A modified total variation regularization approach based on the Gauss-Newton algorithm and split Bregman iteration for magnetotelluric inversion

Abstract

The conductivity distribution of subsurface often contains segmented structure with sharp interfaces, although the magnetotelluric (MT) inversions based on Tikhonov regularization are usually stable, the smoothing interfaces tomography result from high-resistance artifacts and boundary blurring still post a great challenge for MT inversion. On the contrary, Total variation (TV) regularization can deal with the problem of high-impedance artifact and boundary blurring, but its stability is difficult to be guaranteed. In order to invert the sharp interface of conductivity distribution and improve the accuracy of MT inversion, this paper proposes an MT inversion method based on a new modified total variation (MTV) regularization. The improved method transforms the TV model constraint into two different sub-constraints: one is the standard MT inversion constraint with L2 norm, and the other is the standard L2-TV model constraint, then the Gauss-Newton algorithm and split Bregman iteration are employed to separately solve these two different sub-constraint problems. In the inversion experiments, we design a wedge-shaped model and an undulating surface model, the comparison results of accuracy and efficiency show that, among Tikhonov, TV and MTV regularization methods at the same iterations, the proposed regularization method can achieve the lowest reconstruction error and data misfit, thereby eliminating high-resistance artifacts and, in particular, can solve the problem of smoothing interfaces tomography. To this end, a field data testing is also presented to verify the effectiveness and the practicability of the new modified method.