The propagation of VLF radio waves across a coastline is investigated in this thesis. The Earth and ionosphere are assumed to be flat. The coastline is modelled by a straight line across which the electrical properties of the Earth change discontinuously. Only the case of radio waves normally incident upon the coastline is studied. Various models of the Earth-ionosphere waveguide are used in the investigation. The simplest one neglects the Earth's magnetic field and treats the land, sea and ionosphere as constant impedance planes. A more sophisticated model aporoximates the land and sea by semi-infinite, homogeneous, isotropic media and the ionosphere by a vertically inhomogeneous isotropic medium. The next one discussed has an anisotropic ionosphere with the land, sea and ionosphere treated as planes with constant impedance matrices. The final model approximates the land and sea by semi-infinite inhomogeneous isotropic media and the ionosphere by a vertically inhomogeneous, anisotropic medium. Only in the simplest model can the scattered field be obtained in a closed form. In this case the exact formulae obtained yield simple approximations for the scattered field and further study shows that it is possible to obtain these approximations, or equivalent ones, without the calculation of the exact solution. This latter method easily generalises to the other models studied in the thesis. Thus expressions for the scattered field are obtained for all the models. These expressions are used to calculate numerical values of the mode conversion coefficients. The results show that the reflected field is unimportant and that the Earth's magnetic field is an important parameter in the determination of the transmitted field. They also show that scattering is more important at night-time, at high wave frequencies (in the frequency range studied), or with low land conductivities.
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