Random fields and up scaling, towards a more predictive probabilistic quantitative hydrogeology
Résumé
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.
Domaines
Sciences de la Terre
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Licence : CC BY - Paternité
Licence : CC BY - Paternité