## 3 Methodology  
A scenario of underwater data transmission includes transmission nodes and receiver nodes. The communication links of underwater data are characterized by low rates of data transmission; this is mainly because of communication limitations due to the high propagation delays or low bandwidth. The effects of these limitations can be reduced by communicating in shorter distances and by using multi-hop communication for covering longer distances [10]. The propagation of the acoustic signal is affected by the following channel parameters: transmitter signal power (source level, SL), the attenuation through the path of acoustic communication (path loss, PL), underwater noises (noise level, NL) and the multipath and Doppler effects [11]. Table 1[12] shows the typical seabed materials and their properties, which play an important role in the multipath effect. In our study Equation (1) is used to calculate the transmitter's acoustic signal level [11]. \[\mathrm{SL(P,\eta,DI)=}170.8+10\ \mathrm{logP_{tx}+}10\ \log\eta_{tx}+ \mathrm{DI_{tx}} \tag{1}\]  
where \(\mathrm{P_{tx}}\) is the power at transmitter, \(\eta_{tx}\) is the efficiency factor that considers the losses associated with the electrical to acoustic conversion, \(\mathrm{DI_{tx}}\) is the projector directivity index. For the calculation of the path loss it is used [PERSON]'s model [13]. As presented in [9; 14] the absorption that occurs in an underwater communication channel is given by:  
\[\mathrm{A(r,f)=r^{k}\times a(f)^{\frac{r}{1000}}} \tag{2}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Bottom Material** & **Porosity (\%)** & **pl/p** & **cl/c** & **cl (m/s)** \\ \hline Clay & 70 & 1.5 & 1.0 & 1500 \\ Silt & 55 & 1.7 & 1.05 & 1575 \\ Sand & 45 & 1.9 & 1.1 & 1650 \\ Gravel & 35 & 2.0 & 1.2 & 1800 \\ Moraine & 25 & 2.1 & 1.3 & 1950 \\ Chalk & - & 2.2 & 1.6 & 2400 \\ Limestone & - & 2.4 & 2.0 & 3000 \\ Basalt & - & 2.7 & 3.5 & 5250 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Typical seabed materials and their properties. where r is the distance (m), and f the frequency of the signal (kHz), k is the spreading factor and a(f) is the absorption coefficient. The acoustic path loss can be expressed in dB as the sum of spreading loss and absorption loss by:  
\[\mathrm{PL}=\mathrm{k}\times 10\ \log(\mathrm{r})+\frac{\mathrm{r}}{1000}\times 10 \ \log\ \mathrm{a(f)} \tag{3}\]  
The spreading factor k describes the geometry of the acoustic signal propagation. The commonly used values of the spreading factor are k = 2 for the spherical spreading, k = 1 for the cylindrical spreading, and k = 1.5 for the practical spreading. The absorption coefficient (a(f)) is calculate by using the Francois and Garrison formula [5] which depends on frequency, pressure (depth), temperature, salinity, pH and the acoustic propagation velocity, as follows:  
\[10\ \log(\mathrm{a(f)})=\frac{\mathrm{A}_{1}\ \mathrm{P}_{1}\ \mathrm{f}_{1}\ \mathrm{f}^{2}}{\mathrm{f}_{1}^{2}+\mathrm{f}^{2}}+\frac{ \mathrm{A}_{2}\ \mathrm{P}_{2}\ \mathrm{f}_{2}\ \mathrm{f}^{2}}{\mathrm{f}_{2}^{2}+\mathrm{f}^{2}}+ \mathrm{A}_{3}\ \mathrm{P}_{3}\ \mathrm{f}^{2} \tag{4}\]  
where the dependence on the pressure (depth) is given by P\({}_{1}\), P\({}_{2}\), P\({}_{3}\) and the relaxation frequencies of Boric acid and (MgSO4) molecules are given by f\({}_{1}\) and f\({}_{2}\). The effects of temperature are given by the coefficients A\({}_{1}\), A\({}_{2}\), A\({}_{3}\). The first term is related to the contribution of the boric acid (B(OH)\({}_{3}\)), the second term due to the contribution of magnesium sulfate (MgSO\({}_{4}\)) and the third due the contribution of pure water. All the coefficients of Equation (4) are calculated according to [7; 15].