Another look at anisotropy in geostatistics

A thorough geostatistical data analysis includes a careful study of how the data's second-order variation, as characterized by the semivariogram, depends on the relative orientation of data locations. If the semivariogram depends on only the (Euclidean) distance between locations, then the semivariogram is isotropic; otherwise, it is anisotropic. In this article, I take another look at the modeling of anisotropy in geostatistics. A new, more specific classification of types of anisotropy is proposed. More importantly, some heretofore inadequately understood implications of the dependence of various semivariogram attributes on direction are discussed, and the wisdom of some current practices for modeling the direction-dependence of these attributes is questioned.