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Estimation of regionalized compositions: A comparison of three methods

Mathematical Geology

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, ,
DOI: 10.1007/BF02083570

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Abstract

A regionalized composition is a random vector function whose components are positive and sum to a constant at every point of the sampling region. Consequently, the components of a regionalized composition are necessarily spatially correlated. This spatial dependence-induced by the constant sum constraint-is a spurious spatial correlation and may lead to misinterpretations of statistical analyses. Furthermore, the cross-covariance matrices of the regionalized composition are singular, as is the coefficient matrix of the cokriging system of equations. Three methods of performing estimation or prediction of a regionalized composition at unsampled points are discussed: (1) the direct approach of estimating each variable separately; (2) the basis method, which is applicable only when a random function is available that can he regarded as the size of the regionalized composition under study; (3) the logratio approach, using the additive-log-ratio transformation proposed by J. Aitchison, which allows statistical analysis of compositional data. We present a brief theoretical review of these three methods and compare them using compositional data from the Lyons West Oil Field in Kansas (USA). It is shown that, although there are no important numerical differences, the direct approach leads to invalid results, whereas the basis method and the additive-log-ratio approach are comparable. ?? 1995 International Association for Mathematical Geology.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Estimation of regionalized compositions: A comparison of three methods
Series title:
Mathematical Geology
DOI:
10.1007/BF02083570
Volume
27
Issue:
1
Year Published:
1995
Language:
English
Publisher location:
Kluwer Academic Publishers-Plenum Publishers
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
Larger Work Title:
Mathematical Geology
First page:
105
Last page:
127
Number of Pages:
23