Influence of Earth curvature and the terrestrial magnetic field on VLF propagation

Abstract

An account is given of some recent work on the mode theory of VLF ionospheric propagation. Attention is confined to the behavior of the attenuation coefficient of the dominant mode. The ionosphere is assumed to be a sharply bounded and homogeneous ionized medium. It is indicated that earth curvature increases the attenuation rate by as much as a factor of 2 as compared with the corresponding attenuation for a flat earth. The influence of the earth's magnetic field is also shown to be important. In fact, east‐to‐west propagation paths suffer much greater attenuation than west‐to‐east paths. The theoretical results in the present paper appear to agree well with the experimental data of W.L. Taylor.

Attenuation of lightning‐produced sferics in the Earth‐ionosphere waveguide and low‐latitude ionosphere

“…[6] By combining WWLLN's global lightning location data with the 12-24 s of burst waveform data C/NOFS regularly obtains during satellite eclipses, we achieve comprehensive observations of whistlers and sferics. By comparing stroke energy with whistler amplitude, we will show that the sferic waves traveling to the east in the Earth-ionosphere waveguide experience less attenuation than those traveling to the west and are more likely to be observed at all but the shortest distances to the originating stroke, while westward going waves introduce comparatively more energy to the topside ionosphere, as predicted by theory but never adequately measured [Wait and Spies, 1960;Rybachek, 1995]. Additionally, we will show that attenuation in the ionosphere is dominated by the D and E regions, below the orbit of C/NOFS, with little further attenuation between 400 and 850 km.…”

“…The C/NOFS and WWLLN events can be correlated via a simple time-of-flight calculation, so that the stroke energy and whistler amplitude can be compared to theory with the assistance of the Long-Wavelength Propagation Capability (LWPC) software [Ferguson, 1998]. Theory and observation show that VLF waves propagating in the Earth-ionosphere waveguide attenuate as a function of distance and magnetic azimuth from the originating stroke, producing a marked amplitude difference between eastward propagation and westward propagation [Wait and Spies, 1960;Rybachek, 1995]. We are now able to detect this VLF propagation feature in lightning-generated sferics both within the Earth-ionosphere waveguide and in the topside ionosphere.…”

Azimuthal dependence of VLF propagation

“…Similarly, the LWPC model shows an attenuation increase of 2 dB/Mm from eastward‐ to westward‐propagating sferics for equatorial day paths over the Pacific Ocean. The model also gives a 28% to 37% variability of attenuation between propagation directions, relative to northward propagation, compared to 30% for Wait and Spies [] and 58% to 77% for WWLLN.…”

Transequatorial reception of a very-low-frequency transmission

“…The diurnal variation of the phase and amplitude of very-low-frequency radio waves propagated over great distances has been explained [Wait, 1959;Wait and Spies, 1960] with considerable success using the wave-guide mode theory of VLF propagation [Budden, 1961;Wait, 1962]. In the simpler versions of this theory it is assumed that the VLF energy travels in a wave guide formed by an imperfectly conducting, sharply bounded, isotropic ionosphere which is concentric with a perfectly conducting earth.…”