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
D
layer and the lower edge of the
E
layer. Propagation of ELF waves below this exponential layer is considered after calculating the surface impedance
Z_{s}
at an altitude
h
where the local refractive index
n
does 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, where
Z_{s}
was defined at
h
where
|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.