Abstract
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.
Highlights
In many cases including this paper, the surface impedance is a scalar defined to equal the ratio of a horizontal electric component to the perpendicular horizontal magnetic component at the Earth’s surface
To the electric and magnetic fields, the surface impedance primarily depends on time variations of the magnetospheric and ionospheric current system and is secondarily affected by currents and charges induced in the Earth
In a usual situation in practice, geomagnetic data are available and we need to calculate the geoelectric field in order to be able to estimate geomagnetically induced currents (GIC) in a network
Summary
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. 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. The special situation with electric and magnetic fields that are independent of the space coordinates at the Earth’s surface is called the “plane wave case”, which is the most important in practice in connection with the surface impedance Both the secondary reflected field in the air and the fields in the Earth layers propagate vertically and no dependence on x or y exists This is called the “plane wave case”, and the surface impedance characterising the Earth’s conductivity structure only depends on the angular frequency ω (provided that Ey and Bx are Fourier transformed from the time (t) to the frequency (ω) domain). To the derivation of Eq (6) from formula (2), Eq (9) leads to the convolution integral (x)
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