3. Electronic Theses and Dissertations (ETDs) - All submissions
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Item Applications of chaos and fractals to geophysical inversion problems(2019-10-22) Dias, BrandonIn order to gain clear insight into the structure and composition of the Earth and its subsurface, geophysicists and geologists take readings of geophysics responses. Gravitational responses are among the most often recorded datasets and among the most used means of model analysis is the least-squares inversion process. Here; this is demonstrated using synthetic gravitational responses from buried sphere and cylinder models of different density contrasts to the background. The least-squares inversion attempts to utilize initial user chosen parameters to create models which correlate strongly with observed data and thus create potential geological models of the Earth’s subsurface or submerged geological structures. The inversion processes, misfit hyper-functions, basins of attraction and fractal dimensions are studied as functions of initial model parameters. We observe that the fractal dimension and basin of attraction vary with respect to observed model depths and positions. Additionally the fractal dimension is inversely proportional to the degree of damping of the least-squares inversion process. A potential problem with the least-squares inversion method is the possibility for solutions to tend to local minima. These may better fit an observed model response but may not provide a geologically viable option. The equation for the least-squares inversion, as applied to observed models, is altered to induce bifurcations and chaos within solutions. Chaos can be used to move the inversion process out of local minima on the misfit surface, potentially improving the fit of the model response to the data. Bifurcation diagrams are established and the periodicity analysed.Item A study of geomagnetic field time variations over southern Africa using a regional harmonic spline core magnetic field model derived from CHAMP satellite and ground magnetic observations(2019) Nahayo, EmmanuelThe geomagnetic field spatial variation in Southern Africa is characterised by a high horizontal gradient, and its study requires high spatial resolution data. Regional field models are more suitable than global models to study small scale features of the geomagnetic field variation. They use more dense data, hence a good data coverage allows a detailed description of the geomagnetic variation in the area of investigation. In Southern Africa, the ground recording stations are limited (4 magnetic observatories and 38 geomagnetic repeat stations) and satellite data are needed for studies where high spatial and temporal resolution data are required. The southern African region borders the South Atlantic Anomaly (SAA) where the strength of the magnetic field is approximately 30% weaker compared to other regions of the same latitudes. In an attempt of supporting geomagnetic field model data users and investigating the evolution of the South Atlantic Anomaly, a study to develop and derive a southern African regional field model combining CHAMP satellite data with ground-based data showed that the regional model over Southern Africa can be improved by combining both satellite and ground-based data. The internal Earth processes generating the main field can be studied by modelling the core field using inversion of geomagnetic field components measured above the surface of the Earth, and they assist in monitoring the long-term variation of the geomagnetic field on time scales of 1 year and more, therefore giving valuable information on the evolution of the SAA in southern Africa. The study of the geomagnetic field time variation in the southern Africa region was carried out applying the harmonic splines technique on CHAMP satellite and ground data that have been recorded between 2001 and 2010. A Southern Africa Regional Model (SARM) was derived and evaluated using global models, such as International Geomagnetic Reference Field (IGRF-11) and GFZ Reference Internal Magnetic Model (GRIMM), by calculating the difference between SARM and global models. The results of this study suggest that the 200 km gridded SARM model developed from only satellite data is shown to match monthly averaged ground data to within 1.5%, 1.6% and 0.7% for X, Y and Z, respectively, suggesting the temporal variations are valid where ground data are not available. In addition, these results also confirm the earlier findings of the 2007 magnetic jerk and rapid secular variation fluctuations of 2003 and 2004 on the eastern edge of the SAA which extends 1000 km into South Africa. CHAMP satellite and relatively densely spaced (300 km) ground-based data measured over southern African region between 2005 and 2010 are incorporated in a new regional, harmonic spline based, core field model. Our new SACFM-2 model is compared to our previously developed SARM model, a regional model based only on satellite data, and the global CHAOS-6 model developed by Finlay et al. (2016). The results agree well with the CHAOS-6 model (within 0.4%) in the vertical (Z) component and total field (F) that are used to investigate the evolution of the South Atlantic Anomaly in the region. The computed maps of main field of the Z component and total intensity F show a steady decrease of the field between 2005.5 and 2010.5, reaching an average of 40 nT and 50 nT per year, respectively, in the southwest of South Africa, indicating evolution of the South Atlantic Anomaly under Southern Africa and an increase of the geographical area of this feature. In addition, a southern African lithospheric magnetic model (SALMM) over Southern Africa was developed based on the Spherical Cap Harmonic Analysis method using CHAMP satellite measurements at an altitude between 332 km and 365 km, and between 2007.0 and 2009.0 epochs. This lithospheric magnetic model SALMM was compared to a regional model developed by Vervelidou et al. (2018) and the global model MF7. Our lithospheric magnetic model SALMM was interpreted in terms of regional (100s km) geological features and long-wavelength geological magnetic anomalies.Item 3D geophysical modelling used for structural interpretation in southern Mali and northeastern Guinea, West Africa(2017) Yossi, MamadouThis study presents the combined processing, integration and inverse modelling of magnetic and gravity data for first-order crustal scale structures in southern Mali and northeast of Guinea. Southern Mali and northeast Guinea form part of the Palaeoproterozoic Baoulé-Mossi domain, which is part of the West African craton (WAC). The current understanding of the geology region is limited to exploration camp-scale studies with limited borehole investigations, and regional interpretations of historic geophysical datasets. In this study geophysical modelling is used to attempt to advance the understanding of the geology at depth. The combination of geophysical methods is an optimization that can support geophysical interpretations and contribute to the determination of the geological and structural characteristics that are important in understanding the subsurface geology. Geophysical inversion modelling broadly resolved geology and structures under thick sedimentary cover (850-1100, thick) that is interpreted as comprising basinal sediments of the Taoudenni basin, or Cretaceous ferricrete. Geological constraints reduced the non-uniqueness, but could not control the quality. Nonetheless, the architecture, geometry and form of structures and dykes were predicted when compared with experimental analogue models as being a reasonable predictive tool for the behaviour of structures and dykes at depth. The use of surface physical properties added more information to the inversion modelling, but was very limited. The enhancement of magnetic and gravity data, using filters, defined tip damage zones for firstorder scale Yanfolila and Banifing shear zones that host gold mineralisation for example, at the Morila gold mine, and Kalana, Kodieran mines and Komana prospects. Second-order structures were also defined including in the tip damage zones of the Siguiri, Fatou and Syama shear zones, and the Manakoro fault, Madina-Yanfolila fault and Madina fault.Item Surface wave tomography and shear wave velocity structure of the Southwestern block of the Congo craton(2012-02-27) Mangongolo, AzangiRayleigh wave dispersion curves are used to invert for the group velocity maps of the southwestern block of the Congo craton. The group velocity maps were then inverted to obtain the three dimensional shear-wave velocity of the lithosphere beneath the region. In the process, the adjacent Kalahari craton and Damara mobile belt were also mapped to help constrain the southernmost edge of the Congo craton. To obtain the surface wave group velocity tomography, event-station dispersion curves of Rayleigh waves were measured using the multiple filter analysis method. Then the dispersion curves were inverted using the conjugate gradient least-square (CGLSQR) inversion method. To check the reliability of the result, a checkerboard test was performed. The 2-dimensional group velocities and 3-dimensonal shear-wave velocities were found to be faster beneath the southwestern block of the Congo craton and the Kalahari craton and slower in the Damara mobile belt. The group velocity map at 20s period shows that basins are 0 to 3% slower than PREM model. For longer period (50s to 120s), the Central and East African Rift system are ~ 5 % faster, cratons are 5 to 8% faster, and the adjacent mobile belts are 0 to 4% faster than the PREM model. The Afar depression is the slowest, up to 6% slower than the continental PREM model at all periods. The shear-wave velocity maps reveal that (1) the Afar area is the slowest (up to 8% slower than the IASP91 model), (2) the cratons are faster (up to 6% faster than IASP91) than the surrounding mobile belts (up to 2% faster than IASP91). The East African Rifts system is also slow (up to 5%). The Damara mobile belt constitutes a clear separation terrain between the Congo craton and the Kalahari craton. This result is consistent with previous studies by Pasyanos and Nyblade (2007), and Priestly et al. (2006, 2008), who also found faster shear-wave velocities beneath the Kalahari, Congo and Tanzania cratons. The relatively slow seismic velocities (-1 to 2% compared to IASP91) in the Proterozoic Damara mobile belt between the southwestern block of the Congo craton and the Kalahari craton are explained by the view that the Proterozoic lithosphere has hotter rock materials than the SW block of the Congo craton and the Kalahari craton. Our model of faster lithosphere beneath the SW block of the Congo and the Kalahari craton is also consistent with the model of strongly depleted (in basaltic components) lithosphere beneath these craton; compared to less depleted lithosphere beneath the DMB.