The linearized inverse theory of Backus and Gilbert has been used to invert potential difference measurements obtained from direct current resistivity soundings. The resistivity is assumed to be a continuous function of depth, hence many of the difficulties encountered when assuming that the earth is a layered half-space are avoided. An iterative technique is used to construct a resistivity model whose calculated responses agree with the observations, and the model is then appraised to find those features which are uniquely determined by the surface observations. Also, the existence of the Frechet kernels allows direct comparisons of the resolution provided by various electrode geometries and thus the design of electrode arrays to enhance resolution becomes more feasible.

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