Ground effects of space weather investigated by the surface impedance

Abstract

The objective of this paper is to provide a discussion of the surface impedance applicable in connection with studies of geomagnetically induced currents (GIC) in technological systems. This viewpoint means that the surface impedance is regarded as a tool to determine the horizontal (geo)electric field at the Earth's surface, which is the key quantity for GIC. Thus the approach is different from the traditional magnetotelluric viewpoint. The definition of the surface impedance usually involves wavenumber-frequency-domain fields, so inverse Fourier transforming the expression of the electric field in terms of the surface impedance and the geomagnetic field results in convolution integrals in the time and space domains. The frequency-dependent surface impedance has a high-pass filter character whereas the corresponding transfer function between the electric field and the time derivative of the magnetic field is of a low-pass filter type. The relative change of the latter transfer function with frequency is usually smaller than that of the surface impedance, which indicates that the geoelectric field is closer to the time derivative than to the magnetic field itself. An investigation of the surface impedance defined by the space-domain electric and magnetic components indicates that the largest electric fields are not always achieved by the plane wave assumption, which is sometimes regarded as an extreme case for GIC. It is also concluded in this paper that it is often possible to apply the plane wave relation locally between the surface electric and magnetic fields. The absolute value of the surface impedance decreases with an increasing wavenumber although the maximum may also be at a non-zero value of the wavenumber. The imaginary part of the surface impedance usually much exceeds the real part.

Surface electric fields for North America during historical geomagnetic storms

“…We supplement the USGS data with five realistic layered Earth resistivity models for Canada described in Pirjola et al []: the “Quebec,” “Ontario—Model 1,” “Southern Manitoba,” “British Columbia,” and “Nova Scotia” (QUE, ONT, MAN, BRC, and NOV, respectively). We also extend the Great Plains and Central Lowland physiographic regions northward for the Alberta, Saskatchewan, and southwestern Manitoba provinces in Canada.…”

“…Physiographic regions for the United States and southern Canada (dark lines), from the USGS and Pirjola et al [], respectively. Large‐filled circles represent the grid of equivalent elementary current systems in the ionosphere spaced 5° apart used to interpolate magnetic field data.…”

Practical model applicable to investigating the coast effect on the geoelectric field in connection with studies of geomagnetically induced currents

“…The difficulty in the present H polarisation situation arises from the fact that Z u (b) in equation (10) does not go to zero but actually approaches infinity, when |b| increases, so the integral in equation (6) does not converge. However, referring to equations (15) and (16) in [12], we see that the inverse Fourier transform of 1…”

“…However, we should notice that the application of Z d in equations (2) and (8) concerns the transfer through the highly-conducting ocean water whereas Z u is used for relating E d to H d at the ocean floor, and generally large conductivities are more favourable for the plane wave assumption, e.g. [12] and references therein. On the other hand, it must be remembered that the derivation of equations (13) and (15) in [1], which are utilised in equations (2) and (8) above, applies the formula Z d = E d /H d at the ocean floor.…”

“…The former case, where the electric field is perpendicular to the coastline, is more interesting and important regarding GIC studies since it exhibits the pronounced enhancement of the electric field. For the H polarisation, Gilbert ends up at an integral equation for the electric field at the ocean floor and at the land surface, which together form the xy plane of his Cartesian coordinate system with the y axis lying at the coastline (equations (10) and (12) in [4]). In the integral equation, the electric field is a function of x, and the kernel is a modified Bessel function K 0 thanks to the simplifying assumption that the land and the Earth below the ocean constitute a uniform half-space.…”