The Mode Theory of VLF Ionospheric Propagation for Finite Ground Conductivity

The space between the earth and the ionosphere is considered as a waveguide with sharply bounded walls. Employing a representation in terms of spherical wave functions of complex order, the field of a vertical dipole source is calculated for very low frequencies. It is shown that the effect of the finite conductivity of the ground is quite important for propagation to great distances. Good agreement is obtained with the experimental results of J. Heritage.