Effects of lateral ionospheric gradients on ELF propagation

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Abstract
This paper analyzes the propagation of the transverse electromagnetic (TEM) ELF mode when the earth‐ionosphere waveguide is not stratified. It treats a localized disturbance by recasting the wave equation as a two‐dimensional integral equation. Numerical solutions show that such a disturbance behaves like a cylindrical lens filling a narrow aperture. Lateral diffraction, focusing, and reflection can cause the TEM mode to exhibit a standing wave pattern before the disturbance, and a transverse pattern of maxima and minima beyond it. Such phenomena can contribute to the spatial fluctuations occasionally observed in ELF transmissions. The focusing and diffraction diminish when the transverse dimension of the disturbance approaches the width of the first Fresnel zone—typically, several megameters. The analysis models exceedingly widespread inhomogeneities, such as a disturbed polar cap or the day/night hemispheres, as semi‐infinite regions having diffuse boundaries. It then derives full‐wave analytic expressions for the lateral reflection and transmission coefficients of the TEM mode. Reflection can be important in two situations: first, when a great‐circle propagation path is nearly tangential to the boundary of the disturbed polar cap and second, when the TEM mode is obliquely incident on the day/night terminator, in which case a phenomenon analogous to internal reflection can occur.