Abstract: |
Geostatistical data sets are usually multivariate and joint simulation or estimation requires the joint modelling of the spatial continuity. While the inference of a suitable variogram model can be automated to some extent, it may nevertheless be preferable to transform the set of attributes into spatially uncorrelated factors that can be simulated independently. The earliest decorrelation method is principal component analysis (PCA), where the original data are rotated to orthogonal factors. The application of PCA results in spatial decorrelation only in the case of an intrinsic co-regionliastion. A more general decorrelation method is the method of minimum/maximum autocorrelation factors (MAF), where a two structure linear model of coregionalisation is assumed. MAF decorrelates the theoretical model exactly, but the actual data are only approximately decorrelated. MAF is thus a special case of a non-orthogonal approximate diagonaliser of a set of symmetric matrices, here the set of experimental semivariogram or covariance matrices for a specified set of lags. A more general approach for approximate joint diagonalisation (AJD) has been developed in the context of blind source separation. For these AJD algorithms no assumptions are made beyond symmetry of the individual matrices and so they can be applied to a family of experimental semivariogram or covariance matrices. In their application there are no restrictions on the number of matrices to be diagonalised and there is no assumption made about the underlying covariance structure of the multivariate random function. In this paper we give an overview over the different AJD methods and discuss their performance on a number of simulated data sets with different spatial characteristics and compare the performance with MAF or PCA . |
