Magnetic polarization of the Schumann resonances: An asymptotic theory

Horizontal components of extremely low-frequency (ELF) fields in the gyrotropic Earth–ionosphere cavity are expressed through the fields of an isotropic cavity. A linear approximation of the perturbation method with respect to two small parameters is used. These are the impedance z₀ of the isotropic ionosphere and the ratio γ≡z₂/z₁ of the off-diagonal to diagonal elements of the surface impedance matrix of the gyrotropic ionosphere. It is shown that the effect of splitting of the Schumann resonance frequencies caused by the existence of the d.c. geomagnetic field results in an “apparent” angular 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 an elliptical magnetic polarization. An analytical relation for the mentioned phenomena is derived. Explicit expressions for polarization characteristics of the electromagnetic ELF noise excited by an arbitrary number of equatorial thunderstorm centers are obtained. Expected values of the “apparent” angular shift for these sources are estimated. Analysis of the estimated magnitudes shows 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” effect. Equations to calculate the necessary corrections are presented. The results are generalized to the case of an arbitrary latitudinal location of the sources.