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Permanent link (DOI): https://doi.org/10.7939/R31X5C

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Geostatistics with locally varying anisotropy Open Access

Descriptions

Other title
Subject/Keyword
model
Geostatistics
krige
Dijkstra
multidimensional
ISOMAP
anisotropy
Simulation
stationarity
MDS
resource
estimation
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Boisvert, Jeff
Supervisor and department
Deutsch, Clayton (Civil and Environmental Engineering)
Examining committee member and department
Askari-Nasab, Hooman (Civil and Environmental Engineering)
Apel, Derek (Civil and Environmental Engineering)
Nouri, Alireza (Civil and Environmental Engineering)
Schuurmans, Dale (Computer Science)
Dimitrakopolous, Roussos (McGill University)
Department
Department of Civil and Environmental Engineering
Specialization

Date accepted
2010-04-14T20:19:11Z
Graduation date
2010-06
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
Many geological deposits contain nonlinear anisotropic features such as veins, channels, folds or local changes in orientation; numerical property modeling must account for these features to be reliable and predictive. This work incorporates locally varying anisotropy into inverse distance estimation, kriging and sequential Gaussian simulation. The methodology is applicable to a range of fields including (1) mining-mineral grade modeling (2) petroleum-porosity, permeability, saturation and facies modeling (3) environmental-contaminate concentration modeling. An exhaustive vector field defines the direction and magnitude of anisotropy and must be specified prior to modeling. Techniques explored for obtaining this field include: manual; moment of inertia of local covariance maps; direct estimation and; automatic feature interpolation. The methodology for integrating locally varying anisotropy into numerical modeling is based on modifying the distance/covariance between locations in space. Normally, the straight line path determines distance but in the presence of nonlinear features the appropriate path between locations traces along the features. These paths are calculated with the Dijkstra algorithm and may be nonlinear in the presence of locally varying anisotropy. Nonlinear paths do not ensure positive definiteness of the required system of equations when used with kriging or sequential Gaussian simulation. Classical multidimensional scaling is applied to ensure positive definiteness but is found to be computationally infeasible for large models, thus, landmark points are used for efficiency with acceptable losses in precision. The methodology is demonstrated on two data sets (1) net thickness of the McMurray formation in northern Alberta and (2) gold grade in a porphyry copper deposit. Integrating LVA into numerical modeling increases local accuracy and improves leave-one-out cross validation analysis results in both case studies.
Language
English
DOI
doi:10.7939/R31X5C
Rights
License granted by Jeff Boisvert (jbb@ualberta.ca) on 2010-04-14T17:39:48Z (GMT): Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of the above terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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