Spatial Pair-Copula Model of Grade for an Anisotropic Gold Deposit

Abstract

Copulas provide a convenient way to express multivariate distribution. In this study, pair-copula modelling is applied to a gold deposit in Western Ghana. The dataset for the gold deposit has 1500 surface soil samples on an area of 7810 ha. The distribution of the grade appears to be anisotropic and has a non-stationary random process. The objectives of the analysis are to use a spatial pair-copula to model the anisotropic gold grade and to determine regions of highest gold value within the field for a future drilling campaign. In the analysis, possible transformations of the data were compared to reduce the influence of outliers and in the case of copulas achieving a marginal uniform distribution. The anisotropy of the gold grades is described with empirical copula contour plots for each distance class and for two orthogonal directions. The non-stationarity is modelled by regression methods. The residuals from the regression are modelled with both spatial pair copulas and kriging. The different approaches are compared in terms of the mean absolute error (MAE) and root mean square error, using different proportions of the data for training and validation. The pair-copula median with kernel margins had MAE of 17.4 compared to 18.3 for log-normal kriging. An advantage of copulas is that they provide a more accurate model than kriging for the uncertainty associated with predictions.