Effects of lateral ionospheric gradients on ELF propagation

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. INTRODUCTION Even such large inhomogeneities as sporadic-E patches, the polar cap boundary, and the day/night terminator can cause the properties of the earthionosphere waveguide to change markedly over the huge wavelength or Fresnel zone of an extremely low frequency (ELF) signal. Such inhomogeneities can therefore give rise to lateral reflection, diffraction, and focusing of ELF modes. Those phenomena are usually unimportant at higher frequencies where the waveguide can be assumed to be slowly varying in the lateral directions. The integral equation approach, which was first introduced by Wait [1964] to analyze weak VLF scattering, is one means of de•,scribing propagation when the ionosphere is not stratified. Field and Joiner [1979] solved the integral equation for ELF propagation in the presence of ionospheric disturbances that were (1) weak and localized or (2) of arbitrary strength and extent, but azimuthally sym-

Localized ELF nocturnal propagation anomalies

“…Another possible explanation for these anomalous nighttime submarine results (Figure 2) is that the receivers are on great-circle paths that are nearly tangential to the disturbed polar cap, in which shadow zones and interference patterns could occur [Field and Joiner, 1981].…”

Effect of the total solar eclipse of 20 March 2015 on the ELF propagation over high‐latitude paths

“…The dynamics of the Schumann resonance and related questions of ELF propagation in the Earth-ionosphere cavity in the frequency band below 50 Hz as a function of solar irradiance (varying with the transition from day to night) was studied in many works [Greifinger et al, 2005;Melnikov et al, 2004]. Additionally, some authors explored the effects of solar terminator [Field and Joiner, 1982;Nickolaenko, 2007].…”

Three‐dimensional subionospheric VLF field diffraction by a truncated highly conducting cylinder and its application to the Trimpi effect problem

“…There also exist a group of studies dealing with ground wave propagation over the inhomogeneous surface of the Earth [ Soloviev and Agapov , 1997, and references therein]. In most of these studies the authors considered ionospheric inhomogeneities that are small in comparison with a wavelength or path length [ Crombie , 1964; Wait , 1964; Field and Joiner , 1979, 1982; Soloviev , 1985; Poulsen et al , 1990, 1993; Nickolaenko , 1994], and they applied first‐order scattering theory (Born approximation) or direct numerical inversion of the integral equation [ Field and Joiner , 1982] for the sake of getting the solution.…”

“…The appropriate integral equation was derived by Wait [1964], who employed the first‐order scattering theory to solve it. These ideas were developed by Field and Joiner [1979, 1982], Nickolaenko [1994], and Poulsen et al [1990], but the rigid validity criteria were always imposed, so that the obtained results proved to be applicable only to single‐mode propagation (ELF or long‐path VLF propagation). Poulsen et al [1993] extended their single‐mode scattering to the case of multiple modes, but only in the WKB limit that assumes no mode conversion within the disturbed region.…”

“…5, 1079, doi:10.1029/2001RS002499, 2002 Copyright 2002 by the American Geophysical Union. 0048-6604/02/2001RS002499 ison with a wavelength or path length [Crombie, 1964;Wait, 1964;Joiner, 1979, 1982;Soloviev, 1985;Poulsen et al, 1990Poulsen et al, , 1993Nickolaenko, 1994], and they applied first-order scattering theory (Born approximation) or direct numerical inversion of the integral equation [Field and Joiner, 1982] for the sake of getting the solution.…”