Approximated Solutions for ELF Near-Field Propagation Due to a Horizontal Electric Dipole Excitation Near the Sea-Rock Boundary

In this paper, the near-field propagation of extremely low frequency (ELF) wave due to a horizontal electric dipole excitation has been investigated near the boundary between two dielectrics. First, a novel quasi-static approximation is assumed with γ
₂
≈ -iλ so that the integrands of the Fourier-Bessel representations for ELF field are approximated near the poles by adopting Maclaurin's Expansion. Second, by the conditions of k
_2ρ
≪ 1, z/ρ ≪ 1, and d/ρ ≪ 1, the ratio of wave numbers for rock and sea k
₂
/k
₁
is equivalent to an infinitesimal that only fundamental terms of |k
₂
²
γ
₂
|/|k
₁
²
γ
₁
| are reserved for the electromagnetic components. Third, the approximated formulas are derived for ELF near-field propagation generated by a horizontal electric dipole with the above simplifications. Finally, the simplified formulas are verified by an analogy with the exact and approximated formulas, respectively. It demonstrates that the proposed formulas are complementarily essential for evaluations of ELF near field and the plotted Poynting vectors indicate approximately the propagation direction of the energy flow.