# Vertical Correlation and Array Gain Analysis for Vertical Line Array in Deep Water
## 4 Experimental Results
### Correlation and Array Gain in the Shadow Zone  
When the sound source is placed at a depth of 30 m and a horizontal range of 10.3 km, we collect the signal data received by the VLA. The acoustic field is now located in the shadow zone. 30-s samples of the signal are selected and filtered by a band-pass filter with a frequency range of 300-400 Hz in this processing. The top element is still considered as the reference element. The signal received by the reference element in the time domain, frequency domain, and time-frequency domain is presented in Figure 17, respectively. Because of the significant influence of multiple paths during the propagation of sound waves, pulse shape of the received signal in the time domain is not evident and arrival waves at the various time are mixed, as shown in Figure 17a. Similarly, the power output of the VLA is shown in Figure 18 after the conventional beamforming processing. From Figure 18, we can find that there exist two visible peaks appearing at 111\({}^{\circ}\) and 61\({}^{\circ}\)  
Figure 16: Average array gains (AGs) in the direct-arrival zone (**a**) data in the middle measurement period; (**b**) data in the late measurement period. Figure 17: Received signal of the reference element in the shadow zone (**a**) time domain; (**b**) frequency domain; (**c**) time–frequency domain. respectively. According to the experiment configuration, the direction of the received wave is mainly upward in this range. Therefore, the elevation angle of the signal received by hydrophones is 111\({}^{\circ}\), and the grazing lobe angle is 61\({}^{\circ}\). Following Equation (7), the correlation coefficients of the received signal are calculated and shown in Figure 19. It is concluded that the correlation coefficients between two different hydrophones are lower than those in the direct-arrival zone in Figure 8. Besides, correlation coefficients descend significantly as the vertical depths ascend and show periodic oscillation, as shown in Figure 20. This phenomenon occurs mainly because, at long range, sound rays undergo multiple reflections between the sea surface and the bottom. Moreover, the difference in the arrival time of each ray increases and multi-path interference becomes complicated. Figure 19: Correlation coefficients of signal. Figure 20: Variation of correlation coefficient with element depth. Figure 18: Power output after conventional beamforming processing (main lobe of 111\({}^{\circ}\) and grazing lobe of 61\({}^{\circ}\)). To analyze the ray type in the shadow zone, we use the BELLHOP model to calculate the time arrival structure of the eigen-rays received by the reference hydrophone. As shown in Figure 21, we can see that the acoustic field in the shadow zone is mainly composed of the once-bottom-bounce ray (S0B1), once-surface-reflected and once-bottom-reflected ray (S1B1), and the twice-surface-reflected and once-bottom-reflected ray (S2B1). It is concluded that the time arrival structure becomes more complicated than that in the direct-arrival zone because of multiple reflections of sound rays from the ocean surface and the ocean bottom. The amplitudes of three types of the ray are close, as presented in Figure 21. The ray traces of the S0B1 wave, S1B1 wave, and S2B1 wave received by the reference element are further shown in Figure 21, in which we can find that propagation traces between S1B1 wave with the blue line and S2B1 wave are close. Furthermore, the path of S1B1 wave with purple line and the one of S0B1 wave are also similar. However, there exist different propagation paths and distinct time-delay differences between the two groups, which complicates multi-path interference and reduces the vertical correlation of the sound field. Table 2 shows the amplitudes, arrival time, and elevation angles information of S0B1 wave, S1B1 wave, and S2B1 wave, respectively. In this table, the positive and negative values of the arrival angle represent the downward and upward direction of the incident wave, respectively.