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 , and the value of should be no greater than 0.6 in order to keep a good consistency.

中文翻译：

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有损半空间表面附近的垂直磁偶极子的ELF / SLF近场磁场的准静态解

跨越两种不同介质之间边界的偶极天线已广泛用于地球物理勘探，海洋学和水下通信领域。本文提出了一种分析方法，用于分析由于垂直磁偶极子（VMD）引起的极低频（ELF）/超低频（SLF）范围内的近区磁场。由于缺乏可行的分析技术来精确推导这些分量，因此根据准静态定义和等效的无穷小理论引入了两个合理的假设。电磁场分量的最终表达式是指数函数。通过与直接数值解的比较以及在特殊情况下的精确结果，证明了拟准近似的正确性和有效性。，和值应不大于0.6，以保持良好的一致性。