Memory-Efficient Categorical Multi-point Statistics Algorithms Based on Compact Search Trees

Multi-point statistics (MPS) has emerged as an advanced geomodeling approach. A practical MPS algorithm named snesim (simple normal equations simulation), which uses categorical-variable training images, was proposed in 2001. The snesim algorithm generates a search tree to store the occurrence statistics of all patterns in the training image within a given set of search templates before the simulation proceeds. The snesim search tree concept makes MPS simulation central processing unit efficient but consumes large amounts of memory, particularly when three-dimensional training images contain complex patterns and when a large search template is required to ensure optimal reproduction of the image patterns. To crack the memory-restriction bottleneck, we have developed a compact search tree that contains the same information but reduces memory cost by one order of magnitude. Furthermore, the compact structure also accelerates MPS simulation significantly. Such remarkable improvement makes MPS a more practical tool to use in building the large and complex three-dimensional facies models required in the oil and gas industry.