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Acoustic inversion of sediment parameters in muddy bottom environment has received much attention in the field of underwater acoustics. In shallow water, when there is a low-speed layer of unconsolidated sediment, such as mud in which the sound speed is lower than that of the sea water, on the top of a high-speed bottom, the transmission losses at different frequencies will increase periodically under the condition of small grazing angles. Based on this phenomenon, an acoustic inversion method of seabed parameters for low speed sediments is proposed. Firstly, the analytical expressions between the frequency interval of the transmission loss (TL) periodical increasing and geoacoustic parameters, including the sound speed and the thickness of sediment layer and the sound speed of seawater near the bottom, are derived under the condition of small grazing angles. Secondly, using the broadband sound propagation signals received under the thermocline in the 2002 summer acoustic experiment conducted in the Yellow Sea, the TL at small grazing angles increases periodically with the frequency, and it is determined that the sediment of this sea area is a low-speed sediment. Then, taking the analytical expression as the constraint condition and combining with Hamilton's empirical formula, the sound speed, density, thickness of sediment layer and the sound speed and density of the seabed are inverted by matched field processing. Finally, the bottom attenuation coefficients at different frequencies are inverted by using the long-range TL, and the linear relationship between the attenuation coefficients and the frequencies is obtained. The equivalence between the two different bottom models is discussed in the end. The inversion results can provide seabed parameters for the study and application of the sound propagation law in shallow water with a low-speed sediment.
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Keywords:
- low-speed sedimentary seabed /
- geoacoustic inversion /
- matched field processing /
- transmission loss
[1] Gerstoft P, Gingras D F 1996 J. Acoust. Soc. Am. 99 2839
Google Scholar
[2] D’Spain G L, Murray J J, Hodgkiss W S, Booth N O 1995 J. Acoust. Soc. Am. 97 3291
[3] Zhou J X 1985 J. Acoust. Soc. Am. 78 1003
Google Scholar
[4] Zhou J X, Zhang X Z, Rogers P H, Simmen J A, Dahl P H, Jin G L, Peng Z H 2004 IEEE J. Ocean. Eng. 29 988
Google Scholar
[5] 高伟, 王宁, 王好忠 2008 声学学报 33 109
Google Scholar
Gao W, Wang N, Wang H Z 2008 Acta Acustica 33 109
Google Scholar
[6] Carbone N M, Deane G B, Buckingham M J 1998 J. Acoust. Soc. Am. 103 801
Google Scholar
[7] Li Z L, Zhang R H 2004 Chin. Phys. Lett. 21 1100
Google Scholar
[8] 李风华, 张仁和 2000 声学学报 25 297
Google Scholar
Li F H, Zhang R H 2000 Acta Acustica 25 297
Google Scholar
[9] Wu S L, Li Z L, Qin J X 2015 Chin. Phys. Lett. 32 124301
Google Scholar
[10] Li Z L, Zhang R H, Yan J, Li F H, Liu J J 2004 IEEE J. Ocean. Eng. 29 973
Google Scholar
[11] Li Z L 2003 Chin. J. Acoust. 22 176
[12] Li Z L, Zhang R H 2007 Chin. Phys. Lett. 24 471
Google Scholar
[13] Li Z L, Li F H 2010 Chin. J. Oceanol. Limnol. 28 990
Google Scholar
[14] Zhou J X, Zhang X Z 2009 J. Acoust. Soc. Am. 125 2847
Google Scholar
[15] Press F, Ewing M. 1948 Geophysics 13 404
Google Scholar
[16] Rubano L A 1980 J. Acoust. Soc. Am. 67 1608
[17] Kuperman W A, Jensen F B 1980 Bottom-interacting Ocean Acoustics (New York: Plenum Press) pp135−152
[18] Bonnel J, Lin Y T, Eleftherakis D, Goff J A, Stan D, Ross C, James H M, Gopu R P 2018 J. Acoust. Soc. Am. 143 405
Google Scholar
[19] Wan L, Badiey M, Knobles D P, Wilson P S 2018 J. Acoust. Soc. Am. 143 199
Google Scholar
[20] Porter M B, Bucker H P 1987 J. Acoust. Soc. Am. 82 1349
Google Scholar
[21] Porter M, Reiss E L 1984 J. Acoust. Soc. Am. 76 244
Google Scholar
[22] Hamilton E L, Bachman R T 1982 J. Acoust. Soc. Am. 72 1891
Google Scholar
[23] Stoffa P L, Sen M K 1991 Geophysics 56 1794
Google Scholar
[24] Hamilton E L 1980 J. Acoust. Soc. Am. 68 1313
Google Scholar
[25] Gerstoft P, Mecklenbrauker C F 1998 J. Acoust. Soc. Am. 104 808
Google Scholar
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图 1 低声速沉积层海底模型
Figure 1. Bottom model with a low speed sediment layer.
图 2 掠射角1°时对应的海底反射损失
Figure 2. Reflection loss for the grazing angle of 1°.
图 3 小掠射角情况下参数敏感性分析
Figure 3. Sensitivity analyses of the bottom reflection loss to the geoacoustic parameters under the small grazing angle.
图 4 声传播损失与海底反射损失随频率的变化
Figure 4. Comparison between the transmission loss and reflection loss at different frequencies.
图 5 低声速沉积层声学参数联合反演流程
Figure 5. Flowchart of geoacoustic inversion for the sediment with lower sound speed.
图 6 实验期间的水文环境和设备布设 (a) 声速剖面; (b) 设备布设及海深示意图
Figure 6. Water environment and experiment configuration during the experiment: (a) Measured sound speed profile; (b) experimental configuration and water depth.
图 7 声传播损失随频率的变化 (r = 9.2 km, zs = 50.0 m, zr = 53.5 m)
Figure 7. Transmission losses at the different frequencies (
r = 9.2 km, zs = 50.0 m, zr = 53.5 m). 
图 8 给定频率间隔下沉积层厚度与声速的关系
Figure 8. Relationship between the thickness of sediment and its sound speed at the special frequency step.
图 9 参数的一维边缘概率密度分布
Figure 9. One-dimensional marginal posterior probability densities of the parameters.
图 10 声源距离和海深的模糊度表面
Figure 10. Ambiguity surface of source range and water depth.
图 11 代价函数随沉积层和基底衰减系数的模糊度表面
Figure 11. Ambiguity surface of sediment attenuation and basement attenuation.
图 12 反演得到的不同频率的衰减系数
Figure 12. Inverted attenuation coefficients at different frequencies
图 13 利用反演参数计算的不同频率传播损失与实验结果的对比 (a) zr = 22 m; (b) zr = 50 m
Figure 13. Comparison between the numerical TL and experimental TL at different frequencies: (a) zr = 22 m; (b) zr = 50 m.
图 14 不同海底模型的海底反射损失比较 (a) 半无限大海底模型; (b) 双层海底模型; (c) 掠射角0.1°; (d) 掠射角11.6°
Figure 14. Comparison of reflection losses for different bottom models: (a) Uniform liquid half-space bottom model; (b) two layered bottom model; (c) at grazing angle 0.1°; (d) at grazing angle 11.6°.
表 1 低声速沉积海底环境参数
Table 1. Seabed environmental parameters for low-speed sediment simulation.
c1/m·s–1 ρ1/g·cm–3 α1/dB·λ–1 c2/m·s–1 ρ2/g·cm–3 α2/dB·λ–1 d/m c3/m·s–1 ρ3/g·cm–3 α3/dB·λ–1 1488 1.0 0.0 1460 1.4 0.10 5 1620 1.8 0.10 
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表 2 计算得到的不同距离下的有效海底掠射角
Table 2. Effective bottom grazing angles at different ranges.
收发距离/km 1 5 10 20 有效海底掠射角 10.41° 6.16° 2.15° 0.52° 标准差 7.84° 6.44° 3.75° 0.70°
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表 3 待反演参数搜素范围及反演结果
Table 3. Search ranges of the unknown parameters and the inverted results.
c2/m·s–1 ρ2/g·cm–3 c3/m·s–1 ρ3/g·cm–3 d/m r/km h/m 搜索范围 1418—1487 1.1—1.6 1489—1800 — — 9.0—9.4 60—65 最优值 1474.01 1.35 1580.47 1.64 10.32 9.26 64.63 平均值 1474.12 1.39 1581.02 1.64 10.48 9.22 64.65 标准差 2.22 0.07 1.52 0.00 0.98 0.10 0.34
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[1] Gerstoft P, Gingras D F 1996 J. Acoust. Soc. Am. 99 2839
Google Scholar
[2] D’Spain G L, Murray J J, Hodgkiss W S, Booth N O 1995 J. Acoust. Soc. Am. 97 3291
[3] Zhou J X 1985 J. Acoust. Soc. Am. 78 1003
Google Scholar
[4] Zhou J X, Zhang X Z, Rogers P H, Simmen J A, Dahl P H, Jin G L, Peng Z H 2004 IEEE J. Ocean. Eng. 29 988
Google Scholar
[5] 高伟, 王宁, 王好忠 2008 声学学报 33 109
Google Scholar
Gao W, Wang N, Wang H Z 2008 Acta Acustica 33 109
Google Scholar
[6] Carbone N M, Deane G B, Buckingham M J 1998 J. Acoust. Soc. Am. 103 801
Google Scholar
[7] Li Z L, Zhang R H 2004 Chin. Phys. Lett. 21 1100
Google Scholar
[8] 李风华, 张仁和 2000 声学学报 25 297
Google Scholar
Li F H, Zhang R H 2000 Acta Acustica 25 297
Google Scholar
[9] Wu S L, Li Z L, Qin J X 2015 Chin. Phys. Lett. 32 124301
Google Scholar
[10] Li Z L, Zhang R H, Yan J, Li F H, Liu J J 2004 IEEE J. Ocean. Eng. 29 973
Google Scholar
[11] Li Z L 2003 Chin. J. Acoust. 22 176
[12] Li Z L, Zhang R H 2007 Chin. Phys. Lett. 24 471
Google Scholar
[13] Li Z L, Li F H 2010 Chin. J. Oceanol. Limnol. 28 990
Google Scholar
[14] Zhou J X, Zhang X Z 2009 J. Acoust. Soc. Am. 125 2847
Google Scholar
[15] Press F, Ewing M. 1948 Geophysics 13 404
Google Scholar
[16] Rubano L A 1980 J. Acoust. Soc. Am. 67 1608
[17] Kuperman W A, Jensen F B 1980 Bottom-interacting Ocean Acoustics (New York: Plenum Press) pp135−152
[18] Bonnel J, Lin Y T, Eleftherakis D, Goff J A, Stan D, Ross C, James H M, Gopu R P 2018 J. Acoust. Soc. Am. 143 405
Google Scholar
[19] Wan L, Badiey M, Knobles D P, Wilson P S 2018 J. Acoust. Soc. Am. 143 199
Google Scholar
[20] Porter M B, Bucker H P 1987 J. Acoust. Soc. Am. 82 1349
Google Scholar
[21] Porter M, Reiss E L 1984 J. Acoust. Soc. Am. 76 244
Google Scholar
[22] Hamilton E L, Bachman R T 1982 J. Acoust. Soc. Am. 72 1891
Google Scholar
[23] Stoffa P L, Sen M K 1991 Geophysics 56 1794
Google Scholar
[24] Hamilton E L 1980 J. Acoust. Soc. Am. 68 1313
Google Scholar
[25] Gerstoft P, Mecklenbrauker C F 1998 J. Acoust. Soc. Am. 104 808
Google Scholar
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