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Covariance functions are a fundamental tool for modeling the dependencestructure of spatial processes. This work investigates novel constructions forcovariance functions that enable the integration of anisotropies and holeeffects in complex and versatile ways, having the potential to provide moreaccurate representations of dependence structures arising with real-world data.We show that these constructions extend widely used covariance models,including the Mat\'ern, Cauchy, compactly-supported hypergeometric and cardinalsine models. We apply our results to a geophysical data set from arock-carbonate aquifer and demonstrate that the proposed models yield moreaccurate predictions at unsampled locations compared to basic covariancemodels.

Versatile Parametric Classes of Covariance Functions that Interlace Anisotropies and Hole Effects