Estimation of regionalized compositions: A comparison of three methods |
| |
| Authors: | V Pawlowsky R A Olea and J C Davis |
| |
| Institution: | (1) Department de Matemàtica Aplicada III, E.T.S. d'Enginyers de Camins, Canals i Ports, Universitat Politècnica de Catalunya, Gran Capitán s/n, E-08034 Barcelona, Spain;(2) Mathematical Geology Section, Kansas Geological Survey, The University of Kansas, 66047 Lawrence, Kansas |
| |
| 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. |
| |
| Keywords: | closed data log-ratio basis method oil field kriging |
| 本文献已被 SpringerLink 等数据库收录！ |
|
