Multivariate Simulation Using A Locally Varying Coregionalization Model
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Authors
Riquelme, Alvaro
Date
Type
thesis
Language
eng
Keyword
Multivariate geostatistical modeling , Nataf transformation , Cholesky decomposition , Geodesics , Riemannian manifold , Symmetric positive definite
Alternative Title
Abstract
Multivariate spatial modeling is key to understanding the behavior of materials downstream in a mining operation. However, multivariate spatial modeling is challenging when the variables show complex relationships, posing a problem for resource modeling. The thesis proposes three novel methodologies, based on recent developments in geometry, with the unique motivation of extracting as much information as possible from a given multivariate data set sampled in a geographical domain and improving resource estimates results when the multivariate behavior of the data is complex.
The thesis starting point is the relaxation in the assumption of stationarity in the linear correlation coefficient among the different geological attributes, fixed throughout the domain under study in the conventional case. Instead, we consider a model in which the correlation parameter is locally varying, according to the location considered in the domain. Once we set the basis of the model, we propose three methodologies for classical problems in resource estimation.
The first contribution takes advantage of the interpolation of the correlation matrices to characterize the dependency among variables throughout the geologic domain. Once the correlation is interpolated on a grid, multivariate simulation is performed, honoring complex relationships shown in the data.
A second contribution considers using the inference of correlation between the known and missing variables to apply Bayes' rule for data imputation of missing values. Then, we propose a second imputation methodology by exploiting the Cholesky decomposition properties, considering the spatial auto-correlation on the variable of interest.
One of the most important steps when developing a resource estimation project is the definition of stationary spatial domains. The clustering of geological data using the K-means algorithm adapted to our context is a third development of the presented research, accounting for the non-Euclidean nature of the correlation among attributes.
The value of the research is demonstrated in a case study using real geochemical data. Overall, the results show accuracy in the prediction at unsampled locations, accounting for complex relations between the attributes while adding practical value and theoretical insight to multivariate geostatistical modeling.
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Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
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Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Attribution-NonCommercial 3.0 United States
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Attribution-NonCommercial 3.0 United States