## 3 Applications  
Since the third type of interference structure in the shadow zone is formed by the ocean bottom reflection of the high-speed sediment and it is directly related to the geoacoustic parameters, it can be used for geoacoustic inversion. Using this interference structure for geoacoustic inversion has the following advantages:  
1. The interference structure of the shadow zone in the range-frequency domain formed by the ocean bottom reflection of the high-speed sediment is almost the same as the interference structure of the seabed reflection coefficient in the angle-frequency domain. However, for the actual acquisition of the interference spectrum of the ocean bottom reflection coefficient in the angle-frequency domain, it is usually used by beamforming of the vertical array. Accordingly, the experiment has a high cost, and the error caused by the limited array aperture also needs to be considered [11]. However, the interference structure of the shadow zone in the range-frequency domain can be obtained by a single hydrophone. The grazing angle of multi-path signals varies greatly with the range, and thus it has rich angle information and does not need to consider the array aperture problem.  
Figure 4: (**a**) The difference in receiving grazing angles among the four multi –path arrivals; (**b**) \(\Delta t_{1}\), \(\Delta t_{2}\) and their difference; (**c**) the value changes of \(2(\phi_{\text{SB}}-\phi_{\text{B}})\) and \(2(\phi_{\text{BS}}-\phi_{\text{BS}})\) with the receiving range, and their comparison to \(2\pi f\Delta t_{1}\) and \(2\pi f\Delta t_{2}\) when the frequency is 500 Hz; and (**d**) the description of the interference structure of the acoustic shadow zone by the interference fringe calculated by the grazing angle of each multi-path signal in combination with Equations (3) and (5) (B (red line), SB and BS (green line), SBS (yellow line), the range corresponding to the critical angle of the seawater and the basement (white dotted line), and the range corresponding to the critical angle of the sea –water and the sediment (blue dotted line)).  
2. Compared with obtaining the interference structure when the hydrophone is placed on the ocean bottom, the difficulties of the experiment for geoacoustic inversion is lower when the sound source and receiver are located on the sea surface [21].  
Equations (3) and (5) show that the interference structure is determined by the sound speed, density, and thickness of the sedimentary layer and the sound speed and density of the basement, and it has no correlation with the ocean bottom absorption coefficient. The cost function was constructed as follows:  
\[E(\overset{\rightarrow}{m})=\frac{1}{N}\sqrt{\sum_{i=1}^{N}\left(S_{\text{exp }}^{i}(\varphi_{r_{\text{SB}}},f)-S_{\text{cal}}^{i}(\varphi_{r_{\text{SB}}},f; \overset{\rightarrow}{m})\right)^{2}} \tag{16}\]  
where \(S_{\text{exp}}\) and \(S_{\text{cal}}\) are the fringes obtained by actual measurement and the fringes calculated by Equation (3) and Equation (5), respectively, \(N\) is the number of fringes, and \(\varphi_{r_{\text{SB}}}\) is the grazing angle of SB receiving, corresponding to the receiving range. \(\overset{\rightarrow}{m}=\left[\begin{array}{cc}\text{c}_{\text{s}}&\text{ },\rho_{\text{s}}&\text{ },\text{ }d,\text{c}_{\text{b}}&\text{ },\text{ }\rho_{\text{b}},n\end{array}\right]\) is the inversion parameter vector. Since the order of the fringe cannot be known in advance, the order of the fringe \(n\) was also regarded as the inversion parameter, and the rest of the parameters are the same as above.