Model Waveforms of Slow-Tail Sferics

We simulate numerically the propagation of slow-tail sferics, which occupy a wide frequency band from 1 Hz to 10 kHz, in the spherical Earth–ionosphere cavity. The TM wave generated by a vertical lightning discharge is considered. Classic engineering models of a lightning stroke are employed. The calculations use the Williams stroke model as the field source. We assume that the upper boundary of the cavity is an isotropic horizontally stratified ionosphere, and the conductivity of each layer depends on its altitude. The day and night-time models of the vertical conductivity profile, which were used for correct description of the global electromagnetic (Schumann) resonance, are employed. The frequency dependence of the complex propagation constants of the zero- and first-order modes was found by using the full-wave solution in the form of the Riccati equation. The roots of this equation are the eigenvalues of the problem, which are found by iterations. Complex spectra of vertical electric and horizontal magnetic fields are constructed in the form of a series of modes with known propagation constants. Various source-to-observer distances in the day and night-time cavities are considered. The Fourier transform is applied to the complex field spectra to find the waveforms of the sferics. The model data allowed us to obtain the calibration curves for estimating the source-to-observer distance from the delay between the ELF slow tail and the VLF precursor. It is shown that the calibration curves are coincident for the day and night-time propagation conditions.