Stable solutions of the ionospheric fields are derived by a modified matrix multiplication technique for a vertical geomagnetic field and large values of the local refractive index. In an alternate method one ignores the coupling between propagating and attenuated magnetoionic modes at large altitudes in the presence of a dipping geomagnetic field. These two methods are used to integrate fields above the F region and to compute propagation parameters of ELF and VLF waves.
The propagation parameters of ELF fields are dependent on the altitude of the F region and on the geomagnetic field and may exhibit irregular frequency variations. In the VLF range the propagation parameters of terrestrial waves are adequately specified without including the effects of an F region. Application of the reciprocity theorem for a magnetoionic medium shows that an effective excitation of the terrestrial guide requires satellite sources of excessive dipole moments.