3D electromagnetic inversion based on quasi-analytical approximation
Michael Zhdanov; Gabor Hursan
Журнал:
Inverse Problems
Дата:
2000-10-01
Аннотация:
In this paper we address one of the most challenging problems of
electromagnetic (EM) geophysical methods: three-dimensional (3D) inversion
of EM data over inhomogeneous geological formations. The difficulties
in 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, the
inversion is an unstable and ambiguous problem. To overcome
these difficulties we suggest using, for forward modelling, the new
quasi-analytical (QA) approximation developed recently by
Zhdanov et al (ZhdanovMS, DmitrievVI, FangS and HursanG
1999 Geophysics at press). It is based on ideas similar to
those developed by Habashy et al (HabashyTM, GroomRW and
SpiesBR 1993 J. Geophys. Res.98 1759-75) for a
localized nonlinear approximation, and by Zhdanov and Fang
(ZhdanovMS and FangS 1996a Geophysics61 646-65)
for a quasi-linear approximation. We assume that the anomalous
electrical field within an inhomogeneous domain is linearly
proportional to the background (normal) field through a scalar
electrical reflectivity coefficient, which is a function of the
background geoelectrical cross-section and the background EM
field only. This approach leads to construction of the QA
expressions for an anomalous EM field and for the Frechet
derivative operator of a forward problem, which simplifies
dramatically the forward modelling and inversion. To obtain a
stable solution of a 3D inverse problem we apply the
regularization method based on using a focusing stabilizing
functional introduced by Portniaguine and Zhdanov (Portniaguine
O and Zhdanov M S 1999 Geophysics64 874-87). This
stabilizer helps generate a sharp and focused image of anomalous
conductivity distribution. The inversion is based on the
re-weighted regularized conjugate gradient method.
266.7Кб