Theoretical and practical aspects of variography: in particular, estimation and modelling of semi-variograms over areas of limited and clustered or widely spaced data in a two-dimensional South African gold mining context.
Date
2012-01-30
Authors
Morgan, Craig John
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Abstract
This thesis provides a detailed study of the semi-variogram. Included is a
thorough presentation of the theory of semi-variograms, ranging from the
probabilistic model of geostatistics to validity, estimation and modelling of the
semi-variogram. A detailed study of the nugget effect parameter is included in
which the composition of the nugget effect and the concept of measurement error
being part of the nugget effect are explored. The influence that support size has
on the semi-variogram parameters is also presented. Practical guidelines into
modelling the best semi-variogram are given, and the problems associated with
modelling semi-variograms over limited and clustered or widely spaced data is
investigated in detail.
This thesis looks at semi-variograms from a South African deep-level gold
mining standpoint, and its ultimate goal is to provide a thorough investigation of
the semi-variogram from both a theoretical and a practical perspective. Much of
the theory presented is tested against real-life gold mining data sets, and the
theoretical as well as practical implications of semi-variogram estimation and
modelling are discussed. A particularly interesting observation is the potential
under-estimation of the sill, nugget and range parameters of the semi-variogram
when faced with limited, clustered gold mining data.
However, most of the theory presented in this thesis can be generalized to
situations outside of the gold mining industry, and it is believed that many of the
practical results observed can also be used outside of gold mining. Therefore,
although targeted primarily at the gold mining professional, this thesis is equally
valid to interested persons involved in other spatial disciplines.