Diffusion of electromagnetic fields into two-dimensional earth: TE and TM polarization

Abstract

Electromagnetic fields occurring at the earth surface during geomagnetic disturbances drive geomagnetically induced currents (GICs) in electric power transmission grids, submarine cables and railway lines leading to potential problems in the operation of electromagnetic equipment and systems. In order to estimate the potential risk of GlCs on such systems, it is necessary to bow the magnitude of the electric and magnetic fields at the Earth surface. In this paper, diffusion of both TE and TM polarized electromagnetic fields into a non-unlform 2D earth model is studied via the method of auxiliary sources (MAS). The MAS uses elementary electridmagnetic currents placed on auxiliary surfaces to produce the fields resulting from the primary and secondary currents. Electric and magnetic field distributions are shown and analyzed at the Earth surface with lateral conductivity discontinuities (e.g., near coastal regions). I. INTRODUCTION Geomagnetic storms originating from the sun can induce several hundred amps of DC current in technological systems such as pipelines, railway, and power transmission lines. These so-called geomagnetically induced currents (GICs) are a potential source of problems to the systems in which they flow. GICs can cause harmful effects in power lines and transformers, in some cases even causing a collapse of the system (I). Studies have shown that GICs also exist in trans-oceanic cables, thus leading to the problems in the operation of communication systems (Z). Most techniques used to estimate the induced electromagnetic (EM) fields due to geomagnetic origin (which is necessary in order to mitigate any serious space weather effects) consider a simple 1-d layered earth model or neglect contributions from the induced currents within the Earth. However, depending on the distribution of the Earth conductivity, such as near costal regions, the induced EM fields can be significantly affected by secondary EM fields produced by the eddy currents flowing within the Earth. In this work, the method of auxiliary sources (MAS) is used for solving the EM field diffision problem for a non-uniform 2D Earth model. The MAS is a numerical technique which was originally developed for analyzing a wide class of scattering and radiation electro-magnetic problems (l, and references therein). Recently the MAS has been applied to various low frequency electromagnetic induction problems. It has been widely demonstrated to be a general, robust, and accurate numerical method for low frequency electromagnetic induction scattering by highly conducting and permeable targets. Particularly in application to composite objects, the reduced computational complexity of the method shows great potential for simulating realistically complex electromagnetic induction problems (3, and references therein). Briefly, in the MAS, boundary value problems are solved numerically by representing the electromagnetic fields in each domain of the structure under investigation by a finite linear combination of analytic solutions of the relevant field equations, corresponding to sources situated at some distance away from the boundaries of each domain. The 'auxiliary sources' producing these analytical solutions are chosen to be elementary currents and charges located on fictitious auxiliary surtace(s), usually conforming to the actual surface(s) of the structure. In practice, at least as the method is realized here, we only require points on the auxiliary and actual surfaces, without resorting to the detailed mesh stmctures as required by other methods (finite element method, boundary element method, etc.). The two auxiliary surfaces are set up inside and outside the penetrable scattering object. Specifically, the fields outside of the structure are considered to originate from a set of auxiliary sources placed inside the object, and the fields penetrating inside the object arise from a set of auxiliary sources placed outside the object. The fields constructed inside and outside of the object are required to obey the continuity of the tangential magnetic field components and the jump condition for the normal magnetic field components at an array of selected points on the sdace(s) of the structure. The result is a set of matrix equations in which the amplitudes of auxiliary sources are to he determined. Once the amplitude of auxiliary sources is found the