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Bottom backscattering due to roughness seafloor is the main source of shallow water reverberation, especially in the waveguide with downward reflection profile or a calm sea-surface. Empirical backscattering models with a simple form has an important limitation to analyzing other characteristics of reverberation except for the intensity characteristics, which originates from optics and describes the relationship between the bottom backscattering strength and scattering grazing angle of plane-wave in half-infinite space. In the shallow water, such a plane-wave backscattering model cannot be used due to frequency dispersion. The model of bottom backscattering based on physical scattering principle is made to relieve such a limitation, but thereby bringing about another restraint by a geoacoustics model. The bottom backscattering model, which is formulated during modeling the full-wave reverberation theory at small grazing angle in range-independent shallow water waveguide, is simplified by combining with bottom reflection coefficient model which is independent of the geoacoustics model. The bottom reflection coefficient model as referred to the proposed phase parameter P in this paper is equivalent to velocity and density of sediment to describe sound field interacted with sea-bottom. Therefore simplification of bottom backscattering model can be handled by the phase parameter without any knowledge of bottom geoacoustic parameters. The angular dependency and intensity dependency of bottom backscattering due to roughness seafloor at small grazing angle are studied more in depth through such a simplified model. Marking 2/P as the cut-off point, the grazing angle is divided into two stages. Near the critical angle, as grazing angle is greater than 2/P and less than critical grazing angle, the angular dependency of bottom backscattering due to roughness seafloor is weighted by phase parameter of bottom reflection coefficient, while the intensity dependency is independent of phase parameter. At each small grazing angle, as grazing angle is less than 2/P, the angular dependency of bottom backscattering due to roughness seafloor is proportional to incident and scattering grazing angle squared and irrespective of phase parameter of bottom reflection coefficient which is like the empirical bottom backscattering model, while the intensity dependency is proportional to the fourth power of phase parameter. So the bottom has different influences on the angular dependency and intensity dependency of bottom backscattering in different stages of grazing angle.
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Keywords:
- bottom sackscattering model /
- intensity dependency /
- angular dependency /
- small grazing angle approximation
[1] 张仁和, 李文华, 裘辛方, 金国亮 1995 声学学报 20 417
Zhang R H, Li W H, Qiu X F, Jin G L 1995 Acta Acoust. 20 417
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Google Scholar
Liu J J, Li F H, Zhang R H 2006 Acta Acoust. 31 173
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Gao T F 1989 Acta Acoust. 14 126
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Google Scholar
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Shang E C 1979 Acta Ocean. Sin. 1 58
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Google Scholar
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Zhao Z D 2007 Ph. D. Dissertation (Beijing: The University of Chinese Academy of Sciences) (in Chinese)
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图 1 浅海波导环境
Figure 1. Shallow water waveguide environment.
图 2
$\zeta $ 随P参数的变化Figure 2.
$\zeta $ varied with P parameters near critical angle.
图 3 海底甚小掠射角反向散射系数对P参数的依赖
Figure 3. Relationship between P and bottom backscattering coefficient at very low grazing angle.
图 4 海底反向散射模型的比较
Figure 4. Compare with bottom backscattering model with different approximate.
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[1] 张仁和, 李文华, 裘辛方, 金国亮 1995 声学学报 20 417
Zhang R H, Li W H, Qiu X F, Jin G L 1995 Acta Acoust. 20 417
[2] 刘建军, 李风华, 张仁和 2006 声学学报 31 173
Google Scholar
Liu J J, Li F H, Zhang R H 2006 Acta Acoust. 31 173
Google Scholar
[3] 姚万军, 蔡志明, 卫红凯 2009 声学学报 34 223
Google Scholar
Yao W J, Cai Z M, Wei H K 2009 Acta Acoust. 34 223
Google Scholar
[4] Zhou J X, Zhang X Z 2012 J. Acoust. Soc. Am. 131 2611
Google Scholar
[5] Isakson M J, Chotiros N P 2011 J. Acoust. Soc. Am. 129 1237
[6] 彭朝晖, 周纪浔, 张仁和 2004 中国科学G辑 物理学 力学 天文学 34 378
Peng Z H, Zhou J X, Zhang R H 2004 Sci. China (Series G)
34 378 [7] Ivakin A N 1998 J. Acoust. Soc. Am. 103 827
Google Scholar
[8] Ivakin A N 2016 J. Acoust. Soc. Am. 140 657
Google Scholar
[9] Moe J E, Jackson D R 1994 J. Acoust. Soc. Am. 96 1748
Google Scholar
[10] Tang D J, Jackson D R 2017 J. Acoust. Soc. Am. 142 2968
Google Scholar
[11] Shang E C, Gao T F, Wu J R 2008 IEEE J. Ocean Eng. 33 451
Google Scholar
[12] 高天赋 1989 声学学报 14 126
Gao T F 1989 Acta Acoust. 14 126
[13] Tang D J 1997 Internal Conference on Shallow-Water Acoustics Beijing, China, April 21-25, 1997 p323
[14] Gao T F, Shang E C, Tang D J 2001 Theoretical and Computational Acoustics Beijing, China, May 21-25, 2001 p67
[15] Wu J R, Shang E C, Gao T F 2010 AIP Conf. Proc. 1272 314
[16] Wu J R, Shang E C, Gao T F 2010 J. Comput. Acous. 18 209
Google Scholar
[17] 尚尔昌 1979 海洋学报 1 58
Shang E C 1979 Acta Ocean. Sin. 1 58
[18] Zhao Z D, Ma L, Shang E C 2014 J. Comput. Acoust. 22 1440005
Google Scholar
[19] 赵振东 2014 博士学位论文 (北京: 中国科学院大学)
Zhao Z D 2007 Ph. D. Dissertation (Beijing: The University of Chinese Academy of Sciences) (in Chinese)
[20] Goff J A, Jordan T H 1988 J. Geophys. Res. 93 13589
Google Scholar
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