The hydroelectric problem of porous rocks: inversion of the position of the water table from self-potential data

The self-potential (SP) method is a fast and cheap reconnaissance tool sensitive to ground water flow in unconfined aquifers. A model based on the use of Green's functions for the coupled hydroelectric problem yields an integral equation relating the SP field to the distribution of the piezometric head describing the phreatic surface and to the electrical resistivity contrast through this phreatic surface. We apply this model to SP data measured on the south flank of the Piton de la Fournaise volcano, a large shield volcano located on Reunion island, Indian ocean. The phreatic surface, inverted with the help of the Simplex algorithm from the SP data, agrees well with the available information in this area [one borehole and electromagnetic (EM) data]. This interpretation scheme, which we call electrography, has many applications to the crucial problem of water supply in volcanic areas where drilling is expensive.