Using Pattern Counts to Quantify the Difference Between a Pair of Three-Dimensional Realizations

Abstract

When comparing different ways of modeling discrete three-dimensional realizations such as facies, it is useful to have a measure of difference (or similarity) in the geometry of these realizations.We propose a method for evaluating such difference by comparing pattern counts for a small template. Tests on synthetic datasets demonstrate that the proposed difference effectively differentiates between realizations of a Boolean model and those generated using multiple-point statistics with the Boolean realizations as training images. We also observed that multiple-point statistics realizations based on similar training images yield smaller differences to one another compared to those based on training images from dissimilar concepts. This suggests that the proposed difference is a useful tool for comparing discrete three-dimensional realizations.