On the electromagnetic resonant frequencies of the earth ionosphere cavity

The earth ionosphere cavity is capable of supporting resonant electromagnetic modes (Schumann modes) at extremely low frequencies. The usual formula for the frequencies of these resonances is deduced from the waveguide mode theory in which propagation is essentially tangential to the earth's surface. Here an alternative formulation in terms of outwardly and inwardly propagating radial waves is presented and shown to result in the same formula as found from the waveguide mode theory for all reasonable
D
-region ionosphere parameters.