Random fields and up scaling, towards a more predictive probabilistic quantitative hydrogeology - Noetinger, Benoît (Comptes Rendus. Géoscience)
Random fields are becoming a mature tool sharing applications in many area of physics, mechanics and geosciences. In the latter, it is commonly used under the name of geostatistics. Continuous enrichment of geological/geostatistical models leads to manipulating hydrogeological models characterized by many parameters or hyperparameters corresponding to statistical aggregates that may be poorly estimated due to the scarcity of field data. Those parameters are generally support-scale-dependent and uncertain, so some inverse problem and uncertainty analysis must be carried out in practical applications that involve generally some forward calculation for example a fluid flow simulation if one in interested in transfers in the subsurface. Up scaling techniques are still required to find and to restrict in a controlled manner the more relevant parameters, allowing to lower the dimension of the parameter space. In the stochastic case, the interaction between the conductivity spatial distribution and the flow pattern can lead to non trivial behaviours that will be discussed. Fractured media will not be considered. That note does not present original results, but a selection of some potentially fruitful research avenues suggested by previous works.