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We present a new inversion approach, in which the Lagrangian multiplier is set as a variable at each parameterized blocks and automatically determined according to the parameter resolution matrix and spread function analysis. The approach, named Active Constraint Balancing (ACB), tries to balance the constraints of the optimization according to sensitivity for a given problem so that it enhances the resolution as well as the stability of the inversion process. We demonstrate the performance of the ACB by applying it to a two dimensional resistivity tomography, which results in a remarkable enhancement of the spatial resolution.

We have developed a three‐dimensional inverse scheme for carrying out DC resistivity surveys, incorporating complicated topography as well as arbitrary electrode arrays. The algorithm is based on the finite‐element approximation to the forward problem, so that the effect of topographic variation on the resistivity data is effectively evaluated and incorporated in the inversion. Furthermore, we have enhanced the resolving power of the inversion using the active constraint balancing method. Numerical verifications show that a correct earth image can be derived even when complicated topographic variation exists. By inverting the real field data acquired at a site for an underground sewage disposal plant, we obtained a reasonable image of the subsurface structures, which correlates well with the surface geology and drill log data.

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