# Electromagnetic Field Variation of ELF Near-Region Excited by HED in a Homogeneous Half-Space Model
## 4 Spatial Distribution of EM Field Intensity in the Near-Field Region  
### Spatial Distribution of EM Field Intensity  
To further study the ELF near-field distribution of the HED antenna in seawater, we selected the model shown in Figure 2 and used the algorithm to evaluate the distribution of the EM field intensity of the observation plane on the square grid 100 m \(\times\) 100 m at the plane of \(z=1\) m.  
Assuming that the distance from the horizontal antenna to the sea surface is \(d=10\) m, the electric moment is \(ldl=1\)A \(\cdot\) m, \(\varphi=\pi/4\), the working frequency is 10 Hz, the propagation distance is \(\rho=5000\) m, and the height from the observation point to the sea surface is \(z=1\) m; \(\mu_{0}\) and \(\epsilon_{0}\) are the permeability and dielectric constant in a vacuum, respectively. The conductivity and relative permittivity of seawater are \(\sigma_{1}=4\) S/m and \(\epsilon_{1}=80\), respectively. The EM field components changed with the height of the observation point. In the model shown in Figure 2, the coordinate origin is taken as the center, and a square area with a length and width of 100 m is obtained at the plane of \(z=1\) m. The amplitude distributions of each field component were simulated using Delphi software and are shown in Figure 4.  
In the model shown in Figure 2, an HED antenna with a working frequency of 10 Hz is placed underwater at 1 m away from the sea surface. A voltage source is fed at the center point of the antenna. It is considered that the HED antenna is excited by an equal amplitude and phase source in order to analyze the law of field distribution in the underwater HED antenna. The radius of the thin wire is 2 cm. The wavelength of an EM wave at 10 Hz in seawater is approximately equal to 0.5 m for seawater conductivity equal to 4 S/m, and it is about 3 \(\times\) 10\({}^{7}\) m in air.  
The results for electric fields are shown in Figure 4a-c, which include four color intensity plots for the three electric field components and the magnitude of the electric field. \(E_{\rho}\) exhibits maximum field intensity along the \(x\)-axis, and minimum field intensity along the \(y\)-axis, while \(E_{z}\) clearly shows that the shape and polarized direction for the HED antenna are placed along the \(y\)-axis; \(E_{\varphi}\) demonstrates that there is a strong electric field intensity in the \(y\)-axis direction and the fastest attenuation in the \(x\)-axis direction. In addition, the vertical electric component \(E_{z}\) is much stronger than \(E_{\rho}\) and \(E_{\varphi}\) for near-field region distance propagation in any direction, and the minimum attenuation is 15 dB. At the same time, we should also focus on the electric field strength in the \(x\)-axis direction of \(E_{\rho}\) and the \(y\)-axis direction of \(E_{\varphi}\). Similar plots for magnetic fields are shown in Figure 4d-f. Figure 4d,e show the field distribution in air; the field distributions of \(H_{\rho}\) and \(H_{\varphi}\) at 10 Hz are drawn on the \(z\) = 1 m plane above the air-sea interface. It can be seen that \(H_{\rho}\) and \(H_{\varphi}\) have an obvious attenuation mutation point at 40 m, which may be caused by changes in the interface between air and seawater. Meanwhile, we can see that \(H_{\varphi}\) receives the strongest magnetic field strength in the \(x\)-axis direction, the decay rate is the slowest, and the lowest attenuation value is 30 dB, so we should pay attention to the magnetic field strength in this direction. Figure 4f shows that the maximum field intensity of \(H_{z}\) is along the \(x\)-axis, and the minimum field intensity is along the \(y\)-axis, while the radical magnetic component \(H_{z}\) is a little stronger than \(H_{\rho}\) and \(H_{\varphi}\) for near-field region distance in any direction, and the attenuation speed is relatively stable, and the minimum attenuation rate is maintained at 40 dB, which is suitable for near-field region distance propagation.