The 2-D telegraph equation (TDTE)

The 2-D telegraph equation (two-dimensional telegraph equation, TDTE) solves the propagation of ELF waves over the spherical surface of the Earth-ionosphere cavity for an arbitrary source-observer configuration. Instead of seeking global normal modes, it tracks how a wave from a specific source propagates through the cavity and combines at the point of observation.

This approach is flexible: it can model both large individual transients (Q-discharges from strong lightning strikes) and the "background" SR arising from the incoherent superposition of many lightning discharges scattered across the entire planet. It thereby bridges the gap between modeling individual events and modeling the continuous resonance signal.

The TDTE approach for reconstructing global lightning activity was introduced by Prácser et al. (2019) Pracser 2019 and forms the core of the open-source package schupy Bozoki 2019. Compared with the purely analytical model of a uniform cavity, it makes it possible to work with a realistic distribution of sources; compared with FDTD/FEM it is computationally substantially cheaper, which makes it a practical tool for the inversion of measurements.