The electromagnetic field generated by a horizontal electric dipole positioned above a spherical conducting dielectric layer

To derive the spherical harmonic series expression of the electromagnetic field generated by an extremely low frequency (ELF) horizontal electric dipole (HED) in a spherical seawater-air half-space, under the condition that the surface impedance boundary of a uniform spherical conductive dielectric layer is satisfied, the electromagnetic field distribution in the spherical half-space model is calculated using the electromagnetic field reciprocity theorem. Initially, the electromagnetic field equations for a vertical electric dipole (VED) and a vertical magnetic dipole (VMD) over a uniform spherical conductive medium are rigorously derived from the Fock theory of ground wave diffraction. Subsequently, based on these derivations, the electromagnetic field generated by HEDs in a spherical conducting medium in the space above the medium is deduced using the reciprocity theorem of electromagnetic fields. To validate the accuracy of the proposed method, the electric field (Eρ) and the magnetic field (Hρ) of the HED in spherical conducting medium seawater above the air are simulated using MATLAB software. Experimental data indicate that, compared to the results obtained from Pan's Sommerfeld numerical approximation method and Hu's quasi-static method, the calculated results of the proposed method show basic consistency, with an error margin of less than 3 dB, which remains within the permissible range. As the propagation distance increases, the electromagnetic field strength calculated by the proposed method shows the best performance, with the smallest attenuation value of the field strength