Electromagnetic Field of a HED in the Spherical “Earth-Ionosphere” Model and Its Application in Geophysics

Abstract

The controlled source extremely low frequency (CSELF) method bears the potential for deep resource exploitation utilizing the skywave. The “Skywave” denotes the electromagnetic wave propagating through the waveguide formed by the Earth and ionosphere. It has a considerable penetration depth into the lithosphere due to its low-frequency band. Previous research on extremely low-frequency electromagnetic fields with the coupled lithosphere, atmosphere, and planar ionosphere models ignored the effect of the Earth’s curvature. Thus, we aimed to present the exact formulas for horizontal electric dipoles (HED) in a spherical “Earth-ionosphere” model. These new formulas consider the Earth’s curvature as a multilayer medium rather than a homogeneous underground. We introduce three techniques: function combination pairs, addition and subtraction terms, and Padé approximants, to handle slow convergence in numerical calculation. In the spherical waveguide, electromagnetic fields are mutually interfered with and produce oscillations, which is different from the planar model. The influence of Earth’s curvature cannot be neglected with the increase in source–receiver distance, though it is negligible within 3000 km. Furthermore, it is worth noting that apparent resistivity ρθφ enters the waveguide area earlier than ρφθ. This method can be used as Green’s function to simulate the electromagnetic field of actual antennas and 3-D models.