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Very-low-frequency (VLF) (≤100 Hz) acoustic waves exhibit special propagation characteristics in the deep sea, owing to strong penetration capability and interaction with deep geological structures. In a deep sea experiment conducted in the South China Sea, a vertical linear array including 64 elements is moored to the bottom (approximately 4360 m depth) to receive the acoustic signal. In the bearing-time record (BTR) processed by beamforming, a high-energy bottom bounce path is observed from the ship noise received by the bottom-moored vertical linear array, which shows an abrupt increase in energy near a grazing angle of 45°. However, the physical mechanism causing this phenomenon is still unclear, and we investigate it further in this work. According to the data processing, we develop an environmental model of the seabed by combining continuous speed gradient, which arises from long-term geological compaction processes, in the sediment. This model is compared with a traditional stratified model under the assumption of a uniform sediment layer. The wavenumber integration method is adopted in numerical simulation to accurately calculate the pressure field and analyze the cross-media propagation. The numerical simulations show that the positive velocity gradient (increasing from 1600 m/s to 2144 m/s) causes an ‘acoustic turning’ effect, which reradiates substantial acoustic energy back into the water column and generates the observed high-energy bounce paths. This is supported by theoretical analysis in the WKB approximation, where the calculated reflection coefficient shows a sharp transition in the acoustic turning point, explaining the energy fluctuations observed in the experimental BTR. Further analysis shows that the thickness of sediment influences the angular separation between bottom bounce paths, while its sound speed structure determines the turning angle. These findings offer new insights into VLF acoustic propagation in the deep sea and also provide critical evidence for supporting a transition from simplified stratified models to a more realistic model with a continuous gradient structure. Furthermore, the discovery of high-energy bottom bounce paths provides a new way for enhancing the capabilities of underwater detection, and these observed features also provide reliable pressure field characteristics for inverting deep seabed parameters.
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Keywords:
- very low frequency acoustics detection /
- continuous sound speed seabed /
- seabed acoustic bounce /
- acoustic turning
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Google Scholar
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Google Scholar
[9] Kniffin G P, Boyle J K, Zurk L M, Siderius M 2016 J. Acoust. Soc. Am. 139 418
Google Scholar
[10] Urick R 1983 Principles of Underwater Sound (3rd Ed.) (San Francisco: McGraw-Hill Book Company) pp146–150
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Google Scholar
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Google Scholar
[13] Yang K D, Xu L Y, Yang Q L, Duan R 2018 J. Acoust. Soc. Am. 143 EL8
Google Scholar
[14] Duan R, Yang K D, Ma Y L, Yang Q L, Li H 2014 J. Acoust. Soc. Am. 136 EL159
Google Scholar
[15] 朱方伟, 郑广赢, 刘福臣 2021 哈尔滨工程大学学报 42 1510
Google Scholar
Zhu F W, Zheng G Y, Liu F C 2021 J. Harbin Eng. Univ. 42 1510
Google Scholar
[16] Cao R, Yang K D, Ma Y L, Yang Q L, Xia H J, Shi Y 2019 Acta Acust. United Acust. 105 248
Google Scholar
[17] 吴俊楠, 周士弘, 张岩 2016 中国科学: 物理学 力学 天文学 46 094311
Google Scholar
Wu J N, Zhou S H, Zhang Y 2016 Sci. Sin. Phys. Mech. Astron. 46 094311
Google Scholar
[18] 谢亮, 王鲁军, 林旺生 2021 声学学报 46 171
Google Scholar
Xie L, Wang L J, Lin W S 2021 Acta Acust. 46 171
Google Scholar
[19] Chen H Y, Zhu Z R, Yang D S 2024 IEEE J. Oceanic Eng. 49 1127
Google Scholar
[20] Krolik J, Swingler D 1990 IEEE Trans. Acoust. Speech Signal Process. 38 356
Google Scholar
[21] Li C F, Li J B, Ding W W 2015 J. Geophys. Res. Solid Earth. 120 1377
Google Scholar
[22] Zhao M H, Qiu X L, Xia S H, Xu H L, Wang P, Wang T K, Lee C S, Xia K Y 2010 Tectonophysics 480 183
Google Scholar
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图 1 海洋试验场景
Figure 1. Diagram of ocean experiment.
图 2 宽带BTR (20—100 Hz)
Figure 2. BTR for broadband frequencies 20–100 Hz.
图 3 船载AIS记录货轮的航行轨迹
Figure 3. Cargo vessel trajectory recorded by shipboard AIS.
图 4 时延估计结果(互相关)
Figure 4. Time delay estimation results from cross-correlation analysis.
图 5 沉积层含声速梯度的声学模型示意图(${\theta _{\mathrm{w}}}, {\theta _{{\mathrm{sed}}}}$分别为海水及沉积层中的掠射角; ${\theta _{\mathrm{c}}}$为表层海底全反射临界角, $h$为沉积层厚度, ${c_i}~(i = {\mathrm{w}}, {\mathrm{sed}}\text{-}{\mathrm{top}}, {\mathrm{sed}}\text{-}{\mathrm{bot}}, {\mathrm{b}})$分别为海水, 沉积层上、下界面及基底层中的声速, ${\rho _i}~(i = {\mathrm{w}}, {\mathrm{sed}}, {\mathrm{b}})$分别为海水, 沉积层及基底层中的密度)
Figure 5. Schematic diagram of the acoustic model with a varying velocity in the sediment layer (${\theta _{\mathrm{w}}}, {\theta _{{\mathrm{sed}}}}$ are the grazing angles in the seawater and the sediment layer; ${\theta _{\mathrm{c}}}$ is the critical angle at the seabed surface; $h$ is the thickness of the sediment layer; ${c_i}~(i = {\mathrm{w}}, {\mathrm{sed}}\text{-}{\mathrm{top}}, {\mathrm{sed}}\text{-}{\mathrm{bot}}, {\mathrm{b}})$ are the sound speeds in the seawater, at the upper/lower interfaces of the sediment layer, and in the basement layer; ${\rho _i}~(i = {\mathrm{w}}, {\mathrm{sed}}, {\mathrm{b}})$ are the densities of the seawater, the sediment layer, and the basement layer).
图 6 沉积层为均匀声速的声学模型示意图
Figure 6. Schematic diagram of the acoustic model with a constant velocity in the sediment layer.
图 7 均匀沉积层模型下的深层海底路径反射系数
Figure 7. Seabed reflection coefficient for the model with a constant velocity in the sediment layer.
图 8 沉积层含声速梯度模型下的深层海底路径反射系数
Figure 8. Seabed reflection coefficient for the model with a varying velocity in the sediment layer.
图 9 声场传播损失(仿真) (a) 沉积层含声速梯度的仿真结果; (b) 均匀沉积层模型的仿真结果
Figure 9. Acoustic transmission loss field by numerical simulation: (a) Simulation results for the model with a varying velocity in the sediment layer; (b) simulation results for the model with a constant velocity in the sediment layer.
图 10 宽带波束形成的仿真结果 (a) 沉积层含声速梯度的沉积仿真结果; (b) 均匀沉积层模型仿真结果
Figure 10. Broadband beamforming by numerical simulation: (a) Simulation results for the model with a varying velocity in the sediment layer; (b) simulation results for the model with a constant velocity in the sediment layer.
图 11 不同条件下深层海底路径俯仰角
Figure 11. Beam angle of deep bottom path under different conditions.
图 12 突变角度附近的能量变化(归一化)
Figure 12. Normalized energy around the transition angle.
图 13 模型1和模型2的仿真结果 (a) 模型1的宽带波束输出(20—100 Hz); (b) 模型1的声场传播损失; (c) 模型2的宽带波束输出(20—100 Hz); (d) 模型2的声场传播损失
Figure 13. Simulation results for model 1 and model 2: (a) Broadband beam output (20–100 Hz) for model 1; (b) acoustic transmission loss field for model 1; (c) broadband beam output (20–100 Hz) for model 2; (d) acoustic transmission loss field for model 2.
图 14 模型3的仿真结果 (a) 模型3的宽带波束输出(20—100 Hz); (b) 模型3的声场传播损失
Figure 14. Simulation results for model 3: (a) Broadband beam output (20–100 Hz) for model 3; (b) acoustic transmission loss field for model 3.
表 1 模型所用环境参数
Table 1. Environmental parameters used in models.
h/m ${c_{{\mathrm{sed}}}}$/
(${\mathrm{m}} {\cdot} {{\mathrm{s}}^{ - 1}}$)${\rho _{{\mathrm{sed}}}}$/
(${\mathrm{g}} {\cdot} {\mathrm{cm}}^{ - 3}$)${c_{\mathrm{b}}}$/
(${\mathrm{m}} {\cdot} {{\mathrm{s}}^{ - 1}}$)${\rho _{\mathrm{b}}}$/
(${\mathrm{g}} {\cdot} {\mathrm{cm}}^{ - 3}$)声速连续
模型450 1600—2144 1.1 2144 1.7 声速均匀
模型450 1600 1.1 2144 1.7 
DownLoad: CSV
表 2 仿真中模型所用环境参数
Table 2. Environmental parameters used in simulation models.
$h/{\mathrm{m}}$ ${c_{{\mathrm{sed}}}}$/
(${\mathrm{m}} {\cdot} {{\mathrm{s}}^{ - 1}}$)${\rho _{{\mathrm{sed}}}}$/
(${\mathrm{g}} {\cdot} {\mathrm{cm}}^{ - 3}$)${c_{\mathrm{b}}}$/
(${\mathrm{m}} {\cdot}{{\mathrm{s}}^{ - 1}}$)${\rho _{\mathrm{b}}}$/
(${\mathrm{g}} {\cdot} {\mathrm{cm}}^{ - 3}$)模型1 450 1600—1800 1.1 2144 1.7 模型2 450 1600—2500 1.1 2500 1.7 模型3 50 1600—2144 1.1 2144 1.7
DownLoad: CSV
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[1] Smith T A, Rigby J 2022 Ocean Eng. 266 112863
Google Scholar
[2] Liu B T, Huang S B, Zheng B, Chen X F, Zhao J, Qi X R, Li Y, Liu S C 2023 J. Acoust. Soc. Am. 153 415
Google Scholar
[3] Sun D J, Lu M Y, Mei J D, Wang S C, Pei Y Q 2021 J. Acoust. Soc. Am. 150 952
Google Scholar
[4] Yang K F, Zhou T, Hui J, Xu C 2025 Appl. Acoust. 233 110623
Google Scholar
[5] Zhang D L, Gao L S, Sun D J, Teng T T 2022 Appl. Acoust. 188 108549
Google Scholar
[6] Zurk L M, Boyle J K, Shibley J 2013 Asilomar Conference on Signals, Systems and Computers Pacific Grove, USA, November 3–6, 2013 p2130
[7] Mccargar R, Zurk L M 2013 J. Acoust. Soc. Am. 133 EL320
Google Scholar
[8] Mccargar R K, Zurk L M 2012 J. Acoust. Soc. Am. 132 2081
Google Scholar
[9] Kniffin G P, Boyle J K, Zurk L M, Siderius M 2016 J. Acoust. Soc. Am. 139 418
Google Scholar
[10] Urick R 1983 Principles of Underwater Sound (3rd Ed.) (San Francisco: McGraw-Hill Book Company) pp146–150
[11] Gaul R D, Knobles D P, Shooter J A, Wittenborn A F 2007 IEEE J. Ocean. Eng. 32 497
Google Scholar
[12] Duan R, Yang K D, Li H, Yang Q L, Wu F Y, Ma Y L 2019 J. Acoust. Soc. Am. 145 903
Google Scholar
[13] Yang K D, Xu L Y, Yang Q L, Duan R 2018 J. Acoust. Soc. Am. 143 EL8
Google Scholar
[14] Duan R, Yang K D, Ma Y L, Yang Q L, Li H 2014 J. Acoust. Soc. Am. 136 EL159
Google Scholar
[15] 朱方伟, 郑广赢, 刘福臣 2021 哈尔滨工程大学学报 42 1510
Google Scholar
Zhu F W, Zheng G Y, Liu F C 2021 J. Harbin Eng. Univ. 42 1510
Google Scholar
[16] Cao R, Yang K D, Ma Y L, Yang Q L, Xia H J, Shi Y 2019 Acta Acust. United Acust. 105 248
Google Scholar
[17] 吴俊楠, 周士弘, 张岩 2016 中国科学: 物理学 力学 天文学 46 094311
Google Scholar
Wu J N, Zhou S H, Zhang Y 2016 Sci. Sin. Phys. Mech. Astron. 46 094311
Google Scholar
[18] 谢亮, 王鲁军, 林旺生 2021 声学学报 46 171
Google Scholar
Xie L, Wang L J, Lin W S 2021 Acta Acust. 46 171
Google Scholar
[19] Chen H Y, Zhu Z R, Yang D S 2024 IEEE J. Oceanic Eng. 49 1127
Google Scholar
[20] Krolik J, Swingler D 1990 IEEE Trans. Acoust. Speech Signal Process. 38 356
Google Scholar
[21] Li C F, Li J B, Ding W W 2015 J. Geophys. Res. Solid Earth. 120 1377
Google Scholar
[22] Zhao M H, Qiu X L, Xia S H, Xu H L, Wang P, Wang T K, Lee C S, Xia K Y 2010 Tectonophysics 480 183
Google Scholar
[23] Wei X D, Ruan A G, Li J B, Niu X W, Wu Z L, Ding W W 2017 Mar. Geophys. Res. 38 125
Google Scholar
[24] 王海峰, 张振, 杨永, 邓希光, 徐华宁, 朱克超, 何高文 2021 地质通报 40 305
Google Scholar
Wang H F, Zhang Z, Ynag Y, Deng X G, Xu H N, Zhu K C, He G W 2021 Geological Bull. China 40 305
Google Scholar
[25] Hamilton E L 1980 J. Acoust. Soc. Am. 68 1313
Google Scholar
[26] Jensen F B, Kuperman W A, Porter M B, Schmidt H 2011 Computational Ocean Acoustics (2nd Ed.) (New York: Springer) pp38–188
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