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A High-Order, Data-Driven Framework for Joint Simulation of Categorical Variables

  • Ilnur MinniakhmetovEmail author
  • Roussos Dimitrakopoulos
Chapter
Part of the Quantitative Geology and Geostatistics book series (QGAG, volume 19)

Abstract

Relatively recent techniques for categorical simulations are based on multipoint statistical approaches where a training image (TI) is used to derive complex spatial relationships using patterns. In these cases, simulated realizations are driven by the TI utilized, while the spatial statistics of the hard data is not used. This paper presents a data-driven, high-order simulation approach based upon the approximation of high-order spatial indicator moments. The high-order spatial statistics are expressed as functions of spatial distances similar to variogram models for two-point methods. It is shown that the higher-order statistics are connected with lower orders via boundary conditions. Using an advanced recursive B-spline approximation algorithm, the high-order statistics are reconstructed from hard data. Finally, conditional distribution is calculated using Bayes rule and random values are simulated sequentially for all unsampled grid nodes. The main advantages of the proposed technique are its ability to simulate without a training image, which reproduces the high-order statistics of hard data, and to adopt the complexity of the model to the information available in the hard data. The approach is tested with a synthetic dataset and compared to a conventional second-order method, sisim, in terms of cross-correlations and high-order spatial statistics.

Keywords

Training Image Hard Data Variogram Model Unsampled Location Sequential Indicator Simulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

Funding was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant 239019 and mining industry partners of the COSMO Lab (AngloGold Ashanti, Barrick Gold, BHP Billiton, De Beers Canada, Kinross Gold, Newmont Mining, and Vale).

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.COSMO, Stochastic Mine Planning LaboratoryMcGill UniversityMontrealCanada

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