Abstract
Among the techniques used to simulate categorical variables, multiple-point statistics is becoming very popular because it allows the user to provide an explicit conceptual model via a training image. In classic implementations, the multiple-point statistics are inferred from the training image by storing all the observed patterns of a certain size in a tree structure. This type of algorithm has the advantage of being fast to apply, but it presents some critical limitations. In particular, a tree is extremely RAM demanding. For three-dimensional problems with numerous facies, large templates cannot be used. Complex structures are then difficult to simulate.
In this paper, we propose to replace the tree by a list. This structure requires much less RAM. It has three main advantages. First, it allows for the use of larger templates. Second, the list structure being parsimonious, it can be extended to include additional information. Here, we show how this can be used to develop a new approach for dealing with non-stationary training images. Finally, an interesting aspect of the list is that it allows one to parallelize the part of the algorithm in which the conditional probability density function is computed. This is especially important for large problems that can be solved on clusters of PCs with distributed memory or on multicore machines with shared memory.
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References
Arpat G, Caers J (2007) Conditional simulation with patterns. Math Geol 39(2):177–203
Caers J (2005) Petroleum geostatistics. Society of Petroleum Engineers, Richardson
Caers J, Strebelle S, Payrazyan K (2003) Stochastic integration of seismic data and geologic scenarios: a west Africa submarine channel saga. Lead Edge 22(3):192–196
Chugunova T, Hu L (2008) Multiple-point statistical simulations constrained by continuous auxiliary data. Math Geosci 40(2):133–146
Daly C, Caers J (2010) Multipoint geostatistics—an introductory review. First Break 28(9). doi:10.3997/1365-2397.2010020
Daly C, Knudby C (2007) Multipoint statistics in reservoir modelling and in computer vision. In: Petroleum geostatistics 2007, EAGE, Cascais, Portugal
de Vries LM, Carrera J, Falivene O, Gratacos O, Luit JS (2009) Application of multiple point geostatistics to non-stationary images. Math Geosci 41(1):29–42
Dongarra J, Huss-Lederman S, Otto S, Snir M, Walker D (1998) MPI—the complete reference: the MPI core, 2nd edn, vol. 1. MIT Press, Cambridge
Gropp W, Huss-Lederman S, Lumsdaine A, Lusk E, Nitzberg B, Saphir W, Snir M (1998) MPI—the complete reference: the MPI extensions, vol 2. MIT Press, Cambridge
Guardiano F, Strivastava R (1993) Multivariate geostatistics: beyond bivariate moments. In: Soares A (ed) Geostatistics Troia, vol 1. Kluwer Academic, Dordrecht, pp 133–144
Hu L, Chugunova T (2008) Multiple-point geostatistics for modeling subsurface heterogeneity: a comprehensive review. Water Resour Res 44:W11413
Journel A, Zhang T (2006) Necessity of a multiple-point prior model. Math Geol 38(5):591–610
Liu Y (2006) Using the snesim program for multiple-point statistical simulation. Comput Geosci 32:1544–1563
Liu Y, Harding A, Abriel W, Strebelle S (2004) Multiple-point simulation integrating wells, three-dimensional seismic data, and geology. Am Assoc Pet Geol Bull 88(7):905–921
Mariethoz G, Renard P, Straubhaar J (2009) The direct sampling method to perform multiple-points geostatistical simulations. Water Resour Res (submitted)
Okabe H, Blunt MJ (2007) Pore space reconstruction of vuggy carbonates using microtomography and multiple-point statistics. Water Resour Res 43:W12S02
Remy N, Boucher A, Wu J (2009) Applied geostatistics with SGeMS: a user’s guide. Cambridge University Press, New York
Renard P (2007) Stochastic hydrogeology: what professionals really need? Ground Water 45(5):531–541
Rivoirard J, Cojan I, Renard D, Geffroy F (2008) Advances in quantification of process–based models for meandering channelized reservoirs. In: Ortiz J, Emery X (eds) VIII international geostatistics congress, GEOSTATS 2008, Santiago, Chile
Ronayne M, Gorelick S, Caers J (2008) Identifying discrete geologic structures that produce anomalous hydraulic response: an inverse modeling approach. Water Resour Res 44:8
Stien M, Hauge R, Kolbjørnsen O, Abrahamsen P (2007) Modification of the snesim algorithm. In: Petroleum geostatistics 2007, EAGE, Cascais, Portugal
Strebelle S (2002) Conditional simulation of complex geological structures using multiple-points statistics. Math Geol 34(1):1–21
Strebelle S, Remy N (2005) Post-processing of multiple-point geostatistical models to improve reproduction of training patterns. In: Leuangthong O, Deutsch C (eds) Geostatistics Banff 2004. Springer, Berlin, pp 979–988
Suzuki S, Strebelle S (2007) Real–time post–processing method to enhance multiple-point statistics simulation. In: Petroleum geostatistics 2007, EAGE, Cascais, Portugal
Tran TT (1994) Improving variogram reproduction on dense simulation grids. Comput Geosci 20(7):1161–1168
Vargas H, Caetano H, Mata-Lima H (2008) A new parallelization approach for sequential simulation. In: Soares A, Pereira MJ, Dimitrakopoulos R (eds) geoENV VI geostatistics for environmental applications. Springer, Berlin, pp 489–496
Wu J, Zhang T, Journel A (2008) Fast filtersim simulation with score-based distance. Math Geosci 40(7):773–788
Zhang T, Switzer P, Journel AG (2006) Filter-based classification of training image patterns for spatial simulation. Math Geol 38(1):63–80
Zhang T, Pedersen SI, McCormick D (2008) Patched path and recursive servo system in multiple-point geostatistics simulation. In: Proceedings of the eighth international geostatistics congress, vol 2, pp 1119–1124. Gecamin, Santiago
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Straubhaar, J., Renard, P., Mariethoz, G. et al. An Improved Parallel Multiple-point Algorithm Using a List Approach. Math Geosci 43, 305–328 (2011). https://doi.org/10.1007/s11004-011-9328-7
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DOI: https://doi.org/10.1007/s11004-011-9328-7