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In order to build an efficient underwater acoustic sensor network in the Arctic Ocean environment, transmission characteristics of under-ice acoustic channels need comprehensive understanding. The reflecting and scattering of acoustic waves from sea ices have great influences on under-ice acoustic channels. Both topology and structure of sea surface ices are very complex and variable. The physical dimension, acoustic property and interface roughness of sea ices depend not only on local environment, but also on climate and formation time. Therefore, it is of great significance to develop a model of reflecting and scattering of acoustic waves from sea ices for investigating the sound propagation in the under-ice environment. Assuming that sea ices are a multi-layered elastic solid medium and the ice-water interface is rough and satisfies the boundary condition of perturbation, we develop a system of linear equations to solve the coherent reflection coefficient of the incident sound wave from water to sea ice. The coherent reflection coefficient is a function of the frequency of sound wave and incident grazing angle, and is numerically evaluated. The influences of ice thickness and ice-water interface roughness on the coherent reflection coefficient are analyzed. Furthermore, the method of calculating scattering coefficient by using the power spectrum density of the scattering field is introduced. The scattering coefficient as a function of the scattering grazing angle is numerically evaluated. The influences of ice thickness and ice-water interface roughness on scattering coefficient are analyzed. The results show that both the coherent reflection coefficient and the scattering coefficient are dependent on the frequency of acoustic wave, ice thickness and grazing angle. The coherent reflection coefficient is close to 1.0 and the scattering coefficient is less than 0.01 when incident grazing angle is less than 15°. In addition, the frequency of acoustic wave and ice thickness have weak influences on them. However, the frequency of acoustic wave and ice thickness have significant influences on the coherent reflection coefficient and the scattering coefficient when the incident grazing angle is big, say, greater than 30°. In general, the thicker the ice is, the smaller the coherent reflection coefficient and the scattering coefficient are. The coherent reflection coefficient is less than 0.18 when the ice thickness is greater than 10.0 m and the frequency of acoustic waves is greater than 2 kHz. The ice-water interface roughness has great influences on both the coherent reflection coefficient and the scattering coefficient. The rougher of the ice-water interface is, the smaller the coherent reflection coefficient is, and the bigger the scattering coefficient is.
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Keywords:
- sea ices /
- coherent reflection coefficient /
- scattering coefficient /
- under-ice acoustic channels
[1] Li Q H, Wang N, Zhao J P, Huang H N, Yin L, Huang Y, Li Y, Xue S H, Ren X M, Li T (in Chinese)[李启虎, 王宁, 赵进平, 黄海宁, 尹力, 黄勇, 李宇, 薛山花, 任新敏, 李涛 2014 应用声学 33 471]
[2] Gautier D L, Bird K J, Charpentier R R, Grantz A, Houseknecht D W, Klett T R, Moore T E, Pitman J K, Schenk C J, Schuenemeyer J H, Sorensen K, Tennyson M E, Valin Z C, Wandrey C J 2009 Science 324 1175
[3] ACIA 2004 Impacts of a Warming Arctic:Arctic Climate Impact Assessment (Cambridge:Cambridge University Press)
[4] Kang J C, Yan Q D, Sun B, Wen J H, Wang D L, Sun J Y, Meng G L, Kumiko G A 1999 Chin. J. Pol. Res. 11 301 (in Chinese)[康建成, 颜其德, 孙波, 温家洪, 汪大立, 孙俊英, 孟广林, Kumkko G A 1999 极地研究 11 301]
[5] Mikhalevsky P N, Sagen H, Worcester P F, Baggeroer A B 2015 Arctic 68 1
[6] Mikhalevsky P N, Gavrilov A N, Baggeroer A B 1999 IEEE J. Ocean. Eng. 24 183
[7] Marsh H W, Mellen R H 1963 J. Acoust. Soc. Am. 35 552
[8] Duckworth G, LePage K, Farrell T 2001 J. Acoust. Soc. Am. 110 747
[9] LePage K, Schmidt H 1994 J. Acoust. Soc. Am. 96 1783
[10] Alexander P, Duncan A, Bose N 2012 Sci. Edu. 41 250
[11] Langleben M P 1970 J. Geophs. Res. 75 5243
[12] Yang T C, Votaw C W 1981 J. Acoust. Soc. Am. 70 841
[13] Yin J W, Du P Y, Zhu G P, Zhang M H, Han X, Zhang X, Sun H, Sheng X L (in Chinese)[殷敬伟, 杜鹏宇, 朱广平, 张明辉, 韩笑, 张晓, 孙辉, 生雪莉 2016 应用声学 35 58]
[14] Jezek K C, Stanton T K, Gow A J, Lange M A 1990 J. Acouct. Soc. Am. 88 1903
[15] Rothrock D A, Thorndike A S 1980 J. Acoust. Soc. Am. 85 3955
[16] Diachok O I 1976 J. Acoust. Soc. Am. 59 1110
[17] McCammom D F, McDamoel S T 1985 J. Acoust. Soc. Am. 77 499
[18] Yew C H, Weng X 1987 J. Acoust. Soc. Am. 82 342
[19] Ewing W M, Jardetzky W S, Press F 1957 Elastic Waves in Layered Media (New York:McGraw-Hill)
[20] Kuperman W A, Schmidt H 1989 J. Acoust. Soc. Am. 86 1511
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[1] Li Q H, Wang N, Zhao J P, Huang H N, Yin L, Huang Y, Li Y, Xue S H, Ren X M, Li T (in Chinese)[李启虎, 王宁, 赵进平, 黄海宁, 尹力, 黄勇, 李宇, 薛山花, 任新敏, 李涛 2014 应用声学 33 471]
[2] Gautier D L, Bird K J, Charpentier R R, Grantz A, Houseknecht D W, Klett T R, Moore T E, Pitman J K, Schenk C J, Schuenemeyer J H, Sorensen K, Tennyson M E, Valin Z C, Wandrey C J 2009 Science 324 1175
[3] ACIA 2004 Impacts of a Warming Arctic:Arctic Climate Impact Assessment (Cambridge:Cambridge University Press)
[4] Kang J C, Yan Q D, Sun B, Wen J H, Wang D L, Sun J Y, Meng G L, Kumiko G A 1999 Chin. J. Pol. Res. 11 301 (in Chinese)[康建成, 颜其德, 孙波, 温家洪, 汪大立, 孙俊英, 孟广林, Kumkko G A 1999 极地研究 11 301]
[5] Mikhalevsky P N, Sagen H, Worcester P F, Baggeroer A B 2015 Arctic 68 1
[6] Mikhalevsky P N, Gavrilov A N, Baggeroer A B 1999 IEEE J. Ocean. Eng. 24 183
[7] Marsh H W, Mellen R H 1963 J. Acoust. Soc. Am. 35 552
[8] Duckworth G, LePage K, Farrell T 2001 J. Acoust. Soc. Am. 110 747
[9] LePage K, Schmidt H 1994 J. Acoust. Soc. Am. 96 1783
[10] Alexander P, Duncan A, Bose N 2012 Sci. Edu. 41 250
[11] Langleben M P 1970 J. Geophs. Res. 75 5243
[12] Yang T C, Votaw C W 1981 J. Acoust. Soc. Am. 70 841
[13] Yin J W, Du P Y, Zhu G P, Zhang M H, Han X, Zhang X, Sun H, Sheng X L (in Chinese)[殷敬伟, 杜鹏宇, 朱广平, 张明辉, 韩笑, 张晓, 孙辉, 生雪莉 2016 应用声学 35 58]
[14] Jezek K C, Stanton T K, Gow A J, Lange M A 1990 J. Acouct. Soc. Am. 88 1903
[15] Rothrock D A, Thorndike A S 1980 J. Acoust. Soc. Am. 85 3955
[16] Diachok O I 1976 J. Acoust. Soc. Am. 59 1110
[17] McCammom D F, McDamoel S T 1985 J. Acoust. Soc. Am. 77 499
[18] Yew C H, Weng X 1987 J. Acoust. Soc. Am. 82 342
[19] Ewing W M, Jardetzky W S, Press F 1957 Elastic Waves in Layered Media (New York:McGraw-Hill)
[20] Kuperman W A, Schmidt H 1989 J. Acoust. Soc. Am. 86 1511
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