Principles of electrography applied to self-potential electrokinetic sources and hydrogeological applications

Abstract

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.