Programs for kriging and sequential Gaussian simulation with locally varying anisotropy using non-Euclidean distances

Abstract

Geological deposits display nonlinear features such as veins, channels or folds that result in complex spatial anisotropies that are difficult to model with currently available geostatistical techniques. The methodology presented in this paper for incorporating locally varying anisotropy in kriging or sequential Gaussian simulation is based on modifying how locations in space are related. Normally, the straight line path is used; however, when nonlinear features exist the appropriate path between locations follows along the features. The Dijkstra algorithm is used to determine the shortest path/distance between locations and a conventional covariance or variogram function is used. This nonlinear path is a non-Euclidean distance metric and positive definiteness of the resulting kriging system of equations is not guaranteed. Multidimensional scaling (landmark isometric mapping) is used to ensure positive definiteness. In addition to the variogram, the only parameters required for the implementation of kriging or sequential Gaussian simulation with locally varying anisotropy are (1) the local orientation and magnitude of anisotropy and (2) the number of dimensions required for multidimensional scaling. This paper presents a suite of programs that can be used to krige or simulate practically sized geostatistical models with locally varying anisotropy. The programs kt3d_LVA, SGS_LVA and gamv_LVA are provided.