ELF waves in the presence of exponential ionospheric conductivity profiles

Abstract
Based on the theory of Nicolet and Ailkin, the profile of ionospheric conductivity exhibits a nearly exponential variation with altitude through theDlayer and the lower edge of theElayer. Propagation of ELF waves below this exponential layer is considered after calculating the surface impedanceZ_{s}at an altitudehwhere the local refractive indexndoes not necessarily satisfy|n|\gg1. The propagation constant is determined by an iteration process. This model of an isotropic nonhomogeneous ionosphere is a closer approximation of the propagation geometry than are earlier models, whereZ_{s}was defined athwhere|n|gg1. The present model accounts simultaneously for ELF attenuation rates as measured by Jean, and earth-ionosphere cavity resonances as observed by Balser and Wagner.