SLF/ELF fields from VED solved by normalized spherical harmonic functions

Electromagnetic (EM) fields excited by a vertical electric dipole (VED) at the super-low frequency and the extremely low frequency have been widely used in different studies such as space weather, earthquake predictions, geophysical investigations, and communications. Accurate and efficient algorithms are necessary for quick estimations of worldwide EM fields. This study proposes a recursive algorithm to calculate EM fields excited by a VED embedded in a layered spherical model. A set of local/general reflection and transmission coefficients is defined to describe propagations of EM fields in each spherical layer and the outgoing-type waves and the standing-type waves of EM fields are expressed by normalized spherical Bessel/Hankel functions. The normalized spherical Bessel/Hankel functions are not only useful to overcome the overflow problem in calculations of spherical Bessel/Hankel functions but also helpful to speed up the convergence of summation expressions of EM fields, because the normalized spherical Bessel/Hankel functions mitigate small oscillations terms. Calculating the primary fields and the secondary fields of the total EM fields, respectively, is also helpful to reach convergent summations, because their convergence radiuses are different.