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Geostatistics offers a set of methods for modeling, predicting, or simulating geological domains in space. In addition of being an input of some of these methods, indicator direct and cross-variograms convey valuable information on the geometry of the domain layouts and on their contact relationships, in particular, on the surface area of a domain boundary, on the surface area of the contact between two domains, on the propensity for a domain to be in contact with, or separated from, another domain, and on the minimum and maximum distances between points from two domains. Accordingly, the indicator variograms inferred from sparse sampling data can be used to determine whether or not an interpreted model of the subsurface is consistent with the sampling information. The previous concepts are illustrated through a case study corresponding to a porphyry copper deposit.

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We consider spatial matrix-valued isotropic covariance functions in Euclidean spaces and provide a very short proof of a celebrated characterization result proposed by earlier literature. We then provide a characterization theorem to create a bridge between a class of matrix-valued functions and the class of matrix-valued positive semidefinite functions in finite-dimensional Euclidean spaces. We culminate with criteria of the Pólya type for matrix-valued isotropic covariance functions, and with a generalization of Schlather's class of multivariate spatial covariance functions.We then challenge the problem of matrix-valued space-time covariance functions, and provide a general class that encompasses all the proposals on the Gneiting nonseparable class provided by earlier literature.

No abstract