Series expansions for the electric and magnetic fields produced by a line or sheet current source above a layered Earth


  • Risto Pirjola,

  • Ari Viljanen,

  • David Boteler


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.