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Teaching Aid: Minimum/Maximum Autocorrelation Factors for Joint Simulation of Attributes

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Abstract

Multivariate conditional simulation is used to assess the multivariate grade risk in mineral deposits. With the presence of several spatially correlated attributes, it is important to ensure that their joint simulation is carried out properly and that the observed spatial correlation is reproduced in the realizations. The method of minimum/maximum autocorrelation factors (MAF) is a well established and practical technique that can be used for this purpose. MAF offers tremendous advantages over standard full cosimulation, principal component analysis, and stepwise techniques. In what follows, a detailed review of the MAF technique, its applications, and examples are provided to guide the practitioner on its use.

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References

  • Bandarian E, Bloom L, Mueller U (2006) Transformation methods for multivariate geostatistical simulations. In: Proceedings of the IAMG 06 XI-th international congress for mathematical geology

    Google Scholar 

  • Bandarian E, Bloom L, Mueller U (2008) Direct minimum/maximum autocorrelation factors within the framework of a two structure linear model of coregionalization. Comput Geosci 34(3):190–200

    Article  Google Scholar 

  • Boucher A, Dimitrakopoulos R (2009) Block-support simulation of multiple correlated variables. Math Geosci 41(2):215–237

    Article  Google Scholar 

  • Boucher A, Dimitrakopoulos R, Vargas-Guzmán JA (2004) Joint simulations, optimal drillhole spacing and the role of stockpile. In: Quantitative geology and geostatistics, geostatistics Banff, vol 14, pp 35–44

    Google Scholar 

  • David M (1988) Handbook of applied advance geostatistical ore reserve estimation. Elsevier, Amsterdam

    Google Scholar 

  • Desbarats A (2001) Geostatistical modeling of regionalized grain-size distributions using min/max autocorrelation factors. In: Monestiez P, Allard D, Froidevaux R (eds) GeoENV III—geostatistics for environmental applications, Proceedings of the third European conference on geostatistics for environmental applications. Kluwer Academic, Dordrecht, pp 441–452

    Chapter  Google Scholar 

  • Desbarats A, Dimitrakopoulos R (2000) Geostatistical simulation of regionalized pore-size distribution using min/max autocorrelation factors. Math Geol 32(8):919–942

    Article  Google Scholar 

  • Deutsch C, Journel A (1992) GSLIB: Geostatistical software library and user’s guide. Oxford University Press, New York

    Google Scholar 

  • Dimitrakopoulos R, Mackie S (2008) Joint simulation of mine spoil uncertainty for rehabilitation decision making. In: Soares A, Pereira M, Dimitrakopoulos R (eds) GeoENV VI—geostatistics for environmental applications, Proceedings of the sixth European conference on geostatistics for environmental applications. Quantitative geology and geostatistics, vol 15. Springer, Berlin, pp 349–359

    Chapter  Google Scholar 

  • Fonseca M, Dimitrakopoulos R (2003) Assessing risk in grade tonnage curves in a complex copper deposit, northern Brazil, based on an efficient joint simulation of multiple correlated variables. In: Application of computers and operations research in the mineral industries. South African institute of mining and metallurgy, pp 373–382

    Google Scholar 

  • Goovaerts P (1993) Spatial orthogonality of the principal components computed from coregionalized variables. Math Geol 25(3):281–302

    Article  Google Scholar 

  • Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York

    Google Scholar 

  • Goulard M (1989) Inference in a coregionalization model. In: Armstrong M (ed) Geostatistics, vol 1. Kluwer Academic, Dordrecht, pp 397–408

    Google Scholar 

  • Leuangthong O, Deutsch C (2003) Stepwise conditional transformation for simulation of multiple variables. Math Geol 35(2):155–173

    Article  Google Scholar 

  • Matheron G (1973) The intrinsic random functions and their applications. Adv Appl Probab 5:439–468

    Article  Google Scholar 

  • Rondon O, Tran T (2008) Multivariate simulations using min/max autocorrelation factors: practical aspects and case studies in the mining industry. In: Ortiz J, Emery X (eds) Geostats, vol 1, pp 269–278

    Google Scholar 

  • Switzer P, Green A (1984) Min/max autocorrelation factors for multivariate spatial imaging. Technical report no 6, Department of statistics, Stanford University, Stanford, California

  • Tercan A (1999) Importance of orthogonalization algorithm in modeling conditional distributions by orthogonal transformed indicator methods. Math Geol 31(2):155–173

    Google Scholar 

  • Tran T, Murphy M, Glacken I (2006) Semivariogram structures used in multivariate conditional simulation via minimum/maximum autocorrelation factors. Presented at the XI international congress of the international association for mathematical geosciences (IAMG), Liège, Belgium,

  • Vargas-Guzmán J, Dimitrakopoulos R (2003) Computational properties of min/max autocorrelation factors. Comput Geosci 29(6):715–723

    Article  Google Scholar 

  • Wackernagel H (1998) Principal component analysis for autocorrelated data: a geostatistical perspective. Technical report No 22/98/G. Centre de Géostatistique, Ecole des Mines de Paris

  • Wackernagel H (2003) Multivariate geostatistics. Springer, Berlin

    Google Scholar 

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Correspondence to Oscar Rondon.

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Rondon, O. Teaching Aid: Minimum/Maximum Autocorrelation Factors for Joint Simulation of Attributes. Math Geosci 44, 469–504 (2012). https://doi.org/10.1007/s11004-011-9329-6

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  • DOI: https://doi.org/10.1007/s11004-011-9329-6

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