Geostatistics in the presence of multivariate complexities: comparison of multi-Gaussian transforms

Geostatistical simulation of two or more continuous variables is a common requirement in mining applications. In these applications, it is essential to consider the spatial correlation of each variable and the cross-correlations among them. For example, conventional co-simulation methods use a linear model of co-regionalisation to account for univariate and multivariate spatial correlation. However, variogram inference becomes more complex as the number of variables increases. Alternatively, various decorrelation methods can transform the variables into independent factors that can be individually simulated. Back-transformation of the simulated variables restores the multivariate relationships between the original co-regionalised variables. Among the various transformation methods, multi-Gaussian transforms are designed to deal with complex multivariate relationships, such as non-linear, heteroscedastic and geologically constrained relationships. This study compares the following multi-Gaussian transforms: rotation based iterative Gaussianisation, projection pursuit multivariate transform and flow transformation. Case studies with bivariate complexities are used to evaluate and compare the realisations of transformed values. For this purpose, commonly used geostatistical validation metrics are applied, including multivariate normality tests, reproduction of bivariate relationships, and histogram and variogram validation.