Asymptotic Theory of Fields of the Schumann Resonance in the Gyrotropic Earth-Ionosphere Cavity

Abstract

Horizontal components of extremely low frequency (ELF) fields in the gyrotropic Earth–ionosphere cavity are expressed analytically through the corresponding fields of the isotropic one. A linear approximation by two small parameters is used. Those are the isotropic ionosphere impedance z₀ and the ratio gєz₂/z₁ of the off-diagonal to diagonal matrix elements for the surface impedance of the gyrotropic ionosphere. It is shown that the effect of splitting of the Schumann resonance frequencies caused by existence of the d. c. geomagnetic field results in “apparent” angle shift of all ground-based sources of ELF radiation toward the geographic West (“refraction of ELF fields in the gyrotropic Earth–ionosphere cavity”) and excitation of the elliptical magnetic polarization. An analytical relation for the mentioned phenomena is determined. Explicit expressions for polarization characteristics of the electromagnetic ELF noise excited by an arbitrary number of world thunderstorm centers are obtained. Expected values of the “apparent” angle shifts for sources of radiation are estimated. They show that locations of thunderstorm centers and isolated Q-bursts determined with the use of multi-component ELF measurements should be corrected to exclude the “gyrotropic refraction”. The equations for calculating the necessary corrections are presented. The results obtained are generalized to a case of arbitrary latitudinal location of the sources.