Iterative algorithms for fitting a linear model of coregionalization

In geostatistical applications, automated or semi-automated procedures are often used for modeling the spatial correlation structure (simple and cross variograms) of multivariate data. This paper deals with the well-known linear model of coregionalization and presents three iterative algorithms to find out coregionalization matrices that minimize a weighted sum of the squared deviations between sample and modeled variograms. The first one is a variation of Goulard and Voltz’s proposal for variogram fitting with no constraint other than mathematical consistency. The second one uses simulated annealing for fitting subject to constraints on the simple variogram sills. The third one is a nonlinear least squares algorithm for fitting a plurigaussian model. In all three algorithms, the sample variogram matrices need not be entirely known for every lag vector, a situation of interest with heterotopic samplings. To demonstrate the capabilities of the proposed algorithms, a set of computer programs is provided and applied to case studies in mineral resources evaluation.