Reconstruction of the three-dimensional Darcy velocity in a small catchment using self-potential, electrical resistivity, and induced polarization data

One of the ultimate goals of hydrogeophysics is to map the groundwater table throughout a catchment and together with information about hydrogeological properties of the saturated zone, derived from geophysical and hydrogeological data, estimate the Darcy velocity in three dimensions throughout the saturated zone. In this work, we present our first attempts to achieve this goal in the small (~1 km2) catchment area of Roujan (Hérault, France), which is a well characterized hydrogeological research site. Two mutually exclusive conceptual models to relate self-potential data to the determination of the water table were employed using a maximum likelihood approach, where the resulting models were averaged according to Bayesian model averaging. The estimated electrical resistivity structure derived from resistivity surveys was used together with laboratory measurements to estimate the streaming potential coupling coefficient and its spatial variation. Resistivity and induced polarization surveys were employed to determine the spatial variation of the thickness of the aquifer material (clayey silts) overlying the electrically more conductive aquitard (Miocene marls). Induced Polarization measurements were also performed to estimate the specific surface area and its variation in the aquifer. The electrical conductivity of the pore water was sampled throughout the aquifer and the formation factor was estimated in the laboratory. This allowed us to use both the Kozeny and Carman model and site-specific relationships to relate electrical resistivity and normalized chargeability with permeability. A cokriging method was applied to estimate large scale variations in the three-dimensional permeability structure by conditioning to available permeability data and several collocated two-dimensional models of electrical resistivity and normalized chargeability. Our estimates of the variations of the depth to the aquitard, depth to the water table, and the large-scale variations in the permeability structure allowed us to estimate the Darcy velocity throughout the saturated aquifer in the Roujan catchment.