Finite difference analyses of Schumann resonance and reconstruction of lightning distribution

This paper deals with the computation of extremely low frequency propagation associated with the Schumann resonance phenomena and the reconstruction algorithm for source lightning location on the basis of measured Schumann resonance data. The finite difference equations are derived in terms of discretized magnetic fields in the spherical coordinates, introducing the azimuthal symmetry for simplicity. The most reliable electron and neutral density models in the atmosphere and the ionosphere can be used to describe extremely low frequency wave propagation. A linear inverse problem for the reconstruction is formulated using the computed spectra as a set of basis functions to identify lightning distributions with respect to the distances from any observatories to the global thunderstorm centers. Numerical experiments allow us to evaluate properties and precision of the solution in the absence or in the presence of noise in the initial spectral data. The inverse problem is applied to the experimental data collected at a field site in Japan, and distribution of global lightning activity is reconstructed for the data covering the period from March to December 1999. The reconstructed data show a reasonable set of distances from the observatory to well‐known global thunderstorm centers, and they indicate the seasonal drift of lightning activity. The problems that were involved in solving the inverse problem are also discussed.