Impulse response techniques for uncoupled identification of unknown groundwater transmissivity and storativity distributions
Résumé
We address the inverse problem of identifying from some pumping tests unknown spatially distributed transmissivity and storativity occurring in 2D depth-averaged groundwater flow equations. We employ two phases pumping rate to ensure significant effects of the unknown storativity on the transient state at early times before driving this latest to its steady state. Afterwards, the term involving the unknown storativity switches off which in turn uncouples the underlined inverse problem by allowing to focus firstly on identifying the unknown transmissivity distribution in steady flow. Based on impulse response techniques, we relax the common necessary condition into requiring the knowledge of the state at well selected observation locations. Under some reasonable requirements, we prove that the relaxed necessary condition becomes sufficient to ensure identifiability for a wide class of unknown transmissivity distributions. We develop a constructive identification approach using specific adjoint functions defined from the impulse responses at the state observation locations.