A variety of methods have been developed to solve the general problem of determining underground resistivity from surface measurements using two current electrodes and two collinear potential electrodes (Ghosh, 1971; Parker, 1971; Inman et al, 1973; Inman, 1975; Koefoed, 1979). Nevertheless, problems associated with measurement errors, nonlinearities, and nonuniqueness have not been completely resolved. Recently, a method of interpretation of direct current resistivity measurements, using a linearized Backus and Gilbert technique was advanced by Oldenburg (1978). In this method, the resistivity is assumed to be a continuous function of depth, and an iterative technique is used to construct a resistivity model whose calculated responses agree with observations within a prescribed error. The nonuniqueness of the problem was resolved by determining only averages of resistivity at depth. However, even in this method the nonlinearity of the problem prohibits definitive statements about advantages and disadvantages of any particular electrode configuration until a large variety of resistivity structures have been considered. The main problems are (1) a nonlinear resistivity profile, (2) a nonlinear current penetration, (3) a nonlinear dependence of measurable potential on resistivity, and (4) a nonlinear depth investigation characteristic.

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