3-D FDTD Modeling of Long-Distance VLF Propagation in the Earth-Ionosphere Waveguide

Very low frequency (VLF) electromagnetic wave propagation is modeled for the first time over 1,000 km-scale distances using a three-dimensional finite-difference time-domain (FDTD) model of the Earth-ionosphere waveguide. Specifically, propagation paths 2,000 km in length are studied, with each simulation requiring 28k processing cores and over 45 hours of real time and used ~3.9 TB. A variety of propagation scenarios are tested, including daytime and nighttime propagation paths, a realistic ground propagation path extending from the NAA VLF transmitter in Cutler, Maine towards New Mexico, and day-to-night ionospheric transitions. The 3-D FDTD model results are compared with 2-D azimuthally-symmetric FDTD and the Long Wave Propagation Capability (LWPC) results to both validate the 3-D model and to understand the impact a fully 3-D model can have on the propagation predictions. The results in this paper identify under what conditions, and also at what propagation distances, a fully 3-D model is most beneficial.