Vertical correlations of sound field at large depths in deep water
Authors: Li Zheng-Lin , Dong Fan-Chen , Hu Zhi-Guo , Wu Shuang-Lin ,   State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China,   School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China,   Nanjing Marine Radar Institute, Nanjing 211153, China
Published: December 2020

The research on the vertical correlation characteristics of sound field in deep water has important implications for enhancing the vertical array gain and improving the ability to detect the underwater target. Based on a deep-water experiment conducted in the South China Sea, the vertical coherence of sound fields in the direct zone, shadow zone and convergence zone are analyzed with the sound signals received by a vertical line array that covers the maximal depth to 1,866 m. The numerical analysis based on the ray theory is carried out to provide corresponding theoretical explanations to the variations of the vertical correlation characteristics at different ranges and depths. The vertical correlation coefficients in the direct zone are higher than 0.707 for the whole depth and drop very little with the increase of the vertical depth. It is because the main contributions come from direct arrival ray and sea surface reflection ray. The pulse structure is relatively simple, and the time delays of the two rays increase with the space between two receivers increasing. In the shadow zone, sound energy mainly comes from bottom reflection. Therefore, the vertical correlation coefficients are relatively low. Multi-path arrival is observed obviously. Vertical correlation coefficients drop quickly with depth increasing. With range increasing, the time delays of the multi-path pulses decrease. The vertical correlation coefficients at the same depth will increase a little with range increasing. Near the first convergence zone, vertical correlations oscillate periodically with the increase of vertical separation, and share the same distribution pattern with the sound energy along the vertical direction, which is caused by the periodical oscillation of two groups of the refracted rays from water volume. The refracted rays have the same amplitude, therefore, the time delays of the two group of rays increase with receiver depth increasing, and the phase of sound filed fluctuates in <inline-formula><tex-math id="M1">\begin{document}$The research on the vertical correlation characteristics of sound field in deep water has important implications for enhancing the vertical array gain and improving the ability to detect the underwater target. Based on a deep-water experiment conducted in the South China Sea, the vertical coherence of sound fields in the direct zone, shadow zone and convergence zone are analyzed with the sound signals received by a vertical line array that covers the maximal depth to 1,866 m. The numerical analysis based on the ray theory is carried out to provide corresponding theoretical explanations to the variations of the vertical correlation characteristics at different ranges and depths. The vertical correlation coefficients in the direct zone are higher than 0.707 for the whole depth and drop very little with the increase of the vertical depth. It is because the main contributions come from direct arrival ray and sea surface reflection ray. The pulse structure is relatively simple, and the time delays of the two rays increase with the space between two receivers increasing. In the shadow zone, sound energy mainly comes from bottom reflection. Therefore, the vertical correlation coefficients are relatively low. Multi-path arrival is observed obviously. Vertical correlation coefficients drop quickly with depth increasing. With range increasing, the time delays of the multi-path pulses decrease. The vertical correlation coefficients at the same depth will increase a little with range increasing. Near the first convergence zone, vertical correlations oscillate periodically with the increase of vertical separation, and share the same distribution pattern with the sound energy along the vertical direction, which is caused by the periodical oscillation of two groups of the refracted rays from water volume. The refracted rays have the same amplitude, therefore, the time delays of the two group of rays increase with receiver depth increasing, and the phase of sound filed fluctuates in <inline-formula><tex-math id="M1">\begin{document}$\left[ {0,2} {\text{π}}\right]$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20190134_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20190134_M1.png"/></alternatives></inline-formula>periodically. The periodicity causes the sound intensity and the vertical correlation coefficients to have the same oscillation structures. If the rays have the same phases, the main contribution comes from refraction rays, the structure of the pulses is relatively simple and causes vertical correlation to be higher. Otherwise, the main contribution comes from bottom reflected rays, the structure of the pulses is complex, and vertical correlation drops down. <b><i>Corresponding Author: Li Zheng-lin</i></b> $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20190134_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20190134_M1.png"/></alternatives></inline-formula>periodically. The periodicity causes the sound intensity and the vertical correlation coefficients to have the same oscillation structures. If the rays have the same phases, the main contribution comes from refraction rays, the structure of the pulses is relatively simple and causes vertical correlation to be higher. Otherwise, the main contribution comes from bottom reflected rays, the structure of the pulses is complex, and vertical correlation drops down.