Multivariate Modelling of Geological and Geometallurgical Variables

Abstract

The mining and minerals industry is confronted with several challenges that were not common some decades ago. Deep-seated and complex orebodies, low metal grades, and fluctuating commodity prices have an increasingly high impact on the mining industry, potentially reducing profit margins. It follows that accurate modelling of geological and geometallurgical variables is needed to reduce risks associated with most mineral prospects. This modelling needs to include uncertainty in predictions, as well as outcomes, so that mining companies can use value at risk, for example, to make informed business decisions. This thesis, comprises three journal papers and one conference paper. Several mathematical formulations have been used to model geological and geometallurgical variables. These novel modelling methodologies provides more versatile modelling techniques to traditional modelling techniques which are currently employed in the mining and minerals industry. In Chapter 2 (Paper 1) and Chapter 3 (Paper 2), spatial pair-copula models are used to predict the geological grades of an anisotropic gold deposit within and outside a main field. These models are compared with a traditional kriging approach and results show that pair-copulas models provide improved modelling of error structure than kriging. In Chapter 4 (Paper 3), different trivariate copulas were used to model and predict geological variables from a drill core. The models provided better estimates and prediction intervals of geological variables. In general, geological variables have a large number of outlying values and also exhibit tail dependence. Copulas provide a means of dealing with these practical issues. D-vine copula models, which are able to address the massive multivariate nature and non-linear bivariate relationships of geometallurgical variables, are employed to model geometallurgical variables. In most cases, geometallurgical variables have several missing data, which makes modelling and prediction of these variables difficult. Chapter 5 (Paper 4), a novel data imputation algorithm is developed as part of this thesis to address the issue of missing data of geometallurgical variables. The outcomes of this thesis are an improved geostatistical modelling framework and novel data imputation algorithm techniques, providing better estimates and prediction intervals for geological and geometallurgical variables, and with demonstrated application to practical mining case studies.