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Locally stationary kriging, Natural resources evaluation, Geological modelling, non-stationarity, Geostatistics, Locally stationary Gaussian simulation, Local distributions and variograms

Machuca-Mory, David Francisco

Supervisor and department: Deutsch, Clayton V. Civil and Environmental Engineering

Examining committee member and department: Leung, Juliana Civil and Environmental Engineering Sanchez-Azofeifa, Arturo Earth and Atmospheric Sciences Askari-Hasab, Hooman Civil and Environmental Engineering Chilès, Jean-Paul Centre de Géosciences, MINES, ParisTech

Department: Department of Civil and Environmental Engineering

Specialization:

Date accepted: 2010-08-12T21:37:36Z

Graduation date: 2010-11

Degree: Doctor of Philosophy

Degree level: Doctoral

Abstract: In Geostatistical modelling of the spatial distribution of rock attributes, the multivariate distribution of a Random Function defines the range of possible values and the spatial relationships among them. Under a decision of stationarity, the Random Function distribution and its statistics are inferred from data within a spatial domain deemed statistically homogenous. Assuming stationary multiGaussianity allows spatial prediction techniques to take advantage of this simple parametric distribution model. These techniques compute the local distributions with surrounding data and global spatially invariant statistics. They often fail to reproduce local changes in the mean, variability and, particularly, the spatial continuity, that are required for geologically realistic modelling of rock attributes. The proposed alternative is to build local Random Function models that are deemed stationary only in relation to the locations where they are defined. The corresponding location-dependent distributions and statistics are inferred by weighting the samples inversely proportional to their distance to anchor locations. These distributions are locally Gaussian transformed. The transformation models carry information on the local histogram. The distance weighted experimental measures of spatial correlation are able to adapt to local changes in the spatial continuity and are semi-automatically fitted by locally defined variogram models. The fields of local variogram and transformation parameters are used in locally stationary spatial prediction algorithms. The resulting attribute models are rich in non-stationary spatial features. This process implies a higher computational demand than the traditional techniques, but, if data is abundant enough to allow a reliable inference of the local statistics, the proposed locally stationary techniques outperform their stationary counterparts in terms of accuracy and precision. These improved models have the potential of providing better decision support for engineering design.

Language: English

DOI: doi:10.7939-R32990

Rights: 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 these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before 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.





Author: Machuca-Mory, David Francisco

Source: https://era.library.ualberta.ca/


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University of Alberta Geostatistics with Location-Dependent Statistics by David Francisco Machuca-Mory A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mining Engineering Department of Civil and Environmental Engineering ©David Francisco Machuca-Mory Fall 2010 Edmonton, Alberta 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 these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the authors prior written permission. i Examining Committee Clayton V.
Deutsch, Civil and Environmental Engineering Hooman Askari-Hasab, Civil and Environmental Engineering Juliana Leung, Civil and Environmental Engineering Arturo Sanchez-Azofeifa, Earth and Atmospheric Sciences Jean-Paul Chilès, Centre de Géosciences, MINES, ParisTech ii Dedico este trabajo a la felicidad y prosperidad de la Casa Machuca Mory. iii Abstract In Geostatistical modelling of the spatial distribution of rock attributes, the multivariate distribution of a Random Function defines the range of possible values and the spatial relationships among them.
Under a decision of stationarity, the Random Function distribution and its statistics are inferred from data within a spatial domain deemed statistically homogenous.
Assuming stationary multiGaussianity allows spatial prediction techniques to take advantage of this simple parametric distribution model.
These tec...





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