Full 3-D inversion of electromagnetic data on PC

Ž . Ž . Three-dimensional 3-D electromagnetic EM inversion might be believed to require high-performance computers. Ž . 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. Ž . The system of equations is solved using the incomplete Cholesky biconjugate gradient ICBCG method. By applying the w Ž . x 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. q 2001 Elsevier Science B.V. All rights reserved.