Finite difference analyses of Schumann resonance and reconstruction of lightning distribution

Abstract

[1] 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.

Variations of the global lightning distribution revealed from three‐station Schumann resonance measurements

“…[20] Different kinds of noises in experimental measurements, errors in determination of the ELF propagation parameters, unknown frequency dependence of a source spectrum, and a problem of choice of the regularization parameter a in the inverse problem solution were investigated by Shvets [2001], Ando et al [2005a], and Ando and Hayakawa [2007]. It was shown by these studies, in particular, that serious errors in the reconstructed distance profiles are connected with "slow" trends in the experimental field spectra introduced by the source spectrum Idl (w), if it is not flat in the SR frequency range, or/and by uncorrected frequency response of the receiving channels.…”

“…[7] To infer the global lightning distribution from the background SR signal we proposed a technique of inversion of measured power field spectra into the distribution of sources' intensity in reference to an observation station based on distance signatures in SR spectra [Shvets, 2001;Ando et al, 2005a;Ando and Hayakawa, 2007]. Application of a tomography procedure to a set of such distance profiles of lightning intensity related to a network of observation stations allows us to obtain source distribution over the Earth's surface [Shvets, 2000;Shvets et al, 2009].…”

Three‐dimensional finite difference time domain modeling of the Schumann resonance parameters on Titan, Venus, and Mars

“…A finite difference method has been developed by Ando et al [2005] to analyze the SR problems and to reconstruct the lightning distribution in the Earth-ionosphere cavity. Nickolaenko et al [1999Nickolaenko et al [ , 2004 and Nickolaenko and Rabinowicz [2001] gave an analytical solution for the ELF pulses from the lighting strokes in the time domain.…”

A Review of Progress in FDTD Maxwell's Equations Modeling of Impulsive Subionospheric Propagation Below 300 kHz

“…The first group, Otsuyama et al [49], uses the global 3-D model described in [28], [29] and in Section IV to perform FDTD SR calculations. They simulate a lightning strike occurring at the Equator and record the and magnetic fields at distances between 5 and 20 Mm.…”