Magnetic field at the Earth's surface produced by a horizontal line current

Abstract

To evaluate the magnetic field produced at the surface of a plane earth by a fluctuating line current in the upper atmosphere, the exact expression for the magnetic field is approximated by an image construction involving a line current and a current octopole at a complex depth below the surface. The construction is valid for all frequencies low enough that retardation is not important, and for most purposes the current octopole is an unimportant correction. The resulting formulas are simple enough to allow the fields of nonsinusoidal currents to be calculated. As an example, that corresponding to a pulse in the primary current is evaluated.