SPATIAL ORTHOGONALITY OF THE PRINCIPAL COMPONENTS COMPUTED FROM COREGIONALIZED VARIABLES

Within the frame of the linear model of coregionalization, is paper se ts up equations relating the variogram matrix of the principal compone nts extracted from the variance-covariance matrix to the diagonal vari ogram matrices of the regionalized factors. The spatial orthogonality of the principal components is investigated in three situations: the i ntrinsic correlation, two basic structures with independent nugget com ponents, three basic structures with independent nugget components and uncorrelated subsets of variables. Two examples point out that the co rrelation between the principal components may be nonnegligible at sho rt distances, especially if the correlation structure changes accordin g to the spatial scale considered. For one of the two case studies, an orthogonal varimax rotation of the first principal components is foun d to greatly reduce the spatial correlation between some of them.