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Wind-generated noise is ubiquitous in ocean environments and highly influences the passive sonar performance. Since it originates from sources near the ocean surface, one of its physical features is that it largely represents only the intermediate- and high-order modes. The array-level signal-to-noise ratio (SNR), which includes the array-sampled sound intensity, background noise power, and array gain, is an essential quantity determining the sonar array performance. What is investigated in this work is how the array-level SNR of the vertical line array (VLA) varies with the source depth in downward-refracting shallow water, contributed by the modal structure of the surface noise. On the assumption that the modes are well sampled, it is theoretically demonstrated that the SNR varying with the source depth can be approximated as a linear combination of the lower-order mode-amplitude intensities varying with the water depth. Particularly, when the surface noise especially dominates and the water channel is highly downward refractive, this variation can be represented nearly only by the 1st-order mode-amplitude intensity varying with depth. The structure is meaningful in practice. It suggests the SNR will be inherently larger when the source is submerged than it is near the ocean surface, and will be maximized at a source depth slightly below the 1st-order mode peak across different source ranges. The above assertions are demonstrated in a typical downward-refracting shallow-water channel; the effects from the dominant degree of the surface noise, sound speed gradient in water column, and array aperture are investigated numerically. The obtained results are shown below. 1) Under certain circumstances, the variation of SNR with source depth is nearly irrelevant to the source range. 2) When the surface noise is more significant, the largest SNR in a certain source range will be more significantly larger than the SNR for the source near the surface, the corresponding source depth will be closer to that presenting the 1st-order mode’s peak, and the variation of SNR with source depth is increasingly irrelevant to the source range. 3) A stronger downward-refracting sound speed also enhances this SNR superiority and irrelevance to the source range, but causes the source depth presenting the largest SNR to be more deviated from the 1st-order mode’s peak. 4) Although the structure is unraveled on the assumption that the VLA spans the full water column, it can be seen when the VLA does not but covers the low-order modes' main part; when the array aperture is insufficiently large it will become approximately periodic in the source range, with the source depth presenting the largest SNR fluctuating lightly and nearly periodically around the 1st-order mode peak.
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Keywords:
- surface noise /
- array-level signal-to-noise ratio /
- source depth /
- downward-refracting channel /
- source-range irrelevance
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图 1 典型负声速梯度浅海环境
Figure 1. Typical shallow sea environment with negative sound velocity gradient.
图 2 200 Hz声源激发的18阶模态的形状
Figure 2. Shapes of 18 modes excited by a 200 Hz source.
图 3 垂直阵覆盖全水深时风成噪声协方差矩阵特征向量与模态采样的对应关系 (a)归一化特征值; (b) 特征向量与模态采样的相关系数
Figure 3. Corresponding relation analysis between eigenvectors of the surface noise covariance matrix and sampled modes for the vertical line array spanning the full water column: (a) Normalized eigenvalues; (b) correlations between eigenvectors and sampled modes.
图 4 归一化SNR随声源深度的变化结果 (a) 不同声源距离; (b)
${r_{\rm{s}}} = 10\;{\rm{km}}$ (在每个声源范围内, SNR由该范围内的最大SNR归一化)Figure 4. Normalized SNR versus source depths: (a) Different source ranges; (b)
${r_{\rm{s}}} = 10\;{\rm{km}}$ (at each source range the SNR is normalized by the greatest SNR at that range).
图 5 阵列覆盖全水深时不同特征向量 (a)关于SNR的权值; (b)对SNR的贡献随声源深度的变化(关于图中最大值进行了归一化)
Figure 5. For the vertical line array spanning the full water column different eigenvectors': (a) Weights to SNR; (b) contributions to SNR versus source depths(normalized by the greatest value).
图 6 声源距离10 km上归一化SNR随声源深度的变化结果 (a)不同风成噪声强度; (b)
$\alpha = 1000$ 时SNR随声源深度与1阶模态幅度强度随深度变化对比Figure 6. Normalized SNR versus source depths at
${r_{\rm{s}}} = 10\;{\rm{km}}$ : (a) Different α; (b) comparison of source depths and the 1 st-order mode-amplitude intensity varying with water depths for$\alpha = 1000$ .
图 7
$\alpha = 1$ 时不同声源距离上归一化SNR随声源深度的变化结果Figure 7. Normalized SNR versus source depths across different source ranges for
$\alpha = 1$ .
图 8 不同声源距离上归一化SNR随声源深度的变化结果 (a) g = －0.05 s–1; (b) g = –0.07 s–1; (c) g = –0.10 s–1; (d) g = –0.30 s–1
Figure 8. Normalized SNR versus source depths at different source ranges: (a) g = –0.05 s–1; (b) g = –0.07 s–1; (c) g = –0.10 s–1; (d) g = –0.30 s–1.
图 9 不同声速梯度环境中归一化SNR随声源深度的变化结果(
${r_{\rm{s}}} = 10\;{\rm{km}}$ )Figure 9. Normalized SNR versus source depths at
${r_{\rm{s}}} = 10\;{\rm{km}}$ in various gradient cases.
图 10 垂直阵覆盖10—100 m时不同声源距离上归一化SNR随声源深度的变化关系
Figure 10. Normalized SNR versus source depths across different source ranges for the vertical line array spanning from 10 to 100 m in depth.
图 11 垂直阵覆盖50—100 m时(a)不同声源距离上SNR随声源深度的变化结果和(b) 最大SNR对应的声源深度(红色虚线为1阶模态峰值点所在深度)
Figure 11. For the vertical line spanning from 50 to 100 m in depth: (a) Normalized SNR versus source depths; (b) the source depth presenting the largest SNR at different source ranges(The red dashed line is the depth of the peak point of the first-order mode).
图 12 垂直阵覆盖50—100 m时影响SNR的模态采样分析 (a) 模态采样与特征向量相关系数); (b) 不同特征向量对SNR的归一化权值, 通过第11个特征向量的归一化
Figure 12. Analysis of mode’s contribution to the SNR for the vertical line array spanning from 50 to 100 m in depth: (a) The correlation between sampled modes and eigenvectors; (b) the weights of different eigenvectors to the SNR, normalized by that of the 11 th eigenvector.
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[1] Urick R J 1984 Ambient Noise in the Sea (Washington: Undersea Warfare Technology Office) pp2–30
[2] Hamson R M 1985 J. Acoust. Soc. Am. 78 1702
Google Scholar
[3] Zakarauskas P 1986 Canadian Acoust. 14 3
[4] Dahl P, Miller J, Cato D, Andrew R 2007 Acoust. Today 3 23
Google Scholar
[5] Jensen F B, Kuperman W A, Porter M B, Schmidt H 2000 Computational Ocean Acoustics (New York. USA: Springer-Verlag) chap 9, pp338–340
[6] Cron B F, Sherman C H 1962 J. Acoust. Soc. Am. 34 1732
Google Scholar
[7] Kuperman W A, Ingenito F 1980 J. Acoust. Soc. Am. 67 1988
Google Scholar
[8] Liggett W S, Jacobson M J 1965 J. Acoust. Soc. Am. 38 303
Google Scholar
[9] Yang T C, Kwang Y 1997 J. Acoust. Soc. Am. 101 2541
Google Scholar
[10] 周建波, 朴胜春, 刘亚琴, 祝捍皓 2017 物理学报 66 014301
Google Scholar
Zhou J B, Piao S C, Liu Y Q, Zhu H H 2017 Acta Phys. Sin. 66 014301
Google Scholar
[11] Jiang D, Li Z, Qin J, Peng Z, Shao H 2017 Sci. China Phys. Mech. 60 124321
Google Scholar
[12] 蒋光禹, 孙超, 谢磊, 刘雄厚 2019 物理学报 68 024302
Google Scholar
Jiang G Y, Sun C, Xie L, Liu X H 2019 Acta Phys. Sin. 68 024302
Google Scholar
[13] Kay S 1993 Fundamentals of Statistical Signal Processing Volume II: Detection Theory (New Jersey: Prentice Hall) pp197–200, 478–479
[14] Kong D Z, Sun C, Li M Y, Xie L 2021 Defence Technology 17 1414
Google Scholar
[15] Li M Y, Sun C, Zhao H, Willett P 2022 IEEE J. Ocean. Eng. 47 201
Google Scholar
[16] Baggeroer A B, Kuperman W A, Schmidt H 1987 J. Acoust. Soc. Am. 83 571
Google Scholar
[17] Buck J R, Preisig J C, Wage K E 1998 J. Acoust. Soc. Am. 103 1813
Google Scholar
[18] 向龙凤, 孙超, 李明杨 2015 声学学报 40 779
Google Scholar
Xiang L F, Sun C, Li M Y 2015 Acta Acustica 40 779
Google Scholar
[19] Wang N, Liu J Z 2002 Chin. Phys. B 11 456
Google Scholar
[20] Kim K, Woojae S, Keunhwa L 2010 IEEE J. Ocean. Eng. 35 120
Google Scholar
[21] Van Trees H L 2002 Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory (New York: John Wiley & Sons) pp449–450
[22] Neilsen T B, Westwood E K 2002 J. Acoust. Soc. Am. 111 748
Google Scholar
[23] Porter M B 1991 The KRAKEN Normal Mode Program (La Spezia: SCALANT Undersea Research Center)
[24] [25] Wenz G M 1962 J. Acoust. Soc. Am. 34 1936
Google Scholar
[26] Yang T C 1987 J. Acoust. Soc. Am. 82 1736
Google Scholar
[27] 李明杨, 孙超, 邵炫 2014 物理学报 63 204302
Google Scholar
Li M Y, Sun C, Shao X 2014 Acta Phys. Sin. 63 204302
Google Scholar
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