A Simple and Robust Total Variation-Based Inversion Scheme for Transient Electromagnetic Data

Abstract

Transient electromagnetic (TEM) data are conveniently inverted to visualized underground structure with the widely used Occam's inversion. However, in sedimentary environments, Occam's inversion performs poorly in reproducing the sharp boundaries as it produces smoothed results of subsurface geophysical properties. Here, we develop a simple and robust total variation (TV) based inversion scheme for TEM data to preserve sharp boundaries and improve the accuracy of recovered underground structure. To solve the standard L2-TV optimization problem, we propose a reconstructing minimization (RM) approach. The TV-based inversion scheme is divided into two phases. In Phase I the misfit is brought down to a desired level utilizing Occam's inversion. In Phase II we utilize RM approach to implement TV regularization until the convergent result is achieved. Taking advantage of the excellent stability of Occam's inversion, the TV-based inversion scheme has the characteristics of robustness to different initial models. The switch process between Occam's inversion and the RM approach is rather simple to realize due to their similar solution forms. The synthetic and field data examples validate the efficiency and accuracy of the proposed TV-based inversion scheme. We further present a novel analysis based on reconstruction of stabilizer to illustrate the reason for their distinctive behaviors of TV-based inversion and Occam's inversion.

Keywords

• Reconstructing minimization approach
• sharp boundaries
• total variation
• transient electromagnetic inversion