Solution of the Statistical Characteristics of LF Radio-Wave Propagation Phase in the Earth-ionosphere Waveguide based on the S-FDTD Method

The study of low-frequency (LF) radio-wave propagation phase in the Earth-ionosphere waveguide is of great significance for the accuracy enhancement of related systems such as ionospheric sounding, time service, and lightning location. In this article, the stochastic finite-difference time-domain (S-FDTD) algorithm based on the Taylor series expansion idea is used to propose a new method for measuring the uncertainty of LF radio-wave propagation phase in the random media. We study how to obtain the mean value and standard deviation of the propagation phase of the Loran-C one-hop sky waves when the ionosphere is considered to be the random medium. At the same time, the effects of different ionospheric parameters with random characteristics on the propagation phases of sky waves are analyzed. The results of the wave-hop theory are used for validation. The numerical experimental results show that the method can obtain the statistical characteristics of LF radio-wave propagation phase only by a single FDTD simulation. The method can be further extended to obtain the stochastic characteristics of LF radio-wave propagation phases in the complex Earth-random ionosphere waveguide.