Forward Modeling and validation of a new formulation to compute self-potential signals associated with ground water flow

The classical formulation of the coupled hydroelectrical flow in porous media is based on a linear formulation of two coupled constitutive equations for the electrical current density and the seepage velocity of the water phase and obeying Onsager's reciprocity. This formulation shows that the streaming current density is controlled by the gradient of the fluid pressure of the water phase and a streaming current coupling coefficient that depends on the so-called zeta potential. Recently a new formulation has been introduced in which the streaming current density is directly connected to the seepage velocity of the water phase and to the excess of electrical charge per unit pore volume in the porous material. The advantages of this formulation are numerous. First this new formulation is more intuitive not only in terms of establishing a constitutive equation for the generalized Ohm's law but also in specifying boundary conditions for the influence of the flow field upon the streaming potential. With the new formulation, the streaming potential coupling coefficient shows a decrease of its magnitude with permeability in agreement with published results. The new formulation has been extended in the inertial laminar flow regime and to unsaturated conditions with applications to the vadose zone. This formulation is suitable to model self-potential signals in the field. We investigate infiltration of water from an agricultural ditch, vertical infiltration of water into a sinkhole, and preferential horizontal flow of ground water in a paleochannel. For the three cases reported in the present study, a good match is obtained between finite element simulations performed and field observations. Thus, this formulation could be useful for the inverse mapping of the geometry of groundwater flow from self-potential field measurements.