Large-scale 3D subsurface conductivity imaging using full-wave forward modeling

In this paper, we are going to solve for a 3D subsurface imaging over a waste pit of the Department of Energy (DOE) by inversion of the data collected with the very early time electromagnetic system (VETEM). A priori information shows that the buried objects are highly conductive, therefore a full-wave 3D solver is needed. The measurement data are recorded over an area of 72 m times 25.315 m, so large that it is formidable to process the whole data set simultaneously to obtain a subsurface image. Henceforth, some practical techniques are presented to solve for such a large-scale 3D non-linear inversion problem. First of all, a total-current formulation for the forward problem is presented which, augmented by the stabilized bi-conjugate gradient (BCGS) method, improves the efficiency of the forward solver. Secondly, the Frechet derivatives are computed rapidly with the use of the reciprocity theorem. Lastly, to deal with the large size of the measurement area, the divide-and-conquer strategy is invoked on the basis that a real-world problem is of localized property, and the method is called localized inversion. Besides, a sliding window is devised to mitigate the edge effect collateral to the localized inversion