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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alabert F (1987) Stochastic imaging of spatial distributions using hard and soft information. Unpublished master’s thesis, Department of Applied Earth Sciences, Stanford University, Stanford, California
Boucher A, Dimitrakopoulos R (2004) A new joint simulation framework and application in a multivariate deposit. In: Dimitrakopoulos R, Ramazan S (eds) Orebody modelling and strategic mine planning, Perth, WA, 2004
Boucher A, Dimitrakopoulos R (2009) Block simulation of multiple correlated variables. Math Geosci 41(2):215–237
Caers J (2000) Direct sequential indicator simulation. In: Proceedings of 6th international geostatistics congress, Cape Town, South Africa
Deraisme J, Rivoirard J, Carrasco Castelli P (2008) Multivariate uniform conditioning and block simulations with discrete Gaussian model: application to Chuquicamata deposit. In: Ortiz J, Emery X (eds) Proceedings of the eight international geostatistics congress, pp 69–78
Desbarats A, Dimitrakopoulos R (2000) Geostatistical simulation of regionalized pore-size distributions using min/max autocorrelation factors. Math Geol 32(8):919–942
Deutsch C, Journel A (1992) GSLIB—geostatistical software library and user’s guide. Oxford University Press, New York
Deutsch C, Journel A (1998) GSLIB: geostatistical software library and user’s guide, 2nd edn. Oxford University Press, New York
Dowd P (1971) The application of geostatistics to No. 20 level, New Broken Hill Consolidated Ltd. Operations Research Department, Zinc Corporation, Conzinc Riotinto of Australia (CRA), Broken Hill, NSW, Australia
Emery X (2004) Properties and limitations of sequential indicator simulation. Stoch Environ Res Risk Assess 18:414–424
Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York
Goulard M, Voltz M (1992) Linear coregionalization model: tools for estimation and choice of cross-variogram matrix. Math Geol 24(3):269–285
Horta A, Soares A (2010) Direct sequential co-simulation with joint probability distribution. Math Geosci 42(3):269–292
Journel A (1974) Geostatistics for conditional simulation of ore bodies. Econ Geol 69(5):673–687
Journel A (1994) Modeling uncertainty: some conceptual thoughts. In: Dimitrakopoulos R (ed) Geostatistics for the next century. Kluwer Academic, Dordrecht, The Netherlands, pp 30–43
Journel A, Alabert F (1989) Non-Gaussian data expansion in the earth sciences. Terra Nova 1:123–134
Leuangthong O, Deutsch C (2003) Stepwise conditional transformation for simulation of multiple variables. Math Geol 35(2):155–173
Oliver D (2003) Gaussian cosimulation: modeling of the cross-covariance. Math Geol 35(6):681–698
Rao S, Journel A (1997) Deriving conditional distributions from ordinary kriging. In: Baafi E, Schofield N (eds) Geostatistics—Wollongong 96. Kluwer Academic, London, pp 92–102
Rivoirard J (1994) Introduction to disjunctive kriging and non-linear geostatistics. Clarendon Press, Oxford
Soares A (2001) Direct sequential simulation and co-simulation. Math Geol 33(8):911–926
Switzer P, Green A (1984) Min/max autocorellation factors for multivariate spatial imagery. Stanford University, Department of Statistics
Wackernagel H, Petigas P, Touffait Y (1989) Overview of methods for coregionalisation analysis. In: Armstrong M (ed) Geostatistics, vol. 1, pp 409–420
Xu W, Tran T, Srivastava RM, Journel A (1992) Integrating seismic data in reservoir modeling: the collocated cokriging alternative. SPE 24742
Acknowledgements
Professor Julian Ortiz of the University of Chile and our Quantitative Group colleagues, in particular Mike Stewart, are thanked for feedback and discussions about the proposed method prior to the writing of this paper. Any remaining deficiencies are entirely the responsibility of the authors.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Cornah, A., Vann, J. (2012). Non-multi-Gaussian Multivariate Simulations with Guaranteed Reproduction of Inter-Variable Correlations. In: Abrahamsen, P., Hauge, R., Kolbjørnsen, O. (eds) Geostatistics Oslo 2012. Quantitative Geology and Geostatistics, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4153-9_30
Download citation
DOI: https://doi.org/10.1007/978-94-007-4153-9_30
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-4152-2
Online ISBN: 978-94-007-4153-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)