Model sub-ionospheric ELF – VLF pulses

Abstract

The propagation of natural wide-band pulsed radio signals in the spherical Earth – ionosphere cavity is numerically simulated. The frequency band considered is 1–10,000 Hz. We address the TM waves originated from a vertical lightning stroke of the Bruce and Golde, Williams, or Jones model. Major data are based on the Williams’ lightning model. The upper boundary of the cavity is horizontally stratified and the conductivity of each stratum depends on its altitude. We apply several models of vertical conductivity profile, and all of them adequately describe the global electromagnetic (Schumann) resonance. The electromagnetic fields are expanded into a series of normal waves (modes). The frequency dependence of the complex propagation constant of each mode is found by using the full wave solution in the form of Riccati equation. The roots of this equation are found by iterations. Various source–observer distances are used in the waveguides with different height conductivity profiles. The Fourier transform of complex spectra provides the time domain realizations of the wide-band pulsed signals. The results of different model profiles are compared and their correspondence to the known observational data is demonstrated. Computations show that the model pulses similar to either tweek or to slow tail atmospherics. They acquire the form of slow tail atmospherics when the conventional night or day conductivity profiles are used. In this case, a train of VLF oscillations precedes a typical Q-burst. The delay of Q-burst from the VLF precursor grows in proportion to the source – observer distance. The tweek atmospheric emerges combined with the Q-burst when the mesosphere conductivity profile has a section of rapid conductivity increase by 4–5 orders of magnitude in the altitude interval of a few kilometers around 90 km.