Piecewise smooth models for electromagnetic inverse problems

This paper presents a new method for constructing onedimensional electrical conductivity models of the Earth from surface electromagnetic measurements. The construction of these models is a nonlinear inverse problem that can be approached by linearization techniques combined with iterative methods and Tikhonov’s regularization. The standard application of these techniques usually leads to smooth models that represent a continuous variation of conductivity with depth. In this work we describe how these methods can be modified to incorporate what is known in Computer Vision as the line process (LP) decoupling technique, which has the ability to include discontinuities in the models. This results in piecewise smooth models which are often more adequate for representing stratified media. We have implemented a relaxation technique to construct these types of models and present numerical experiments and an application to field data. These examples illustrate the performance of the combined LP and Tikhonov’s regularization method. Keywords—Magnetotelluric, electromagnetic soundings, regularization, inversion.