Skip to main content
Log in

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

  • Published:
Mathematical Geosciences Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • 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

    Article  Google Scholar 

  • Arpat GB, Caers JK (2007) Conditional simulation with patterns. Math Geol 39(2):177–203

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Caers J (2005) Petroleum geostatistics. SPE interdisciplinary primer series. Society of Petroleum Engineers, Richardson

    Google Scholar 

  • Chilès JP, Delfiner P (1999) Geostatistics: Modeling spatial uncertainty. Series in Probability and Statistics. Wiley, New York

    Google Scholar 

  • Davies G, Smith LJr (2006) Structurally controlled hydrothermal dolomite reservoir facies: an overview. AAPG Bull 90(11):1641–1690

    Article  Google Scholar 

  • Deutsch C, Journel A (1998) GSLIB: Geostatistical software library and user’s guide. Oxford University Press, New York

    Google Scholar 

  • Deutsch CV, Wang L (1996) Hierarchical object-based stochastic modeling of fluvial reservoirs. Math Geol 28(7):857–880

    Article  Google Scholar 

  • Dubrule O, Kostov C (1986) An interpolation method taking into account inequality constraints: I. Methodology. Math Geol 18(1):33–51

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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 

  • 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

    Article  Google Scholar 

  • Goovaerts P (1997) Geostatistics for natural resources evaluation. Applied geostatistics series. Oxford University Press, New York

    Google Scholar 

  • Gringarten E (1998) FRACNET: Stochastic simulation of fractures in layered systems. Comput Geosci 24(8):729–736

    Article  Google Scholar 

  • Haldorsen HH, Damsleth E (1990) Stochastic modeling. J Pet Sci Technol 42:404–412

    Google Scholar 

  • 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 

  • Holden L, Hauge R, Skare A, Skorstad A (1998) Modeling of fluvial reservoirs with object models. Math Geol 30(5):473–496

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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 

  • Journel AG (2006) The necessity of multiple-point prior model. Math Geol 38(5):591–610

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Lantuéjoul C (2002) Geostatistical simulation: models and algorithms. Springer, Berlin

    Google Scholar 

  • Ledez D (2003) Modélisation d’objets naturels par formulation implicite. PhD thesis, INPL, Nancy, France

  • 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 

  • 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

    Article  Google Scholar 

  • Serra J (1988) Image analysis and mathematical morphology: theoretical advances, vol 2. Academic Press, London

    Google Scholar 

  • 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 

  • Stoyan D, Kendall W, Mecke J (1995) Stochastic geometry and its applications. Wiley, New York

    Google Scholar 

  • Strebelle S (2002) Conditional simulation of complex geological structures using multiple-point statistics. Math Geol 34(1):1–21

    Article  Google Scholar 

  • Viseur S (2004) Caractérisation de réservoirs turbiditiques: simulations stochastiques basées-objet de chenaux méandriformes. Bull Soc Géol Fr 175(1):11–20

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Yao T (1998) Conditional spectral simulation with phase identification. Math Geol 30(3):285–308

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vincent Henrion.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Henrion, V., Caumon, G. & Cherpeau, N. ODSIM: An Object-Distance Simulation Method for Conditioning Complex Natural Structures. Math Geosci 42, 911–924 (2010). https://doi.org/10.1007/s11004-010-9299-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11004-010-9299-0

Keywords

Navigation