[1] An algorithm is developed to interpret self-potential (SP) data in terms of distribution of Darcy velocity of the ground water. The model is based on the proportionality existing between the streaming current density and the Darcy velocity. Because the inverse problem of current density determination from SP data is underdetermined, we use Tikhonov regularization with a smoothness constraint based on the differential Laplacian operator and a prior model. The regularization parameter is determined by the L-shape method. The distribution of the Darcy velocity depends on the localization and number of non-polarizing electrodes and information relative to the distribution of the electrical resistivity of the ground. A priori hydraulic information can be introduced in the inverse problem. This approach is tested on two synthetic cases and on real SP data resulting from infiltration of water from a ditch.

[1] We propose an algorithm to invert self-potential signals measured at the ground surface of the Earth to localize hydromechanical disturbances or to the pattern of groundwater flow in geothermal systems. The self-potential signals result from the divergence of the streaming current density. Groundwater flow can be either driven by topography of the water table, free convection, or deformation of the medium. The algorithm includes the electrical resistivity distribution of the medium obtained independently by DC resistance tomography or electromagnetic methods or by coding the assumed geology in terms of distribution of the electrical resistivity accounting for the effect of the temperature and salinity distributions and possibly constraints from borehole measurements. Inversion of the distribution of the source current density from ground surface and borehole self-potential measurements is achieved by solving the inverse problem using Tikhonov regularization solutions that are compatible with the physics of the primary flow problem. By introducing assumptions regarding the smoothness or the compactness of the source and the three-dimensional distribution of the electrical resistivity of the system, the inverse problem can be solved in obtaining the threedimensional distribution of the current source density in the ground. However, an annihilator can be added to the inverted source geometry without affecting the measured self-potential field. Annihilators can be obtained from boundary conditions. Synthetic models and a sandbox experiment are discussed to demonstrate the validity of the algorithm. An application is presented to the geothermal field of Cerro Prieto, Baja California, Mexico, using literature data. Inversion of the self-potential and resistivity data allows observing a plume of hot groundwater rising to the ground surface in the central part of the investigated area and discharging to the ground surface in the southwest part. The temperature anomaly associated with the existence of this plume is independently observed by interpolating borehole temperature measurements. We found a good agreement between the distribution of the temperature and the inverted source current density. The proposed method appears therefore as a noninvasive method for remote detection and three-dimensional mapping of subsurface groundwater flow.Citation: Jardani, A., A. Revil, A. Bolève, and J. P. Dupont (2008), Three-dimensional inversion of self-potential data used to constrain the pattern of groundwater flow in geothermal fields,