Fast modeling of cross-covariances in the LMC: A tool for data integration

Abstract

Although modeling of cross-covariances by fitting the linear model of coregionalization (LMC) is considered a cumbersome task, cross-covariances are the key for integration of data for multiple attributes in environmental hydrology, aquifer and reservoir characterizations using multivariate geostatistics. This paper proposes a novel method of modeling cross-covariances in the linear model of coregionalization (LMC). The classic minimum/maximum autocorrelation factors (MAF) method is analyzed and found to be a good tool to discriminate the elementary nested structures of directional sample covariance matrices. Thus, separate modeling of the scalar sample covariance for each MAF factor may allow to obtain the complete LMC model for the original attributes after a back rotation of the diagonal model covariance matrix of directional factors. However, such a back rotation is not computable following the classic MAF formulation. This paper introduces an ambi-rotational minimum/maximum autocorrelation factors (AMAF) method that allows a back and forth double rotation of the directional diagonal model covariance matrix for factors. This approach provides a device for modeling of the full matrix of directional covariance and cross-covariance for the original attributes in the LMC without recurring to iterations. In this way, the use of multivariate geostatistics for data integration is allowed avoiding collocated approaches or rotation and modeling of data factor scores. The method is illustrated with an example for covariances for three attributes.