Accurate mapping of the electrical conductivity and of the redox potential of the groundwater is important in delineating the shape of a contaminant plume. A map of redox potential in an aquifer is indicative of biodegradation of organic matter and of concentrations of redox-active components; a map of electrical conductivity provides information on the mineralisation of the groundwater. Both maps can be used to optimise the position of pumping wells for remediation. The self-potential method (SP) and electrical resistivity tomography (ERT) have been applied to the contaminant plume associated with the Entressen landfill in south-east France. The self-potential depends on groundwater flow (electrokinetic contribution) and redox conditions ("electro-redox" contribution). Using the variation of the piezometric head in the aquifer, the electrokinetic contribution is removed from the SP signals. A good linear correlation (R²=0.85) is obtained between the residual SP data and the redox potential values measured in monitoring wells. This relationship is used to draw a redox potential map of the overall contaminated site. The electrical conductivity of the subsoil is obtained from 3D-ERT analysis. A good linear correlation (R²=0.91) is observed between the electrical conductivity of the aquifer determined from the 3D-ERT image and the conductivity of the groundwater measured in boreholes. This indicates that the formation factor is nearly homogeneous in the shallow aquifer at the scale of the ERT. From this correlation, a map of the pore water conductivity of the aquifer is obtained. Keywords: self-potential, redox potential, electrical resistivity tomography, fluid conductivity, contaminant plume

The constitutive coupled equations describing ionic transport in a porous shale are obtained at the scale of a representative elementary volume by volume averaging the local Nernst‐Planck and Stokes equations. The final relationships check the Onsager reciprocity to the first order of perturbation of the state variables with respect to the thermostatic state. This state is characterized by a modified version of the Donnan equilibrium model, which accounts for the partition of the counterions between the Stern and diffuse Gouy‐Chapman layers. After upscaling the local equations the material properties entering the macroscopic constitutive equations are explicitly related to the porosity of the shale, its cation exchange capacity, and some textural properties such as the electrical cementation exponent entering Archie's law. This new model is then applied to predict the salt filtering and electrodiffusion efficiencies of a shale layer.

The electrical potential field passively recorded at the ground surface of the Earth (and termed self‐potential) can be analyzed to determine the shape and the depth of the piezometric surface. The coupling between hydraulic flow and electrical current density is electrokinetic in nature. The electrokinetic coupling coefficient entering into the integral equation relating the depth of the water table to self‐potential signals is analyzed for various types of porous materials. It is simply related to the electrical conductivity of the pore water. In steady state conditions each element of the water table can be seen as an elementary dipole with an inclination locally perpendicular to the water table and strength proportional to the water table elevation. Then, we propose three methods to obtain the shape and range of possible depths of the water table from the study of the self‐potential distribution recorded at the ground surface. The nonuniqueness of the solution is removed if one knows either the electrokinetic coupling coefficient or the water table at one location and under the assumption of the spatial homogeneity of the electrokinetic coupling coefficient. Two field cases are discussed to show the success of the proposed methods for estimating the shape and depth of the water table at two different scales of investigations. They concern the study of self‐potential signals associated with the shape of the water table in the vicinity of a pumping well and in the flank of the Kilauea volcano.