Random partitioning and adaptive filters for multiple-point stochastic simulation

  • Mansoureh Sharifzadehlari
  • Nader Fathianpour
  • Philippe Renard
  • Rassoul Amirfattahi
Original Paper
First Online:
  • 124 Downloads

Abstract

Multiple-point geostatistical simulation is used to simulate the spatial structures of geological phenomena. In contrast to conventional two-point variogram based geostatistical methods, the multiple-point approach is capable of simulating complex spatial patterns, shapes, and structures normally observed in geological media. A commonly used pattern based multiple-point geostatistical simulation algorithms is called FILTERSIM. In the conventional FILTERSIM algorithm, the patterns identified in training images are transformed into filter score space using fixed filters that are neither dependent on the training images nor on the characteristics of the patterns extracted from them. In this paper, we introduce two new methods, one for geostatistical simulation and another for conditioning the results. At first, new filters are designed using principal component analysis in such a way to include most structural information specific to the governing training images resulting in the selection of closer patterns in the filter score space. We then propose to combine adaptive filters with an overlap strategy along a raster path and an efficient conditioning method to develop an algorithm for reservoir simulation with high accuracy and continuity. We also combine image quilting with this algorithm to improve connectivity a lot. The proposed method, which we call random partitioning with adaptive filters simulation method, can be used both for continuous and discrete variables. The results of the proposed method show a significant improvement in recovering the expected shapes and structural continuity in the final simulated realizations as compared to those of conventional FILTERSIM algorithm and the algorithm is more than ten times faster than FILTERSIM because of using raster path and using small overlap specially when we use image quilting.

Keywords

Multiple-point Principal component analysis Geostatistics FILTERSIM 
This is a preview of subscription content, log in to check access

References

  1. Abdollahifard MJ (2016) Fast multiple-point simulation using a data-driven path and an efficient gradient-based search. Comput Geosci 86:64–74CrossRefGoogle Scholar
  2. Aitokhuehi I, Durlofsky LJ (2005) Optimizing the performance of smart wells in complex reservoirs using continuously updated geological models. J Pet Sci Eng 48:254–264CrossRefGoogle Scholar
  3. Alcolea A, Renard P, Mariethoz G, Bertone F (2009) Reducing the impact of a desalination plant using stochastic modeling and optimization techniques. J Hydrol 365:275–288CrossRefGoogle Scholar
  4. Arpat GB, Caers J (2007) Conditional simulation with patterns. Math Geosci 39(2):177–203Google Scholar
  5. Caers J, Hoffman T (2006) The probability perturbation method: a new look at Bayesian inverse modeling. Math Geol 38(1):81–100CrossRefGoogle Scholar
  6. Carvalho PRM, Costa JFCL, Rasera LG, Varella LES (2016) Geostatistical facies simulation with geometric patterns of a petroleum reservoir. Stoch Environ Res Risk Assess. doi: 10.1007/s00477-016-1243-5 Google Scholar
  7. Chatterjee S, Mohanty MM (2015) Automatic cluster selection using gap statistics for pattern-based multi-point geostatistical simulation. Arab J Geosci 9(8):7691–7704CrossRefGoogle Scholar
  8. Cox TF, Cox MA (1994) Multidimensional scaling. Chapman & Hall, LondonGoogle Scholar
  9. Duda R, Hart P, Stork D (2001) Pattern classification. Wiley, HobokenGoogle Scholar
  10. Efros AA, Freeman WT (2001) Image quilting for texture synthesis and transfer. Paper presented at the ACM SIGGRAPH conference on computer graphics, Los AngelesGoogle Scholar
  11. Endres DM, Schindelin JE (2003) A new metric for probability distributions. IEEE Trans Inf Theo 49(7):1858–1860CrossRefGoogle Scholar
  12. Fukunaga K (2013) Introduction to statistical pattern recognition. Acad Press, CambridgeGoogle Scholar
  13. Gardet C, Ravalec M, Gloaguen E (2016) Pattern-based conditional simulation with a raster: a few techniques to make it more efficient. Stoch Environ Res Risk Assess 30(2):429–446CrossRefGoogle Scholar
  14. Guardiano FB, Srivastava RM (1993) Multivariate geostatistics: beyond bivariate moments. In: Soares AO (ed) Proceeding of geostatistics Troia 1992. Springer, Netherlands, pp 133–144Google Scholar
  15. Honarkhah M, Caers J (2010) Stochastic simulation of patterns using distance-based pattern modeling. Math Geosci 42:487–517CrossRefGoogle Scholar
  16. Jolliffe I (1986) Principal component analysis. Springer, New YorkCrossRefGoogle Scholar
  17. Mahmud K, Mariethoz G, Caers J, Tahmasebi P, Baker A (2014) Simulation of earth textures by conditional image quilting. Water Resour Res. doi: 10.1002/2013WR015069 Google Scholar
  18. Mariethoz G, Renard P, Caers J (2010) Bayesian inverse problem and optimization with iterative spatial resampling. Water Resour Res 46:17. doi: 10.1029/2010WR009274 Google Scholar
  19. Mattoccia S, Tombari F, Di Stefano L (2008) Reliable rejection of mismatching candidates for efficient ZNCC template matching. In: Image processing. ICIP 2008. 15th IEEE international, pp 849–852Google Scholar
  20. Michael H, Boucher A, Sun T, Caers J, Gorelick S (2010) Combining geologic-process models and geostatistics for conditional simulation of 3-D subsurface heterogeneity. Water Resour Res 46:W05527CrossRefGoogle Scholar
  21. Renard P (2007) Stochastic hydrogeology: What professionals really need? Ground Water 45(5):531–541CrossRefGoogle Scholar
  22. Sarma P, Durlofsky LJ, Aziz K (2008) Kernel principal component analysis for efficient, differentiable parameterization of multipoint geostatistics. Math Geosci 40(1):3–32CrossRefGoogle Scholar
  23. Scholkopf B, Smola AJ (2002) Learning with Kernels. MIT Press, Cambridge, p 664Google Scholar
  24. Scholkopf B, Smola AJ, Muller KR (1998) Nonlinear component analysis as a Kernel eigenvalue problem. Neur Comput 10:1299–1319CrossRefGoogle Scholar
  25. Strebelle S (2002) Conditional simulation of complex geological structures using multiple-point statistics. Math Geol 34(1):1–21CrossRefGoogle Scholar
  26. Strebelle S, Cavelius C (2013) Solving speed and memory issues in multiple-point statistics simulation program SNESIM. Math Geosci 46:171–186CrossRefGoogle Scholar
  27. Strebelle S, Payrazyan K, Caers J (2002) Modeling of a deep water turbidite reservoir conditional to seismic data using multiple-point geostatistics. In: SPE annual technical conference and exhibition, number SPE 77425. Society of Petroleum EngineersGoogle Scholar
  28. Tahmasebi P, Hezarkhani A, Sahimi M (2012) Multiple-point geostatistical modeling based on the cross-correlation functions. Comput Geosci 16:779–797CrossRefGoogle Scholar
  29. Tan X, Tahmasebi P, Caers J (2014) Comparing training-image based algorithms using an analysis of distance. Math Geosci 46(2):149–169CrossRefGoogle Scholar
  30. Tang Y, Zhang J, Jing L, Li H (2015) Digital elevation data fusion using multiple-point geostatistical simulation. IEEE J Sel Top Appl Earth Obs Remote Sens 8(10):4922–4934CrossRefGoogle Scholar
  31. Wu J (2007) 4D seismic and multiple-point pattern data integration using geostatistics. Ph.D. thesis dissertation, Stanford UniversityGoogle Scholar
  32. Wu J, Boucher A, Zhang T (2008) A SGeMS code for pattern simulation of continuous and categorical variables: FILTERSIM. Comput Geosci 34:1863–1876CrossRefGoogle Scholar
  33. Zhang T (2006) Filter-based training pattern classification for spatial pattern simulation. Ph.D. Dissertation. Stanford University. Stanford CA, pp 137Google Scholar
  34. Zhang T, Switzer P, Journel AG (2006) Filter-base classification of training image patterns for spatial simulation. Math Geol 38(1):63–80CrossRefGoogle Scholar
  35. Zhang T, Du Y, Huang T, Yang J, Lu F, Li X (2016) Reconstruction of porous media using ISOMAP-based MPS. Stoch Environ Res Risk Assess 30(1):395–412CrossRefGoogle Scholar
  36. Zhang T, Du Y, Li B, Zhang A (2017a) Stochastic reconstruction of spatial data using LLE and MPS. Stoch Environ Res Risk Assess 31(1):243–256CrossRefGoogle Scholar
  37. Zhang T, Gelman A, Laronga R (2017b) Structure and texture-based fullbore image reconstruction. Math Geosci 49:195–215CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringIsfahan University of TechnologyIsfahanIran
  2. 2.Center of Hydrogeology and GeothermicsUniversity of NeuchâtelNeuchâtelSwitzerland
  3. 3.Department of Mining EngineeringIsfahan University of TechnologyIsfahanIran

Personalised recommendations