Quasi-Static Solution for ELF/SLF near-Zone Field of a Vertical Magnetic Dipole near the Surface of a Lossy Half-Space

Abstract

Dipole antennas over the boundary between two different media have been widely used in the fields of geophysics exploration, oceanography, and submerged communication. In this paper, an analytical method is proposed to analyse the near-zone field at the extremely low frequency (ELF)/super low frequency (SLF) range due to a vertical magnetic dipole (VMD). For the lack of feasible analytical techniques to derive the components exactly, two reasonable assumptions are introduced depending on the quasi-static definition and the equivalent infinitesimal theory. Final expressions of the electromagnetic field components are in terms of exponential functions. By comparisons with direct numerical solutions and exact results in a special case, the correctness and effectiveness of the proposed quasi-static approximation are demonstrated. Simulations show that the smallest validity limit always occurs for component H2z, and the value of k2ρ should be no greater than 0.6 in order to keep a good consistency.

Propagation Characteristics of Extremely Low-Frequency Electromagnetic Waves in a Uniformly Infinite Polar “Sea-Sea Ice” Half-Space

“…However, due to the existence of discrete singular points in the complex plane, VOLUME XX, 2017 obtaining a highly precise numerical solution becomes cumbersome. In the following decades, scholars simplified the Sommerfeld integral method to varying degrees to obtain the propagation characteristics of EMWs in different media [5][6][7][8][9], but the process of solving it mathematically is highly complex., which makes it very difficult to apply in studies on ocean exploration.…”