On Some Consistency Conditions for Geostatistical Change-of-Support Models

This work deals with a family of geostatistical models used in application fields concerned with a change of support, such as mineral resources evaluation and polluted soil management. Three models are examined: the discrete Gaussian, Hermitian and Laguerrian models, which rely on a transformation of the variable of interest (mineral grade or pollutant concentration) defined on point and block supports into variables with Gaussian or gamma univariate distributions and isofactorial bivariate distributions. The focus is given to the relationships between the transformed variables at both supports, and to the conditions that these relationships imply on the model parameters. Additionally, guidelines are given for improving the variogram analysis of the transformed variables and for validating the change-of-support model.