Multivariate Applications

The area of multivariate geostatistics is a fertile one for mining (and environmental) applications. Spatial Variables modelled in geosciences often display inter-related patterns of variability. A proper modelling of these inter-variable spatial relationships is bound to improve the economic and financial evaluation of say, mining projects. This is because the contribution of various metals to the profitability of an operation is hardly ever obtained through a linear transfer function between in-situ resources and mineable reserves, hence an adequate reproduction of multivariate spatial patterns is necessary to properly assess the true potential of a project.

Consider the case of modelling more than one variable (e.g. gold and copper in a porphyry, grade and contaminants in an iron or disseminated nickel orebody; multivariate trace elements in geochemistry, coal or environmental science, etc.). If we perform independent modelling of our multivariate set, the resulting models will not reproduce the correlation between these variables: e.g. the high gold grade core in the porphyry may or may not be a high copper grade area, the occurrences of massive nickel sulphides in disseminated mineralisation may or may not have high arsenic grades attached to them… A technique that overlooks the modelling of ‘cross-structures’, seen in cross-variograms, would miss the crux of the problem in some situations and a key component will be lost when evaluating the potential of a project through the above mentioned transfer function.

Such a modelling requires a consistent model of co-regionalisation to allow for the modelling of spatial correlation intra-variables (say gold with gold, copper with copper) and inter-variables (say gold with copper). The assumptions of stationarity inherent in the use of such a model will be stricter because they apply to domains that need to display an acceptable level of statistical homogeneity for all variables and their spatial correlations. Depending on the nature of the spatial relationship between the variables under consideration (sometimes the variables display different patterns of variability at different spatial scales), different models of correlation may be used (intrinsic correlation, linear model of co-regionalisation, complex model of co-regionalisation).

For more details on multivariate applications, refer to Wackernagel (1995).