Enhanced Multiple-Point Statistical Simulation with Backtracking, Forward Checking and Conflict-Directed Backjumping
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During a conventional multiple-point statistics simulation, the algorithm may not find a matched neighborhood in the training image for some unsimulated pixels. These pixels are referred to as the dead-end pixels; the existence of the dead-end pixels means that multiple-point statistics simulation is not a simple sequential simulation. In this paper, the multiple-point statistics simulation is cast as a combinatorial optimization problem, and the efficient backtracking algorithm is developed to solve this optimization problem. The efficient backtracking consists of backtracking, forward checking, and conflict-directed backjumping algorithms that are introduced and discussed in this paper. This algorithm is applied to simulate multiple-point statistics properties of some synthetic training images; the results show that no anomalies occurred in any of the produced realizations as opposed to previously published methods for solving the dead-end pixels. In particular, in simulating a channel system, all the channels generated by this method are continuous, which is of paramount importance in fluid flow simulation applications. The results also show that the presence of hard data does not degrade the quality of the generated realizations. The presented method provides a robust algorithmic framework for performing MPS simulation.
KeywordsMultiple-point statistics Constraint satisfaction problem Backtracking Generalized arc consistency Conflict-directed backjumping
The author would like to thank the Geoscience Research Centre (GRC) of TOTAL EP UK for funding and supporting this research. The author also would like to thank Tatiana Chugunova (TOTAL SA) for providing one of the training images, and her constructive comments and suggestions during the development of this work.
- Beldiceanu N, Carlsson M, Rampon JX (2010) Working version of SICS. https://sofdem.github.io/gccat/gccat/titlepage.html. Accessed 27 July 2018
- Jeavons P, Krokhin A, Živný S (2014) The complexity of valued constraint satisfaction. Bull EATCS 113:21–55Google Scholar
- Lhomme O (1993) Consistency techniques for numeric CSPs. IJCAI 93:232–238Google Scholar
- Prosser P (1993) Hybrid algorithms for the constraint satisfaction problem. Comput Intell 9:268–299. https://doi.org/10.1111/j.1467-8640.1993.tb00310.x CrossRefGoogle Scholar
- Russell SJ, Norvig P (2010) Artificial intelligence: a modern approach. Pearson Education Limited, Kuala Lumpur, pp 202–233Google Scholar
- Strebelle S (2003) New multiple-point statistics simulation implementation to reduce memory and cpu-time demand. In: Proceedings to the IAMG 2003Google Scholar
- Suzuki S, Strebelle S (2007) Real-time post-processing method to enhance multiple-point statistics simulation. In: EAGE. Petroleum Geostatistics 2007, Cascais, Portugal. https://doi.org/10.3997/2214-4609.201403072