Geostatistics with compositional data, an overview

This paper presents an overview of results for the geostatistical analysis of collocated multivariable data sets, in which the variables form a composition, i.e. where the components inform of the relative important 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 the compositional constraints, the role of pre- and post-transformations like logratios or multivariate normal score transforms, and block-support upscaling. Proofs of all statements are included in an appendix.