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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
$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 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. Corresponding Author: Li Zheng-lin $\end{document}$\left[ {0,2} {\text{π}}\right]$ 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. [1] 周士弘, 张仁和, 陶晓东, 龚敏, 郝隆盛 1998 自然科学进展 8 342
Google Scholar
Zhou S H, Zhang R H, Tao X D, Gong M, Hao L S 1998 Progress in Natural Science 8 342
Google Scholar
[2] Guo L H, Gong Z X, Wu L X 2001 Chin. Phys. Lett. 18 1366
Google Scholar
[3] Li Z L, Zhang R H, Yan J, Li F H, Liu J J 2004 IEEE J. Oceanic Eng. 29 973
Google Scholar
[4] Wan L, Zhou J X, Rogers P H, Knobles D P 2009 Acoust. Phys. 55 383
Google Scholar
[5] 赵梅, 胡长青 2010 声学技术 29 365
Google Scholar
Zhao M, Hu C Q 2010 Technical Acoustics 29 365
Google Scholar
[6] 王鲁军, 彭朝晖, 李整林 2011 声学学报 36 596
Wang L J, Peng C H, Li Z L 2011 Acta Acustica 36 596
[7] 张仁和, 张双荣, 肖金泉, 孙庚辰, 王孟新 1981 声学学报 1 9
Zhang R H, Zhang S R, Xiao J Q, Sun G C, Wang M X 1981 Acta Acustica 1 9
[8] Wang Q, Zhang R H 1992 J. Acoust. Soc. Am. 92 932
Google Scholar
[9] 宫在晓 2001 博士学位论文(北京: 中国科学院声学研究所)
Gong Z X 2001 Ph. D. Dissertation (Beijing: The Institute of Acoustics of the Chinese Academy of Sciences) (in Chinese)
[10] Urick R J, Lund G R 1968 J. Acoust. Soc. Am. 43 723
Google Scholar
[11] Urick R J 1973 J. Acoust. Soc. Am. 54 115
Google Scholar
[12] Colosi J A, Chandrayadula T K, Voronovich A G, Ostashev V E 2013 J. Acoust. Soc. Am. 134 3119
Google Scholar
[13] Li J, Li Z L, Ren Y 2016 Chin. Phys. B 25 124310
Google Scholar
[14] 李鋆 2017 博士学位论文(北京: 中国科学院声学研究所)
Li J 2017 Ph. D. Dissertation (Beijing: The Institute of Acoustics of the Chinese Academy of Sciences) (in Chinese)
[15] 胡治国, 李整林, 张仁和, 任云, 秦继兴, 何利 2016 65 014303
Google Scholar
Hu Z G, Li Z L, Zhang R H, Ren Y, Qin J X, He L 2016 Acta Phys. Sin. 65 014303
Google Scholar
[16] 胡治国, 李整林, 秦继兴, 任云, 张仁和 2016 中国科学: 物理学 力学 天文学 46 094304
Hu Z G, Li Z L, Qin J X, Ren Y, Zhang R H 2016 Scientia Sinica Physica, Mechanica & Astronomica 46 094304
[17] 胡治国, 李整林, 张仁和, 任云, 李鋆 2016 声学学报 41 758
Hu Z G, Li Z L, Zhang R H, Ren Y, Li J 2016 Acta Acustica 41 758
[18] Collins M D, Westwood E K 1991 J. Acoust. Soc. Am. 89 1068
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[19] Collins M D 1993 J. Acoust. Soc. Am. 93 1736
Google Scholar
[20] Jensen F B, Kuperman W A, Porter M B, Schmidt H 2011 Computational Ocean Acoustics (2nd Ed.) (New York: Springer) p147 p36
[21] Wu S L, Li Z L, Qin J X 2015 Chin. Phys. Lett. 32 124301
Google Scholar
[22] Li Z L, Li F H 2010 Chin. J. Oceanol. Limnol. 28 990
Google Scholar
[23] Porter M B, Bucker H P 1987 J. Acoust. Soc. Am. 82 1349
Google Scholar
[24] 翁晋宝 2015 博士学位论文(北京: 中国科学院声学研究所)
Weng J B 2015 Ph. D. Dissertation (Beijing: The Institute of Acoustics of the Chinese Academy of Sciences) (in Chinese)
[25] 张仁和, 李风华 1999 中国科学 A 29 241
Zhang R H, Li F H 1999 Science in China (Series A)
29 241 [26] 翁晋宝, 李风华, 郭永刚 2015 声学学报 40 207
Weng J B, Li F H, Guo Y G 2015 Acta Acustica 40 207
[27] 翁晋宝, 李风华, 郭永刚 2016 声学学报 41 330
Weng J B, Li F H, Guo Y G 2016 Acta Acustica 41 330
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图 1 海上实验设备布放示意图
Figure 1. The configuration of the experiment.
图 2 拖曳换能器发射声信号的周期
Figure 2. The cycle of the source signals from a towed transducer.
图 3 O2到O1传播路径上海深随距离的变化
Figure 3. The bathymetry along the propagation track from O2 to O1.
图 4 实验期间的海水声速剖面
Figure 4. Sound speed profile during the experiment.
图 5 O2到O1 传播路径上二维声传播损失对比 (a)实验结果; (b) RAM模型计算结果
Figure 5. TL along the propagation track from O2 to O1: (a) Experimental result; (b) numerical result.
图 6 距离2.0 km处垂直阵声场垂直互相关 (a) 实验结果; (b) 模型结果
Figure 6. The vertical cross-correlation of sound fields in the whole array at the range of 2.0 km: (a) Experimental results; (b) numerical results.
图 7 距离2.0 km处声场垂直相关随间距的变化, 其中参考阵元深度102 m, 虚线为参考值0.707
Figure 7. The vertical correlation coefficients at the range of 2.0 km for the reference depth at 102 m, where the dashed line representing the reference value 0.707.
图 8 直达区内2.0 km距离处不同接收深度本征声线和时间到达结构 (a), (b) 167 m; (c), (d) 357 m; (e), (f) 1453 m
Figure 8. Eigenrays and arrivals received at three different depths at the range of 2.0 km in the direct zone: (a), (b) 167 m; (c), (d) 357 m; (e), (f) 1453 m.
图 9 直达区内2.0 km距离处不同接收深度多途到达结构比较 (a) 实验结果; (b) 模型结果
Figure 9. Comparison of the experimental multipath structures on the vertical line array at the range of 2.0 km in the direct zone with numerical ones: (a) Experimental result; (b) numerical result.
图 10 直达区内对声场起主要贡献的两条声线, 其中声源深度126 m, 接收深度1453 m
Figure 10. The two main rays contributing to the sound field in the direct zone, where the source and receiver are at the depth of 126 and 1453 m, respectively.
图 11 直达区内对声场起主要贡献的两条声线的初始掠射角及时间到达结构 (a) 声源处的掠射角; (b) 时间到达结构(声源深度126 m, 接收深度1453 m)
Figure 11. The two main rays contributing to the sound field in the direct zone: (a) The grazing angles at source location; (b) the arrivals of the two rays (The source and receiver are at the depth of 126 and 1453 m, respectively).
图 12 由射线模型计算的距离2.0 km处对声场起主要贡献的两条本征声线DR和SR的(a) 到达时间差和(b) 相位差随接收深度的变化
Figure 12. Numerical travel time differences (a) and phase differences (b) of the two eigenrays (DR and SR) with the increase of the receiving depth at the range of 2.0 km from Bellhop model.
图 14 距离4.2 km处垂直阵声场垂直互相关 (a) 实验结果; (b) 模型结果
Figure 14. The vertical cross-correlation of sound fields in the whole array at the range of 4.2 km: (a) Experimental results; (b) numerical results.
图 15 距离4.2 km处两个不同参考深度上声场垂直相关随间距的变化 (a) 参考深度102 m; (b) 参考深度357 m
Figure 15. The vertical correlation coefficients at two different reference depths at the range of 4.2 km: (a) For reference depth 102 m; (b) for reference depth 357 m.
图 16 直达区内4.2 km距离处不同接收深度的本征声线和时间到达结构 (a), (b) 167 m; (c), (d) 357 m; (e), (f) 1453 m
Figure 16. Eigenrays and arrivals received at three different depths at the range of 4.2 km in the direct zone: (a), (b) 167 m; (c), (d) 357 m; (e), (f) 1453 m.
图 17 直达区内4.2 km距离处垂直阵深度覆盖范围内的多途到达结构比较 (a) 实验结果; (b) 模型结果
Figure 17. Comparison of the experimental multipath structures from the receivers on the vertical line array at the range of 4.2 km in the direct zone with numerical ones: (a) Experimental result; (b) Numerical result.
图 18 距离13.6 km处垂直阵声场垂直互相关 (a) 实验结果; (b) 模型结果
Figure 18. The vertical cross-correlation of sound fields in the whole array at the range of 13.6 km: (a) Experimental results; (b) numerical results.
图 19 距离33.2 km处垂直阵声场垂直互相关 (a) 实验结果; (b) 模型结果
Figure 19. The vertical cross-correlation of sound fields in the whole array at the range of 33.2 km: (a) Experimental results; (b) numerical results.
图 20 第一影区内两个不同距离处声场垂直相关随间距的变化, 其中参考深度102 m, 接收距离分别为13.6 km 和33.2 km
Figure 20. Comparison of the vertical correlation coefficients at two different ranges of 13.6 km and 33.2 km in the first shadow zone for the reference depth at 102 m.
图 21 第一影区内接收深度865 m处不同收发距离的本征声线和时间到达结构 (a), (b) 13.6 km; (c), (d) 33.2 km
Figure 21. Eigenrays and arrivals received at the depth of 865 m for two different ranges in the first shadow zone: (a), (b) 13.6 km; (c), (d) 33.2 km.
图 22 第一影区内距离13.6 km处垂直阵深度覆盖范围内的多途到达结构比较 (a) 实验结果; (b) 模型结果
Figure 22. Comparison of the experimental multipath structures from the receivers on the vertical line array at the range of 13.6 km in the first shadow zone with numerical ones: (a) Experimental result; (b) numerical result.
图 23 第一影区内距离33.2 km处垂直阵深度覆盖范围内的多途到达结构比较 (a) 实验结果; (b) 模型结果
Figure 23. Comparison of the experimental multipath structures from the receivers on the vertical line array at the range of 33.2 km in the first shadow zone with numerical ones: (a) Experimental result; (b) numerical result.
图 24 距离50 km处垂直阵声场垂直互相关 (a) 实验结果; (b) 模型结果
Figure 24. The vertical cross-correlation of sound fields in the whole array at the range of 50 km: (a) Experimental results; (b) numerical results.
图 25 距离50 km处两个不同参考深度上声场垂直相关随间距的变化 (a) 参考深度102 m; (b) 参考深度634 m
Figure 25. The vertical correlation coefficients at two different reference depths at the range of 50 km: (a) For reference depth 102 m; (b) for reference depth 634 m.
图 26 第一会聚区附近(50−60 km)声传播损失比较 (a) 实验结果; (b) 模型结果
Figure 26. TL results near the first convergence zone (50−60 km): (a) For experimental result; (b) for numerical result.
图 27 距离50 km处归一化声强随接收深度变化的实验结果与仿真结果对比
Figure 27. Comparison of the normalized experimental sound energy with numerical results at the range of 50 km.
图 28 第一会聚区附近50 km距离处不同接收深度的本征声线和时间到达结构 (a), (b) 167 m; (c), (d) 836 m; (e), (f) 1453 m
Figure 28. Eigenrays and arrivals at three different depths at the range of 50 km near the first convergence zone: (a), (b) 167 m; (c), (d) 836 m; (e), (f) 1453 m.
图 29 第一会聚区附近距离50 km处垂直阵深度覆盖范围内的多途到达结构比较 (a) 实验结果; (b) 模型结果
Figure 29. Comparison of the experimental multipath structures from the receivers on the vertical line array at the range of 50 km near the first convergence zone with numerical ones: (a) Experimental result; (b) numerical result.
图 30 由射线模型计算的距离50 km处对声场起主要贡献的两组水体反转声线的到达时间差(a)和相位差随接收深度(b)的变化
Figure 30. Numerical travel time differences (a) and phase differences (b) of the two groups of refraction eigenrays from water volume with the increase of the receiving depth at the range of 50 km from Bellhop model.
表 1 海底底质采样测量样品分析参数表
Table 1. Sediment parameters analyzed from core sampling.
深度范围/cm 实测声速/m·s–1 湿密度/g·cm–3 声衰减系数/dB·m–1 孔隙度/% 中值粒径/mm 沉积物类型 0–28 1583 1.65 137.06 62.60 0.0053 粘土质粉砂 28–55 1597 1.56 74.02 65.08 0.0274 粉砂 55–80 1663 1.57 118.80 67.59 0.0287 粉砂 80–105 1695 1.45 127.50 74.93 0.0127 粘土质粉砂 105–130 1631 1.55 108.91 68.22 0.0157 粉砂 130–155 1516 1.44 104.86 75.38 0.0062 粘土质粉砂 155–180 129 1.37 66.73 77.98 0.0059 粘土质粉砂 180–205 1508 1.33 127.47 80.77 0.0052 粘土质粉砂 205–230 1540 1.30 111.89 84.07 0.0046 粘土质粉砂 230–250 1533 1.26 121.37 85.00 0.0050 粘土质粉砂 250–280 1547 1.26 159.41 85.55 0.0057 粘土质粉砂 280–305 1565 1.21 255.70 83.24 0.0045 粘土质粉砂 平均值 1584 1.41 126.14 75.87 0.0106 –- 
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[1] 周士弘, 张仁和, 陶晓东, 龚敏, 郝隆盛 1998 自然科学进展 8 342
Google Scholar
Zhou S H, Zhang R H, Tao X D, Gong M, Hao L S 1998 Progress in Natural Science 8 342
Google Scholar
[2] Guo L H, Gong Z X, Wu L X 2001 Chin. Phys. Lett. 18 1366
Google Scholar
[3] Li Z L, Zhang R H, Yan J, Li F H, Liu J J 2004 IEEE J. Oceanic Eng. 29 973
Google Scholar
[4] Wan L, Zhou J X, Rogers P H, Knobles D P 2009 Acoust. Phys. 55 383
Google Scholar
[5] 赵梅, 胡长青 2010 声学技术 29 365
Google Scholar
Zhao M, Hu C Q 2010 Technical Acoustics 29 365
Google Scholar
[6] 王鲁军, 彭朝晖, 李整林 2011 声学学报 36 596
Wang L J, Peng C H, Li Z L 2011 Acta Acustica 36 596
[7] 张仁和, 张双荣, 肖金泉, 孙庚辰, 王孟新 1981 声学学报 1 9
Zhang R H, Zhang S R, Xiao J Q, Sun G C, Wang M X 1981 Acta Acustica 1 9
[8] Wang Q, Zhang R H 1992 J. Acoust. Soc. Am. 92 932
Google Scholar
[9] 宫在晓 2001 博士学位论文(北京: 中国科学院声学研究所)
Gong Z X 2001 Ph. D. Dissertation (Beijing: The Institute of Acoustics of the Chinese Academy of Sciences) (in Chinese)
[10] Urick R J, Lund G R 1968 J. Acoust. Soc. Am. 43 723
Google Scholar
[11] Urick R J 1973 J. Acoust. Soc. Am. 54 115
Google Scholar
[12] Colosi J A, Chandrayadula T K, Voronovich A G, Ostashev V E 2013 J. Acoust. Soc. Am. 134 3119
Google Scholar
[13] Li J, Li Z L, Ren Y 2016 Chin. Phys. B 25 124310
Google Scholar
[14] 李鋆 2017 博士学位论文(北京: 中国科学院声学研究所)
Li J 2017 Ph. D. Dissertation (Beijing: The Institute of Acoustics of the Chinese Academy of Sciences) (in Chinese)
[15] 胡治国, 李整林, 张仁和, 任云, 秦继兴, 何利 2016 65 014303
Google Scholar
Hu Z G, Li Z L, Zhang R H, Ren Y, Qin J X, He L 2016 Acta Phys. Sin. 65 014303
Google Scholar
[16] 胡治国, 李整林, 秦继兴, 任云, 张仁和 2016 中国科学: 物理学 力学 天文学 46 094304
Hu Z G, Li Z L, Qin J X, Ren Y, Zhang R H 2016 Scientia Sinica Physica, Mechanica & Astronomica 46 094304
[17] 胡治国, 李整林, 张仁和, 任云, 李鋆 2016 声学学报 41 758
Hu Z G, Li Z L, Zhang R H, Ren Y, Li J 2016 Acta Acustica 41 758
[18] Collins M D, Westwood E K 1991 J. Acoust. Soc. Am. 89 1068
Google Scholar
[19] Collins M D 1993 J. Acoust. Soc. Am. 93 1736
Google Scholar
[20] Jensen F B, Kuperman W A, Porter M B, Schmidt H 2011 Computational Ocean Acoustics (2nd Ed.) (New York: Springer) p147 p36
[21] Wu S L, Li Z L, Qin J X 2015 Chin. Phys. Lett. 32 124301
Google Scholar
[22] Li Z L, Li F H 2010 Chin. J. Oceanol. Limnol. 28 990
Google Scholar
[23] Porter M B, Bucker H P 1987 J. Acoust. Soc. Am. 82 1349
Google Scholar
[24] 翁晋宝 2015 博士学位论文(北京: 中国科学院声学研究所)
Weng J B 2015 Ph. D. Dissertation (Beijing: The Institute of Acoustics of the Chinese Academy of Sciences) (in Chinese)
[25] 张仁和, 李风华 1999 中国科学 A 29 241
Zhang R H, Li F H 1999 Science in China (Series A)
29 241 [26] 翁晋宝, 李风华, 郭永刚 2015 声学学报 40 207
Weng J B, Li F H, Guo Y G 2015 Acta Acustica 40 207
[27] 翁晋宝, 李风华, 郭永刚 2016 声学学报 41 330
Weng J B, Li F H, Guo Y G 2016 Acta Acustica 41 330
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