Mode conversion and refraction effects in the Earth-ionosphere waveguide for VLF radio waves

An approximate theory of multimode propagation in a nonuniform curved terrestrial waveguide is presented. The starting point is the calculation of the mode conversion in a waveguide with an abrupt change of reflecting height and wall impedance. The extension to cascaded sections is then developed. Other approaches are also considered. Finally, some attention is paid to the influence of the angle between the direction of propagation and the terminator (i.e., the sunrise or sunset line). Although no detailed comparison between theory and experiment is made, the results are compatible with much of the observational data reported in the literature.