Multivariate correlation in the framework of support and spatial scales ofvariability

This paper extends the concept of dispersion variance to the multivariate c ase where the change of support affects dispersion covariances and the matr ix of correlation between attributes. This leads to a concept of correlatio n between attributes as a function of sample supports and size of the physi cal domain. Decomposition of dispersion covariances into the spatial scales of variability provides a tool for computing the contribution to variabili ty from different spatial components. Coregionalized dispersion covariances and elementary dispersion variances are defined for each multivariate spat ial scale of variability This allows the computation of dispersion covarian ces and correlation between attributes without integrating the cross-variog rams. A correlation matrix, for a second-order stationary field with point support and infinite domain, converges toward constant correlation coeffici ents. The regionalized correlation coefficients for each spatial scale of v ariability, and the cases where the intrinsic correlation hypothesis holds are Sound independent of support and size of domain. This approach opens po ssibilities for multivariate geostatistics with data taken at different sup port. Two numerical examples from soil textural data demonstrate the change of correlation matrix with the size of the domain. In general, correlation between attributes is extended from the classic Pearson correlation coeffi cient based on independent samples to a most general approach for dependent samples taken with different support in a limited domain.