ELF-EM fields in the multi-layer spherical 'Earth-ionosphere' model based on WKB

With a high signal-to-noise ratio and a great depth of exploration, the wireless electromagnetic method (WEM) has wide applications in the exploration of deep mineral resources and oil and gas reservoirs. Extremely low-frequency electromagnetic (ELF) waves emitted from a horizontal antenna are used to achieve synchronous acquisition for different receivers of multi-coverage information in a global region. However, previous research based on a planar model ignored the curvature of the Earth. This work focuses on the electromagnetic fields (EM fields) in the model of a spherical 'Earth ionosphere' to extend the coverage of WEM. By transferring the EM fields from a vertical electric dipole (VED) as well as a vertical magnetic dipole (VMD) in the multi-layered medium of the Earth, we obtain the formulae for the EM fields emitted by a horizontal electric dipole (HED) by using a reciprocity theorem. The correctness of the proposed method is verified by comparing it with the approximate analytical formula and previous work. Based on the above results, we have studied the propagation and frequency characteristics of electromagnetic fields in a spherical waveguide consisting of the ionosphere and earth. The results show that the electromagnetic fields under the spherical model produce interference effects that are different from those of the planar model. The electromagnetic response of the layered Earth was then discussed, and its potential as an electromagnetic technique for exploring the deep Earth was demonstrated.