Inversion of DC profiles using 1D piecewise continuous models

This paper presents a method for constructing coupled, one-dimensional electrical conductivity models of the Earth from surface geoelectric measurements. The construction of the individual 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 a previous work, we described 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. In this work, the case of several resistivity soundings located along a line transect is considered. For every sounding site, a one-dimensional model is developed, and the models are horizontally coupled in order to include information from neighboring sites. Numerical experiments and application to field data are presented. In both cases, it is assumed that the data are contaminated by static shift effects. The algorithm automatically takes these effects into account. The examples illustrate the performance of the combined LP and Tikhonov's regularization method in the solution of difficult practical problems.