# Vertical Correlation and Array Gain Analysis for Vertical Line Array in Deep Water
## 4 Experimental Results
### Correlation and Array Gain in the Direct-Arrival Zone
Substituting the measured SSP into the BELLHOP model, we calculate the time arrival structure of the eigen-rays received by the reference hydrophone in Figure 9. The source depth and receiving range are the same as the actual sea trial conditions. It is apparent that the direct ray (D) and the once-surface-reflected ray (S1B0) are the main components of the sound field, whose energy is higher than other rays. For example, taking the amplitude of the D wave as the reference standard, we find that the amplitudes of the once-bottom-bounce ray (S0B1), and once-surface-reflected and once-bottom-reflected ray (S1B1) are nearly 13.6 dB lower than D wave as the form of dB. This finding occurs mainly because the sound wave incident to the ocean bottom at larger grazing angles will suffer more severe reflection attenuation. As a consequence, the acoustic field in the direct-arrival zone is dominated by D wave and S1B0 wave. To further explain the high correlation, Table 1 lists the arrival time and elevation angle of D wave and S1B0 wave for the reference element. From the table, we can see that the amplitude difference between D wave and S1B0 wave is about \(7.6\times 10^{-5}\)\(\upmu\)Pa, namely 2.78 dB, and the arrival time and arrival angles between these two ray components are nearly equal to each other. This phenomenon is similar to other elements. Figure 8: Correlation coefficients of signal. Figure 9: Time arrival structure of the eigen-rays (2.4 km). Ray trace clearly reflects the propagation path of sound energy so that the sound field distribution can be qualitatively interpreted. According to the calculation results above, the ray trace of D wave and S1B0 wave received by the reference element are presented in Figure 10. The abscissa represents the horizontal range from the sound source to the receiver. We can see that these two waves propagate almost along the same path and have nearly the same receiving amplitude, arrival time, and arrival angle, which makes their coherent superposition. Ray theory can quantitatively analyze the high vertical correlation of sound field. In the direct-arrival zone, we only consider the D wave and S1B0 wave, and other ray components can be ignored. Figure 11 displays the interference schematic diagram of two rays. We assume that the environment is range independent, the sound speed between the source and receiver is a constant, and the sea surface is absolutely soft. Thus, the sound rays travel along a straight line and are perfectly reflected by the sea surface. The signal received is the superposition of D wave and S1B0 wave, which can be written as [20]. Figure 5:0 \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **Amplitude (uPa)** & **Arrival Time (s)** & **Arrival Angle (\({}^{\circ}\))** & **Number of Surface-Reflection** & **Number of Bottom-Reflection** \\ \hline D & \(2.78\times 10^{-4}\) & 1.529 & 15.28 & 0 & 0 \\ S1B0 & \(2.02\times 10^{-4}\) & 1.529 & 15.95 & 1 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Structure of D and S1B0 wave. Figure 11: Interference schematic diagram of two sound rays. Figure 10: The ray trace of D wave and S1B0 wave. signal also contains the sound energy of other paths, thus, the two curves show difference. The same interpretation method can be extended to non-isosonic profile. The noise correlation is another significant factor in the evaluation of AG. Generally speaking, because of the high SNR, it is difficult to separate the signal and noise when receiving data. Furthermore, the ambient noise is not expected to change during a short time. Hence, the data received before the signal transmission is regarded as the noise. We measured the actual marine environmental noise to do the next analysis. Figure 13 shows the noise correlation coefficients corresponding to different element interval-to-wavelength ratio. The blue line, red line, and yellow line in Figure 13 denote the measured ambient noise, the isotropic noise model, and the surface noise model.