Computational Geosciences

, Volume 17, Issue 2, pp 417–429 | Cite as

Image transforms for determining fit-for-purpose complexity of geostatistical models in flow modeling

  • Orhun Aydin
  • Jef Caers
Original Paper


Increased diversity of water or energy resources has led to an increased complexity in models aimed at representing accurately dynamic behavior and geological variability in such systems. In terms of variability of properties at least, simple layered models have mostly been replaced with more complex geostatistical models. The newest trend is to replace covariance-based models with geologically more realistic models such as Boolean, multiple-point, surface-, or process-based models. In this paper, we address the following question: given some design purpose or a set of flow-based decision variables, does adding more complexity increase predictability and ultimately improve decisions based on such models? In this paper, we do not attempt to make any generalizing statements or answer this question with yes/no, but provide some initial ideas on practical workflows to discover the needed complexity. We do treat complexity only in the context of decision making under uncertainty. Two workflows are proposed: complexifying versus simplifying. In these workflows, we attempt to extract, using image transforms, relevant features of the variability between geostatistical realizations that are related to uncertainty in flow dynamics. A simple distance-based calibration between the static variability and dynamic variability provides a means to decide on what the relevant complexity of geostatistical models should be for the given purpose.


Complexity Uncertainty Geostatistics Image transforms Distance-based modeling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ballard., D.: Generalizing the Hough transform to detect arbitrary shapes. Pattern Recogn. 13, 111–122 (1980)CrossRefGoogle Scholar
  2. 2.
    Borg, I., Groenen, P.: Modern Multidimensional Scaling: Theory and Applications. Springer, New York (1997)CrossRefGoogle Scholar
  3. 3.
    Caers, J.: Petroleum Geostatistics, 89 p. Society of Petroleum Engineers, Austin (2005)Google Scholar
  4. 4.
    Caers, J.: Modeling Uncertainty in the Earth Sciences, 246 p. Wiley, Chichester (2011)CrossRefGoogle Scholar
  5. 5.
    Christie, M., Cliffe, A., Dawid, P., Senn, S.: Simplicity, Complexity and Modelling, 220 p. Wiley, Chichester (2011)CrossRefGoogle Scholar
  6. 6.
    Dubuisson, M.P., Jain, A.: A modified Hausdorff distance for object matching. In: Proc. International Conference on Pattern Recognition, pp. 566–568 (1994)Google Scholar
  7. 7.
    Gonzales, R.C., Woods, R.E.: Digital Image Processing Using MATLAB. Pearson Prentice Hall, Upper Saddle River (2004)Google Scholar
  8. 8.
    Otsu, N.: A threshold selection method from gray-level histograms. IEEE Trans. Syst. Man Cybern. 9, 62–66 (1979)CrossRefGoogle Scholar
  9. 9.
    Rissanen, J.: Stochastic Complexity in Statistical Inquiry. Series in Computer Science. World Scientific, Singapore (1989)Google Scholar
  10. 10.
    Scheidt, C., Caers, J.: Representing spatial uncertainty using distances and kernels. Math. Geosci. 41(4), 397–419 (2009)CrossRefGoogle Scholar
  11. 11.
    Scheidt, C., Caers, J.: Uncertainty quantification in reservoir performance using distances and kernel methods—application to a West-Africa deepwater turbidite reservoir. SPE J. 14(4), 680–692 (2009)Google Scholar
  12. 12.
    Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948)Google Scholar
  13. 13.
    Spiegelhalter, D., Best, N., Bradley, C., Angelika, V.D.: Bayesian measures of model complexity and fit. J. R. Stat. Soc. Ser. B Stat. Methodol. 64, 583–639 (2002)CrossRefGoogle Scholar
  14. 14.
    Suzuki, S., Caers, J.: A distance-based prior model parameterization for constraining solutions of spatial inverse problems. Math. Geosci. 40(4), 445–469 (2008)CrossRefGoogle Scholar
  15. 15.
    Williams, Mansfield, MacDonald, Bush: Top-down reservoir modeling. In: SPE Annual Technical Conference and Exhibition, pp. 2–8. Society of Petroleum Engineers, Houston (2004)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Energy Resources Engineering DepartmentStanford UniversityStanfordUSA

Personalised recommendations