Method of auxiliary sources for calculating the magnetic and electric fields induced in a layered Earth

Abstract

Time varying ionospheric currents caused by geomagnetic storms originating from the Sun induce electric currents in expansive technological networks located on the Earth's surface. These so-called geomagnetically induced currents (GICs) can be damaging to the systems in which they flow. The ability to estimate the magnitude of GICs is, therefore, desirable in order to mitigate any serious effects from this common space weather occurrence. A necessary element in determining GICs is the accurate calculation of the geoelectric field due to ionospheric current sources. Until now, methods for calculating these fields have primarily focused on computational efficiency. These methods are inaccurate to varying degrees and almost entirely restricted to layered or one-dimensional models of the Earth's conductivity. This work introduces a new technique to the geomagnetic induction problem known as the method of auxiliary sources (MAS). The MAS uses elementary electric/magnetic currents placed on auxiliary surfaces to produce the fields resulting from the primary ionospheric current and secondary currents induced in the Earth. Numerical results for a single- and two-layer Earth model show that the MAS is extremely accurate over the frequency range of interest in geomagnetic induction (0– 1 Hz ). The MAS is not, however, limited to layered Earth models and can be used with general three-dimensional structures. Furthermore, it is shown that by using the MAS, it is possible to determine the fields at any location and with any resolution on the surface or within the Earth. The combination of accuracy and flexibility demonstrate the potential of the MAS for studying complicated geomagnetic induction problems.