The waveguide mode theory of propagation of ELF electromagnetic waves over the spherical surface of the Earth

Abstract

The theoretical formulation of the propagation of ELF radio waves, which can be used for the study of Schumann resonances, is developed without making use of the Debye-Watson approximation for the Hankel functions. The modal equations thus obtained are compared with those for a plane wave in a planar waveguide to show that there is a formal resemblance between the two but that the planar approximation does not hold in a strict physical sense. The thin shell approximation leads to the same formulation as the planar approximation if we assume that v( v + 1) = ( k 0 aS) 2.