## 3 Numerical Simulation Analysis
### Influence of Interface on the Calculation Accuracy of Scattering Field in Marine Environment  
In the directional point source method, the deep-sea channel interface is considered far from the target, and the interface slightly affects the sound scattering field near the target. Therefore, the sound scattering field near the target should be replaced by the sound scattering field of the free field. The influence of the interface on the sound scattering field is ignored. In actual problems, the interface has an impact on the scattering of the target. Therefore, this section considers establishing the deep-sea acoustic channel model under the 50 Hz condition. The target is a spherical shell with a radius of 10 m and a thickness of 0.1 m, the density of the spherical shell is \(\rho_{\mathrm{s}}\) = 7850 kg/m\({}^{3}\), the Young's modulus is \(E_{\mathrm{s}}\) = \(2\times 10^{11}\) Pa, the Poisson's ratio is \(\mu_{\mathrm{s}}\) = 0.33, and the sea surface is an absolute soft boundary. The seabed is an absolute hard boundary, the sound velocity in water is c = 1500 m/s, and density is \(\rho\) = 1000 kg/m\({}^{3}\). The incident wave is along the positive \(\times\) direction with a frequency of 50 Hz, as seen in Figure 1, and the distance from the target to the lower boundary is 270 m. The sound scattering field with the distance from the target to the upper interface of 20, 30, and 180 m is calculated and compared with the finite element model. For Figure 5b,c, although the two curves fit well, a deviation remains. Secondary scattering causes the deviation. When the target is equivalent to the directional point source, the existence of the interface is ignored, and the interface does not cause secondary scattering. In the actual channel, multiple scattering of scattered waves back to the target occurs after passing through the interface. The closer the target is to the interface, the greater the secondary scattering and the poorer the accuracy of the directivity point source. Figure 4: A comparison of the sound pressure of the scattering field calculated by the equivalent calculation of different near field and far field sound pressures and the result of direct finite element calculation: (**a**) 0\({}^{\circ}\) direction; (**b**) 80\({}^{\circ}\) direction. Figure 6 shows that, when the target is 20 m away from the interface, a big deviation exists between the results of the directivity point source method and the FEM. The calculation results reach a relatively stable state at 30 m from the interface. The two curves are in good agreement when the target is 180 m away from the interface, indicating that, when close to the sea surface, ignoring the influence of the surface impedance of the elastic structure on the sea surface may bring certain errors. Figure 7 presents a diagram of the sound scattering field of a spherical shell located at different positions of the channel when a plane wave is obliquely incident upwards. The scattered sound field between the target and the upper interface shown in Figure 7a is very large, reaching 1 Pa, indicating that the ratio of the secondary scattering accounting for the sound scattering field is large and the sound scattering field between the target and the interface shown in Figure 7b is very small, further indicating that, when the target is far from the interface, the multiple scattering between the target and the interface accounts for a small proportion of the scattered sound field. Figure 6 clearly shows that, when the target is very close to the interface, the calculation results of the target sound scattering field that are calculated by the directional point source method and the FEM are very different as the distance between the target and the boundary increases. The calculation result of the directional point source is near the finite element calculation result, which indicates that, when the distance to the sea surface is short, ignoring the influence of the surface impedance of the elastic structure on the sea surface may bring certain errors.