Published in Geophysical Research Letters, Volume 34, Issue 24, December 21, 2007.
NOTE: At the time of publication, the author Bwalya Malama was not yet affiliated with Cal Poly.
The definitive version is available at https://doi.org/10.1029/2007GL031907.
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.
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