Mathematical Geosciences

, Volume 49, Issue 6, pp 797–814 | Cite as

Weighted Pivot Coordinates for Compositional Data and Their Application to Geochemical Mapping

  • Karel HronEmail author
  • Peter Filzmoser
  • Patrice de Caritat
  • Eva Fišerová
  • Alžběta Gardlo


The log ratio methodology converts compositional data, such as concentrations of chemical elements in a rock, from their original Aitchison geometry to interpretable real orthonormal coordinates, thereby allowing meaningful statistical processing and visualization. However, it must be taken into account that the original concentrations can be flawed by detection limit or imprecision problems that can severely affect the resulting coordinates. This paper aims to construct such orthonormal log ratio coordinates, called weighted pivot coordinates, that capture the relevant relative information about an original component and treat the redundant information in a controlled manner. Theoretical developments are supported by a thorough simulation study. Weighted pivot coordinates are then applied to the geochemical mapping of catchment outlet sediments from the National Geochemical Survey of Australia illustrating their advantage over possible alternatives.


Aitchison geometry Orthonormal coordinates Pivot coordinates Geochemical mapping National Geochemical Survey of Australia 



The insightful and constructive reviewer reports from Dr. Raimon Tolosana-Delgado and two anonymous reviewers are gratefully acknowledged; they helped to greatly improve the paper. The authors thank and acknowledge also the participants of the first GeoMap Workshop (held in Olomouc, Czech Republic, 17–20 June 2014) which provoked discussions leading to the present contribution. The paper was supported by the Grant COST Action CRoNoS IC1408 and the infrastructural part was supported from NPU I (LO1304).


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© International Association for Mathematical Geosciences 2017

Authors and Affiliations

  1. 1.Department of Mathematical Analysis and Applications of Mathematics, Faculty of SciencePalacký University OlomoucOlomoucCzech Republic
  2. 2.Institute of Statistics and Mathematical Methods in EconomicsVienna University of TechnologyViennaAustria
  3. 3.Research School of Earth SciencesThe Australian National UniversityCanberraAustralia
  4. 4.Institute of Molecular and Translational Medicine, Faculty of Medicine and DentistryPalacký University OlomoucOlomoucCzech Republic
  5. 5.Department of Clinical BiochemistryUniversity Hospital OlomoucOlomoucCzech Republic

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