Multi-point Geostatistical Algorithm for Simulating the Subsurface using Non-linear Mapping function

Abstract

The simulation of complex geology and heterogeneous subsurface isalways a difficult and challenging job. Variogram-based techniques have onlyconsidered two-point statistics, and they may not always be sufficient torepresent the complex subsurface structures. In this paper, a pattern-basedmulti-point geostatistical algorithm is proposed. The patterns are classifiedinto different clusters to reduce the computational time during the sequentialsimulation. An automatic cluster number selection algorithm is proposed using anon-linear mapping function. The self organised maps (SOM), non-linear mappingfunctions, are applied to classify the patterns by projecting thehigh-dimensional data to the two-dimensional lattice. The cluster numbers areautomatically selected based on the U-matrix generated by the SOM. Thesimulation was performed by measuring the similarity of the conditioning dataevent with the class prototypes using the L2-norm.

The method is validated by a number of examples of conditional andunconditional simulations. The resultsshow that the spatial continuity is well reproduced in all examples ofconditional as well as unconditional simulations. The results were thencompared with filtersim technique;and results revealed that the proposed algorithm performed better than the filtersim in all examples presented inthis paper.