Implementation of the Iterative Proportion Fitting Algorithm for Geostatistical Facies Modeling

In geostatistics, most stochastic algorithm for simulation of categorical variables such as facies or rock types require a conditional probability distribution. The multivariate probability distribution of all the grouped locations including the unsampled location permits calculation of the conditional probability directly based on its definition. In this article, the iterative proportion fitting (IPF) algorithm is implemented to infer this multivariate probability. Using the IPF algorithm, the multivariate probability is obtained by iterative modification to an initial estimated multivariate probability using lower order bivariate probabilities as constraints. The imposed bivariate marginal probabilities are inferred from profiles along drill holes or wells. In the IPF process, a sparse matrix is used to calculate the marginal probabilities from the multivariate probability, which makes the iterative fitting more tractable and practical. This algorithm can be extended to higher order marginal probability constraints as used in multiple point statistics. The theoretical framework is developed and illustrated with estimation and simulation example.