A modified form of the Smith-Pitteway full-wave program is used in conjunction with various lower ionospheric profiles to calculate the propagation characteristics of ELF/VLF waves from a source in the magnetosphere, through the ionosphere. Expressions are developed which give the ratio of the power transmitted into the earth's surface to the power incident on the top of the ionosphere, as a function of the number of wave-hops in the earth-ionosphere waveguide. This depends upon the wave polarization after each hop and a limiting polarization is found after several hops. Numerical evaluation of these expressions is presented and discussed.
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