Transformation Methods for Multivariate Geostatistical Simulation—Minimum/Maximum Autocorrelation Factors and Alternating Columns Diagonal Centres

Abstract

To speed up multivariate geostatistical simulation it is common to transform the set of attributes into spatially uncorrelated factors that can be simulated independently. The main method in recent years has been minimum/maximum autocorrelation factors, either based on the coefficient matrices of a two structure linear model of coregionalisation (LMC) or on a pair of experimental covariance matrices. In both cases there is an underlying assumption that the covariance structure of the data set can be adequately modelled using a two structure LMC. We consider an extension that removes the restriction imposed by this assumption by using the experimental matrices for a larger set of lags. The method relies on an iterative algorithm that approximately diagonalises a set of symmetric matrices, and is referred to as the Alternating Columns-Diagonal Centres method. We use the Jura data set to evaluate the extent to which factors obtained from each method are spatially decorrelated and to assess the effect of the transformation method on the simulated attributes.