Lightning Sferics: Analysis of the Instantaneous Phase and Frequency Inferred From Complex Waveforms

Analysis of very low frequency lightning waveforms, or radio sferics, can contribute to research into lower ionosphere perturbations and the corresponding atmospheric chemistry. Lightning waveforms can also be characterized on the basis of their propagation distance from receivers in order to study radio wave propagation. A bank of average waveforms, that is, the waveform bank, <1,000km with a spatial resolution of 10km has been produced, based on the lightning waveforms recorded in Europe on 8 August 2014. These average lightning waveforms at different distances exhibit a sequence of consecutive maxima resulting from ionospheric reflections, named sky waves. The spectral waveform bank shows a sequence of consecutive modal maxima at different frequencies depending on distance. The Hilbert transform is applied to produce complex lightning waveforms, which provide additional information to the original real waveforms alone, that is, the instantaneous phase and frequency. The time differences calculated from the instantaneous phases of complex lightning waveforms give the minimum arrival time difference error when compared to other analyzed signal processing methods. The derivative of the instantaneous phase, that is, the instantaneous frequency, represents the amplitude-weighted average of frequency components at maximum amplitude according to theory and numerical simulation. In real experiments, the instantaneous frequency can be understood as the median value of the real frequency distribution calculated at maximum amplitude. It is found that the instantaneous frequencies at maximum amplitudes are distance dependent. This finding might enable the development of a novel method to determine lightning distances in the future.