# Study of Low-Frequency Hydroacoustic Waves' Behavior at the Shelf of Decreasing Depth
## 5 Analysis of the Results  
Based on the data of the model calculations at certain points on the route that coincided with sounding points, vertical profiles of pressure distribution from the surface to the bottom were constructed. Model pressure distribution curves at the transmitter operating frequency of 22 Hz from the surface to the bottom are shown against the experimental curves in Figure 4. Based on these curves, polynomial equations of the most suitable degree were constructed according to which the model energy density at each receiving station was calculated by means of Equation (1) and the model energy density was calculated at each of the receiving stations (for stations P1-P7: 3.715, 1.133, \(2.14\times 10^{-1}\), \(1.08\times 10^{-1}\), \(2.18\times 10^{-2}\), \(2.05\times 10^{-3}\), \(6.30\times 10^{-7}\) J/m\({}^{3}\)). The graph of their changes is shown in Figure 7. The graph of the experimental data changes is also shown in this figure. All the obtained model calculations provided overestimated results in comparison with the experimental data, which, in our opinion, is due to the fact that the model is very approximate and does not take into account many of the effects of the propagation of hydroacoustic waves in the shallow sea, and also does not take into account the contribution of the damped and undamped Rayleigh-type waves spreading along the \"water-bottom\" boundary. Nevertheless, at many of the receiving stations, the model curves are similar to the experimental ones and display a relatively reliable distribution of the pressure created by the hydroacoustic transmitter at a frequency of 22 Hz from the surface to the bottom. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(\epsilon_{p}\) & \(\epsilon_{s}\) & \(\rho\) \\ \hline Precipitation & 1600 m/s & 400 m/s & 1.9 g/sm\({}^{3}\) \\ \hline Semi-infinite granite space & 5400 m/s & 3300 m/s & 2.79 g/sm\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Medium parameters used for the simulation. Figure 6: Solution domain. Figure 7: Graphs of the hydroacoustic energy density changes in the model calculations and experimental research. A significant difference in the behavior of the model and the experimental curves was noted at stations 6 and 7 (see Figure 4 P6 and P7, respectively). Judging by the upper part of the drawing and the slope of the curve to the right and not to the left (as model calculations show), this contribution was made by an undamped Rayleigh-type wave propagating along the \"water-bottom\" boundary, the value of the generated pressure of which is about 4-5 Pa, which is also consistent with the calculated data given in Table 2 for these stations in the column \"Transmitter/Hydroacoustics, %\" and well as the conclusions of [12]. Let us analyze in more detail the experimental results given above. In the analysis, we will take into account that a hydroacoustic wave propagates along the wedge-shaped shelf. The loss of energy of the hydroacoustic wave propagating along the wedge-shaped shelf is determined by several factors. If the depth of the sea is several times greater than the wavelength, then the main causes of energy loss are sound absorption by water and its scattering by the sea surface. With decreasing frequency, the influence of the sea bottom begins to prevail in the attenuation of the hydroacoustic wave. This effect manifests itself as an increase in the dissipation of wave energy by the bottom soil. For wavelengths greater than the depths of the sea, the fraction of energy that is absorbed from the water layer into the sea bottom and is converted into elastic waves of the water-bottom interface increases. With an increase in the wavelength, the generation of Rayleigh waves and body waves begin to play a major role in attenuating the energy of the hydroacoustic wave. The influence of the wedge on the frequency and spatial dependence of the energy of the hydroacoustic wave emitted from the water layer can be estimated as follows.