Inversion techniques applied to resistivity inverse problems

Reviews various inversion techniques applied to resistivity inverse problems, and proposes a fairly different approach. The advantages and disadvantages of various resistivity inversion methods are briefly summarized. A good inversion method must simultaneously minimize the effects of data error and model parameter errors. The necessary requirements for inversion of any geophysical data are a fast forward algorithm for calculating theoretical data for initial model parameters, and a technique for calculating derivatives of the data with respect to the model parameters. Unfortunately, the second requirement is not readily available for two-dimensional (2D) or three-dimensional (3D) inverse resistivity problems. A few workers have examined the problem of resistivity inversion, but no claim has yet been made for an optimum inverse method for 2D or 3D resistivity data. Most resistivity inversion methods are also restricted to surface electrode arrays. A multi-dimensional resistivity inversion method using perturbation analysis and reciprocity is proposed. The theoretical basis for this method is briefly developed. This approach is an efficient way of calculating the derivatives of data with respect to the model parameters because the inverse formulation thereby developed is a linearized form of the general non-linear problem.