On the field representations in the ELF range

Abstract

Spectral propagation characteristics of ELF atmospherics or slow-tail wave forms are usually determined from mode theory or a residue series representation [Jean et al., 1961; Jones, 1970; Taylor and Sao, 1970; Hughes and Theisen, 1970]. The azimuthal or distance variation of the fields is characterized by Legendre functions of complex order where special simplified forms exist near the source, in the asymptotic range, or near the antipode. The successive Schumann resonances (or circumferential resonances of the earth to ionosphere cavity, which are excited by the worldwide distribution of thunderstorm activity) can be described by Legendre polynomials of increasing integer order n [Wait, 1962; Large and Wait, 1968]. The Legendre polynomials or zonal harmonics can be also used at higher frequencies; special summation techniques are required to assure a more rapid convergence of the series [Johler and Berry, 1962], and the representation of zonal harmonics yields fields consistent with other representations [Galejs, 1969, Figure 4].