New Developments in Covariance Modeling and Coregionalization for the Study and Simulation of Natural Phenomena

Geostatistics focus on modeling natural phenomena by univariate or multivariate spatial random fields. Most applications rely on the choice of a stationary model to represent the studied phenomenon. It is now acknowledged that this model is not flexible enough to adequately represent a natural phenomenon showing behaviors that vary substantially in space (a simple example of such heterogeneity is the problem of estimating overburden thickness in the presence of outcrops). For the univariate case, a few non-stationary models were developed recently. However, these models do not have compact support, which limits in practice their range of application. There is a definite need to enlarge the class of univariate non-stationary models, a first goal pursued by this thesis.