Dispersive propagation of trans-ionospheric pulse pairs in ionosphere

As the most powerful natural radio waves on earth, trans-ionospheric pulse pairs (TIPPs) are emitted by lightning and have been recorded by several satellites. TIPPs commonly consist of two radio pulses with a clear ionospheric dispersion. Here, we calculate the propagation of TIPPs across the ionosphere by use of a method accurate for sub-cycle radio pulses. One can directly obtain dispersed waveforms in the time domain and then reproduce satellite-recorded frequency spectra. Our work affords a simple and robust tool to directly compare with observation data, which should be helpful to deduce original undispersed waveforms of TIPPs and characteristics of high-energy electrons produced by lightning.