Fast direct sampling for multiple-point stochastic simulation

Multiple-point statistics simulation has recently attracted significant attention for the simulation of complex geological structures. In this paper, a fast direct sampling (FDS) algorithm is presented based on a fast gradient descent pattern matching strategy. The match is directly extracted from the training image (TI) and so the method does not require intensive preprocessing and database storage. The initial node of the search path is selected randomly but the following nodes are selected in a principled manner so that the path is conducted to the right match. Each node is selected based on the matching accuracy and the behavior of the TI in the previous node. A simple initialization strategy is presented in this paper which significantly accelerates the matching process at the expense of a very naïve preprocessing stage. The proposed simulation algorithm has several outstanding advantages: it needs no (or very limited) preprocessing, does not need any database storage, searches for the match directly in the TI, is not limited to fixed size patterns (the pattern size can be easily changed during simulation), is capable of handling both continuous and categorical data, is capable of handling multivariate data, and finally and more importantly, is a fast method while maintaining high standards for the matching quality. Experiments on different TIs reveal that the simulation results of FDS and DS are comparable in terms of pattern reproduction and connectivity while FDS is far faster than DS.