Focusing geophysical inversion images

A critical problem in inversion of geophysical data is developing a stable inverse problem solution that can simultaneously resolve complicated geolog ical structures. The traditional way to obtain a stable solution is based o n maximum smoothness criteria. This approach, however, provides smoothed un focused images of real geoelectrical structures. Recently, a new approach t o reconstruction of images has been developed based on a total variational stabilizing functional. However, in geophysical applications it still produ ces distorted images. In this paper we develop a new technique to solve thi s problem which we call focusing inversion images. It is based on specially selected stabilizing functionals, called minimum gradient support (MGS) fu nctionals, which minimize the area where strong model parameter variations and discontinuity occur. We demonstrate that the MGS functional, in combina tion with the penalization function, helps to generate clearer and more foc used images for geological structures than conventional maximum smoothness or total variation functionals. The method has been successfully tested on synthetic models and applied to real gravity data.