A regularized three-dimensional magnetotelluric inversion with a minimum gradient support constraint

SUMMARY Most 3-D magnetotelluric (MT) inversions are classified as a regularized inversion with a smoothness constraint. These inverse algorithms provide smooth solutions but cannot clearly image sharp geo-electrical interfaces. In this paper, we introduce the minimum gradient support (MGS) functional to regularize the 3-D MT inverse problem. This functional has a property whereby the functional seeks a structure with minimum volume containing large conductivity gradients. Therefore, the MGS functional can be used to search for a model with a sharp boundary. We apply the MGS functional to 3-D MT inversion to obtain a clear and accurate image of geo-electrical interfaces. In addition, the modified scattering equation approach introduced in the modified iterative dissipative method (MIDM) is applied to forward calculation, which is based on integral equation (IE) formulation and allows us to efficiently reduce the time required for forward calculation with high accuracy. The quasi-Newton iterative method is used to optimize the objective functional. It is a kind of iterative method with simplified calculation of the inverse Hessian matrix using Broyden–Fletcher–Goldfarb–Shanno (BFGS) update. The convergence of this iterative method is guaranteed with inexact line searches. We also modify the adaptive approach for optimum selection of the regularization parameter so as to fit the inverse algorithm of this study. Three synthetic models are investigated, and the obtained results are compared with those obtained by a smoothing inversion. Based on the comparison, we confirm that the MGS inversion can provide higher resolution when geo-electrical interfaces are sharp. This property will help us to determine reliable electrical structures by the MT exploration method.

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