×

zbMATH — the first resource for mathematics

Multivariate categorical modeling with hierarchical truncated pluri-Gaussian simulation. (English) Zbl 1421.86029
Summary: Multiple categorical variables such as mineralization zones, alteration zones, and lithology are often available for geostatistical modeling. Each categorical variable has a number of possible categorical outcomes. The current approach for numerical modeling of categorical variables is to either combine the categorical variables or to model them independently. The collapse of multiple categorical variables into a single variable with all combinations is impractical due to the large number of combinations. In some cases, lumping categorical variables is justified in terms of stationary domains; however, this decision is often due to the limitations of existing techniques. The independent modeling of each categorical variable will fail to reproduce the collocated joint categorical relationships. A methodology for the multivariate modeling of categorical variables utilizing the hierarchical truncated pluri-Gaussian approach is developed and illustrated with the Swiss Jura data set. The multivariate approach allows for improved reproduction of multivariate relationships between categorical variables.
MSC:
86A32 Geostatistics
62H99 Multivariate analysis
Software:
GSLIB
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Acar, S., Process development metallurgical studies for gold cyanidation process, Miner Metall Process, 33, 161-171, (2016)
[2] Angove, J.; Acar, S.; Adams, MD (ed.), Metallurgical test work: gold processingoptions, physical ore properties, and cyanide management, 131-140, (2016), Amsterdam
[3] Arroyo, D.; Emery, X.; Pelez, M., An enhanced Gibbs sampler algorithm for non-conditional simulation of Gaussian random vectors, Comput Geosci, 46, 138-148, (2012)
[4] Astrakova A, Oliver DS, Lantuéjoul C (2015) Truncation map estimation based on bivariate probabilities and validation for the truncated pluriGaussian model. arXiv preprint arXiv:150801090
[5] Babak, O.; Deutsch, CV, Collocated cokriging based on merged secondary attributes, Math Geosci, 41, 921, (2008) · Zbl 1178.86016
[6] Barnett, RM; Deutsch, CV, Multivariate imputation of unequally sampled geological variables, Math Geosci, 47, 791-817, (2015) · Zbl 1323.86018
[7] Barnett, RM; Manchuk, JG; Deutsch, CV, Projection pursuit multivariate transform, Math Geosci, 46, 337-359, (2014) · Zbl 1322.86007
[8] Black WE (2016) Multivariate geostatistical prediction of geochemical measurements for use in mineral prospectivity modeling. Ph.D. thesis, University of Alberta, Edmonton, Alberta. https://doi.org/10.7939/R37659M2R
[9] Bye A (2011) Case studies demonstrating value from geometallurgy initiatives. In: GeoMet 2011—1st AusIMM international geometallurgy conference 2011. AusIMM: Australasian Institute of Mining and Metallurgy, pp 9-30
[10] Deutsch CV, Journel AG (1998) Geostatistical software library and users guide, 2nd edn. Oxford University Press, Oxford
[11] Deutsch, JL; Palmer, K.; Deutsch, CV; Szymanski, J.; Etsell, TH, Spatial modeling of geometallurgical properties: techniques and a case study, Nat Resour Res, 25, 161-181, (2016)
[12] Emery, X.; Cornejo, J., Truncated Gaussian simulation of discrete-valued, ordinal coregionalized variables, Comput Geosci, 36, 1325-1338, (2010)
[13] Emery, X.; Arroyo, D.; Peláez, M., Simulating large Gaussian random vectors subject to inequality constraints by Gibbs sampling, Math Geosci, 46, 265-283, (2014) · Zbl 1322.65030
[14] Galli, A.; Gao, H., Rate of convergence of the Gibbs sampler in the Gaussian case, Math Geol, 33, 653-677, (2001) · Zbl 1011.86008
[15] Galli, A.; Beucher, H.; Loch, G.; Doligez, B.; etal.; Armstrong, M. (ed.); Dowd, PA (ed.), The pros and cons of the truncated Gaussian method, No. 7, 217-233, (1994), Dordrecht
[16] Garza, RAP; Titley, SR; Pimentel, BF, Geology of the Escondida porphyry copper deposit, Antofagasta region, Chile, Econ Geol, 96, 307-324, (2001)
[17] Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, Oxford
[18] Hunt, JA; Berry, RF, Geological contributions to geometallurgy: a review, Geosci Can, 44, 103-118, (2017)
[19] Lantuéjoul C, Desassis N (2012) Simulation of a Gaussian random vector: a propagative version of the Gibbs sampler. In: The 9th international geostatistics congress, Oslo, Norway
[20] León Carrera MF, Barbier M, Le Ravalec M (2018) Accounting for diagenesis overprint in carbonate reservoirs using parametrization technique and optimization workflow for production data matching. J Pet Explor Prod Technol. https://doi.org/10.1007/s13202-018-0446-3
[21] Renard D, Beucher H, Doligez B (2008) Heterotopic bi-categorical variables in pluri-Gaussian truncated simulation. In: Proceedings of the eighth international geostatistics congress geostats, Citeseer, pp 289-298
[22] Rossi ME, Deutsch CV (2014) Mineral resource estimation. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5717-5
[23] Scheffel, R.; Guzman, A.; Dreier, J., Development metallurgy guidelines for copper heap leach, Miner Metall Process, 33, 187-199, (2016)
[24] Silva DS (2018) Enhanced geologic modeling with data-driven training images for improved resources and recoverable reserves. Ph.D. thesis, University of Alberta, Edmonton, Alberta
[25] Silva, DSF; Deutsch, CV, Multiple imputation framework for data assignment in truncated pluri-Gaussian simulation, Stoch Environ Res Risk Assess, 31, 2251-2263, (2017)
[26] Silva, DS; Jewbali, A.; Boisvert, JB; Deutsch, CV, Drillhole placement subject to constraints for improved resource classification, CIM J, 9, 21-32, (2018)
[27] Spall JC (2005) Introduction to stochastic search and optimization: estimation, simulation, and control, vol 65. Wiley, New York
[28] Tonder, EV; Deglon, D.; Napier-Munn, T., The effect of ore blends on the mineral processing of platinum ores, Miner Eng, 23, 621-626, (2010)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.