Propagation and Time-of-Arrival of VLF Pulses in the Earth-Ionosphere Waveguide

Very low frequency (VLF) propagation in the earth-ionosphere waveguide has been of interest for many decades. Most computational capabilities have been performed for a single frequency, with time-dependent results (such as those applied to lightning) obtained by inverse-Fourier-transforming these single-frequency components over a spectrum of frequencies. But if time-of-arrival (TOA) of a wave pulse is of interest, a less computationally-intensive method can be employed. Since a single spectral field component in the waveguide may be represented as a sum of modal fields, and since the group velocity is different for each mode, only the mode with the largest group velocity - the lowest order mode - need be calculated to obtain TOA information. This principle is demonstrated in detail for a simple waveguide, and applied to the earth-ionosphere waveguide.