Which Experimental Variogram for the Structural Inference: A Methodological Study

Abstract

Knowing the lack of robustness of the classical variogram in the case of positively skewed distributions, the use of a variogram deduced from the non centered covariance has been successfully proposed in the fisheries domain (Guiblin et al., 1995).

However, examples of soil pollutants on former industrial sites have shown that despite their theoretical equality the classical variogram and the one deduced from the non centered covariance can lead to very different structures (Jeannée and de Fouquet, 2000). From that point of view, how can the structural inference be improved by the combined use of both tools?

To answer this question, a gaussian random function, its lognormal transform and its median truncation are simulated with a spherical model and various ranges. The tools are compared using on one hand variogram and covariance clouds and on the other hand the variance of the error between the regional variogram, that we want to infer, and the experimental variogram, the only one known in practice.