This article considers a method for solving the direct and the inverse problems in the presence of H-polarization for the fundamental three-layer model of deep magnetotelluric sounding with vertical tectonic faults and horizontal high-conductivity S-layers in a poorly conducting crystalline matrix. The conductivities may vanish on parts of the vertical cracks or the horizontal S-layers, i.e., in this model S-layers and vertical faults may degenerate into an insulator.In 1950 Tikhonov [1] proposed using the frequency dependence of the impedance Z(e0) of the Earth's natural field to study the interior structure of the Earth. The impedance is the ratio of the electric field tangential component to the magnetic field tangential component measured on the Earth's surface as a function of frequency co. Previous research [4,5] has shown that the interpretation of deep magnetotelluric sounding (MTS) data is essentially influenced by the presence of nonhomogeneities in the surface layer overlying the crystalline foundation. The interpretation of deep MTS data is substantially affected also by tectonic faults, which are cracks in the Earth's crust formed in the process of tectonic motions and deformations that are induced in the crustal rocks by tectonic tensile, compressive, or shearing forces. These cracks influence the interpretation of deep MTS data because they may easily leak electric current from the surface sedimentary layer to the conducting half-space below the crystalline base. The location of faults is usually known. It is required to determine their geophysical parameters.In this article, we consider the two-dimensional inverse problem in the presence of H-polarization for the fundamental three-layer model of deep MTS with tectonic faults. The conductivity for this model is defined by the formula
The iterative asymptotic method for solving inverse problems for partial differential equations was developed for the case of slowly varying coefficients. The method constructs a sequence that is proved to converge asymptotically to the solution of the inverse problem. We indicate cases in which this sequence uniformly converges to the solution of the inverse problem.
An approximation model is proposed for an elliptical equation with complex rapidly varying coefficients. An efficient numerical method is developed and implemented. A problem of geoelectricity requiring solution of an equation in this setting is investigated.Numerical solution of elliptical equations with variable coefficients must consider coefficient "contrasts," i.e., the ratio of their maximum and minimum values. High contrast leads to certain difficulties with solution. Problems with high-contrast coefficients arise in many applications, and specifically in 5geoelectricity. The typical structure of the medium is characterized by resistivities ranging from 10 ohm/m to 1 ohm/re. The development of electromagnetic sounding and prospecting methods also leads to mathematical problems with high-contrast coefficients.Special-purpose methods have been developed in geoelectricity for calculation of fields in media where conductivity changes abruptly with depth and varies smoothly along the Earth's surface [1][2][3][4]. Recently, researchers have begun focusing on problems for so-called media with faults. In these media, thin high-conductivity regions are embedded in a poorly conducting layer. Electromagnetic field calculations in such media must allow for rapid variation of the equation coefficients in both horizontal and vertical directions [5,6].The article introduces a convenient approximation of the elliptical equation with coefficients of maximum contrast, develops and implements a numerical method for solving the resulting problem, and analyzes the numerical results in a problem dealing with the effect of faults on electromagnetic fields.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.