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 1000 km scale distances using a 3-D finite-difference time-domain (FDTD) model of the Earth-ionosphere waveguide. Specifically, propagation paths of 2000 km in length are studied, with each simulation requiring 28k processing cores and over 45 h of real time and using ~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, ME, USA, toward 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 understand the impact a fully 3-D model can have on the propagation predictions. The results in this article identify under what conditions and also at what propagation distances, a fully 3-D model is most beneficial.