The report presents results of a numerical study of EM propagation under diffuse anistropic ionospheres at the extremely low frequencies of 45 Hz and 75 Hz. Waveguide mode parameters are presented under both day and night ambient conditions for several values of ground conductivity as a function of geomagnetic flux density, dip angle, and direction of propagation. (Author).

The study presents the results of a theoretical analysis of the propagation of electromagnetic waves in the very-low-frequency (VLF) and extremely-low-frequency (ELF) ranges in the earth-ionosphere cavity during solar flares. The calculations, which are based upon nominal models of ambient conditions and solar-flare x-ray fluxes and spectra, result in mode-attenuation coefficients which are in good general agreement with observations. The propagation is enhanced relative to ambient conditions at ELF and upper VLF frequencies but is degraded in the lower VLF range. This general behavior is quite insensitive to the details of the assumed x-ray spectrum, the main requirement being a sufficient concentration of x-ray energy in the 1 - 8 A wavelength band. This class of spectrum tends to cause a moderate lowering of the D-region accompanied by an increase in the height gradient of conductivity in the reflection region; this in turn causes the observed phenomena at ELF and VLF during sudden ionospheric disturbances. (Author).

Extremely low frequency (ELF) propagation formulas are derived for dipole sources radiating in a spherical earth-ionosphere waveguide. In these formulas, the earth and ionosphere boundaries are modeled as scalar surface impedances. The spherical waveguide formulas are applied to predict the electromagnetic fields produced by vertical and horizontal electric dipoles (located on the surface of the earth) at antipodal ranges for several frequencies and propagation conditions. These results are used to establish the maximum ranges of validity of ELF propagation formulas that are based on the earth-flattening approximation. Numerous derivations are given in the appendices.