Multiple-Mode Interference and Phase Standard Deviation of VLF Wave Propagation in an Anisotropic Earth–Ionosphere Waveguide

In this paper, the multiple-mode interference (MMI) and phase standard deviation of very low frequency (VLF) wave propagation in an anisotropic earth-ionosphere waveguide are treated analytically. The phase stability of a VLF wave is dependent on the characteristics of each propagable mode, such as the excitation factor, the attenuation rate, the phase velocity, as well as their derivatives with respect to the effective ionosphere height. Computations show that the phase stability in the multiple-mode zone is much poorer than that in the single-mode zone, and the phase standard deviations evaluated considering the ionospheric anisotropy are more consistent with the measured data. It is also found that there exist pronounced directional differences in the interference distributions, and the effect of MMI is weakened as the geomagnetic inclination angle increases. By comparison of the phase standard deviation and the field strength, we find that the maxima of the phase standard deviation coincide with the minima of the field strength. Moreover, the MMI zone is much broader in nighttime than in daytime, and in an anisotropic waveguide, the interference will present evident aggregation at certain heights.