Mathematical Geosciences

, Volume 41, Issue 5, pp 491–508 | Cite as

Subsurface Characterization Using a Cellular Automaton Approach

  • H. M. SchuttelaarsEmail author
  • F. M. Dekking
  • C. Berentsen
Open Access


In this paper, a random Cellular Automaton model is developed to characterise heterogeneity of geological formations. The CA-model is multilateral and can be easily applied in both two and three dimensions. We demonstrate that conditioning on well data is possible and the method is numerically efficient. To construct the model, the subsurface is subdivided into N cells, with an initial lithology assigned to each cell. Rules to update the current cell states are chosen from a set of rules, independently for each cell. The model converges typically in less than 50 iterations to a steady state or periodic solution. Within one period the realisations exhibit similar statistical properties. The final fraction of the various lithologies can be tuned by choosing the proper initial fractions. In this way, geological knowledge of those fractions can be satisfied.


Transition probability Two and three dimensional characterisation Well-data 


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Copyright information

© The Author(s) 2009

Open AccessThis is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • H. M. Schuttelaars
    • 1
    Email author
  • F. M. Dekking
    • 1
  • C. Berentsen
    • 2
    • 3
    • 4
  1. 1.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands
  2. 2.Department of Earth SciencesUniversity of UtrechtUtrechtThe Netherlands
  3. 3.Faculty of Civil Engineering and GeosciencesDelft University of TechnologyDelftThe Netherlands
  4. 4.Shell International Exploration and ProductionRijswijkThe Netherlands

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