VLF modes below an idealized anisotropic ionosphere

The cylindrical shell between the earth and a homogeneous or exponentially varying ionosphere model is excited by vertically or horizontally polarized line sources; these fields are related to dipole fields in a spherical shell. Because of ionospheric anisotropy, the vertically polarized source also excites TM field components with wave numbers corresponding to TE modes, and a horizontally polarized source excites TE fields corresponding to TM modes, particularly for the higher frequencies at nighttime and for propagation westward. Among the field components tangential to the ground surface, TM fields tend to dominate with the exception of TE modes at daytime and for lower frequencies at night. TM modes dominate in the nighttime mode sum (or interference pattern) for propagation eastward, but the two lower TE modes contribute significantly if propagation is westward. Simplified computational models that neglect the radial component of the earth's static magnetic field are justified under daytime conditions. At nighttime such calculations provide extreme changes in the attenuation rates and phase velocity variations, which are opposite to the ones observed with a dipping static magnetic field. The direction dependence of the phase velocity is eliminated by decreasing the strength of the static magnetic field.