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Mathematical Geosciences

, Volume 51, Issue 4, pp 485–526 | Cite as

Geostatistics for Compositional Data: An Overview

  • Raimon Tolosana-DelgadoEmail author
  • Ute Mueller
  • K. Gerald van den Boogaart
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Abstract

This paper presents an overview of results for the geostatistical analysis of collocated multivariate data sets, whose variables form a composition, where the components represent the relative importance of the parts forming a whole. Such data sets occur most often in mining, hydrogeochemistry and soil science, but the results gathered here are relevant for any regionalised compositional data set. The paper covers the basic definitions, the analysis of the spatial codependence between components, mapping methods of cokriging and cosimulation honoring compositional constraints, the role of pre- and post-transformations such as log-ratios or multivariate normal score transforms, and block-support upscaling. The main result is that multivariate geostatistical techniques can and should be performed on log-ratio scores, in which case the system data-variograms-cokriging/cosimulation is intrinsically consistent, delivering the same results regardless of which log-ratio transformation was used to represent them. Proofs of all statements are included in an appendix.

Keywords

Simplex Variogram Cokriging Co-simulation 

Notes

Acknowledgements

This paper was compiled during research visits between Perth and Freiberg within the project “CoDaBlockCoEstimation”, jointly funded by the German Academic Exchange Service (DAAD) and Universities Australia. The authors warmly thank Vera Pawlwowsky-Glahn and Juan José Egozcue for their constructive comments on a previous version of this manuscript.

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Copyright information

© International Association for Mathematical Geosciences 2018

Authors and Affiliations

  1. 1.Helmholtz-Zentrum Dresden-Rossendorf, Helmholtz Institute Freiberg for Resource TechnologyFreibergGermany
  2. 2.School of ScienceEdith Cowan UniversityJoondalupAustralia
  3. 3.Institut für StochastikTechnische Universität “Bergakademie” FreibergFreibergGermany

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