The U-Wedge Transformation Method for Mutlivariate Geostatistical Simulation
Faculty of Computing, Health and Science
School of Engineering / Natural Resources Modelling and Simulation Research Group
To speed up multivariate geostatistical simulation it is common to transform the set of attributes into spatially uncorrelated factors that can be simulated independently. Spatial decorrelation methods are usually based on the diagonalisation of the variance/covariance and semivariogram matrices of the set of attributes for a chosen family of lag spacings. These matrices are symmetric and there are several efficient methods for the approximate joint diagonalisation of a family of symmetric matrices. One of these is the uniformly weighted exhaustive diagonalisation with Gauss iterations (U-WEDGE) method. In contrast to the method of minimum/maximum autocorrelation factors (MAF), where a two structure linear model of coregionalisation is assumed, U-WEDGE can be applied directly to the set of experimental semivariogram matrices without having to place restrictions on the number of structures in the linear model of coregionalisation, thus removing one of the restrictions placed on the subsequent modelling of the spatial structure of the factors. We use an iron-ore data set to illustrate the method and present a comparison between the simulated attributes obtained from U-WEDGE and MAF with the full co-simulation of the attributes.