Abstract
Geostatistical models should be checked to ensure consistency with conditioning data and statistical inputs. These are minimum acceptance criteria. Often the first and second-order statistics such as the histogram and variogram of simulated geological realizations are compared to the input parameters to check the reasonableness of the simulation implementation. Assessing the reproduction of statistics beyond second-order is often not considered because the “correct” higher order statistics are rarely known. With multiple point simulation (MPS) geostatistical methods, practitioners are now explicitly modeling higher-order statistics taken from a training image (TI). This article explores methods for extending minimum acceptance criteria to multiple point statistical comparisons between geostatistical realizations made with MPS algorithms and the associated TI. The intent is to assess how well the geostatistical models have reproduced the input statistics of the TI; akin to assessing the histogram and variogram reproduction in traditional semivariogram-based geostatistics. A number of metrics are presented to compare the input multiple point statistics of the TI with the statistics of the geostatistical realizations. These metrics are (1) first and second-order statistics, (2) trends, (3) the multiscale histogram, (4) the multiple point density function, and (5) the missing bins in the multiple point density function. A case study using MPS realizations is presented to demonstrate the proposed metrics; however, the metrics are not limited to specific MPS realizations. Comparisons could be made between any reference numerical analogue model and any simulated categorical variable model.
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References
Arpat, G. B., and Caers, J., 2007, Conditional simulation with patterns: Math. Geol., v. 39, no. 2, p. 177–203.
Boisvert, J. B., Pyrcz, M. J., and Deutsch, C. V., 2007, Multiple-point statistics for training image selection: Nat. Resour. Res., v. 16, no. 4, p. 313–321.
Caers, J., 2001, Geostatistical reservoir modeling using statistical pattern recognition: J. Petrol. Sci. Eng., v. 29, no. 3, p. 177–188.
Caers, J., Strebelle, S., and Payrazyan, K., 2003, Stochastic integration of seismic and geological scenarios: a submarine channel saga: Leading Edge, v. 22, no. 3, p. 192–196.
Davis, B. M., 1987, Uses and abuses of cross-validation in geostatistics: Math. Geol., v. 19, no. 3, p. 241–248.
Deutsch, C. V., 1992, Annealing techniques applied to reservoir modeling and the integration of geological and engineering (well test) data: PhD thesis, Stanford University, Stanford, CA.
Deutsch, C. V., and Journel, A. G., 1998, GSLIB—geostatistical software library and user’s guide: Oxford University Press, New York, p. 369.
Eskandari, K., 2008, Growthsim: a complete framework for integrating static and dynamic data into reservoir models: Ph.D. thesis, University of Texas at Austin, 199 p.
Guardiano, F., and Srivastava, M., 1993, Multivariate geostatistics, beyond bivariate moments, in Soares, A., ed., Geostatistics Troia ‘92: Springer, v. 1, p. 133–144.
Harding, A., Strebelle, S., Levy, M., Thorne, J., Xie, D., Leigh, S., Preece, R., and Scamman, R., 2004, Reservoir facies modeling: new advances in MPS, in Leunangthong, O., and Deutsch, C. V., eds., Proceedings of the Seventh International Geostatistics Congress: Banff, Alberta, 10 p.
Leuangthong, O., McLennan, J. A., and Deutsch, C. V., 2004, Minimum acceptance criteria for geostatistical realizations: Nat. Resour. Res., v. 13, no. 3, p. 131–141.
Liu, Y., Harding, A., Abriel, W., and Strebelle, S., 2004, Multiple-point statistics simulation integrating wells, seismic data and geology: AAPG Bull., v. 88, no. 7, p. 905–921.
Lyster, S., and Deutsch, C. V., 2008, MPS simulation in a Gibbs sampler algorithm, in 8th International Geostatistics Congress Chile: GECAMIN Ltd, Santiago, Chile, v. 1, p. 79–86.
Oreskes, N., Shrader-Frechette, K., and Belitz, K., 1994, Verification, validation, and confirmation in the earth sciences: Science, v. 263, no. 5147, p. 641–646.
Ortiz, J. M., and Deutsch, C. V., 2004, Indicator simulation accounting for multiple point statistics: Math. Geol., v. 36, no. 5, p. 545–565.
Pyrcz, M. J., Gringarten, E., Frykman, P., and Deutsch, C. V., 2006, Representative input parameters for geostatistical simulation, in Coburn, T. C., Yarus, R. J., and Chambers, R. L., eds., Stochastic Modeling and Geostatistics: Principles, Methods and Case Studies, Volume II: AAPG Computer Applications in Geology 5: American Association of Petroleum Geologists, p. 123–137.
Strebelle, S., 2002, Conditional simulation of complex geological structures using multiple-point statistics: Math. Geol., v. 34, no. 1, p. 1–22.
Strebelle, S., 2007, Simulation of petrophysical property trends within facies geobodies, in Petroleum Geostatistics: EAGE.
Strebelle, S., Payrazyan, K., and Caers, J., 2003, Modeling of a deepwater turbidite reservoir conditional to seismic data using multiple-point geostatistics: SPE J., v. 8, no. 3, p. 227–235.
Wu, J., Zhang, T., and Journel, A., 2008, Fast FILTERSIM simulation with score-based distance: Math. Geosci. doi:10.1007/s11004-008-9157-5.
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Boisvert, J.B., Pyrcz, M.J. & Deutsch, C.V. Multiple Point Metrics to Assess Categorical Variable Models. Nat Resour Res 19, 165–175 (2010). https://doi.org/10.1007/s11053-010-9120-2
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DOI: https://doi.org/10.1007/s11053-010-9120-2