Ionospheric Variability Effects on Impulsive ELF Antipodal Propagation About the Earth Sphere

Analytical and numerical solutions to extremely low-frequency electromagnetic wave propagation in the earth-ionosphere waveguide nearly always assume average (mean) material properties at each position of interest and only solve for the average (mean) electric and magnetic fields. However, numerically assuming only an average state of the ionosphere yields calculated output electromagnetic field waveforms that are not as rich and complex as measured electromagnetic fields. Furthermore, there is great uncertainty in the content of the ionosphere at any given moment. In this paper, global stochastic finite-difference time-domain models of the earth-ionosphere waveguide are generated for the first time. These models use the Galerkin-based polynomial chaos expansion method to efficiently calculate both the mean and variance of the electric and magnetic fields due to uncertainties and variances in the state of the ionosphere. The proposed method is validated through comparisons with brute-force Monte Carlo results.