# Study of Low-Frequency Hydroacoustic Waves' Behavior at the Shelf of Decreasing Depth
## 3 Experimental Data Processing
The energy density of the hydroacoustic waves propagating along the shelf were calculated by utilizing the polynomial equations given in Table 1 for all the receiving stations, according to the first formula. \[E_{r}=\int\limits_{0}^{h}\frac{\left(S_{h}(z)\right)^{2}}{2\rho_{w}c_{w}^{2}}dz, \tag{1}\]  
where \(S_{h}(z)\) is the polynomial equation of the curve at sea depth \(h\). In accordance with [3; 6], we assume that the signal transmitted by the low-frequency hydroacoustic transmitter reaches the laser strainmeter in the form of surface waves. In this case, the main contribution to the displacement of the earth crust was made by the damped Rayleigh-type surface waves. The amplitude of these waves decays exponentially with the depth of the earth crust. Therefore, the elastic energy density of the Rayleigh-type surface waves can be calculated using the following Equation (2). \[E_{r}=\int\limits_{0}^{\lambda_{b}}\frac{\rho_{b}\omega^{2}{A_{0}}^{2}\exp(-4 \pi z/\lambda_{b})}{2\cos\left(\theta\right)^{2}}dz, \tag{2}\]  
where \(A_{0}\) is the displacement amplitude at the frequency of the transmitted signal, equal to half of the wave amplitude at the frequency of 22 Hz, singled out from the laser strainmeter record. \(\lambda_{b}\) is the Rayleigh-type wavelength at the \"air-earth crust\" boundary and is equal to 104.5 m. The calculation results are shown in Table 2. Table 2 also shows the data for the share of the hydroacoustic energy density at each receiving station that was calculated from the energy density of the transmitter, taking into account the cylindrical divergence of the transmitted signal and the share of the density of the hydroacoustic energy transformed into the density of seismic acoustic energy at each receiving station, taking into account the cylindrical divergence of the Rayleigh-type waves. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No**} & \multirow{2}{*}{**Sea Depth, m.**} & \multirow{2}{*}{ \begin{tabular}{c} **Distance from** \\ Transmitter, m.** \\ \end{tabular}  } & & \multicolumn{2}{c}{**Wave Amplitude at the**} \\  & & & & **Polynomial Equation** & **Frequency of 22 Hz,** \\  & & & & **Singled out from the Laser** \\  & & & & **Strainmeter Record, nm** \\ \hline \multirow{2}{*}{\(1\)} & \multirow{2}{*}{\(37\)} & \multirow{2}{*}{\(335\)} & \(\text{S}_{37}(z)=(3.2835124^{+}10^{-7})x^{2}\) – & & \\  & & & \((4.5340116*^{-10})^{-5}x^{2}\)\(\text{e}^{-6}\) & \(0.0024484*^{2}\text{e}^{-5}\) & \multirow{2}{*}{\(14.6\)} \\  & & & \(0.0643262*^{2}\text{e}^{+}\) & \(0.8225148*^{2}\) & \(-4.5942522*^{2}\text{e}^{2}\) & \\  & & & \(21.798353*^{2}\text{e}-4.9269574\) & & \\ \hline \multirow{2}{*}{\(2\)} & \multirow{2}{*}{\(37.5\)} & \multirow{2}{*}{\(502\)} & \(\text{S}_{37}(z)=(8.8507925*^{-10})^{5}x^{4}\) – \(0.0085366*^{2}\text{e}^{3}\) & \multirow{2}{*}{\(16.4\)} \\  & & & \(0.1861208*^{2}\text{e}^{2}+6.2774712*^{2}+2.4975244\) & & \\ \hline \multirow{2}{*}{\(3\)} & \multirow{2}{*}{\(36.2\)} & \multirow{2}{*}{\(674\)} & \(\text{S}_{36}(z)=(-1.1161644*^{10}-4)^{5}x^{2}+0.0063251*^{2}\) & \multirow{2}{*}{\(28.7\)} \\  & & & \(-0.0895405*^{2}\text{e}^{-}\) & \(<5.0292998*^{2}\text{e}^{-}\) & \(-0.206082\) \\ \hline \multirow{2}{*}{\(4\)} & \multirow{2}{*}{\(30\)} & \multirow{2}{*}{\(970\)} & \(\text{S}_{30}(z)=(1.2446708*^{10}-4)^{5}x^{4}\) – \(0.0112489*^{2}\text{e}^{3}\) & \multirow{2}{*}{\(26.7\)} \\  & & & \(0.2185657*^{2}\text{e}^{2}+3.8794756*^{2}+0.9499853\) & & \\ \hline \multirow{2}{*}{\(5\)} & \multirow{2}{*}{\(20\)} & \multirow{2}{*}{\(1148\)} & \(\text{S}_{20}(x)=(1.641604*^{10}-4)^{5}x^{4}\) – \(0.0135414*^{2}\text{e}^{3}\) & \multirow{2}{*}{\(28.1\)} \\  & & & \(0.2436404*^{2}\text{e}^{2}+1.2073308*^{2}+1.462406\) & & \\ \hline \multirow{2}{*}{\(6\)} & \multirow{2}{*}{\(10\)} & \(1252\) & \(\text{S}_{10}(z)=0.0561111*^{2}\text{e}^{-}2-0.9616667*^{2}\text{e}+6.2055556\) & \multirow{2}{*}{\(24.4\)} \\ \cline{1-1} \cl