Series expansions for the electric and magnetic fields produced by a line or sheet current source above a layered Earth
Article first published online: 7 DEC 2012
Copyright 1999 by the American Geophysical Union.
Volume 34, Issue 2, pages 269–280, March-April 1999
How to Cite
1999), Series expansions for the electric and magnetic fields produced by a line or sheet current source above a layered Earth, Radio Sci., 34(2), 269–280, doi:10.1029/1998RS900034., , and (
- Issue published online: 7 DEC 2012
- Article first published online: 7 DEC 2012
- Manuscript Accepted: 2 DEC 1998
- Manuscript Received: 9 JUL 1998
The electric and magnetic fields that an overhead, infinitely long line current produces at the surface of a uniform Earth have rapidly converging series expansions, derived earlier. In this paper we make an extension by letting the Earth have a layered conductivity structure characterized by a surface impedance. By investigating the behavior of the surface impedance as a function of the wave number and using an analogy with the uniform-Earth case, approximate series expansions can be derived for the electric and magnetic fields at the Earth's surface. The accuracy of the expansions is considered by numerical examples, in which the line current simulates an auroral electrojet. An increase in the period of oscillation, as well as an increase of the Earth's resistivity, tends to decrease the agreement between field values calculated from the series expansions and from exact integral expressions. However, the inaccuracies are insignificant compared with uncertainties involved in the simplified geophysical model. A sheet current having a finite width is a more appropriate model of an auroral electrojet than a line current. We therefore also present the formulas for the electric and magnetic fields due to a sheet current obtained by integrating the line current expansions.