CDFSIM: Efficient Stochastic Simulation Through Decomposition of Cumulative Distribution Functions of Transformed Spatial Patterns
- 422 Downloads
Simulation of categorical and continuous variables is performed using a new pattern-based simulation method founded upon coding spatial patterns in one dimension. The method consists of, first, using a spatial template to extract information in the form of patterns from a training image. Patterns are grouped into a pattern database and, then, mapped to one dimension. Cumulative distribution functions of the one-dimensional patterns are built. Patterns are then classified by decomposing the cumulative distribution functions, and calculating class or cluster prototypes. During the simulation process, a conditioning data event is compared to the class prototype, and a pattern is randomly drawn from the best matched class. Several examples are presented so as to assess the performance of the proposed method, including conditional and unconditional simulations of categorical and continuous data sets. Results show that the proposed method is efficient and very well performing in both two and three dimensions. Comparison of the proposed method to the filtersim algorithm suggests that it is better at reproducing the multi-point configurations and main characteristics of the reference images, while less sensitive to the number of classes and spatial templates used in the simulations.
KeywordsPattern-based simulation Clustering Patterns coding Conditional simulation Training image
We thank the Associate Editor of Mathematical Geosciences handling our manuscript and the anonymous reviewers for their detailed comments that have helped improve the manuscript. The work in this paper was funded by Natural Science and Engineering Research Council of Canada CRDPJ 411270-10, Discovery Grant 239019, and the industry members of the COSMO Stochastic Mine Planning Laboratory: AngloGold Ashanti, Barrick Gold, BHP Billiton, De Beers, Newmont Mining and Vale.
- Arpat GB (2004) Sequential simulation with patterns. PhD thesis, Stanford UniversityGoogle Scholar
- Daly C (2004) Higher order models using entropy, Markov random fields and sequential simulation. In: Leuangthong O, Deutsch CV (eds) Geostatistics Banff. Kluwer, Dordrecht, pp 215–225Google Scholar
- Deutsch CV (2002) Geostatistical reservoir modeling. Oxford University Press, New YorkGoogle Scholar
- Goovaerts P (1998) Geostatistics for natural resources evaluation. Oxford University Press, New YorkGoogle Scholar
- Guardiano FB, Srivastava RM (1993) Multivariate geostatistics: beyond bivariate moments. In: Soares (ed) Geostatistics Troia ‘92. Kluwer, Dordrecht, pp 133–144Google Scholar
- Journel AG (1997) Deterministic geostatistics: a new visit. In: Baafi E, Schofield N (eds) Geostatistics Woolongong ‘96. Kluwer, Dordrecht, pp 213–224Google Scholar
- Remy N, Boucher A, Wu J (2008) Applied geostatistics with SGeMS: a user’s guide. Cambridge University Press, CambridgeGoogle Scholar
- Strebelle S (2000) Sequential simulation drawing structures from training images. PhD thesis, Stanford UniversityGoogle Scholar
- Tjelmeland H, Eidsvik J (2004) Directional Metropolis: hastings updates for conditionals with nonlinear likelihoods. In: Geostatistics Banff 2004, vol 1. Springer, Berlin, pp 95–104Google Scholar