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Multivariate Spatial Modeling of Metallurgical Rock Properties Open Access


Other title
Multivariate simulation
Parameter uncertainty
Nonlinear variables
Multiscale modeling
Multiple imputation
Unequal sampling
Type of item
Degree grantor
University of Alberta
Author or creator
Deutsch, Jared L
Supervisor and department
Askari-Nasab, Hooman (Civil and Environmental Engineering)
Etsell, Thomas (Chemical and Materials Engineering)
Examining committee member and department
Etsell, Thomas (Chemical and Materials Engineering)
Askari-Nasab, Hooman (Civil and Environmental Engineering)
Gómez-Hernández, Jaime (Universitat Politècnica de València)
Boisvert, Jeffrey (Civil and Environmental Engineering)
Hamann, Andreas (Renewable Resources)
Department of Civil and Environmental Engineering
Mining Engineering
Date accepted
Graduation date
Doctor of Philosophy
Degree level
High resolution spatial numerical models of metallurgical properties constrained by geological controls and more extensively measured grade and geomechanical properties constitute an important part of geometallurgy. The spatial modeling of metallurgical rock properties has unique challenges. Metallurgical properties of interest may average nonlinearly, and the nonlinear behaviour may be unquantified due to substantial costs associated with sample collection and testing. The large scale of the samples presents an additional challenge in the modeling of these variables as the support volume for metallurgical properties may be 1-2 orders of magnitude larger than typical metal assays. Practical challenges including the highly multivariate nature of geometallurgical data sets, undersampling and complex optimization requirements complicate the problem. Addressing these challenges requires an integrated statistical approach. In this thesis, a consistent framework for quantifying and modeling the nonlinear behaviour of metallurgical rock properties is introduced. This integrated approach is composed of three parts: a nonlinear modeling and inference strategy, a multivariate downscaling algorithm, and an integrated geostatistical approach to multivariate modeling of metallurgical properties. The first contribution of this thesis is a novel semi-parametric Bayesian updating algorithm which has been developed to infer nonlinear behaviour given multiscale measurements of metallurgical rock properties and related linear properties. This approach may be applied to fit a power law which is demonstrated to be a flexible model for nonlinear modeling. The second contribution addresses the challenge of highly multiscale data by the development of a direct sequential simulation method for the downscaling of metallurgical rock properties given highly multivariate information. The stochastic downscaling procedure developed is exact and respects intrinsic constraints, such as requirements for non-negativity. The third contribution is the development of a consistent framework for geostatistical modeling of metallurgical variables in the presence of constraints, nonlinear variables, multiscale data, missing data, and complex relationships. This approach, and a number of the algorithms developed in this thesis are applied in a geometallurgical case study of a South American copper-molybdenum porphyry deposit. The thesis statement: an integrated statistical approach for the multivariate spatial modeling of metallurgical rock properties will lead to better mine and mill operation strategies to maximize mine value. Developments in this thesis facilitate the integrated approach which is applied to the case study demonstrating the value of this integrated statistical framework.
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
Citation for previous publication
Deutsch, J. L., Palmer, K., Deutsch, C. V., Szymanski, J., & Etsell, T. H. (2015). Spatial Modeling of Geometallurgical Properties: Techniques and a Case Study. Natural Resources Research, 1-21.Deutsch, J. L., Szymanski, J., & Etsell, T. H. (2014). Metallurgical Variable Re-expression for Geostatistics, presented at 16th Annual International Association for Mathematical Geology Conference in New Delhi, India.Deutsch, J.L., Szymanski, J., Etsell, T.H. and Deutsch, C.V. (2015) Downscaling and Multiple Imputation of Metallurgical Variables, presented at 17th Annual International Association for Mathematical Geology Conference in Freiberg, Germany.

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