Derivation of characteristics of the relation between geomagnetic and geoelectric variation fields from the surface impedance for a two-layer earth

Abstract

The surface impedance is defined to give the ratio between horizontal geoelectric and geomagnetic variation fields at the earth’s surface in the frequency domain. Studying the properties of the surface impedance enables conclusions about the corresponding relation between the surface electric and magnetic variation fields in the time domain. In particular, it is possible to perform an investigation about assumptions that lead to a proportionality between the geoelectric field and the time derivative of the geomagnetic field and about situations that make the electric field and the variations of the magnetic field proportional. The results are directly applicable to the research of geomagnetically induced currents (GIC) driven by the geoelectric field in technological networks at the earth’s surface. Thus, the main objective of this paper is not in traditional magnetotellurics but in studies of ground effects of space weather. We use a two-layer earth model, which is simple enough to have a precise analytic formula for the surface impedance. It is shown in this paper that a poorly-conducting upper layer above a highly-conducting bottom is favourable to the electric field (and GIC) being proportional to the magnetic time derivative at the earth’s surface whereas a thin highly-conducting upper layer above a less-conducting bottom results in a surface electric field (and GIC) proportional to magnetic variations.