Evaluation of multivariate Gaussian transforms for geostatistical applications

Abstract

Abstract Traditional geostatistical simulation techniques rely on the assumption of multi-Gaussianity. Although the normal score transform is widely used to convert data to a Gaussian distribution, it only guarantees that the normal scores will be univariate Gaussian and the variables may still have complex multivariate relationships. For this reason, multi-Gaussian transforms became popular for simplifying multivariate geostatistical modelling. This study evaluates three multi-Gaussian transforms: flow transformation, projection pursuit multivariate transform, and rotation based iterative Gaussianisation. Three two-dimensional synthetic case studies were designed with complex multivariate relationships to make it difficult to produce good multivariate Gaussian distributions. The quality of the fitted transforms, the forward transformation of data from the same population and the back transformation from a standard multivariate Gaussian distribution were assessed based on statistical indices and visual inspection. The methods were also evaluated using a real case study with eight variables from the Prominent Hill copper deposit in South Australia. The effects of multi-Gaussian transforms on the reproduction of variograms, univariate and bivariate statistics were qualitatively and quantitatively investigated.