Mathematical Geosciences

, Volume 46, Issue 7, pp 815–840 | Cite as

A Multiple Training Image Approach for Spatial Modeling of Geologic Domains

  • Daniel A. SilvaEmail author
  • Clayton V. Deutsch


Characterization of complex geological features and patterns remains one of the most challenging tasks in geostatistics. Multiple point statistics (MPS) simulation offers an alternative to accomplish this aim by going beyond classical two-point statistics. Reproduction of features in the final realizations is achieved by borrowing high-order spatial statistics from a training image. Most MPS algorithms use one training image at a time chosen by the geomodeler. This paper proposes the use of multiple training images simultaneously for spatial modeling through a scheme of data integration for conditional probabilities known as a linear opinion pool. The training images (TIs) are based on the available information and not on conceptual geological models; one image comes from modeling the categories by a deterministic approach and another comes from the application of conventional sequential indicator simulation. The first is too continuous and the second too random. The mixing of TIs requires weights for each of them. A methodology for calibrating the weights based on the available drillholes is proposed. A measure of multipoint entropy along the drillholes is matched by the combination of the two TIs. The proposed methodology reproduces geologic features from both TIs with the correct amount of continuity and variability. There is no need for a conceptual training image from another modeling technique; the data-driven TIs permit a robust inference of spatial structure from reasonably spaced drillhole data.


Geostatistics MPS Training image Linear opinion pool Entropy Geologic domains 



The research work was supported by the industry sponsors of the Centre of Computational Geostatistics at University of Alberta. Also, we thank three anonymous reviewers for their valuable and constructive comments. Finally, thanks to Teck Resources Inc. and the Red Dog Mine for providing the dataset used in the example.


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Copyright information

© International Association for Mathematical Geosciences 2014

Authors and Affiliations

  1. 1.Department of Civil and Environmental Engineering, 3-133 Markin/CNRL Natural Resources Facility, Center for Computational GeostatisticsUniversity of AlbertaEdmontonCanada

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