Theoretical investigations into very low frequency radio wave propagation.

The propagation of VLF radiowaves between the Earth and the ionosphere has been discussed theoretically within the context of waveguide mode theory. Due to the high reflectivity of the lower ionosphere to electromagnetic waves at thesefrequencies, propagation to great distances within the Earth-ionosphere waveguide, with little attenuation, is possible. This fact makes these frequencies ideal for the use in global navigational systems. OMEGA is one such system and this is quoted throughout as an example of a phase type navigation aid. The theoretical variations of the field strength with distance along the guide have been calculated for propagation over various types of terrain. The theory can be extended to include the dependence on receiver height within the waveguide. This will have practical application when OMEGA is installed in aircraft. The theory has been developed to model propagation over discontinuities in the lower wall of the waveguide. The mode conversion coefficients are calculated for propagation over a spherical Earth and beneath a realistic anisotropic ionosphere. Variations of the important first few mode conversion coefficients with frequency, conductivity and azimuth are illustrated. These conversion coefficients are utilised to calculate the theoretical field strengths as a discontinuity is crossed. Propagations across sea-land and land-sea boundaries are illustrated and propagation across the Greenland ice cap is modelled and compared to experimental results. The discontinuity theory has been developed, for the first time, to model propagation over a height discontinuity in the lower wall of the waveguide. This can be extended to calculate variations of the theoretical field strength as a mountain range is traversed. The theoretical trends are similar to those observed in practice. Finally, the ionospheric inversion problem is considered. The Backus and Gilbert theory is reformulated within the context of ionospheric physics. A new method has been developed for calculating the derivatives of the ionospheric reflection matrix, starting from the Pitterway Full Wave technique. This has proved invaluable in producing a significant saving in computing time and has made the implementation of the inversion technique on a computer possible. An example of inverting VLF steep incidence sounding data highlights the fundamental problem of inversion, namely, one of non-uniqueness.