- pretations. First, individually these wedges are less than 100 km in the east?west dimension. The loads imposed by bodies of such a size may have been too R.G. Cawthorn, S.J. Webb / Tectonophysics 330 (2001) 195?209202 Fig. 7. (a) Observed gravity profile across the entire Bushveld Complex from Nietverdiend (west) to Lydenburg (east) on Fig. 3 (from Meyer and De Beer, 1987). The two dashed lines are the computed gravity profiles for the models shown in Fig. 7c; dotted?dashed line for continuous Bushveld if the crust has a uniform thickness of 35 km, and dashed line if a depressed crustal model is used. (b) The interpretation of Meyer and De Beer (1987). Vertical shading indicates the Bushveld Complex. (c) Proposed simplified structure of the crust after isostatic readjustment in response to an intrusion 7-km-thick and continuous lateral extent of 400 km. Densities of rock types are indicated. small to have caused the crust to flex (Kearey and Vine, 1996). Second, the currently inward-dipping sheet model is shown in Fig. 6a. From palaeomagnetic evidence (summarised by Eales et al., 1993) these sheets were emplaced horizontally, as shown in Fig. 6b. If it is accepted that the crust was significantly weaker at the time of emplacement of the Bushveld (as suggested by Grotzinger and Royden, 1990), or that the loads were adequate to cause flexuring, the crust would have been deflected most underneath the thickest portions of these wedges, as shown in Fig. 6c. Such a geometry results in dips opposite from that seen today. It is only when the Bushveld is considered as being connected at depth that its lateral extent is sufficient to create a load large enough to cause the crust to bend and reach isostatic equilibrium in the centre. A typical Bouguer gravity profile across the Bush- veld Complex is shown by the solid line in Fig. 7a, from Meyer and De Beer (1987), who modelled it as two dipping sheets, which are not connected (Fig. 7b). Since the distance between the termination of these two limbs is about 200 km, the inference in this inter- pretation is that they never were connected. This grav- ity model is based on the assumption that the weight of the Bushveld Complex is sufficiently small so that the rigidity of the crust was able to sustain the excess load without undergoing major deformation or read- justment. This assumption may not be valid. The Bushveld Complex is 6?8 km thick (Fig. 2), and has an average density of 3050 kg m23. If it was contin- uous over an area of 65,000 km2 (Eales and Cawthorn, 1996), it would have been large enough to have caused flexure in the entire crust. Two recent examples of isostatic readjustment can be quoted to illustrate such responses. They illustrate rebound due to removal of load, rather than subsi- dence due to addition of load, but demonstrate the rapidity at which isostatic readjustments of the crust occur. Fennoscandia was covered by an ice-sheet R.G. Cawthorn, S.J. Webb / Tectonophysics 330 (2001) 195?209 203 Fig. 8. Evolution of the entire (approximately 35 km-thick) continental crust in response to the intrusion of the Bushveld Complex. (a) Intrusion of 7 km-thick body at a depth of 3-km. (b) Effect of isostatic readjustment. The 6-km depression of the base of the crust has been drawn as a gentle basin, but its exact morphology is not well-constrained. (c) Injection of 2-km-thick Bushveld Granite derived from melting at the base of the crust. The basin shown in the centre of the body would have filled rapidly with sediment and would influence the final shape and depth of the mafic rocks of the Bushveld Complex. Erosion of the section shown in Fig. 8c has taken place to expose the edges of the Bushveld Complex. 2.5 km thick 20,000 yr ago that caused depression of the crust by 600?700 m. Melting of the ice-sheet was complete about 10,000 yr ago, and the crust is now rising at a rate of over 1 cm per year (Kearey and Vine, 1996). Ice-sheets have tremendous lateral extent and may not provide an adequate analogue for the Bushveld Complex, although the density and thick- ness of the ice-sheet were much less than the Bush- veld Complex. In terms of size a more comparable analogue would be lakes such as Lake Bonneville, in western Utah (May et al., 1991) and Lake Minchin in the central Andes (Bills et al., 1994). The ancient shorelines of these now-dry lakes record a history of hydro-isostatic deflection. These lakes are roughly 200 km by 400 km by 140 m deep (Minchin) and 300 km by 400 km by 350 m deep (Bonneville), and caused depression of the crust and mantle by 20?40 and 50 m respectively. Whereas these loads occur on relatively thin lithosphere compared to the Kaapvaal craton, they demonstrate that loads of this wavelength can cause isostatic readjustment. By comparison, the mafic rocks of the Bushveld Complex have an average density some three times greater than ice and water, and are of a thickness some 3?20 times greater than the ice and water in these examples. We conclude that isostatic compensation upon emplacement of the Bushveld Complex would have been inevitable and rapid. The Bouguer gravity response of a continuous Bushveld has been forward modelled in Fig. 7 to produce isostatic equilibrium in the centre of the intrusion, and shows that the base of the crust should have been depressed by 6 km as a consequence (as shown in Fig. 7c). In this calculation we have assumed an initially homogeneous crust of thickness 35 km with a density of 2700 kg m23, the intrusion of a 7 km-thick body with a bulk density of 3050 kg m23, and a mantle density of 3300 kg m23. This model is simplistic, since it ignores the effects of crustal and mantle strength, and assumes perfect isostatic re-equilibration at its centre. However, the calculation is adequate to demonstrate that significant subsidence would have occurred, and that this effect needs to be considered in any interpretation of the gravity data. Emplacement of some 2 km of granitic rocks of the Bushveld Complex immediately postdates the mafic phase of the Bushveld Complex. The ages of the two events are not distinguishable in terms of conven- tional age determinations (Walraven et al., 1990). It has been suggested (Schweitzer et al., 1997) that the granite was formed by melting at the base of the crust as a result of heat liberated during underplating and interaction between the deep crust and the mafic magma. Fig. 8c shows the effect of this process in that the mafic rocks could have sunk a further 2 km as granite melt is extracted from underlying rocks and emplaced directly above the mafic sequence. The mafic sequence would therefore occupy a basinal structure deep below its original level in the centre. If the mafic rocks were emplaced below 3 km of roof rocks (Schweitzer et al., 1995), as indicated in Fig. 8a, the total depth to the top of the intrusion may be considerable (Fig. 8c). This depression is then assumed to have been filled by sedimentary rocks. The only place where a plausible sequence of such sedimentary rocks is still preserved at outcrop is near Moloto (Fig. 1), where Martini (1998) has described the deposition of the Loskop Formation as occurring immediately after emplacement of the Bushveld Complex, and emphasised that the nature of these immature conglomerates implies extremely rapid uplift and rugged topographic relief in the source area. The extent to which such rocks may have filled this rapidly subsiding basin is unknown. 6. Interpretation of the gravity profile The first-order gravity structure of the crust can now be examined in the light of this model. The Bouguer anomaly map (Fig. 3) shows the mafic rocks of the Bushveld Complex to have a well-defined 60?70 mGal anomaly relative to a regional back- ground of 2140 mGal. In fact, the entire Kaapvaal craton has significantly low Bouguer values compared to its surrounding regions. The density contrast between the mafic rocks and most of the crustal rocks is so large (350 kg m23) that the crustal sequence is not subdivided into different rock types in Fig. 7. Hence, a cross-section comprising rocks with only three densities is shown in Fig. 7; crustal rocks (density 2700 kg m23), the mafic phase of the Bushveld Complex (density 3050 kg m23), and mantle (density 3300 kg m23). The mafic rocks of the Bushveld Complex are assigned a uniform R.G. Cawthorn, S.J. Webb / Tectonophysics 330 (2001) 195?209204 thickness of 7 km, which continues under the central area. The gravity anomaly, created by a model in which the crust is of constant thickness (35 km), i.e. one with no compensation, shows that above the mafic rocks the Bouguer gravity anomaly reaches 100 mGal (Fig. 7a, dash?dot profile) relative to background. However, if the crust underneath the Bushveld Complex is assumed to have been depressed by 6 km, by isostatic response as explained above, the central gravity anomaly completely disappears (Fig. 7a, dashed profile), and closely matches the observed gravity profile from western to eastern Bushveld. This model is extremely simplistic, but demon- strates that the previous gravity models in which the consequences of isostasy were ignored are seriously flawed. When isostacy is considered, a crustal struc- ture with continuity between the eastern and western limbs of the Bushveld Complex is consistent with the gravity data. R.G. Cawthorn, S.J. Webb / Tectonophysics 330 (2001) 195?209 205 Fig. 9. Detailed west?east cross-section, taken at latitude 24.938 S, from longitude 25?31.58 E, incorporating the observed surface geology and inferred structural interpretation, as described in the text, and the observed (solid line) and calculated (dashed line) gravity profiles. Note that there is extreme vertical exaggeration in this section. The extended length of the profile relative to Fig. 7 was used to ensure that regional variations are accounted for, and that nearby interfering anomalies were modelled (such as the Far Western Limb outlier at 130 km). The densities (in kg m23) selected for these different units are taken from the compilation of Mare et al. (2001), and were: Stormberg Group (basic and felsic volcanics) ? 2700; Dwyka, Ecca and Beaufort Groups of the Karoo Supergroup (clastic sedimentary rocks) ? 2600; Waterberg Supergroup (clastic) ?2600; Bushveld Granite ? 2650; Bushveld mafic rocks ? 3050; Rooiberg Group (felsic volcanics) ? 2650; Transvaal Supergroup (clastic and chemical sedimentary rocks) ? 2700; undifferentiated basement (mainly granitic gneiss, with some pre- Transvaal Supergroup sedimentary sequences) ? 2700; and mantle.The constraints on the modelling were the surface geology, and agreement with seismic lines, where available (generally quite short relative to length of gravity section), e.g. Campbell (1990). However, it must be emphasised that this is only one possible interpretation that is consistent with the gravity data. The apparent abrupt vertical displacements at about 250 and 450 km along the section are updomes and not faults, but given the scale of the section they are shown as near-vertical boundaries. Note that the base of the crust has been isostatically depressed by about 6 km in this interpretation, which is the fundamental difference between this and all previously published models. Inspection of the geological map in Fig. 1 shows that there are numerous complications to such a simple synclinal shape to the Bushveld Complex. A more realistic cross-section than in Fig. 7 is shown in Fig. 9, and is accurately modelled along the traverse shown in Fig. 3. The detailed geology and appropriate density contrasts are incorporated in this section. There is one part of the cross-section that remains unresolved. At 330 km along the section, correspond- ing to longitude 28.258 in Fig. 3 there is a gravity high. It has been modelled here as an upfold of the mafic rocks of the Bushveld Complex, but may be related to a pre-Karoo volcanic sequence identified in bore core by Frick and Walraven (1985). However, being composed of basalt to trachyte the density of these rocks may not be adequate to produce the observed Bouguer anomaly. The variations in thickness of the Transvaal Supergroup shown in the model in the centre of the basin are unconstrained. However, the main purpose of Fig. 9 is to demonstrate that, given the available constraints of surface geology, density measurements, and a few peripheral seismic lines, the gravity data do not exclude the existence of a contin- uous Bushveld if the crust is assumed to have bent under the load. A future analysis of flexure parameters will permit evaluation of crustal strength at the time of Bushveld emplacement, but will depend upon careful analysis of the dip, load emplaced and timing of various defor- mation events. 6.1. Transvaal Supergroup inliers The gently dipping, synformal base of the complex, implied in Fig. 8, is inaccurate in detail. Numerous diapiric structures disturb this regular shape (Sharpe and Chadwick, 1982; Hartzer, 1995; Uken and Watkeys, 1997). These occur in both limbs, and on a variety of scales; for example, the relatively small Malope and Fortdraai Domes in the east (Fig. 1), over which the Critical and Main Zones may be extensively thinned (Sharpe and Chadwick, 1982; Marlow and Van der Merwe, 1977; Uken and Watkeys, 1997), and the larger, more complex inliers, such as the eastern Marble Hall and Dennil- ton Domes, and western Crocodile River Dome (Hartzer, 1995). In these larger inliers (Dennilton, Marble Hall and Crocodile River Domes), Hartzer (1995) suggested that at least some of the deforma- tion predated the emplacement of the mafic rocks, although they had also been metamorphosed and reactivated by the emplacement of the Bushveld Complex. The Fortdraai and Malope Domes are rela- tively small structures disrupting the continuity of the Bushveld Complex. The question arises as to whether the same model applies to all the structures. Hartzer (1995) suggested that these structural domes had been reactivated by the Bushveld Complex, but had also acted as barriers to lateral spreading of the magmas. He recorded metamorphic temperatures in these domes up to 5308C and 2.5 kbar pressure. Such high thermal gradients cannot be achieved by any regional or tectonic metamorphism, and require a magmatic heat source. Modelling such metamorphic conditions places constraints on the location of such a magma, which is here presumed to have been the Bushveld Complex. Hartzer (1995) presented a model in which he suggested that the Bushveld Complex thinned in proximity to these structures, and did not overlie them. With such a model, meta- morphic temperatures of 5008C could not be produced across 20-km-wide domal structures. Such metamorphic temperatures in these domes imply that the Bushveld Complex had to have been thick and continuous across these original structures. The suggestion that there had been pre-magmatic structural deformation is not questioned here, but their final disposition as inliers is attributed to doming due to the loading by the Bushveld Complex. Similar metamorphic grades have been reported in the Dennilton Dome (Hartzer, 1995), and so a similar model may be proposed. On the scale of the section (Fig. 9) these two domes appear as fault blocks with near-vertical contacts. In reality, they are domes, but the horizontal distance over which updoming occurred is too short to show accurately. In fact, near surface, the Crocodile River Dome is fault- bounded, but the intense folding in the interior of this structure suggests that it is largely diapiric. In the section (Fig. 9), it is assumed that uplift or tecton- ism has resulted in the complete erosion of the Bush- veld Complex over these two domes, but that the Bushveld Complex continues in between them, as is supported by the presence of Upper Zone rocks at Rhenosterhoekspruit (Fig. 1), north of the section in Fig. 9. R.G. Cawthorn, S.J. Webb / Tectonophysics 330 (2001) 195?209206 7. Other limbs The unique sequences in the eastern and western limbs listed above are not well-developed in the far western, northern and southeastern limbs. In the far west, only the lowermost layers are preserved and so comparison with the western limb is not possible (Eales and Cawthorn, 1996). In the southeastern limb only Lower and Upper Zone rocks are preserved, and so the chromitite layers, the Merensky Reef and the Pyroxenite Marker are not developed (Buchanan, 1975). In the northern limb, the Lower Zone contains more olivine and chromitite than the eastern or western limbs (Hulbert and Von Gruenewaldt, 1982). However, there is a Pyroxenite Marker and many thick magnetitite layers (Van der Merwe, 1976), and so some similarities with eastern and western limbs do exist. It is possible that all these limbs were interconnected and that the observed variations are merely lateral facies changes of the type seen from north of south in both the eastern and western limbs. However, it is not possible to prove unequivocally on petrological grounds that all limbs are sufficiently comparable and that they were once connected, as can be proposed for the eastern and western limbs. Hence, connectivity between these other limbs of the Bushveld Complex must remain speculative. 8. Conclusions In terms of rock types, sequences, mineral compo- sitions and isotopic ratios, the western and eastern limbs of the Bushveld Complex display many extre- mely remarkable similarities. Numerous unique and distinctive layers and sequences that occur in both limbs cannot be attributed to normal magmatic differ- entiation processes. Such similarities suggest that they were once contiguous. Petrologically the two limbs appear to have formed in the same magma chamber by processes having extreme lateral persistence. Yet, previous gravity interpretations have argued that they are not connected. A re-examination is presented here of the principles and assumptions behind these gravity models. Consid- eration of the isostatic effects upon the crust of the emplacement of mafic rock, 6?8 km thick and cover- ing 65,000 km2, suggests that depression of the base of the crust by up to 6 km may have occurred. As a result, it is concluded that it is perfectly plausible to construct a gravity profile, entirely consistent with that observed across the Bushveld Complex, in which the mafic rocks are continuous in the central region. This geometrical situation is possible, provided that the continental crust is depressed by 6 km under the Bushveld Complex as a consequence of isostatic readjustment due to the enormous mass of the mafic rocks. Acknowledgements We thank Chris Hatton, Andrew Mitchell, Edgar Stettler, Dennis Harry, Pierre Hattingh, Martin Bott and an anonymous referee for many valuable comments on various versions of this manuscript, and Mike Knoper for many discussions. Di Du Toit and Lyn Whitfield drafted the diagrams. We are also grateful to the Council for Geoscience for permission to reproduce a portion of the gravity map of the Republic of South Africa. 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A review of regional variations in facies and grade distribution of the Merensky Reef, western Bushveld Complex with some mining implications. In: Anhaeusser, C.R. (Ed.), XVth CMMI Congress. S. Afr. Instn. Mining Metall., Johannesburg, South Africa, vol. 3, pp. 183?194. Von Gruenewaldt, G., 1973. The Main and Upper Zones of the Bushveld Complex in the Roossenekal area, eastern Transvaal. Trans. Geol. Soc. S. Afr. 76, 207?227. Walraven, F., 1987. Geochronological and isotopic studies of Bush- veld Complex rocks from the Fairfield borehole at Moloto, northeast of Pretoria. S. Afr. J. Geol. 90, 352?360. Walraven, F., 1997. Geochronology of the Rooiberg Group, Trans- vaal Supergroup, South Africa. Economic Geology Research Unit, University of the Witwatersrand, Johannesburg, South Africa, Information Circular 316, 21 p. R.G. Cawthorn, S.J. Webb / Tectonophysics 330 (2001) 195?209208 Walraven, F., Darracott, B.W., 1976. Quantitative interpretation of a gravity profile across the western Bushveld Complex. Trans. Geol. Soc. S. Afr. 79, 22?26. Walraven, F., Armstrong, R.A., Kruger, F.J., 1990. A chronostrati- graphic framework for the north-central Kaapvaal Craton, the Bushveld Complex and Vredefort structure. Tectonophysics 171, 23?48. Wessel, P., Smith, W.H.F., 1995. New version of the generic mapping tools released. EOS Trans. Am. Geophys. Union 76, 329. R.G. Cawthorn, S.J. Webb / Tectonophysics 330 (2001) 195?209 209 Appendix D This appendix presents Nguuri et al. (2001) in its published format. Consequently, the formatting, layout, figure numbering and table titles do not follow the rest of the thesis. My contribution to this paper has been important; I made one of the diagrams and contributed to the text. 353 GEOPHYSICAL RESEARCH LETTERS, VOL. 28, NO. 13, PAGES 2501-2504, JULY 1, 2001 Crustal structure beneath southern Africa and its implications for the formation and evolution of the Kaapvaal and Zimbabwe cratons T. K. Nguuri,1 J. Gore,2 D. E. James,3 S. J. Webb,4 C. Wright,1 T. G. Zengeni,2 O. Gwavava,2 J. A. Snoke,5 and Kaapvaal Seismic Group6 Abstract. The formation of Archean crust appears to in- volve processes unique to early earth history. Initial results from receiver function analysis of crustal structure beneath 81 broadband stations deployed across southern Africa re- veal significant differences in the nature of the crust and the crust-mantle boundary between Archean and post-Archean geologic terranes. With the notable exception of the colli- sional Limpopo belt, where the crust is thick and the Moho complex, the crust beneath undisturbed Archean craton is typically thin (? 35?40 km), unlayered, and characterized by a strong velocity contrast across a relatively sharp Moho. This crustal structure contrasts markedly with that beneath post-Archean terranes and beneath Archean regions affected by large-scale Proterozoic events (the Bushveld complex and the Okwa/Magondi belts), where the crust tends to be rel- atively thick (? 45?50 km) and the Moho is complex. 1. Introduction With few exceptions, the oldest crustal cores of the con- tinents formed during Archean time [e.g. de Wit et al., 1992; Windley, 1995]. Evidence presented below indicates that the process of crustal formation in the Archean differed from that of post-Archean time. In this paper we highlight characteristics which distinguish the Archean crust and the crust/mantle interface from that of disturbed Archean and post-Archean terranes. The evidence from this study sug- gests that the M-discontinuity (Moho) beneath undisturbed Archean terranes tends to be a relatively simple interface characterized by a significant velocity contrast of at least 1 km/s. In contrast, Archean terranes that have been mod- ified by Proterozoic events typically exhibit complex Moho signatures and comparatively thick crustal sections, similar to what is observed in the Proterozoic mobile belts border- ing the cratons. 1Bernard Price Institute of Geophysical Research, University of the Witwatersrand, Wits, South Africa 2Department of Physics, University of Zimbabwe, Harare, Zimbabwe 3Department of Terrestrial Magnetism, Carnegie Institution of Washington, Washington, DC, USA 4Department of Geophysics, University of the Witwatersrand, Wits, South Africa 5Department of Geological Sciences, Virginia Tech, Blacks- burg, VA, USA 6http://www.ciw.edu/kaapvaal Copyright 2001 by the American Geophysical Union. Paper number 2000GL012587. 0094-8276/01/2000GL012587$05.00 Seismic station locations and a schematic outline of the principal geologic provinces of southern Africa are shown in Figure 1. The Archean Kaapvaal and Zimbabwe cratons form the continental nucleus of southern Africa. The in- tracratonic Bushveld Complex, the outcrop limbs of which are shown in Figure 1, is the largest known layered mafic in- trusion in the world (0.5?1.0 ? 106 km3) [Von Gruenewaldt et al., 1985]. It disrupted the northern Kaapvaal craton ca. 2.05 Ga and is seen as a major geologic domain, extending westward as far as Botswana [H. Kampunzu, pers. comm., 2000], far beyond the region of Bushveld outcrop and well into the mantle [James et al., 2001]. Sandwiched between the cratons is the Limpopo mobile belt, a collisional ter- rane formed when the Kaapvaal and Zimbabwe cratons were consolidated in late Archean time [Van Reenen et al., 1992]. The Limpopo belt is divided into a Northern Marginal Zone, a Central Zone, and a Southern Marginal Zone. Evidence presented below confirms that the two marginal zones are overthrust belts atop cratonic crust and that the Central Zone was a deep zone of tectonic deformation. The Kaapvaal 16?E 20?E 24?E 28?E 32?E 36?E 32?S 28?S 24?S 20?S 16?S 11 16 22 29 37 59 6061 62 63 64 65 66 67 68 69 70 71 72 74 75 78 79 02 05 09 10 14 15 19 20 26 27 28 33 34 35 36 42 43 44 48 49 53 54 58 01 03 04 07 08 12 13 17 18 23 24 25 30 31 32 38 39 40 45 46 47 50 51 52 55 56 57 73 76 77 80 81 82 Bushveld Complex Namibia Botswana Ma go nd i B elt Okwa Belt Kh ei ss B el t Cape Fold Belt Namaqua-Natal Belt Kaa pva al C rato n Limpopo Belt Zim bab we Cra ton LBTB SUR LBTB Figure 1. Location map for the southern Africa seismic array with a schematic overlay of southern African geological provinces. Station symbols in light gray denote stations deployed during the first year of the experiment, symbols in dark gray denote stations deployed during the second year of the experiment, and symbols in white denote stations deployed for the full two years of the experiment. Black squares denote global digital seismic stations. 2501 2502 NGUURI ET AL.: CRUSTAL STRUCTURE BENEATH SOUTHERN AFRICA 0 10 20 30 40 50 60 70 80 90 100 23 20 23 33 28 24 13 3 15 5 3 15 21 14 16 5 20 4 21 29 25 24 10 32 9 8 24 2 10 8 25 9 26 7 23 17 9 29 9 9 5 17 sa78 sa80 sa79 sa72 sa76 sa75 sa71 sa58 sa63 sa54 sa52 sa60 sa50 sa59 sa62 sa49 lbtb sa43 sa39 sa40 sa38 sa37 sa34 sa32 sa36 sa33 sa31 sa35 sa30 sa26 sa25 sa27 sa24 sa28 bosa sa18 sa19 sa17 sa20 sa14 sa15 sa13 Zimbabwe Craton Kaapvaal Craton Depth (km) 0 10 20 30 40 50 60 70 80 90 100 22 1616818241513 18323027 314302030107 1314 1626815 21156216201024177 10456 sa77 sa70 sa73 sa67 sa66 sa74 sa68 sa69 sa65 sa55 sa57 sa56 sa51 sa53 sa46 sa47 sa45 sa48 sa42 sa64 sa61 sa29 sa23 sa22 sa16 sa12 sa11 sa09 sa81 sa10 sa82 sa08 sa07 sur sa05 sa04 sa03 sa02 sa01 Limpopo: N. Marginal Zone Limpopo: Central Zone Limpopo: S. Marginal Zone Bushveld Province Okwa Belt Kheis Belt Namaqua-Natal Belt Cape Fold Belt Depth (km) CRATONIC NONCRATONIC Figure 2. One-dimensional phasing depth images for southern Africa based on receiver function stacks as described in text. Im- ages organized north to south by geologic province. The station name and number of events included in the stack are shown to the right of each trace. The dominant signal on the depth images is the Ps conversion from the Moho. Thin crust and strong am- plitude Ps Moho conversions are associated with undisturbed cra- ton; Moho images for disrupted craton and post-Archean terranes tend to be more diffuse and of smaller amplitude. Areas of dis- rupted craton, including the Bushveld Complex and the Magondi belt affecting the southwest corner of the Zimbabwe craton have been classified as ?noncratonic,? as is the Limpopo belt. Sev- eral stations in the vicinity of the Bushveld Complex and along a zone extending westward into the Okwa belt are grouped as part of the Kaapvaal craton, although their structure suggests they were affected by Proterozoic events (see text). craton is bounded on the south and east by the subduction- related Namaqua-Natal Proterozoic orogenic belt (ca 1.1? 1.9 Ga) and on the west by the Kheis overthrust belt (ca 2.0 Ga) [de Wit et al., 1992]. The complex region north of the Kheis belt and west of the Limpopo belt and Zimbabwe craton is part of the ? 2 Ga Okwa and Magondi belts. The geology of the Okwa/Magondi region remains poorly under- stood owing to complex tectonic and magmatic overprinting of Proterozoic events on Archean basement, as well as to the fact that extensive Kalahari sand cover obscures much of the regional geology. The Cape Fold belt in the southernmost part of the region of study is Phanerozoic in age. 2. Data and Methodology The southern Africa seismic experiment utilized 55 broad- band REFTEK/STS2 instruments deployed at 81 stations between April 1997 and July 1999. The continuously recorded data of the portable experiment were supplemented by data from three global digital stations in the region of the ar- ray (Figure 1). We processed 35 teleseismic events to yield a comprehensive set of high-quality receiver functions (see [Ammon, 1991] for review and other references). Receiver functions were corrected for moveout, binned by station and stacked at depth intervals of 0.5 km between 1 km and 101 km. The resulting spatial (phasing depth) spike series im- age reflects primarily the S-velocity discontinuity structure beneath each station [Dueker and Sheehan, 1998; Gurrola et al., 1994]. The crustal model for the moveout correc- tion is based on a refraction seismic model for the Kaapvaal with an average P-wave velocity for the crust of 6.5 km/sec, Poisson?s ratio of 0.25, and Moho depth of 38 km [Durrheim and Green, 1992]. The phasing depth images for the south- ern Africa array are plotted in Figure 2 and arranged by geological province. The first (zero-depth) peak, partially truncated, is simply the coherence peak of P-wave arrivals. Subsequent peaks on the records are related to velocity dis- continuities at depth. As seen from Figure 2, only one con- sistent Ps signal occurs, and it is readily associated with the Moho. The results shown in Figure 2 are summarized in the form of a color-coded map of Moho depth in Figure 3. As the velocity-depth model was constructed by averaging seismic refraction results for the Kaapvaal craton, the model may be an underestimate of mean crustal velocity and crustal thickness for off-craton or modified cratonic regions. Crustal thickness data tabulated by station may be downloaded from www.ciw.edu/kaapvaal/pubs/crust/nguuri table1.pdf. 3. Results Phasing depth images based on receiver functions are shown in Figure 2, arranged by geologic province. The or- ganization of stations by province is ambiguous in places, notably in the Okwa/Magondi belt of eastern Botswana, where cratonic structures are overprinted by late Archean and Proterozoic (2 Ga) events, and in the general vicinity of 16?E 20?E 24?E 28?E 32?E 36?E 32?S 28?S 24?S 20?S 16?S 26 29 32 35 38 41 44 47 50 53 56 NAMIBIA BOTSWANA ZIMBABWE R.S.A. Zimbabwe Craton Limpopo Belt Kaapvaal Craton Namaqua-Natal Mobile Belt Cape Fold Belt Kheis Belt Okwa Terrane Magondi Mobile Bel t Crustal Thickness (km ) Bushveld Complex Figure 3. Color-coded contour map of depth to Moho beneath the southern Africa array based on phasing depth images of Fig- ure 2 and as tabulated in the electronic supplement to this paper. Crustal thickness color scale is shown on right. Thin crust tends to be associated with undisturbed areas of craton, particularly in the southern and eastern parts of the Kaapvaal craton and in the Zimbabwe craton north of the Limpopo belt. Greater crustal thickness is associated with the Bushveld region and its westward extension into the Okwa and Magondi belts. Crustal thickness is also greater in the central zone of the Limpopo belt and in the Proterozoic Namaqua-Natal mobile belt. NGUURI ET AL.: CRUSTAL STRUCTURE BENEATH SOUTHERN AFRICA 2503 the Bushveld, where the boundary between disturbed and undisturbed craton is poorly defined. The crust beneath Proterozoic belts and cratonic terranes modified in Protero- zoic time is in almost all cases thicker than that beneath the cratons. 3.1. Kaapvaal and Zimbabwe cratons. Stations located within undisturbed Kaapvaal or Zim- babwe craton typically have sharp, large amplitude Ps con- verted signals from the Moho. Distinctive among the cra- tonic results are those from stations located in the Zim- babwe craton, where Moho depths, with one exception, clus- ter between 34 and 37 km. Results for the Kaapvaal cra- ton exhibit more variability, with crustal thickness vary- ing between about 33 and 45 km, but averaging close to 38 km. Most of the Kaapvaal stations exhibiting greater crustal thickness are situated in regions immediately adja- cent to the Bushveld and Okwa/Magondi terranes, suggest- ing that crustal modification in Proterozoic time may have been more widespread than is indicated by surface geology. Crustal reworking in the Proterozoic would be consistent with tomographic results [James et al., 2001] which show that most of the northern stations of the Kaapvaal craton overlie modified mantle characterized by lower seismic ve- locities. Thus the stations in the extended region of the Bushveld and Okwa/Magondi Proterozoic terranes may rep- resent disturbed rather than stable craton. 3.2. Bushveld and Okwa/Magondi terranes. The crust thickens systematically across the boundary between undisturbed craton and stations near and in the Bushveld Complex and the Okwa/Magondi terranes. As seen in Figure 3, the lithosphere disturbance associated with the Bushveld event appears to be part of a broad zone of 2 Ga activity that may extend from the Bushveld into the Okwa/Magondi belt of similar age in eastern Bostwana. Rel- ative to the undisturbed craton to the south, that entire re- gion is characterized by thick crust and lower upper mantle velocities [James et al., 2001]. The evidence reported here for a thick crust and a relatively diffuse Moho beneath the Bushveld is consistent with the notion of a broadly continu- ous mafic body at depth [Cawthorn and Webb, 2001; Webb et al., 2000]. The substantial load of material added to the crust during the Bushveld event appears to have produced a downward crustal flexure of several km [Webb et al., 2000]. The nature of the 2 Ga crustal overprint associated with the Okwa/Magondi belt is poorly understood, although it is evident from the wealth of diamond production that the Archean geotherms were not significantly elevated during the Proterozoic event. 3.3. Limpopo belt. The intercratonic Limpopo belt remains the subject of geological debate over its presumed origin as an Archean collisional zone [Van Reenen et al., 1987; Van Reenen et al., 1992]. Depth images for the marginal zones are typical of cratonic structure, both in character of the Ps conver- sion and in crustal thickness. The northern marginal zone is underlain by crust about 37 km thick, typical of the ad- jacent Zimbabwe craton, and the southern marginal zone has a crust around 40-42 km thick, consistent with that of the adjacent Kaapvaal craton (see Figure 2). The cen- tral Limpopo belt, the site of pervasive deformation during the collision of the Kaapvaal and Zimbabwe cratons in the Archean, displays particularly complex structure. In some instances (e.g., stations sa66 and sa67) the identification of the Moho is ambiguous and could be resolved only with con- straints from two-station surface wave phase velocity inver- sions, where thicker crust is required to satisfy the dispersion data. The broad and comparatively weak Ps images have maxima that indicate depths between 40 and 53 km and are indicative of a structurally complex Moho. While there is some evidence for a deep crustal discontinuity at about 30-35 km depth beneath some stations, interstation surface wave phase velocity inversion results show unambiguously that the crust must be in excess of 40?45 km thick beneath the Limpopo Central Zone (unpublished data). As with the Bushveld, the relatively thick crust beneath the Limpopo is not compensated by higher elevations, suggestive of a dense lower crust. 3.3.1. Kheis belt The clear cratonic signatures of the northern and southern marginal zones of the Limpopo belt are not evident in the Kheis Thrust belt of the western Kaapvaal (Figure 1). Although the Kheis belt is known from nodule studies to overlie the craton, the observed Ps Moho signals are weak. The lack of a purely ?cratonic? signature is consistent with tomographic images of the upper mantle, where strong positive seismic velocity perturbations in the mantle beneath the central region of the craton diminish be- neath the Kheis belt [James et al., 2001]. The crust beneath the Kheis belt is generally thin (< 40 km), however, more characteristic of the undisturbed cratonic crust to the east than of the extended Bushveld and Okwa/Magondi terranes to the north. 3.4. Namaqua-Natal and Cape Fold belts. While results are comparatively sparse for the Namaqua- Natal and Cape Fold belts, measurements of crustal thick- ness are typically 40?50 km throughout the Namaqua-Natal belt and northern Cape Fold belt. Within the Cape Fold belt, the crust thins to about 30 km near the African coast. 4. Discussion Among the most significant findings of the present study is evidence for pervasive Proterozoic (ca 2 Ga) modifica- tion and thickening of Archean crust across a broad east- west zone bounded on the east by the Bushveld and on the west by the Okwa/Magondi terranes. The area of thickened crust corresponds closely to the zone of reduced upper man- tle velocities found from body wave tomography [James et al., 2001]. Moho Ps conversions for stations in this region of disturbed craton tend to be low in amplitude and in some cases ambiguous, suggesting that the Moho is a weak and/or transitional (e.g., > 5 km) boundary. One possible interpre- tation of the poor Ps signals is that they reflect Proterozoic age magmatic underplating or reworking of Archean crust (e.g., [Griffin and O?Reilly, 1987]). While magmatic addi- tion to the crust is plausible beneath the Bushveld Complex, the cause of increased crustal thickness elsewhere in the re- gion of Proterozoic overprinting is not so apparent. Both crustal thickness and the Moho signature observed in the region of modified Archean crust are similar to those ob- served at stations in the Proterozoic Namaqua-Natal belt. Durrheim and Mooney found that Archean crust world- wide is typically 27?40 km thick, whereas Proterozoic crust 2504 NGUURI ET AL.: CRUSTAL STRUCTURE BENEATH SOUTHERN AFRICA is about 40?55 km thick, with higher velocity material (> 7 km/s) at its base [Durrheim and Mooney, 1994]. Our find- ings are in substantial agreement with that conclusion. The thinnest crust (35?40 km) is found beneath those regions of the Kaapvaal and Zimbabwe cratons that have been undis- turbed since Archean time. The clear Ps Moho conversions for undisturbed craton indicate a strong velocity contrast (1 km/s or more) across a sharp Moho. Seismic refraction re- sults and studies of crustal xenoliths suggest that the lower crust of cratonic southern Africa may be less mafic on av- erage (and hence less dense and lower velocity) than that of post-Archean lower crust [Durrheim and Mooney, 1994; Griffin and O?Reilly, 1987; Rudnick and Fountain, 1995]. Results from this study, while not definitive, are consistent with an intermediate or intermediate-to-mafic lower crustal composition beneath undisturbed cratons. The central zone of the Limpopo belt is characterized not only by thick crust (up to 50 km or more) and com- plex Moho structure, but geologic evidence indicates that 20-30 km of crustal uplift and exhumation have taken place since Archean time [Treloar et al., 1992]. If correct, this im- plies that the crustal section beneath the Limpopo belt in the Archean was comparable to the thickest crust observed today anywhere in the world. Acknowledgments. The Kaapvaal Project involves the efforts of more than 100 people affiliated with about 30 insti- tutions. Details of participants and a project summary can be found at the Kaapvaal website www.ciw.edu/kaapvaal. We owe a special debt to Dr. Rod Green who sited and constructed almost all of the stations of the southern Africa experiment and kept them running during the course of the experiment. As usual, su- pertech Randy Kuehnel was indispensable. Particular thanks are owed to the able crew of the PASSCAL Instrument Center. We thank Andy Nyblade and Walter Mooney for thoughtful and very helpful reviews of the original manuscript. This work was sup- ported by the National Science Foundation Continental Dynamics Program, the National Research Foundation of South Africa and by universities, Geological Surveys, and exploration companies in South Africa, Zimbabwe, and Botswana. Map figures were pro- duced with GMT [Wessel and Smith, 1991]. References Ammon, C.J., The isolation of receiver effects from teleseismic P waveforms, Bull. Seismol. Soc. Am., 81, 2504?2510, 1991. Cawthorn, R.G., and S.J. Webb, Connectivity between the west- ern and eastern limbs of the Bushveld Complex, Tectono- physics, 330, 195?209, 2001. de Wit, M.J., C. Roering, R.J. Hart, R.A. Armstrong, C.E.J. de Ronde, R.W.E. Green, M. Tredoux, E. Peberdy, and R.A. Hart, Formation of an Archaean continent, Nature, 357 (6379), 553?562, 1992. Dueker, K.G., and A.F. Sheehan, Mantle discontinuity structure beneath the Colorado Rocky Mountains and High Plains, J. Geophys. Res., 103, 7153?7169, 1998. Durrheim, R.J., and R.W.E. Green, A seismic refraction investi- gation of the Archaean Kaapvaal Craton, South Africa, using mine tremors as the energy source, Geophys. J. Int., 108, 812? 832, 1992. Durrheim, R.J., and W.D. Mooney, Evolution of the Precam- brian lithosphere: Seismological and geochemical constraints, J. Geophys. Res., 99, 15,359?15,374, 1994. Griffin, W.L., and S.Y. O?Reilly, The composition of the lower crust and the nature of the continental Moho-xenolith evi- dence, in Mantle xenoliths, edited by P.H. Nixon, pp. 413?432, John Wiley & Sons, Chichester, United Kingdom, 1987. Gurrola, H., J.B. Minster, and T.J. Owens, The use of velocity spectrum for stacking receiver functions and imaging upper mantle discontinuities, Geophys. J. Int., 117, 427?440, 1994. James, D.E., M.J. Fouch, J.C. VanDecar, S. van der Lee, and Kaapvaal Seismic Group, Tectospheric structure beneath south- ern Africa, Geophys. Res. Lett., this issue, 2001. Rudnick, R.L., and D.M. Fountain, Nature and composition of the continental crust: A lower crustal perspective, Rev. Geo- phys., 33 (3), 267?309, 1995. Treloar, P.J., M.P. Coward, and N.B.W. Harris, Himalayan- Tibetan analogies for the evolution of the Zimbabwean Craton and Limpopo belt, Precamb. Res., 55, 571?587, 1992. Van Reenen, D.D., J.M. Barton, C.A. Roering, C.A. Smith, and J.F. Van Schalkwyk, Deep crustal response to continental colli- sion: The Limpopo belt of southern Africa, Geology (Boulder), 15, 11?14, 1987. Van Reenen, D.D., C. Roering, L.D. Ashwal, and M.J. de Wit, Regional geological setting of the Limpopo belt, Precamb. Res., 55, 1?5, 1992. Von Gruenewaldt, G., M.R. Sharpe, and C.J. Hatton, The Bushveld Complex: Introduction and review, Economic Ge- ology, 80, 803-812, 1985. Webb, S.J., T. Nguuri, D.E. James, and T.H. Jordan, Crustal thickness supports Bushveld continuity, Eos Trans. AGU, Sup- plement, 81 (19), S175, 2000. Wessel, P., and W.H.F. Smith, Free software helps map and dis- play data, Eos Trans. AGU, 72, 445-446, 1991. Windley, B.F., The evolving continents, 526 pp., John Wiley and Sons Ltd., Chichester, England, 1995. T. K. Nguuri and C. Wright, Bernard Price Institute of Geo- physical Research, University of the Witwatersrand, Wits 2050, South Africa. J. Gore, T. G. Zengeni and O. Gwavava, Department of Physics, University of Zimbabwe, Harare, Zimbabwe. D. E. James, Department of Terrestrial Magnetism, Carnegie Institution of Washington, 5241 Broad Branch Rd., N.W., Wash- ington, DC 20015, USA. (e-mail: james@dtm.ciw.edu) S. J. Webb, Department of Geophysics, University of the Wit- watersrand, Wits 2050, South Africa. J. A. Snoke, Department of Geological Sciences, Virginia Tech, Blacksburg, VA 24061, USA. Kaapvaal Seismic Group, http://www.ciw.edu/kaapvaal. (Received November 6, 2000; revised March 14, 2001; accepted March 16, 2001.) Appendix E This appendix contains the fortran programs used to calculate the gravity response as detailed in Chapter 3 and 5. Original code derived from Lees and VanDecar (1991). Program: gravity_crustal_elev_regional.f as used in Chapter 3. program gravity_crustal_elev_regional implicit undefined (a-z) C Original code is from John VanDecar gravity.f but was linked to C subroutines that John used C used in the tomography inversion. This version can be run C independently of VanDecar?s tomographic inversion and only C requires the subroutine DELAZ5. This subroutine was provided by C John VanDecar, who obtained it from Brian Savage and traces back C to Kanamori. C C SJW January 2005, fixed some bugs in formatting C SJW February 28, 2005 C (large parts from gravity.f by John Vandecar) C This code takes lat long crustal thickness values that C have been interpolated to an even grid and C calculates the value of total value and vertical C component of gravity C at various latitudes and longitudes on a spherical surface. C 8901234567890123456789012345678901234567890123456789012345678901 C C Bug fix March 27, 2005 C Fixed definitions of sph prims lat and longs. C renamed lat long variables to make more sense C (See book 4, pages 3-5 for explanation) C C April 2, 2005 added get arg capabilities. C To compile this program use: C cl gravity_crustal_regional where cl is a little script that C will compile and link the program C C (Old method: C f77 gravity_crustal_elev_regional.f -o gravity_crustal_elev_regional) C Actually this still works.... C C To run this program use: C Cgravity_crustal_elev_regional 300 300 300 50 50 50 50 300 0 100 200 0 > C grav_moho_elev_den_regional_out_1.dat C C where the numbers are the density contrasts across the Moho C in the 12 tectonic regions (see tectonic_regions.txt for C details. C C April 3, 2005 C added crustal regionalization information C will need to make density an array C C April 4, 2005 358 C file of crustal thicknesses now ready. C character*80 calcpoints, crustthick character argv*10 character dummy*5 character type*5 integer maxsiz parameter (maxsiz = 200) integer i,j,k,l,m,n integer geo(maxsiz,maxsiz) integer iargc C iargc is part of getarg real deltrad,deltdeg,deltkm,azes,azesdg,azse,azsedg real edist, colatcalcr(maxsiz), colatr(maxsiz) real dellong real delcolat, dist real gper(maxsiz,maxsiz), grav, gravvert real lat(maxsiz),long(maxsiz), longr(maxsiz) real longmaxr(maxsiz), longminr(maxsiz) real latcalc(maxsiz), longcalc(maxsiz) real longcalcr(maxsiz) real radius, rmid(maxsiz,maxsiz) real thick(maxsiz,maxsiz) double precision bigg, f, pi double precision densityc(maxsiz) double precision density double precision colatminr(maxsiz), colatmaxr(maxsiz) double precision dellongr, delcolatr double precision rtop, rbot, thickavg, volume C functions external getarg, edist, DELAZ5 C Units for values: bigg(m^3/(kg*s^2)), densityc(kg/m^3), C radius(km) parameter (pi=3.141592654) parameter (f=180.0/pi) parameter (bigg = 6.67d-11) parameter (radius = 6371.0) parameter (thickavg = 41.0) C data densityc /450./ C data densityc /400./ C data densityc /350./ C data densityc /300./ C data densityc /250./ C data densityc /200./ C data densityc /150./ C data densityc /100./ C data densityc /50./ C These MUST be 1/2 of a degree (not 50 km) 359 C so that cell walls line up dellong = 0.5 dellongr = dble(0.5/f) delcolat = 0.5 delcolatr = dble(0.5/f) i = 0 j = 0 k = 0 l = 0 C later the input files be changed to be part of the run C statement with cread: calcpoints='calculate_gravity_here_sorted.xy' crustthick= & 'padded_crustal_thickness-elev_for_gravity_geo_sorted.xyz' C Read in the values of density for geo regions C or based on thicknesses using getarg see syntax in c tectonic_regions.txt n = iargc() call getarg(1,argv) read(argv,*) type if (type.eq.'geol') then goto 5 else if (type.eq.'thic') then goto 6 else goto 9 end if 5 do m = 2,n call getarg(m, argv) read(argv,*) densityc(m-1) write(0,*) type, m, m-1, n, argv, densityc(m-1) enddo goto 10 6 do m = 2,n call getarg(m, argv) read(argv,*) densityc(m-1) write(0,*) type, m, m-1, n, argv, densityc(m-1) enddo goto 10 9 write(0,*) type write(0,*) "first field must be geol or thic" stop 10 continue 360 C Read in the positions that gravity will be calculated C at. This is over the whole range of the area, but C can be more limited, hence indicies (k,l) can be different C from i,j. C The file is in lat long, but we need colatitude and long. C The interval is by half degrees. Reads in fine. Be sure C to use sorted file. C write(*,*)" k, l, latcalc(l), longcalc(k) " open(unit=15,file=calcpoints,status='old',form='formatted') do k = 1,49 do l = 1,41 read(15,*) longcalc(k), latcalc(l) C write(*,*) k,l, longcalc(k), latcalc(l) enddo enddo close(15) C Testing works fine! C do k = 1,49 C do l = 1,41 C write(*,*) k,l, longcalc(k), latcalc(l) C enddo C enddo C Read in the crustal thickness values. These are the values C determined from the crustal thickness studies, and extracted C from the gridded data for more even coverage. C They have been padded in the region outside of the study C to the average value of the thickness C File has been formatted and sorted. C These lat longs need different names from the previous for C distinction when doing the distance and angle calculation C C Add regional information to the crustal thickness C values geo(i,j) dummy C write(*,*) "i,j, long(i), lat(j), thick(i,j), geo(i,j), dummy" open(unit=16,file=crustthick,status='old') do i = 1,49 do j = 1,41 read(16,*) long(i),lat(j),thick(i,j),geo(i,j),dummy C write(*,*) i,j,long(i),lat(j),thick(i,j),geo(i,j) C write(*,*) dummy enddo enddo close(16) C Testing works fine! C write(*,*) "i,j, long(i), lat(j), thick(i,j)" C do i = 1,49 C do j = 1,41 C write(*,*) i,j, long(i), lat(j), thick(i,j) C enddo C enddo C Check that all constants etc are what they should be. C write(*,*) "pi,f, bigg, radius, dellong" C write(*,*) "dellongr, delcolat, delcolatr, thickavg" C 361 C write(*,*) pi, f, bigg, radius, dellong C write(*,*) dellongr, delcolat, delcolatr, thickavg C write(0,*) "done with prelim checks" C Some paramters for volume calculation C in radians C C Note: MUST loop through all as thick(i,j) C changes. Many will be zero, have added a check to C to skip any where thick(i,j) equals 41 km. grav = 0.0 i = 0 j = 0 do k = 1,49 do l = 1,41 longcalcr(k) = real((longcalc(k)*1.0/f)) colatcalcr(l) = real((-latcalc(l)+90.0)*1.0/f) do i = 1,49 C do i = 23,24 do j = 1,41 C This works to deflect all calculations for depth of 41.0 C write(0,*)"doing calculation",long(i),lat(j),rmid(i,j) C Checked ok. rtop = dble(radius - thick(i,j)) rbot = dble(radius - thickavg) rmid(i,j) = real((rtop+rbot)/2.0) if (rmid(i,j).ne.6330.0) then C Now we need a series of if, elseif statements C to incorporate the regional geology effects. if (type.eq.'geol') then if (geo(i,j).eq.1) then density = densityc(1) else if (geo(i,j).eq.2) then density = densityc(2) else if (geo(i,j).eq.3) then density = densityc(3) else if (geo(i,j).eq.4) then density = densityc(4) else if (geo(i,j).eq.5) then density = densityc(5) else if (geo(i,j).eq.6) then density = densityc(6) else if (geo(i,j).eq.7) then density = densityc(7) else if (geo(i,j).eq.8) then density = densityc(8) else if (geo(i,j).eq.9) then 362 density = densityc(9) else if (geo(i,j).eq.10) then density = densityc(10) else if (geo(i,j).eq.11) then density = densityc(11) else if (geo(i,j).ge.12) then density = densityc(12) endif C write(0,*) type, density, thick(i,j), geo(i,j) C write(0,*) long(i), lat(j) C Now the same thing for thickness variations C else if (type.eq.'thic') then if (thick(i,j).ge.24.0.AND.thick(i,j).lt.26.0) then density = densityc(1) else if (thick(i,j).ge.26.0.AND.thick(i,j).lt.28.0) then density = densityc(2) else if (thick(i,j).ge.28.0.AND.thick(i,j).lt.30.0) then density = densityc(3) else if (thick(i,j).ge.30.0.AND.thick(i,j).lt.32.0) then density = densityc(4) else if (thick(i,j).ge.32.0.AND.thick(i,j).lt.34.0) then density = densityc(5) else if (thick(i,j).ge.34.0.AND.thick(i,j).lt.36.0) then density = densityc(6) else if (thick(i,j).ge.36.0.AND.thick(i,j).lt.38.0) then density = densityc(7) else if (thick(i,j).ge.38.0.AND.thick(i,j).lt.40.0) then density = densityc(8) else if (thick(i,j).ge.40.0.AND.thick(i,j).lt.42.0) then density = densityc(9) else if (thick(i,j).ge.42.0.AND.thick(i,j).lt.44.0) then density = densityc(10) else if (thick(i,j).ge.44.0.AND.thick(i,j).lt.46.0) then density = densityc(11) else if (thick(i,j).ge.46.0.AND.thick(i,j).lt.48.0) then density = densityc(12) else if (thick(i,j).ge.48.0.AND.thick(i,j).lt.50.0) then density = densityc(13) else if (thick(i,j).ge.50.0.AND.thick(i,j).lt.52.0) then density = densityc(14) else if (thick(i,j).ge.52.0.AND.thick(i,j).lt.54.0) then density = densityc(15) else if (thick(i,j).ge.54.0.AND.thick(i,j).lt.56.0) then density = densityc(16) else if (thick(i,j).ge.56.0.AND.thick(i,j).lt.58.0) then density = densityc(17) endif C write(0,*) type, density, thick(i,j) C write(0,*) long(i), lat(j) end if longr(i) = (long(i))/f longmaxr(i) = longr(i) + (dellongr/2.0) longminr(i) = longr(i) - (dellongr/2.0) C Checked ok. 363 C write(*,*) "long(i), longr(i), dellongr" C write(*,*) "longmaxr, longminr" C write(*,*) long(i), longr(i), dellongr C write(*,*) longmaxr(i), longminr(i) C Needs to be double precision for later. colatr(j) = (-lat(j) + 90)/f colatminr(j) = dble(colatr(j) - (delcolatr/2.0d0)) colatmaxr(j) = dble(colatr(j) + (delcolatr/2.0d0)) C Checked ok. C write(*,*) "lat(j), colatr(j), delcolatr" C write(*,*) "colatminr(j), colatmaxr(j)" C write(*,*) lat(j), colatr(j), delcolatr C write(*,*) colatminr(j), colatmaxr(j) volume = dble(dellongr)*(rtop**3-rbot**3) & *(dcos(colatminr(j))-dcos(colatmaxr(j)))/3.0d0 C Checked ok. C write(*,*) "volume,colatminr(j),colatmaxr(j),dellongr" C write(*,*) volume,colatminr(j),colatmaxr(j),dellongr C This is total gravity not vert comp for the moment... gper(i,j) = volume*bigg*1.0d5*density C write(*,*)"check gper", gper C C write(*,*) "sending to edist" C write(*,*) radius,colatcalcr(l),longcalcr(k) C write(*,*) rmid(i,j),colatr(j),longr(i) C Everything sent to edist must be real dist = edist(radius, colatcalcr(l), longcalcr(k), & rmid(i,j), colatr(j), longr(i)) C write(*,*) "value back is", dist C write(*,*) "latcalc, longcalc",longcalc(k),latcalc(j) C Total value of gravity (want only vert component!) C The factor of 1000 is to go from km to m grav = grav + (gper(i,j)*1000.0)/(dist**2) C This uses the midpoint call DELAZ5(latcalc(l),longcalc(k),lat(j),long(i), & deltrad,deltdeg,deltkm,azes,azesdg,azse, & azsedg,0) 364 C write(*,*)latcalc(l),longcalc(k),lat(j),long(i), C & deltrad,deltdeg gravvert = gravvert + (gper(i,j)*1.0d3)* & (dble(radius)-dble(rmid(i,j))* & (dcos(dble(deltrad))))/(dble(dist)**3) C write(*,*) k,l,radius,latcalc(l), colatcalcr(l) C write(*,*) longcalc(k), longcalcr(k) C write(*,*) i,j, rmid(i,j),colatr(j),longr(i) C write(*,*) grav, dist, gper(i,j) C write(*,*) " " C write(*,*) i,j,dellongr,rtop,rbot C write(*,*) lat(j), colatr(j), colatminr(j),colatmaxr(j) C write(*,*) thick(i,j), rmid(i,j), volume C write(*,*) " " else goto 25 endif 25 continue enddo enddo write(*,*) k,l,longcalc(k), latcalc(l), gravvert, grav grav = 0.0 gravvert = 0.0 enddo enddo C stop end c --------------------------------------------------------------------- real function edist(r1, t1, p1, r2, t2, p2) c . . get euclidian distance from 2 sets of spherical polar coordinates c . . . r = radius c . . . t = colatitude c . . . p = longitude real r1, t1, p1, r2, t2, p2 real x1, y1, z1, x2, y2, z2 x1 = r1*sin(t1)*cos(p1) y1 = r1*sin(t1)*sin(p1) z1 = r1*cos(t1) x2 = r2*sin(t2)*cos(p2) y2 = r2*sin(t2)*sin(p2) z2 = r2*cos(t2) c write(*,*)"r1,t1,p1,r2,t2,p2 in edist" c write(*,*) r1,t1,p1 c write(*,*) r2,t2,p2 c write(*,*) "x1, y1, z1, x2, y2, z2" c write(*,*) x1, y1, z1 c write(*,*) x2, y2, z2 edist = sqrt((x1-x2)**2+(y1-y2)**2+(z1-z2)**2) 365 return end c---------------------------------------------------------------------- SUBROUTINE DELAZ5( THEI, ALEI, THSI, ALSI, DELT, DELTDG, 2DELTKM, AZES, AZESDG, AZSE, AZSEDG, I ) ! This is an old Fortran subroutine to compute the ! distance and azimuths between two points. ! Point A: Latitude THEI, Longitude ALEI ! Point B: Latitude THSI, Longitude ALSI ! If the coordinates are in geographical coordinates in deg,then ! I=0 ! If the coordinates are in geocentric in radia, then I=1 ! These are the input parameters. ! Outputs are: ! 0 DELT=distance in radian ! 1 DELTDG=distance in degree ! 2 DELTKM=distance in km ! 3 AZES=azimuth of Point B as viewed from Point A (radian) ! 4 AZESDEG=azimuth of Point B as viewed from Point A ! (radian) (degree) ! 5 AZSE=azimuth of Point A as viewed from Point B (radian) ! 6 AZSEDEG=azimuth of Point A as viewed from Point B ! (radian) (degree) ! Brian Savage (orig from Kanamori) DOUBLE PRECISION C, AK, D, E, CP, AKP, DP, EP, 2A, B, G, H, AP, BP, GP, HP IF(I) 50, 50, 51 C IF COORDINATES ARE GEOGRAPH DEG I=0 C IF COORDINATES ARE GEOCENT RADIAN I=1 50 THE=1.745329252E-2*THEI ALE=1.745329252E-2*ALEI THS=1.745329252E-2*THSI ALS=1.745329252E-2*ALSI c AAA=0.9931177*TAN(THE) AAA=0.993277*TAN(THE) THE=ATAN(AAA) c AAA=0.9931177*TAN(THS) AAA=0.993277*TAN(THS) THS=ATAN(AAA) GO TO 32 51 THE=THEI ALE=ALEI THS=THSI ALS = ALSI 32 CONTINUE C= SIN(THE) AK=-COS(THE) D=SIN(ALE) E= -COS(ALE) A= AK*E B= -AK*D G=-C*E H=C*D CP=SIN(THS) AKP=-COS(THS) DP=SIN(ALS) EP = -COS(ALS) AP = AKP*EP BP=-AKP*DP 366 GP=-CP*EP HP=CP*DP C1=A*AP+B*BP+C*CP IF( C1-0.94 ) 30, 31, 31 30 IF(C1+0.94) 28, 28, 29 29 DELT=ACOS(C1) 33 DELTKM=6371.0*DELT C3 = (AP-D)**2+(BP-E)**2+CP**2-2.0 C4 = (AP-G)**2+(BP-H)**2+(CP-AK)**2-2.0 C5 = (A-DP)**2+ (B-EP)**2+C**2-2.0 C6 = (A-GP)**2+(B-HP)**2+(C-AKP)**2-2.0 DELTDG = 57.29577951*DELT AZES = ATAN2(C3, C4 ) IF ( AZES ) 80, 81, 81 80 AZES = 6.283185308+ AZES 81 AZSE = ATAN2( C5, C6 ) IF ( AZSE ) 70, 71 , 71 70 AZSE=6.283185308+AZSE 71 AZESDG=57.29577951*AZES AZSEDG=57.29577951*AZSE RETURN 31 C1=(A-AP)**2+(B-BP)**2+(C-CP)**2 C1= SQRT(C1) C1=C1/2.0 DELT = ASIN(C1) DELT= 2.0*DELT GO TO 33 28 C1=(A+AP)**2+(B+BP)**2+(C+CP)**2 C1 = SQRT(C1 ) C1= C1/2.0 DELT = ACOS(C1) DELT = 2.0*DELT GO TO 33 END 367 Program grav_tomo_sue.f as used in chapter 5. program grav_tomo_sue implicit undefined (a-z) C SJW February 15, 2005 C Large parts from gravity.f by John Vandecar C but modified not to require the tomographic code C subroutines. C The tomography voxel volume is entered as files. C This code takes slowness values from the kaapvaal C tomography results and determines a density value C for each slowness value at the model locations C which are given in lat long. From this 3D array C of density values the vertical graviational anomaly C on the surface of a sphere is determined. C Now accounts for vertical component of gravity. C C C Need to change to accommodate file out changes.... C C April 11, 2005 now accounts for layer between crustal C thickness and 50 km thickness. C C C To compile use: f77 grav_tomo_sue.f -o grav_tomo_sue C C C To run use: C C filename density-tomo_factor mindepth maxdepth > fileout C C usage: grav_tomo_sue -2.4 0 400 > grav_tomo_400_f-2.4 C grav_tomo_sue -2.4 0 300 > grav_tomo_300_f-2.4 C grav_tomo_sue -2.4 0 600 > grav_tomo_600_f-2.4 C grav_tomo_sue -2.4 0 700 > file_out_2.4 (should fail) C C grav_tomo_sue -2.4 0 0 > file_test_1_out_2.4 (works,first C layer test) C C C real pi, f parameter (pi=3.14159265) parameter (f=180.0/pi) character*80 calcpoints, crustthick, dummy2 character*80 gravout character*80 mod3id, hitcnt character*80 radslow character argv*10 integer dummy1 integer i,j,k,l, m, n integer ir, it, ip integer minir, maxir integer minip, maxip 368 integer minit, maxit integer numr, numt, nump integer iargc real deltrad,deltdeg,deltkm,azes,azesdg,azse,azsedg real edist, clatmid(500), colatcalc(500) real colatmids, clatmids real density(37, 49, 47) real densityc, dellong, delcolat, dist real factor real gpers(37, 49, 47) real gper(500,500), grav, gravvert real hit3d(37, 49, 47), hitmin real lat(500),long(500), longr(500), longmid(500) real longs, longmids, longmidsf, latmids real latcalc(500), longcalc(500), longcalcf(500) real mindepth, maxdepth real pvelo(37) real radslw(37) real radius, rmids real slow3d(37, 49, 47) real thick(500,500) real valr(37), valt(49), valp(47) double precision bigg double precision clatmin(500), clatmax(500), colat(500) double precision colatmins, colatmaxs double precision rtops, rbots double precision rtop, rbot, volume external getarg, edist, DELAZ5 C Units for values: bigg(m^3/(kg*s^2)), densityc(kg/m^3), C radius(km) data bigg /6.67d-11/ C data densityc /450./ C data densityc /300./ C data densityc /400./ data radius /6371./ data hitmin /5.0/ data factor /-2.4/ C These MUST be 1/2 of a degree (not 50 km) C so that cell walls line up dellong = dble(0.5/f) delcolat = dble(0.5/f) k = 0 l = 0 numr = 37 numt = 49 nump = 47 C later the input files be changed to be part of the run C statement with cread as in John's code: C for now just hardwire as this doesn't really change. 369 calcpoints='calculate_gravity_here_sorted.xy' mod3id = 'mod.P01a' hitcnt = 'hitcnt.P01a' radslow = 'radslw.ascii' gravout = 'grav_tomo_out.llz' crustthick='padded_crustal_thickness_for_gravity_geo_sorted.xyz' C Read in the value of factor (for density) and thickness wanted n = iargc() call getarg(1, argv) read(argv, *) factor C write(0,*) n, factor call getarg(2, argv) read(argv, *) mindepth minir = int((-0.02)* mindepth + 37) C write(0,*) n, mindepth, minir call getarg(3, argv) read(argv, *) maxdepth maxir = int((-0.02)* maxdepth + 37) C write(0,*) n, maxdepth, maxir if (maxdepth.ge.600) then write(0,*) "Maxdepth must be less than 600, STOP" stop endif C Read in the crustal thickness values for first layer. These C are the values C determined from the crustal thickness studies, and extracted C from the gridded data for more even coverage. C They have been padded in the region outside of the study C to the average value of the thickness (41 km) C File has been formatted and sorted. C These lat longs need different names from the previous for C distinction when doing the the distance and angle calculation C C Add regional information to the crustal thickness C values geo(i,j) dummy C write(0,*) "i,j, long(i), lat(j), thick(i,j), dummy1, dummy2" open(unit=14,file=crustthick,status='old') do i = 1,49 do j = 1,41 read(14,*) long(i),lat(j),thick(i,j),dummy1,dummy2 C write(0,*) i,j,long(i),lat(j),thick(i,j), dummy1, dummy2 enddo enddo close(14) C Read in the positions that gravity will be calculated C at. This is over the whole range of the area, but C can be more limited, hence indicies (k,l) can be different 370 C from i,j. C The file is in lat long, but we need colatitude and long. C The interval is by half degrees. Reads in fine. Be sure C to use sorted file.(calculate_gravity_here_sorted.xy) C Check everything is being read in correctly (yes) C write(*,*)"k,l,latcalc(l),longcalc(k)-these are calc points " open(unit=15,file=calcpoints,status='old',form='formatted') do k = 1,49 do l = 1,41 read(15,*) longcalc(k), latcalc(l) C write(*,*) k,l, longcalc(k), latcalc(l) enddo enddo close(15) C Remember that valt (lat) is in rads in colat without neg sign C Remember that valp (long) is in rads c . . read three-dimensional velocity model from standard input open(unit=16,file=mod3id,form='unformatted') read(16)valr,valt,valp read(16)slow3d close(16) C Check this is correct (remember this is in rads): C Remember that valt (lat) is in rads in colat without neg sign C Remember that valp (long) is in rads C write(*,*) "valr, valt, valp, slow3d" C do ir = 1, numr C do it = 1,numt C do ip = 1, nump C write(*,*) valr(ir),valt(it),valp(ip),slow3d(ir,it,ip) C write(*,*) valr(ir),valt(it)*f,valp(ip)*f,slow3d(ir,it,ip) C enddo C enddo C enddo C write(*,*) "done with slow3d" C Remember that valr(1) is 4731 and valr(37) is 6371 (step 50 km C at top, but 100 km at 4731) C See notes page 126 book 3. C Remember that valt (lat) is in rads in colat without neg sign C Remember that valp (long) is in rads c . . read in hit count open(unit=17,file=hitcnt,form='unformatted') read(17)valr,valt,valp read(17)hit3d close(17) C Check this is correct: C write(*,*) "valr, valt, valp, hitme" C do ir = 1, numr C do it = 1,numt C do ip = 1, nump C write(*,*) valr(ir),valt(it),valp(ip),hit3d(ir,it,ip) C write(*,*) valr(ir),valt(it)*f,valp(ip)*f,hit3d(ir,it,ip) C enddo C enddo 371 C enddo C write(*,*) "done with hitcount" C . . read in the background velocity model (previously output C . . from gravity_sue.f) C . . output file from gravity_sue.f is: radslw.ascii C . . was created from: C . . Write out the radial slowness model and velocity C write(13,*) valr(ir), radslw, pvel(iouprt,valr(ir)) C Read it in here to get the IASPEI model C C write(*,*)"valr(ir), radslw, pvelo(iouprt,valr(ir)) (IASPEI)" open(unit=18,file=radslow,status='old',form='formatted') do ir = 1, numr read(18,*) valr(ir), radslw(ir), pvelo(ir) C write(*,*) ir, valr(ir), radslw(ir), pvelo(ir) enddo close(18) C write(*,*) "done with reading in background" C Everything reads in fine. Now to start calculating! C For this version, leave top layer in. This will be C mostly replaced in final version with crustal thicknesses. C Zero out loops grav = 0.0 C Position gravity is calculated at: do k = 1,49 do l = 1,41 longcalcf(k) = real((longcalc(k)/f)) colatcalc(l) = real((-latcalc(l)+90.0)/f) C Need to work on this option a bit more C Also to do first layer separatly... C To get radius starting from 6371 down to 5771 use: C do ir = 37,25, -1 C To get radius starting from 6321 down to 5771 C (ie 600 km depth) use: C Radius values now set by input from starting statement C It can start at 37, if it does start at 37, that means the C first layer is the "inbetween" layer for making up the C rest of the crustal thickness. C minir = 37, maxir = 29, goes from 0 to 400 km depth C because of the way John set up the indicies. do ir = minir,maxir, -1 if(ir.eq.37) then minit = 4 maxit = 44 minip = 4 maxip = 44 else minit = 1 maxit = 49 minip = 1 maxip = 47 372 end if do it = minit,maxit do ip = minip,maxip C If hit count is less than 5, totally skip C all calculations. C write(*,*) "k,l,ir,it,ip,hit3d(ir,it,ip)" C write(*,*) k,l,ir,it,ip,hit3d(ir,it,ip), grav if(hit3d(ir,it,ip).ge.hitmin)then C do gravity calculation C C first do gravity calculation for in between layer: C This accounts for that awkward layer between the crustal C thickness and first full layer of the tomography C if(ir.eq.37) then C If thickness is less than or equal to 50 km AND C For thickness greater than 50 km (note that the rtop C is really rbot, BUT we want them like this so that the C volume is "negative" so that this will be subtracted from C the sum) rtops = dble(radius - thick(ip+3,it-3)) rbots = dble(radius - 50.0) rmids = real((rtops+rbots)/2.0) C write(0,*) ir,it,ip,thick(ip+3,it-3),rtops,rbots,rmids else C Calculate volume of sp cube for tomo C rtops - for radius of Sphere top C rtops = dble(valr(ir)) rbots = dble(valr(ir-1)) rmids = (valr(ir) + valr(ir-1))/2.0 end if C ***************** C write(*,*) "ir, rtops, rbots, rmids" C write(*,*) ir, rtops, rbots, rmids C CoLatitude of sphere cube in radians colatmins = dble(valt(it) - delcolat/2.0) colatmids = real(valt(it)) colatmaxs = dble(valt(it) + delcolat/2.0) latmids = -(colatmids*f) + 90 C Longitude of sphere cube in radians longs = valp(ip) longmids = real(valp(ip)) 373 longmidsf=(longmids*f) volume = dble(dellong)*(rtops**3-rbots**3) & *(dcos(colatmins)-dcos(colatmaxs))/3.0d0 C write(0,*) ir,it,ip,latmids,longmidsf,volume C Now determine density for current block: if(ir.eq.37) then density(ir,it,ip) = -slow3d(ir-1,it,ip) & /(slow3d(ir-1,it,ip)*radslw(ir-1) & + radslw(ir-1)**2)/factor C write(0,*) ir,it,ip,latmids,longmidsf,density(ir,it,ip) else density(ir,it,ip) = -slow3d(ir,it,ip) & /(slow3d(ir,it,ip)*radslw(ir) + radslw(ir)**2)/factor C write(0,*) ir,it,ip,latmids,longmidsf,density(ir,it,ip) endif C First calculate gravity, then vertical component. C This is total gravity not vert comp to start with gpers(ir,it,ip) = volume*bigg*1.0d5*density(ir,it,ip) C ****************** C write(*,*) "volume, density, gpers" C write(*,*) volume, density(ir,it,ip), gpers(ir,it,ip) C ******************* C write(*,*) "sending to edist" C write(*,*) radius,colatcalc(l),longcalcf(k) C write(*,*) radius, latcalc(l), longcalc(k) C write(*,*) rmids,colatmids,longmids C write(*,*) rmids,it,valt(it)*f,delcolat,longmidsf dist = edist(radius, colatcalc(l), longcalcf(k), & rmids, colatmids, longmids) C Total value of gravity (want only vert component!) C The factor of 1000 is to go from km to m C include grav for comparison (Note 1.0d6 is for both C km/m AND gm/kg conversions) grav = grav + (gpers(ir,it,ip)*1.0d6)/(dist**2) call DELAZ5(latcalc(l),longcalc(k),latmids,longmidsf, & deltrad,deltdeg,deltkm,azes,azesdg,azse, & azsedg,0) 374 C To check DELAZ C ******************************** C write(*,*)"latcalc(l),longcalc(k),latmids,longmidsf, C & deltrad,deltdeg" C write(*,*)latcalc(l),longcalc(k),latmids,longmidsf, C & deltrad,deltdeg C (Note 1.0d6 is for both C km/m AND gm/kg conversions) gravvert = gravvert + (gpers(ir,it,ip)*1.0d6)* & (dble(radius)-dble(rmids)* & (dcos(dble(deltrad))))/(dble(dist)**3) C write(*,*) k,l,radius,latcalc(l), colatcalc(l) C write(*,*) longcalc(k), longcalcf(k) C write(*,*) ir, it, ip,rmids,latmids,longmidsf C write(*,*) grav, dist, gpers(ir,it,ip) C write(*,*) " " C C write(*,*) "end of loop ", ip C write(*,*) k,l,ir,it,ip C C write(*,*) i,j,dellong,rtop,rbot C write(*,*) lat(j), colat(j), clatmin(j),clatmax(j) C write(*,*) thick(i,j), rmid(i,j), volume C write(*,*) " " else goto 45 45 continue endif enddo enddo enddo C write(*,*) "k,l,longcalc(k), latcalc(l), gravvert, grav" write(*,*) k,l,longcalc(k), latcalc(l), gravvert, grav C write(*,*) "GRAVITY VERT**********" C write(*,*) longcalc(k), latcalc(l), gravvert open(unit=19,file=gravout,status='unknown') write(19,*) k,l,longcalc(k),latcalc(l),gravvert,grav grav = 0.0 gravvert = 0.0 enddo enddo close(19) stop end 375 C ***************************************** c --------------------------------------------------------------------- real function edist(r1, t1, p1, r2, t2, p2) c . . get euclidian distance from 2 sets of spherical polar coordinates c . . . r = radius c . . . t = colatitude (in radians) c . . . p = longitude (in radians) real r1, t1, p1, r2, t2, p2 real x1, y1, z1, x2, y2, z2 x1 = r1*sin(t1)*cos(p1) y1 = r1*sin(t1)*sin(p1) z1 = r1*cos(t1) x2 = r2*sin(t2)*cos(p2) y2 = r2*sin(t2)*sin(p2) z2 = r2*cos(t2) c write(*,*)"r1,t1,p1,r2,t2,p2 in edist" c write(*,*) r1,t1,p1 c write(*,*) r2,t2,p2 c write(*,*) "x1, y1, z1, x2, y2, z2" c write(*,*) x1, y1, z1 c write(*,*) x2, y2, z2 edist = sqrt((x1-x2)**2+(y1-y2)**2+(z1-z2)**2) return end c---------------------------------------------------------------------- SUBROUTINE DELAZ5( THEI, ALEI, THSI, ALSI, DELT, DELTDG, 2DELTKM, AZES, AZESDG, AZSE, AZSEDG, I ) ! This is an old Fortran subroutine to compute the ! distance and azimuths between two points. ! Point A: Latitude THEI, Longitude ALEI ! Point B: Latitude THSI, Longitude ALSI ! If the coordinates are in geographical coordinates in deg, then I=0 ! If the coordinates are in geocentric in radia, then I=1 ! These are the input parameters. ! Outputs are: ! 0 DELT=distance in radian ! 1 DELTDG=distance in degree ! 2 DELTKM=distance in km ! 3 AZES=azimuth of Point B as viewed from Point A (radian) ! 4 AZESDEG=azimuth of Point B as viewed from Point A (radian) (degree) ! 5 AZSE=azimuth of Point A as viewed from Point B (radian) ! 6 AZSEDEG=azimuth of Point A as viewed from Point B (radian) (degree) ! Brian Savage (orig from Kanamori?) DOUBLE PRECISION C, AK, D, E, CP, AKP, DP, EP, 2A, B, G, H, AP, BP, GP, HP IF(I) 50, 50, 51 C IF COORDINATES ARE GEOGRAPH DEG I=0 C IF COORDINATES ARE GEOCENT RADIAN I=1 50 THE=1.745329252E-2*THEI ALE=1.745329252E-2*ALEI THS=1.745329252E-2*THSI ALS=1.745329252E-2*ALSI c AAA=0.9931177*TAN(THE) AAA=0.993277*TAN(THE) THE=ATAN(AAA) 376 377 c AAA=0.9931177*TAN(THS) AAA=0.993277*TAN(THS) THS=ATAN(AAA) GO TO 32 51 THE=THEI ALE=ALEI THS=THSI ALS = ALSI 32 CONTINUE C= SIN(THE) AK=-COS(THE) D=SIN(ALE) E= -COS(ALE) A= AK*E B= -AK*D G=-C*E H=C*D CP=SIN(THS) AKP=-COS(THS) DP=SIN(ALS) EP = -COS(ALS) AP = AKP*EP BP=-AKP*DP GP=-CP*EP HP=CP*DP C1=A*AP+B*BP+C*CP IF( C1-0.94 ) 30, 31, 31 30 IF(C1+0.94) 28, 28, 29 29 DELT=ACOS(C1) 33 DELTKM=6371.0*DELT C3 = (AP-D)**2+(BP-E)**2+CP**2-2.0 C4 = (AP-G)**2+(BP-H)**2+(CP-AK)**2-2.0 C5 = (A-DP)**2+ (B-EP)**2+C**2-2.0 C6 = (A-GP)**2+(B-HP)**2+(C-AKP)**2-2.0 DELTDG = 57.29577951*DELT AZES = ATAN2(C3, C4 ) IF ( AZES ) 80, 81, 81 80 AZES = 6.283185308+ AZES 81 AZSE = ATAN2( C5, C6 ) IF ( AZSE ) 70, 71 , 71 70 AZSE=6.283185308+AZSE 71 AZESDG=57.29577951*AZES AZSEDG=57.29577951*AZSE RETURN 31 C1=(A-AP)**2+(B-BP)**2+(C-CP)**2 C1= SQRT(C1) C1=C1/2.0 DELT = ASIN(C1) DELT= 2.0*DELT GO TO 33 28 C1=(A+AP)**2+(B+BP)**2+(C+CP)**2 C1 = SQRT(C1 ) C1= C1/2.0 DELT = ACOS(C1) DELT = 2.0*DELT GO TO 33 END