Statistical tests for validating geostatistical simulation algorithms

Geostatistical simulation relies on the definition of a stochastic model (e.g. a random field characterized by the set of its finite-dimensional distributions), a spatial domain and an algorithm used to construct realizations of the model over the domain. In practice, most algorithms are approximate, because their implementation requires simplifications or because the convergence to the model is only asymptotic. This work addresses the problem of evaluating the ability of a given algorithm to reproduce the underlying model. Several statistical tests are proposed in order to detect whether the fluctuations observed between the sample statistics (in particular, the spatial average, variance and regional semi-variogram) and the associated theoretical statistics (mean value, dispersion variance and semi-variogram) are inconsistent with the random field model and domain size. The tests are illustrated on a few examples and a set of computer programs is provided.