Focusing geophysical inversion images

A critical problem in inversion of geophysical data is developing a stable inverse problem solution that can si­ multaneously resolve complicated geological structures. The traditional way to obtain a stable solution is based on maximum smoothness criteria. This approach, however, provides smoothed unfocused images of real geoelectri­ cal structures. Recently, a new approach to reconstruc­ tion of images has been developed based on a total varia­ tional stabilizing functional. However, in geophysical ap­ plications it still produces distorted images. In this paper we develop a new technique to solve this problem which we call focusing inversion images. It is based on specially selected stabilizing functionals, called minimum gradi­ ent support (MGS) functionals, which minimize the area where strong model parameter variations and disconti­ nuity occur. We demonstrate that the MGS functional, in combination with the penalization function, helps to generate clearer and more focused images for geologi­ cal structures than conventional maximum smoothness or total variation functionals. The method has been suc­ cessfully tested on synthetic models and applied to real gravity data.