ELF waves in the presence of exponential ionospheric conductivity profiles

Based on the theory of Nicolet and Ailkin, the profile of ionospheric conductivity exhibits a nearly exponential variation with altitude through the layer and the lower edge of the layer. Propagation of ELF waves below this exponential layer is considered after calculating the surface impedance at an altitude where the local refractive index does not necessarily satisfy . 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, where was defined at where . The present model accounts simultaneously for ELF attenuation rates as measured by Jean, and earth-ionosphere cavity resonances as observed by Balser and Wagner.