Bivariate Matérn covariances with cross-dimple for modeling coregionalized variables

Modeling the spatial correlation structure of coregionalized data is a frequent task in numerous fields of the natural sciences. Even in the isotropic case, experimental covariances may exhibit complex features, such as a maximum cross-correlation attained at non-collocated locations (dimple or hole effect). Current construction principles for multivariate covariance models on Euclidean spaces do not allow accounting for such a property. We propose a spectral approach to modify cross-covariancefunctions of the isotropic bivariate Matérn model in order to obtain a cross-dimple. Our model admits analytic expressions in terms of special functions. Our findings are illustrated through applications to data sets from the fields of mining and geochemistry.