The relation between ionospheric profiles and ELF propagation in the Earth-ionosphere transmission line

Abstract

Based on an approximate wave solution, it is shown that, for reflexion of ELF waves from a given ionosphere described by a simple profile of ionization density, the phase-integral method may be used above a certain level, and the ionosphere may be abolished below this level. The height of ELF reflexion thus determined is independent of angle incidence, but not of frequency. The level is the one where the ionosphere passes from rapidly varying to slowly varying behavior, judged in relation to the local wavelength. An approximate solution is obtained to the mode problem in the Earth-ionosphere transmission line in terms of four crossing plane waves, one pair having O wave polarization and the other X wave polarization. The velocity of phase propagation is calculated, and also the rate of attenuation due to leakage of energy into the region above the level of reflexion. The attenuation rate due to collisional absorption below the level of reflexion is also calculated using a method similar to that employed for dielectric loss in an engineering transmission line. As the frequency descends through the ELF band, penetration of the D-region occurs in succession for the O and X waves, leading to reflexion from the E-region at the Schumann resonant frequency and penetration of the ionosphere at micropulsation frequencies. Under quiet day-time ionospheric conditions the penetration frequency-band for the D-region is around 20–60 Hz in middle and high latitudes, but around 75–100 Hz at the equator. At a frequency low enough to be reflected primarily from the E-region under quiet ionospheric conditions, an increase in D-region ionization that is just sufficient to transfer primary reflexion from the E-region to the D-region results in an increase in the rate of attenuation. On the other hand, when once reflexion is firmly established at the lower level, further increase of ionization in the D-region causes a reduction in the rate of attenuation. Similar effects are expected to occur at night in association with a sub- E-region ledge of ionization. Small variations in the ionization profile of such a ledge are the likely cause of night-time fluctuations of transmission at 45 and 75 Hz.