Non-multi-Gaussian Multivariate Simulations With Guaranteed Reproduction of Inter-variable Correlations

A. Cornah, John Vann

    Research output: Chapter in Book/Conference paperConference paper

    Abstract

    Stochastic modeling of interdependent continuous spatial attributes is now routinely carried out in the minerals industry through multi-Gaussian conditional simulation algorithms. However, transformed conditioning data frequently violate multi-Gaussian assumptions in practice, resulting in poor reproduction of correlation between variables in the resultant simulations. Furthermore, the maximum entropy property that is imposed on the multi-Gaussian simulations is not universally appropriate. A new Direct Sequential Cosimulation algorithm is proposed here. In the proposed approach, pair-wise simulated point values are drawn directly from the discrete multivariate conditional distribution under an assumption of intrinsic correlation with local Ordinary Kriging weights used to inform the draw probability. This generates multivariate simulations with two potential advantages over multi-Gaussian methods: (1) inter-variable correlations are assured because the pair-wise inter-variable dependencies within the untransformed conditioning data are embedded directly into each realization; and (2) the resultant stochastic models are not constrained by the maximum entropy properties of multi-Gaussian geostatistical simulation tools.

    Original languageEnglish
    Title of host publicationGeostatistics Oslo 2012: Quantitative Geology and Geostatistics
    Place of PublicationDordrecht, The Netherlands
    PublisherSpringer
    Pages371-382
    Volume17
    ISBN (Print)9789400741522
    DOIs
    Publication statusPublished - 2012
    Event9th International Geostatistics Congress - Oslo, Norway
    Duration: 11 Jun 201215 Jun 2012

    Conference

    Conference9th International Geostatistics Congress
    CountryNorway
    CityOslo
    Period11/06/1215/06/12

    Fingerprint

    simulation
    conditioning
    entropy
    Gaussian method
    minerals industry
    kriging
    modeling
    attribute
    distribution

    Cite this

    Cornah, A., & Vann, J. (2012). Non-multi-Gaussian Multivariate Simulations With Guaranteed Reproduction of Inter-variable Correlations. In Geostatistics Oslo 2012: Quantitative Geology and Geostatistics (Vol. 17, pp. 371-382). Dordrecht, The Netherlands: Springer. https://doi.org/10.1007/978-94-007-4153-9_30
    Cornah, A. ; Vann, John. / Non-multi-Gaussian Multivariate Simulations With Guaranteed Reproduction of Inter-variable Correlations. Geostatistics Oslo 2012: Quantitative Geology and Geostatistics. Vol. 17 Dordrecht, The Netherlands : Springer, 2012. pp. 371-382
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    title = "Non-multi-Gaussian Multivariate Simulations With Guaranteed Reproduction of Inter-variable Correlations",
    abstract = "Stochastic modeling of interdependent continuous spatial attributes is now routinely carried out in the minerals industry through multi-Gaussian conditional simulation algorithms. However, transformed conditioning data frequently violate multi-Gaussian assumptions in practice, resulting in poor reproduction of correlation between variables in the resultant simulations. Furthermore, the maximum entropy property that is imposed on the multi-Gaussian simulations is not universally appropriate. A new Direct Sequential Cosimulation algorithm is proposed here. In the proposed approach, pair-wise simulated point values are drawn directly from the discrete multivariate conditional distribution under an assumption of intrinsic correlation with local Ordinary Kriging weights used to inform the draw probability. This generates multivariate simulations with two potential advantages over multi-Gaussian methods: (1) inter-variable correlations are assured because the pair-wise inter-variable dependencies within the untransformed conditioning data are embedded directly into each realization; and (2) the resultant stochastic models are not constrained by the maximum entropy properties of multi-Gaussian geostatistical simulation tools.",
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    Cornah, A & Vann, J 2012, Non-multi-Gaussian Multivariate Simulations With Guaranteed Reproduction of Inter-variable Correlations. in Geostatistics Oslo 2012: Quantitative Geology and Geostatistics. vol. 17, Springer, Dordrecht, The Netherlands, pp. 371-382, 9th International Geostatistics Congress, Oslo, Norway, 11/06/12. https://doi.org/10.1007/978-94-007-4153-9_30

    Non-multi-Gaussian Multivariate Simulations With Guaranteed Reproduction of Inter-variable Correlations. / Cornah, A.; Vann, John.

    Geostatistics Oslo 2012: Quantitative Geology and Geostatistics. Vol. 17 Dordrecht, The Netherlands : Springer, 2012. p. 371-382.

    Research output: Chapter in Book/Conference paperConference paper

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    T1 - Non-multi-Gaussian Multivariate Simulations With Guaranteed Reproduction of Inter-variable Correlations

    AU - Cornah, A.

    AU - Vann, John

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    N2 - Stochastic modeling of interdependent continuous spatial attributes is now routinely carried out in the minerals industry through multi-Gaussian conditional simulation algorithms. However, transformed conditioning data frequently violate multi-Gaussian assumptions in practice, resulting in poor reproduction of correlation between variables in the resultant simulations. Furthermore, the maximum entropy property that is imposed on the multi-Gaussian simulations is not universally appropriate. A new Direct Sequential Cosimulation algorithm is proposed here. In the proposed approach, pair-wise simulated point values are drawn directly from the discrete multivariate conditional distribution under an assumption of intrinsic correlation with local Ordinary Kriging weights used to inform the draw probability. This generates multivariate simulations with two potential advantages over multi-Gaussian methods: (1) inter-variable correlations are assured because the pair-wise inter-variable dependencies within the untransformed conditioning data are embedded directly into each realization; and (2) the resultant stochastic models are not constrained by the maximum entropy properties of multi-Gaussian geostatistical simulation tools.

    AB - Stochastic modeling of interdependent continuous spatial attributes is now routinely carried out in the minerals industry through multi-Gaussian conditional simulation algorithms. However, transformed conditioning data frequently violate multi-Gaussian assumptions in practice, resulting in poor reproduction of correlation between variables in the resultant simulations. Furthermore, the maximum entropy property that is imposed on the multi-Gaussian simulations is not universally appropriate. A new Direct Sequential Cosimulation algorithm is proposed here. In the proposed approach, pair-wise simulated point values are drawn directly from the discrete multivariate conditional distribution under an assumption of intrinsic correlation with local Ordinary Kriging weights used to inform the draw probability. This generates multivariate simulations with two potential advantages over multi-Gaussian methods: (1) inter-variable correlations are assured because the pair-wise inter-variable dependencies within the untransformed conditioning data are embedded directly into each realization; and (2) the resultant stochastic models are not constrained by the maximum entropy properties of multi-Gaussian geostatistical simulation tools.

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    Cornah A, Vann J. Non-multi-Gaussian Multivariate Simulations With Guaranteed Reproduction of Inter-variable Correlations. In Geostatistics Oslo 2012: Quantitative Geology and Geostatistics. Vol. 17. Dordrecht, The Netherlands: Springer. 2012. p. 371-382 https://doi.org/10.1007/978-94-007-4153-9_30