A simplified theory of ELF propagation in the Earth-ionosphere transmission line

An approximate theory of ELF propagation in the Earth-ionosphere transmission line is developed by combining the reflection theory of Booker and Lefeuvre (1977) with Greifinger and Greiferinger's (1978, 1979) treatment of the effect of ionization below the level of reflection. The theory allows for the influence of the Earth's magnetic field, for reflection from the gradient on the underside of the D region (or, at night, of a ledge below the E region), for reflection from the gradient on the underside of the E region, and for reflection from the gradient on the topside of the E region. The procedure is to compare local vertical gradient with local wavelength, thereby classifying altitude into intervals where the gradient is high and ones where it is low. Where the gradient is low, the phase-integral treatment is adequate. An interval where the gradient is high may, to a first approximation, be replaced by a discontinuity. The amount of the discontinuity is the difference between the refractive indices at the top and bottom of the interval of high gradient, judged in relation to local wavelength. It is then a matter of combining reflections from the several discontinuities. This requires calculation of the complex phase-changes between the discontinuities. But these are the intervals where the phase-integral treatment is available. To a beter approximation, there is a non-zero phase-change associated with an interval of high gradient. The method for incorporating this is described.