Understanding anisotropy computations

Most descriptions of anisotropy make, reference to reduced distances and co nversion of anisotropic models to isotropic counterparts and equations are presented for a certain class of range-anisotropic models. Many description s state that sill anisotropy is modelled using a range-anisotropic structur e having a very elongated ellipse. The presentations typically have few or no intervening steps. Students and applied researchers rarely follow these presentations and subsequently regard the programs that compute anisotropic variograms as black-boxes, the contents of which are too complex to try to understand. We provide the geometry necessary to clarify those computation s. In so doing, we provide a general way to model any type of anisotropy (r ange, sill, power; slope, nugget) on an ellipse. We note cases in the liter ature in which the printed descriptions of anisotropy on an ellipse do not match the stated or coded models. An example is provided in which both rang e- and sill-anisotropic structures are fitted to the experimental variogram values from an elevation data set using the provided equations and weighte d nonlinear, regression. The original variogram values are plotted with the fitted surfaces to view the fit and anisotropic structure in many directio ns at once.