Quasi‐analytical approximations and series in electromagnetic modeling

Abstract

The quasi‐linear approximation for electromagnetic forward modeling is based on the assumption that the anomalous electrical field within an inhomogeneous domain is linearly proportional to the background (normal) field through an electrical reflectivity tensor λ⁁. In the original formulation of the quasi‐linear approximation, λ⁁ was determined by solving a minimization problem based on an integral equation for the scattering currents. This approach is much less time‐consuming than the full integral equation method; however, it still requires solution of the corresponding system of linear equations. In this paper, we present a new approach to the approximate solution of the integral equation using λ⁁ through construction of quasi‐analytical expressions for the anomalous electromagnetic field for 3-D and 2-D models. Quasi‐analytical solutions reduce dramatically the computational effort related to forward electromagnetic modeling of inhomogeneous geoelectrical structures. In the last sections of this paper, we extend the quasi‐analytical method using iterations and develop higher order approximations resulting in quasi‐analytical series which provide improved accuracy. Computation of these series is based on repetitive application of the given integral contraction operator, which insures rapid convergence to the correct result. Numerical studies demonstrate that quasi‐analytical series can be treated as a new powerful method of fast but rigorous forward modeling solution.

Multisheet modelling of the electrical conductivity structure in the Fennoscandian Shield

“…In MIDM, the conventional scattering equation is modified to a scattering equation with a contracting kernel, which is then solved iteratively in equivalence to Neumann series summation. This method has been applied recently to a variety of multisheet (Pankratov, 1991) and volume 3-D (Avdeev et al, , 1998Kuvshinov et al, 1999;Singer et al, 1999;Zhdanov et al, 1999) problems. By replacing the Neumann series summation with Krylov subspace iteration, significant improvement of convergence has been reported in Avdeev et al (2000), resulting in a solution acceleration of about one order of magnitude.…”

New Geophysical Technique for Mineral Exploration and Mineral Discrimination Based on Electromagnetic Methods

“…For EM methods, Kambalda-style models have been the subject of previous 3-D EM forward modeling studies such as Stolz et al (1995) and Zhdanov et al (2000). However, there are specific limitations on EM methods for the practical exploration of Kambalda-style NiS exploration in Australia and these are imposed by the following factors (Trench and Williams, 1994): a) the generally small size of the deposits (0.5 to 3.0 Mt); b) the extreme depth of weathering in the regolith; and c) the abundance of anomalous responses from noneconomic targets.…”

Electromagnetic Scattering Approximations Revisited

“…Since Γ QA , in general, contains non-diagonal values possible cross-polarization is included (at least to a certain extent). This approximation is known as the QuasiAnalytical (QA) approximation [11]. We now revisit Eq.…”

“…Several approximations to the EM scattering problem have therefore been proposed in the past. Among these are the extended Born approximation (EBA) [10], the local non-linear (LN) approximation [10], the quasi-analytical (QA) approximation [11], the quasi-linear (QL) approximation [12] and the Diagonal Tensor Approximation (DTA) [13]. In order to handle more complex media including larger contrasts and possible anisotropy, also higher-order versions of these methods have been introduced.…”