Abstract
Because of the ill-posedness and high non-uniqueness of the 3D d.c. resistivity inverse problem, we cannot find a stable and unique solution solely on the basis of fitting data. To stabilize the inverse problem and find a minimum-structure solution, Tikhonov regularization is often applied. This usually involves the minimization of the second-order model derivatives, which is equivalent to the application of nonlinear interpolation in model space. For the same purpose, we propose to regularize data and invert a large number of interpolated measurements with an estimated data covariance matrix. Because the potential field distribution is generally smooth, interpolation can be an effective tool to fill in the missing data on the surface and construct 2D data slices. Inverting 2D data slices along with the use of model regularization turns out to be more attractive, because it can more tightly constrain the near-surface structure roughnesses. It also gives parameterization for the model regularization more flexibility. In addition, inverting a large number of interpolated data with an efficient algorithm does not require additional computational effort.
Published Version
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