Spatial simulation of geologic variables

Analytical formulation of a general simulation model for generation of anisotropic as well as isotropic synthetic patterns in one, two, or three dimensions is proposed. It has significance for the purpose of modeling geologic properties such as ore grades, reservoir porosity, mineral distribution, fracture spacings, aperture, orientations, etc. General procedures for such a simulation by the autoregressive process are given for model parameters estimation and synthetic pattern generation. The model works on the square net basis and generates sequential patterns first along any desired direction for unidimensional simulation and then two-dimensional patterns are constructed with reference to two orthogonal unidimensional sequences. Applications to synthetic two-dimensional pattern are shown for isotropic cases with different model parameters. The extension of the model to three-dimensional space is readily available.