Full 3-D inversion of electromagnetic data on PC

Abstract

Three-dimensional (3-D) electromagnetic (EM) inversion might be believed to require high-performance computers. However, with the rapid progress of recent computer technology, running 3-D inversions on personal computers (PC) is becoming a rational choice. This paper describes an attempt to carry out full 3-D inversions of synthetic frequency-domain EM data on a PC. In the inversion, a staggered-grid finite difference scheme is used to solve for the secondary electric field. The system of equations is solved using the incomplete Cholesky biconjugate gradient (ICBCG) method. By applying the static divergence correction proposed by Smith [Geophysics 61 (1996) 1319–1324], the rates of convergence are dramatically improved, and the forward calculation per source location on a medium-size grid takes only a few minutes on a PC. The sensitivities of the EM responses to subsurface resistivity changes are calculated from forward solutions using the reciprocity relation. An inverse problem is formulated so that a model is found that has a smooth structure and at the same time is close to an initial model, and is solved with an iterative least-squares method. A synthetic example for an airborne EM survey shows that the lateral extents of 3-D bodies are well resolved, and the vertical coil coaxial system gives a better lateral resolution than the horizontal coil coplanar system. An example for a ground EM survey shows that expanding the survey coverage or aperture is needed to improve the resolution at depth.