Modeling electromagnetic propagation in the Earth-ionosphere waveguide

The ionosphere plays a role in radio propagation that varies strongly with frequency. At extremely low frequency (ELF: 3-3000 Hz) and very low frequency (VLF: 3-30 kHz), the ground and the ionosphere are good electrical conductors and form a spherical Earth-ionosphere waveguide. Many giants of the electromagnetics (EMs) community studied ELF-VLF propagation in the Earth-ionosphere waveguide, a topic which was critically important for long-range communication and navigation systems. James R. Wait was undoubtedly the most prolific publisher in this field, starting in the 1950s and continuing well into the 1990s. Although it is an old problem, there are new scientific and practical applications that rely on accurate modeling of ELF-VLF propagation, including ionospheric remote sensing, lightning remote sensing, global climate monitoring, and even earthquake precursor detection. The theory of ELF-VLP propagation in the Earth-ionosphere waveguide is mature, but there remain many ways of actually performing propagation calculations. Most techniques are based on waveguide mode theory with either numerical or approximate analytical formulations, but direct finite-difference time-domain (FDTD) modeling is now also feasible. Furthermore, in either mode theory or FDTD, the ionospheric upper boundary can be treated with varying degrees of approximation. While these approximations are understood in a qualitative sense, it is difficult to assess in advance their applicability to a given propagation problem. With a series of mode theory and FDTD simulations of propagation from lightning radiation in the Earth-ionosphere waveguide, we investigate the accuracy of these approximations. We also show that fields from post-discharge ionospheric currents and from evanescent modes become important at lower ELF (≲500 Hz) over short distances (≲500 km). These fields are not easily modeled with mode theory, but are inherent in the FDTD formulation of the problem. In this way, the FDTD solution bridges the gap between analytical solutions for fields close to and far from the source