Source optimization in the inverse geoelectrical problem

In electrical tomography, to determine the conductivity of a body or of a region of the earth, currents are injected on the surface and surface voltage responses are measured. Then the data are inverted to a conductivity distribution which matches the measurements. Usually all available data are used in the belief that pertinent information in the complete data set will be utilized. However, only part of the data contains useful information. This paper addresses means of specifying the optimal data so that pertinent data or data combinations can be interpreted while less pertinent or irrelevant data or data combinations are ignored. It is suggested to reconstruct only those projections of the unknown conductivity distribution which can be reliably restored from the data with a given noise level. Information about these projections is contained in the eigenvalues of the currents to voltage mapping. Reconstruction of only these projections simplifies the inversion procedure. A numerical example is given for the geoenvironmental problem of monitoring a contaminated area.