3D electromagnetic inversion based on quasi-analytical approximation

Abstract

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 twofold. 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 (Zhdanov M S, Dmitriev V I, Fang Sand Hursan G 1999 Geophvsics at press). It is based on ideas similar to those developed by Habashy et al (Habashy T M, Groom R Wand Spies B R 1993 J. Geophvs. Res. 98 1759-75) for a localized nonlinear approximation, and by Zhdanov and Fang (Zhdanov M S and Fang S 1996a Geophysics 61646-65) 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 0 and Zhdanov M S 1999 Geophvsics 64 874-87). 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.

Two‐dimensional magnetotelluric inversion of blocky geoelectrical structures

“…However, in this case we should take into account the nonlinear character of the transformations (A1) and (A2). Zhdanov [1999, 1999b] and Zhdanov and Hursan [2000] have developed a more efficient approach to the solution of this problem, based on so-called reweighted regularized conjugate gradient (RCG) method. In the framework of this approach the variable weighting matrix b w e is precomputed on each iteration, b w e ¼ b w en ¼ b w e b m n ð Þ based on the values b m n , obtained on the previous iteration.…”

“…This idea was also implemented in inversion of three-dimensional (3-D) controlled-source MT (CSMT) data over the structures with sharp geoelectrical boundaries [Portniaguine and Zhdanov, 1999b;Zhdanov and Hursan, 2000]. In this paper we demonstrate that this approach helps to generate much more ''focused'' and resolved images of blocky geoelectrical structures than conventional MT inversion methods.…”

Contrast Source Inversion Method: State of Art

“…We note that Zhdanov and Hursan [34] used an additive regularization with a weighted norm similar to (50).…”

Marine controlled-source electromagnetic interferometry

“…A more sophisticated processing approach is to apply an inversion for the subsurface conductivity distribution (for an overview see Avdeev, 2005). The inversion can be based on CSEM data only (e.g., Zhdanov & Hursan, 2000;Plessix & Mulder, 2008), include structural information from seismics (e.g., MacGregor & Sinha, 2000;Harris et al, 2009;Key, 2009) or jointly invert seismic and CSEM data (e.g., Hu et al, 2009).…”