Three-dimensional source inversion of self-potential data

[ 1] The self-potential (SP) method has long been used for a variety of geophysical applications because of its ease of acquisition, but has suffered from difficulty in interpretation of the data. Self-potential signals result from a source term that is coupled with the earth resistivity and appropriate boundary conditions. This work describes an inversion methodology for determining the self-potential sources from measured SP and resistivity data. The SP source inversion is a linear problem, though it is complicated by nonuniqueness that is common to potential-field problems. The linear operator is also poorly conditioned because of the limited set of measurements, which are often constrained to the earth's surface. Our approach utilizes model regularization that selects a class of solutions which fit the data with sources that are spatially compact. Large variations in sensitivity due to distance and resistivity structure throughout the model are addressed through the use of a scaling term derived from the Green's functions that define the linear operator. A significant benefit of these methods is the resolution of targets at depth from surface measurements alone. This inversion technique is first illustrated with a simple synthetic data set. In a second example we apply this approach to a field data set taken from previously published literature and investigate the effects of different resistivity structure assumptions on the inversion results. The spatial distribution of sources provides useful information that can subsequently be interpreted in terms of physical processes that generate the SP data.