Mathematical Geosciences

, Volume 46, Issue 5, pp 625–645 | Cite as

Conditioning of Multiple-Point Statistics Facies Simulations to Tomographic Images

  • Tobias LochbühlerEmail author
  • Guillaume Pirot
  • Julien Straubhaar
  • Niklas Linde
Special Issue


Geophysical tomography captures the spatial distribution of the underlying geophysical property at a relatively high resolution, but the tomographic images tend to be blurred representations of reality and generally fail to reproduce sharp interfaces. Such models may cause significant bias when taken as a basis for predictive flow and transport modeling and are unsuitable for uncertainty assessment. We present a methodology in which tomograms are used to condition multiple-point statistics (MPS) simulations. A large set of geologically reasonable facies realizations and their corresponding synthetically calculated cross-hole radar tomograms are used as a training image. The training image is scanned with a direct sampling algorithm for patterns in the conditioning tomogram, while accounting for the spatially varying resolution of the tomograms. In a post-processing step, only those conditional simulations that predicted the radar traveltimes within the expected data error levels are accepted. The methodology is demonstrated on a two-facies example featuring channels and an aquifer analog of alluvial sedimentary structures with five facies. For both cases, MPS simulations exhibit the sharp interfaces and the geological patterns found in the training image. Compared to unconditioned MPS simulations, the uncertainty in transport predictions is markedly decreased for simulations conditioned to tomograms. As an improvement to other approaches relying on classical smoothness-constrained geophysical tomography, the proposed method allows for: (1) reproduction of sharp interfaces, (2) incorporation of realistic geological constraints and (3) generation of multiple realizations that enables uncertainty assessment.


Multiple-point statistics Multiple-point direct sampling Geophysical tomography Conditioning 



This research was funded by the Swiss National Science Foundation (SNF) and is a contribution to the ENSEMBLE project (grant no. CRSI22_132249). We would like to thank Philippe Renard for many helpful suggestions during the course of this study. We thank the three anonymous reviewers for their constructive comments that helped to improve the manuscript.


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Copyright information

© International Association for Mathematical Geosciences 2013

Authors and Affiliations

  • Tobias Lochbühler
    • 1
    Email author
  • Guillaume Pirot
    • 2
  • Julien Straubhaar
    • 2
  • Niklas Linde
    • 1
  1. 1.Applied and Environmental Geophysics Group, Faculty of Geosciences and EnvironmentUniversity of LausanneLausanneSwitzerland
  2. 2.Center for Hydrogeology and GeothermicsUniversity of NeuchâtelNeuchâtelSwitzerland

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