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Application of Logratios for Geostatistical Modelling of Compositional Data Open Access


Other title
MultiGaussian Kriging
Compostional Data
Type of item
Degree grantor
University of Alberta
Author or creator
Job, Michael R
Supervisor and department
Dr. Clayton Deutsch (Civil and Environmental Engineering)
Examining committee member and department
Thundat, Thomas (Chemical and Materials Engineering)
Boisvert, Jeff (Civil and Environmental Engineering)
Deutsch, Clayton (Civil and Environmental Engineering)
Department of Civil and Environmental Engineering
Mining Engineering
Date accepted
Graduation date
Master of Science
Degree level
Numeric data for earth sciences often represent fractions or percentages of a whole, such as the chemical or mineralogical composition of a rock. The individual components are non-negative and have a constant sum of 100%. Satisfying these constraints at unsampled locations after estimation or simulation is a practical requirement, but not guaranteed by conventional mapping and modelling techniques. The components are constrained to the constant sum, which means that they are not free to vary independently, and there is at least one negative correlation. Standard statistical techniques are therefore not suited to compositional data, so transformations using the logarithms of the component ratios (logratios) are used to overcome these problems. Linear averaging and back-transformation of logratios results in a geometric rather than an arithmetic mean, which will result in a bias. A procedure using normal scores transformation of the logratio values and multiGaussian kriging was devised to overcome this bias. The key objective is to avoid estimating the logratios directly and then back-transforming into original data units. Instead, the conditional distributions of the components are modelled. Ordinary kriging, multiGaussian kriging and conditional simulation were used on data from the Alberta Oil Sands to assess the performance of the compositional geostatistics approach.
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.
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