Improving Filtersim Simulation Algorithm of Multiple-Point Geostatistics Using New Training Image Based Adaptive Filters and Supervised Hard Data Conditioning

Abstract

Summary Simulations based on Multiple-point statistics (MPS) form a class of newly developed techniques that have received great attention in recent years and are mainly used to map spatial complexity and heterogeneity of geological phenomenon. One of the most commonly used pattern based multiple-point geostatistical simulation algorithm is called Filtersim. In the conventional Filtersim algorithm, the detected patterns in training images are transformed into filter score space using a fixed number of filters that are neither dependent on the training images nor on the characteristics of patterns extracted from them. Through using principal component analysis in current study, a set of new filters are designed in such a way to include most structural information specific to the governing training image resulting in the selection of closer patterns in the filter score space. Comparing the results of applying our proposed filters to that of conventional Filtersim algorithm shows a significant improvement in recovering expected shapes and structural continuity in the final simulated realizations. Introduction MPS simulation is capable of reproducing complex geological patterns that cannot be modeled by two-point statistics moments such as variograms. One of the commonly used pattern-based approach, FILTERSIM, introduces filters to summarize high dimensional patterns into a filter score space. Then, it classifies the patterns into a limited number of classes. FILTERSIM uses six predefined filters, which are not specific to the Training Image. The aim of current research is to introduce new improvements to the initial FILTERSIM technique through defining new adaptive filters. Methodology and Approaches In contrast to original FILTERSIM method, our approach uses some filters which are designed specifically for any given Training Image using PCA analysis. In addition, our approach uses a combination of raster path and random partitioning methods in the course of simulation. The raster path approach results in simulations showing a good continuity of the patterns. The random partitioning is a new feature that allows better simulated realizations as compared to the straightforward use of the raster path. Results and Conclusions The newly proposed approach have been tested on some training images and the results have been compared with previous pattern-based algorithms. Through visual inspection and some discrepancy measures it is shown that the simulated realizations obtained by our approach are much closer to the training image than those obtained with the other methods. In particular, the continuity of the patterns is better preserved with the proposed method.