3D electromagnetic inversion based on quasi-analyticalapproximation

Abstract

In this paper we address one of the most challenging problems ofelectromagnetic (EM) geophysical methods: three-dimensional (3D) inversionof EM data over inhomogeneous geological formations. The difficultiesin the solution of this problem are two-fold. On the one hand,3D EM forward modelling is an extremely complicated and time-consuming mathematical problem itself. On the other hand, theinversion is an unstable and ambiguous problem. To overcomethese difficulties we suggest using, for forward modelling, the newquasi-analytical (QA) approximation developed recently byZhdanov et al (Zhdanov M S, Dmitriev V I, Fang S and Hursan G1999 Geophysics at press). It is based on ideas similar tothose developed by Habashy et al (Habashy T M, Groom R W andSpies B R 1993 J. Geophys. Res. 98 1759-75) for alocalized nonlinear approximation, and by Zhdanov and Fang(Zhdanov M S and Fang S 1996a Geophysics 61 646-65)for a quasi-linear approximation. We assume that the anomalouselectrical field within an inhomogeneous domain is linearlyproportional to the background (normal) field through a scalarelectrical reflectivity coefficient, which is a function of thebackground geoelectrical cross-section and the background EMfield only. This approach leads to construction of the QAexpressions for an anomalous EM field and for the Frechetderivative operator of a forward problem, which simplifiesdramatically the forward modelling and inversion. To obtain astable solution of a 3D inverse problem we apply theregularization method based on using a focusing stabilizingfunctional introduced by Portniaguine and Zhdanov (PortniaguineO and Zhdanov M S 1999 Geophysics 64 874-87). Thisstabilizer helps generate a sharp and focused image of anomalousconductivity distribution. The inversion is based on there-weighted regularized conjugate gradient method.