Advertisement

Mathematical Geosciences

, Volume 42, Issue 8, pp 911–924 | Cite as

ODSIM: An Object-Distance Simulation Method for Conditioning Complex Natural Structures

  • Vincent HenrionEmail author
  • Guillaume Caumon
  • Nicolas Cherpeau
Article

Abstract

Stochastic simulation of categorical objects is traditionally achieved either with object-based or pixel-based methods. Whereas object-based modeling provides realistic results but raises data conditioning problems, pixel-based modeling provides exact data conditioning but may lose some features of the simulated objects such as connectivity. We suggest a hybrid dual-scale approach to combine both shape realism and strict data conditioning. The procedure combines the distance transform to a skeleton object representing coarse-scale structures, plus a classical pixel-based random field and threshold representing fine-scale features. This object-distance simulation method (ODSIM) uses a perturbed distance to objects and is particularly appropriate for modeling structures related to faults or fractures such as karsts, late dolomitized rocks, and mineralized veins. We demonstrate this method to simulate dolomite geometry and discuss strategies to apply this method more generally to simulate binary shapes.

Keywords

Geostatistics Gibbs sampler Gaussian stochastic process Object-based simulation Implicit representation Euclidean distance transform 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allard D, Froideveaux R, Biver P (2006) Conditional simulation of multi-type non stationary Markov object models respecting specified proportions. Math Geol 38(8):959–986 CrossRefGoogle Scholar
  2. Arpat GB, Caers JK (2007) Conditional simulation with patterns. Math Geol 39(2):177–203 CrossRefGoogle Scholar
  3. Boisvert J, Leuangthong O, Ortiz J, Deutsch CV (2008) A methodology to construct training images for vein-type deposits. Comput Geosci 34(5):491–502 CrossRefGoogle Scholar
  4. Caers J (2005) Petroleum geostatistics. SPE interdisciplinary primer series. Society of Petroleum Engineers, Richardson Google Scholar
  5. Chilès JP, Delfiner P (1999) Geostatistics: Modeling spatial uncertainty. Series in Probability and Statistics. Wiley, New York Google Scholar
  6. Davies G, Smith LJr (2006) Structurally controlled hydrothermal dolomite reservoir facies: an overview. AAPG Bull 90(11):1641–1690 CrossRefGoogle Scholar
  7. Deutsch C, Journel A (1998) GSLIB: Geostatistical software library and user’s guide. Oxford University Press, New York Google Scholar
  8. Deutsch CV, Wang L (1996) Hierarchical object-based stochastic modeling of fluvial reservoirs. Math Geol 28(7):857–880 CrossRefGoogle Scholar
  9. Dubrule O, Kostov C (1986) An interpolation method taking into account inequality constraints: I. Methodology. Math Geol 18(1):33–51 CrossRefGoogle Scholar
  10. Emery X, Lantuéjoul C (2006) TBSIM: A computer program for conditional simulation of three-dimensional Gaussian random fields via the turning bands method. Comput Geosci 32(10):1615–1628 CrossRefGoogle Scholar
  11. Favilene O, Cabello P, Arbués P, Munoz JA, Cabrera L (2009) A geostatistical algorithm to reproduce lateral gradual facies transitions. Comput Geosci 35:1642–1651 CrossRefGoogle Scholar
  12. Freulon X, de Fouquet C (1993) Conditioning a Gaussian model with inequalities. In: Soares A (ed) Geostatistics Tróia ’92, vol 1. Kluwer Academic, Dordrecht, pp 201–212 Google Scholar
  13. Geman S, Geman D (1984) Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell 6(6):721–741 CrossRefGoogle Scholar
  14. Goovaerts P (1997) Geostatistics for natural resources evaluation. Applied geostatistics series. Oxford University Press, New York Google Scholar
  15. Gringarten E (1998) FRACNET: Stochastic simulation of fractures in layered systems. Comput Geosci 24(8):729–736 CrossRefGoogle Scholar
  16. Haldorsen HH, Damsleth E (1990) Stochastic modeling. J Pet Sci Technol 42:404–412 Google Scholar
  17. Henrion V, Pellerin J, Caumon G (2008) A stochastic methodology for 3D cave systems modeling. In: Ortiz J, Emery X (eds) Proceedings of the eight international geostatistics congress, vol 1. Gecamin ltd, Santiago, pp 525–533 Google Scholar
  18. Holden L, Hauge R, Skare A, Skorstad A (1998) Modeling of fluvial reservoirs with object models. Math Geol 30(5):473–496 CrossRefGoogle Scholar
  19. Jones M, Baerentzen J, Sramek M (2006) 3d distance fields: A survey of techniques and applications. IEEE Trans Visual Comput Graphics 12(4):581–599 CrossRefGoogle Scholar
  20. Journel AG (1994) Modeling uncertainty: Some conceptual thoughts. In: Dimitrakopoulos R et al (eds) Geostatistics for the next century. Kluwer, Dordrecht, pp 30–43 Google Scholar
  21. Journel AG (2006) The necessity of multiple-point prior model. Math Geol 38(5):591–610 CrossRefGoogle Scholar
  22. Labourdette R, Lascu I, Mylroie J, Roth M (2007) Process-like modeling of flank margin caves: From genesis to burial evolution. J Sediment Res 77(10):965–979 CrossRefGoogle Scholar
  23. Lantuéjoul C (2002) Geostatistical simulation: models and algorithms. Springer, Berlin Google Scholar
  24. Ledez D (2003) Modélisation d’objets naturels par formulation implicite. PhD thesis, INPL, Nancy, France Google Scholar
  25. Renard P, Caers J (2008) Conditioning facies simulations with connectivity data. In: Ortiz J, Emery X (eds) Proceedings of the eight international geostatistics congress, vol 2. Gecamin ltd, Santiago, pp 597–606 Google Scholar
  26. Saito T, Toriwaki J (1994) New algorithms for Euclidean distance transformation of an n-dimensional digital picture with applications. Pattern Recognit 27(11):1551–1565 CrossRefGoogle Scholar
  27. Serra J (1988) Image analysis and mathematical morphology: theoretical advances, vol 2. Academic Press, London Google Scholar
  28. Srivastava R, Frykman P, Jensen M (2004) Geostatistical simulation of fracture networks. In: Leuangthong O, Deutsch C (eds) Proceedings of the seventh international geostatistics congress, vol 1. Springer, Berlin, pp 295–304 Google Scholar
  29. Stoyan D, Kendall W, Mecke J (1995) Stochastic geometry and its applications. Wiley, New York Google Scholar
  30. Strebelle S (2002) Conditional simulation of complex geological structures using multiple-point statistics. Math Geol 34(1):1–21 CrossRefGoogle Scholar
  31. Viseur S (2004) Caractérisation de réservoirs turbiditiques: simulations stochastiques basées-objet de chenaux méandriformes. Bull Soc Géol Fr 175(1):11–20 CrossRefGoogle Scholar
  32. Yin Y, Wu S, Zhang C, Li S, Yin T (2009) A reservoir skeleton-based multiple point geostatistics method. Sci China Ser D, Earth Sci 52:171–178 CrossRefGoogle Scholar
  33. Yao T (1998) Conditional spectral simulation with phase identification. Math Geol 30(3):285–308 CrossRefGoogle Scholar

Copyright information

© International Association for Mathematical Geosciences 2010

Authors and Affiliations

  • Vincent Henrion
    • 1
    Email author
  • Guillaume Caumon
    • 1
  • Nicolas Cherpeau
    • 1
  1. 1.Centre de Recherches Pétrographiques et Géochimiques, École Nationale Supérieure de GéologieNancy-UniversitéVandoeuvre-lès-NancyFrance

Personalised recommendations