Regularizing Data In 3D Dc Resistivity Tomography

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