Numerical integral method for ELF fields excited by vertical electric dipole in asymmetric earth-ionosphere cavity

Extremely low frequency (ELF) propagation formulas for vertical electric dipole sources radiating in a spherical uniform earth-ionosphere cavity have been derived.These formulas have a range dependence characterized by either the Legendre function of the first kind of complex degree v and order zero or one of its first two derivatives.It is difficult to get the value of the Legendre function unless through appropriate approximations.In this paper, a new numerical integral method for the Legendre function is present.It is more efficient and accurate, and can be used in wider frequency band.The field excited vertical dipole at several frequencies are calculated through the numerical integral method.The fields calculated can image the physical phenomena of ELF propagation in earth-ionosphere cavity, and the frequencies of Schumem resonance is the same as previous researches.