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全球性气候变暖的持续使极地科学成为国际科研热点. 极地声学技术研究在近年国内学者的努力下取得了长足进展, 但在基础理论研究方面还有很多需要攻坚的难题. 极地冰声传播受弹性波导影响严重, 特殊的材料物理特性、复杂的边界条件以及极端恶劣的环境均给相关研究推进带来挑战. 针对冰声波导模型精细化构建难题, 本文从海冰物理特性概述、冰声传播理论模型构建、冰声传播特征方程数值求解以及冰声参数评估与选取四个方向出发, 回顾并梳理了极地海冰声波导建模关键技术的发展历程与研究现状, 分析了国内外冰声传播研究进展, 讨论并展望了冰声波导建模技术的未来研究重点以及其在极地开发中的应用潜力, 以期为后续极地声学理论与应用研究的开展提供有益参考.With the continued global warming, polar science has become one of the research hotspots. Regarding polar acoustics, much progress has been made due to the efforts made by scientists in the world. With the enhancement of stereoscopic monitoring capacity in polar regions, the acoustic theory and technologies applicable to Arctic sea-ice, which have long been overlooked as a branch of acoustics, are now dawning more and more attention. The propagation of elastic waves in the Arctic sea-ice is governed by its waveguide, and the understanding of which faces a grave challenge due to the unique material properties and complex internal structure of sea-ice, along with the asymmetric fluid-solid coupling at its boundaries and the inaccessibility for in-situ experiments, which is caused by the extreme condition. Aiming at an effectively and precisely modeling technique of acoustic propagation in sea-ice, including its waveguide, in this paper, the progress, the development, and the status of corresponding researches are reviewed. For a better understanding of the modeling of sea-ice, Arctic sea-ice, i.e. its formation condition, geometries, mechanical properties, microstructures, and the acoustic propagation, is briefly introduced. Different approaches to modeling the propagation of elastic waves in ice-floe based on explicit/implicit boundary conditions are presented and explained in detail. The resulting transcendental characteristic equation describing the acoustic propagation needs to be solved in a complex space for the severe energy leakage at the water-ice interface, and the necessary numerical methods of solving this equation are then explained and compared with each other. Since accurate parameters are imperative in having a satisfactory fidelity for any physical model, the acoustic parameters of Arctic sea-ice, historical evolution and experimental results, along with its assessment techniques are also presented, and a set of sound velocity parameters of Arctic sea-ice are provided for modeling. The roughness of the ice-water interface is discussed case-by-case depending on its spatial scale in comparison with acoustic wavelength for its influence on the elastic waveguide. The perspectives and potential applications of the sea-ice acoustic waveguide within the frame of promoting sustainable development of the polar region are also discussed.
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Keywords:
- polar sea-ice /
- polar acoustics /
- acoustic waveguide /
- research progress
[1] 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 471Google Scholar
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 2014 Appl. Acoust. 33 471Google Scholar
[2] Climate Change Indicators: Arctic Sea Icehttps://www.epa.gov/climate-indicators/climate-change-indicators-arctic-sea-ice [2021-1-1]
[3] 李培基 1996 冰川冻土 18 72Google Scholar
Li P J. 1996 J. Glaciol. Geocryol. 18 72Google Scholar
[4] Grenfell T C, Maykut G A. 1977 J. Glaciol. 18 445Google Scholar
[5] Nakamura N, Oort A H 1988 J. Geophys. Res-Atmos. 93 9510Google Scholar
[6] Magnusdottir G, Deser C, Saravanan R. 2004 J. Climate 17 857Google Scholar
[7] England M R, Polvani L M, Sun L, Deser C, Saravanan R 2020 Nature Geosci. 13 1Google Scholar
[8] Milne A R, Ganton J H 1964 J. Acoust. Soc. Am. 36 855Google Scholar
[9] Xu X Q, Lin J M, Fang S K 2020 Earthquake Research in China 34 264Google Scholar
[10] 朱广平, 殷敬伟, 陈文剑, 胡思为, 周焕玲, 郭龙祥 2017 声学学报 42 152Google Scholar
Zhu G P, Yin J W, Chen W J, Hu S W, Zhou H L, Guo L X 2017 Acta Acustica 42 152Google Scholar
[11] Kinda G B, Simard Y, Gervaise C, Mars J I, Fortier L 2015 J. Acoust. Soc. Am. 138 2034Google Scholar
[12] Tian Y N, Han X, Yin J W, Liu Q Y, Li L 2019 J. Acoust. Soc. Am. 146 2482Google Scholar
[13] Yin J W, Liu B, Zhu G P, Xie Z N 2018 Sensors 18 3461Google Scholar
[14] Schwarz J, Weeks W F. 1977 J. Glaciol. 19 499Google Scholar
[15] Untersteiner N 1986 The Geophysics of Sea Ice (America: Springer US) pp1–8
[16] Lebedev V V 1938 Probl. Arkt. Antarkt. 5 9
[17] 李志军 康建成 2001 冰川冻土 23 383Google Scholar
Li Z J Kang J C 2001 J. Glaciol. Geocryol. 23 383Google Scholar
[18] 李冰洁, 庞小平, 季青 2019 极地研究 31 258Google Scholar
Li B J, Pang X P, Ji Q 2019 Chin. J. Polar Res. 31 258Google Scholar
[19] Press F, Ewing M 1951 Eos Transactions American Geophysical Union 32 673Google Scholar
[20] Petrich C, Eicken H 2010 Sea Ice (2nd Ed.) (America: Wiley-Blackwell) pp23–77
[21] Cox G F N, Richter J A, Weeks W F, Mellor M 1984 a Proceedings of the 3rd International Offshore Mechanics and Arctic Engineering Symposium New Orleans, Louisiana, February 12–17, 1984 p126
[22] Richter-Menge J A, Cox G F N 1984 Proceedings of the 3rd International Offshore Mechanics and Arctic Engineering Symposium New Orleans, Louisiana, February 12–17, 1984 p194
[23] Timco G W, Weeks W F 2010 Cold Reg. Sci. Technol. 60 107Google Scholar
[24] Weeks W F, Gow A J 1980 J. Geophys. Res. 85 137
[25] Stander E, Michel B 1989 Cold Reg. Sci. Technol. 17 153Google Scholar
[26] Diez A, Eisen O 2015 Cryosphere 9 367Google Scholar
[27] Diez A, Eisen O 2015 Cryosphere 9 385Google Scholar
[28] Vaughan M J, Prior D J, Jefferd M, Brantut N, Mitchell T M, Seidemann M 2017 J. Geophys. Res-Sol. 122 7076Google Scholar
[29] Sayers C M 2018 Geophys. J. Int. 1 1
[30] Jeffries M G Wright W H 1988 Proceedings of the 3 rd International Offshore Mechanics and Arctic Engineering Symposium New Orleans, Louisiana, February 12–17, 1984 p201
[31] 孙俊英 2000 冰川冻土 22 3Google Scholar
Sun J Y 2000 J. Glaciol. Geocryol. 22 3Google Scholar
[32] Sato Y 1951 Bulletin of the Earthquake Research Institute University of Tokyo XXIX 223
[33] Miller B E 1990 J. Acoust. Soc. Am. 89 1668Google Scholar
[34] Yang T C, Giellis G R 1994 J. Acoust. Soc. Am. 96 2993Google Scholar
[35] Miklowitz J, Kaul R K 1984 J. Appl. Mech. 46 969
[36] Rose J L 2000 J. Acoust. Soc. Am. 107 1807Google Scholar
[37] Lamb H 1917 Proc. R. Soc. London A93 114
[38] 邓明晰 1996 声学学报 21 429Google Scholar
Deng M X 1996 Acta Acustica 21 429Google Scholar
[39] Zhu Z M, Wu J R 1995 J. Acoust. Soc. Am. 98 1057Google Scholar
[40] Solie L P, Auld B A 1973 J. Acoust. Soc. Am. 54 50Google Scholar
[41] Osborne M F M, Hart S D 1945 J. Acoust. Soc. Am. 17 1Google Scholar
[42] Dayal V, Vinay K K 1989 J. Acoust. Soc. Am. 85 2268Google Scholar
[43] Wu J R, Zhu Z M 1992 J. Acoust. Soc. Am. 91 861Google Scholar
[44] Press F, Ewing M 1951 J. Appl. Phys. 22 892Google Scholar
[45] Landschulze M 2018 Near Surf. Geophys. 16 493Google Scholar
[46] Yang T C, Yates T W 1995 J. Acoust. Soc. Am. 97 971Google Scholar
[47] Graff K F 1975 Wave Motion in Elastic Solid (London: Oxford University Press)
[48] Thomson W T 1950 J. Appl. Phys. 21 89Google Scholar
[49] Haskell N A 1953 Bull. Seismol. Soc. Am. 43 86Google Scholar
[50] Knopoff L A 1964 Bull. Seismol. Soc. Am. 54 431Google Scholar
[51] Randall M J 1967 Bull. Seismol. Soc. Am. 57 1299Google Scholar
[52] Lowe M J S 1995 IEEE T. Ultrason. Ferr. 42 525Google Scholar
[53] Yu L Y, Tian Z H 2015 Nondestruct. Test. Eva. 3 1Google Scholar
[54] Press F, Harkrider D G, Seafeldt C A 1961 Bull. Seismol. Soc. Am. 51 495Google Scholar
[55] Thrower E N 1965 J. Sound Vib. 2 210Google Scholar
[56] Watson T H 1970 Bull. Seismol. Soc. Am. 60 161Google Scholar
[57] Fred, Schwab 1970 Bull. Seismol. Soc. Am. 60 1491Google Scholar
[58] Schwab F A, Knopoff L 1972 Methods in Computational Physics: Advances in Research and Applications (Vol. 11) (New York: Academic Press) pp87–180
[59] Mal A K, Kundu T 1987 Review of Progress in Quantitative NDE (Vol. 6) (New York: Springer US) pp109–116
[60] M. J. S. Lowe 1993 Ph. D. Dissertation (London: University of London)
[61] Barshinger J N, Rose J L 2004 IEEE T. Ultrason. Ferr. 51 1547Google Scholar
[62] 刘增华, 何存富, 吴斌 2005 无损检测 27 225Google Scholar
Liu Z H, He C F, Wu B 2005 Non Destructive Testing 27 225Google Scholar
[63] 龚家元 2010 硕士学位论文(哈尔滨: 哈尔滨工程大学)
Gong J Y 2010 M. S. Dissertation (Harbin: Harbin Engineering University) (in Chinese)
[64] 马丁一, 张宇翔, 谢志南, 高家辉, 殷敬伟 2019 声学技术 4 479
Ma D Y, Zhang Y X, Xie Z N, Gao J H, Yin J W 2019 Technic. Acoustics 4 479
[65] 赵凤文 1991 哈尔滨船舶工程学院学报 2 110
Zhao S W 1991 J. Harbin Engineer. Univ. 2 110
[66] Adamou A T I, Craster R V 2004 J. Acoust. Soc. Am. 116 1524Google Scholar
[67] Karpfinger F, Gurevich B, Bakulin A 2008 J. Acoust. Soc. Am. 124 859Google Scholar
[68] Karpfinger F, Valero H P, Gurevich B, Bakulin A, Sinha B 2010 Geophysics 75 H19Google Scholar
[69] 王献忠, 吴卫国, 庞福振, 孔祥韶 2015 振动与冲击 34 13Google Scholar
Wang X Z, Wu W G, Pang F Z, Kong X S 2015 J. Vibrat. Shock 34 13Google Scholar
[70] Zharnikov T V, Syresin D E, Hsu C J 2013 J. Acoust. Soc. Am. 134 1739Google Scholar
[71] Quintanilla F H, Lowe M, Craster R 2015 AIP Conf. Proc. 1650 739Google Scholar
[72] Sinha, B K, Tiersten H F 1981 J. Appl. Phys. 52 7196Google Scholar
[73] Jen C K, Safaai-Jazi A, Farnell W G 1986 IEEE T. Ultrason. Ferr. 33 634Google Scholar
[74] Porter M B, Reiss E L 1985 J. Acoust. Soc. Am. 77 S13Google Scholar
[75] Brazier-Smith P R, Scott J F M 1991 J. Sound Vib. 145 503Google Scholar
[76] 何世平, 汤渭霖, 范军 2005 声学学报 30 249Google Scholar
He S P, Tang W L, Fan J 2005 Acta Acustica 30 249Google Scholar
[77] Ivansson S 1992 J. Acoust. Soc. Am. 89 1894Google Scholar
[78] Wang N Wang H Z 2010 J. Comput. Acoust. 18 159Google Scholar
[79] Wang H Z, Wang N, Gao D Z 2012 J. Acoust. Soc. Am. 131 1047Google Scholar
[80] Mccammon D F, Mcdaniel S T 1985 J. Acoust. Soc. Am. 77 499Google Scholar
[81] Ewing M, Crary A P, Jr A M T 1934 Physics 5 165Google Scholar
[82] Crary, A P 1954 EOS Transact. Am. Geophys. Union 35 293Google Scholar
[83] Hunkins K 1960 J. Geophys. Res. 65 3459Google Scholar
[84] Schwartz J 1970 Revue Decologie Et De Biologie. Du. Sol. 354
[85] Timco G W, Frederking R M W 1996 Cold Reg. Sci. Technol. 24 1Google Scholar
[86] Cox G F, Weeks W F 1988 Army Cold Regions Research & Engineering Laboratory Crrel Report 88 13
[87] Eicken H, Krouse H R, Kadko D, Perovich D K 2002 J. Geophys. Res. 107 8046Google Scholar
[88] Cox G F N Weeks W F 1974 J. Glaciol. 13 109Google Scholar
[89] Johnston M Timco G W 2002 Proceedings of the 16 th IAHR International Symposium on Ice 2 194
[90] Ackley S F, Hibler W D, Kugzruk F K, Kovacs A, Weeks W F 1974 Oceans IEEE 1 109Google Scholar
[91] Andreas E L, Lange M A, Ackley S F, Wadhams P 1993 J. Geophys. Res-Oceans 98 12Google Scholar
[92] Mcphee M G 2002 J. Geophys. Res-Oceans 107 11Google Scholar
[93] Adolphs U 1999 J. Geophys. Res-Oceans 104 13Google Scholar
[94] Robinson N J, Stevens C L, McPhee M G 2017 Geophys. Res. Lett. 44 1814Google Scholar
[95] Ech-Cherif El-Kettani M, F Luppé, Guillet A 2004 Ultrasonics 42 807Google Scholar
[96] Johnston M, Masterson D, Wright B 2009 Proceedings 20 th POAC Conference 9 120
[97] Marical P, Ech-Cherif El-Kettani M, Predoi M V 2007 Ultrasonics 47 1Google Scholar
[98] Ech-Cherif El-Kettani M, Marical P, Hamitouche Z 2009 IEEE T. Ultrason. Ferr. 56 2023Google Scholar
[99] Oliver J, Crary A P, Cotell R 1954 EOS Transact. Am. Geophys. Union 35 282Google Scholar
[100] Sutherland G Rabault J 2016 J. Geophys. Res-Oceans 121 1984Google Scholar
[101] Marsan D, Weiss J, Larose E, Métaxian J 2012 J. Acoust. Soc. Am. 131 80Google Scholar
[102] Marsan D, Weiss J, Moreau L, Gimbert F, Doble M, Larose E, Grangeon J 2019 J. Acoust. Soc. Am. 145 1600Google Scholar
[103] Moreau L, Lachaud C, Thery R, Predoi M V, Marsan D, Larose E, Weiss J, Montagnat M 2017 J. Acoust. Soc. Am. 142 2873Google Scholar
[104] Moreau L, Boué P, Serripierri A, Weiss J, Hollis D, Pondaven I, Vial B, Garambois S, Larose É, Helmstetter A, Stehly L, Hillers G, Gilbert O 2020 J. Geophys. Res-Oceans 125
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[1] 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 471Google Scholar
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 2014 Appl. Acoust. 33 471Google Scholar
[2] Climate Change Indicators: Arctic Sea Icehttps://www.epa.gov/climate-indicators/climate-change-indicators-arctic-sea-ice [2021-1-1]
[3] 李培基 1996 冰川冻土 18 72Google Scholar
Li P J. 1996 J. Glaciol. Geocryol. 18 72Google Scholar
[4] Grenfell T C, Maykut G A. 1977 J. Glaciol. 18 445Google Scholar
[5] Nakamura N, Oort A H 1988 J. Geophys. Res-Atmos. 93 9510Google Scholar
[6] Magnusdottir G, Deser C, Saravanan R. 2004 J. Climate 17 857Google Scholar
[7] England M R, Polvani L M, Sun L, Deser C, Saravanan R 2020 Nature Geosci. 13 1Google Scholar
[8] Milne A R, Ganton J H 1964 J. Acoust. Soc. Am. 36 855Google Scholar
[9] Xu X Q, Lin J M, Fang S K 2020 Earthquake Research in China 34 264Google Scholar
[10] 朱广平, 殷敬伟, 陈文剑, 胡思为, 周焕玲, 郭龙祥 2017 声学学报 42 152Google Scholar
Zhu G P, Yin J W, Chen W J, Hu S W, Zhou H L, Guo L X 2017 Acta Acustica 42 152Google Scholar
[11] Kinda G B, Simard Y, Gervaise C, Mars J I, Fortier L 2015 J. Acoust. Soc. Am. 138 2034Google Scholar
[12] Tian Y N, Han X, Yin J W, Liu Q Y, Li L 2019 J. Acoust. Soc. Am. 146 2482Google Scholar
[13] Yin J W, Liu B, Zhu G P, Xie Z N 2018 Sensors 18 3461Google Scholar
[14] Schwarz J, Weeks W F. 1977 J. Glaciol. 19 499Google Scholar
[15] Untersteiner N 1986 The Geophysics of Sea Ice (America: Springer US) pp1–8
[16] Lebedev V V 1938 Probl. Arkt. Antarkt. 5 9
[17] 李志军 康建成 2001 冰川冻土 23 383Google Scholar
Li Z J Kang J C 2001 J. Glaciol. Geocryol. 23 383Google Scholar
[18] 李冰洁, 庞小平, 季青 2019 极地研究 31 258Google Scholar
Li B J, Pang X P, Ji Q 2019 Chin. J. Polar Res. 31 258Google Scholar
[19] Press F, Ewing M 1951 Eos Transactions American Geophysical Union 32 673Google Scholar
[20] Petrich C, Eicken H 2010 Sea Ice (2nd Ed.) (America: Wiley-Blackwell) pp23–77
[21] Cox G F N, Richter J A, Weeks W F, Mellor M 1984 a Proceedings of the 3rd International Offshore Mechanics and Arctic Engineering Symposium New Orleans, Louisiana, February 12–17, 1984 p126
[22] Richter-Menge J A, Cox G F N 1984 Proceedings of the 3rd International Offshore Mechanics and Arctic Engineering Symposium New Orleans, Louisiana, February 12–17, 1984 p194
[23] Timco G W, Weeks W F 2010 Cold Reg. Sci. Technol. 60 107Google Scholar
[24] Weeks W F, Gow A J 1980 J. Geophys. Res. 85 137
[25] Stander E, Michel B 1989 Cold Reg. Sci. Technol. 17 153Google Scholar
[26] Diez A, Eisen O 2015 Cryosphere 9 367Google Scholar
[27] Diez A, Eisen O 2015 Cryosphere 9 385Google Scholar
[28] Vaughan M J, Prior D J, Jefferd M, Brantut N, Mitchell T M, Seidemann M 2017 J. Geophys. Res-Sol. 122 7076Google Scholar
[29] Sayers C M 2018 Geophys. J. Int. 1 1
[30] Jeffries M G Wright W H 1988 Proceedings of the 3 rd International Offshore Mechanics and Arctic Engineering Symposium New Orleans, Louisiana, February 12–17, 1984 p201
[31] 孙俊英 2000 冰川冻土 22 3Google Scholar
Sun J Y 2000 J. Glaciol. Geocryol. 22 3Google Scholar
[32] Sato Y 1951 Bulletin of the Earthquake Research Institute University of Tokyo XXIX 223
[33] Miller B E 1990 J. Acoust. Soc. Am. 89 1668Google Scholar
[34] Yang T C, Giellis G R 1994 J. Acoust. Soc. Am. 96 2993Google Scholar
[35] Miklowitz J, Kaul R K 1984 J. Appl. Mech. 46 969
[36] Rose J L 2000 J. Acoust. Soc. Am. 107 1807Google Scholar
[37] Lamb H 1917 Proc. R. Soc. London A93 114
[38] 邓明晰 1996 声学学报 21 429Google Scholar
Deng M X 1996 Acta Acustica 21 429Google Scholar
[39] Zhu Z M, Wu J R 1995 J. Acoust. Soc. Am. 98 1057Google Scholar
[40] Solie L P, Auld B A 1973 J. Acoust. Soc. Am. 54 50Google Scholar
[41] Osborne M F M, Hart S D 1945 J. Acoust. Soc. Am. 17 1Google Scholar
[42] Dayal V, Vinay K K 1989 J. Acoust. Soc. Am. 85 2268Google Scholar
[43] Wu J R, Zhu Z M 1992 J. Acoust. Soc. Am. 91 861Google Scholar
[44] Press F, Ewing M 1951 J. Appl. Phys. 22 892Google Scholar
[45] Landschulze M 2018 Near Surf. Geophys. 16 493Google Scholar
[46] Yang T C, Yates T W 1995 J. Acoust. Soc. Am. 97 971Google Scholar
[47] Graff K F 1975 Wave Motion in Elastic Solid (London: Oxford University Press)
[48] Thomson W T 1950 J. Appl. Phys. 21 89Google Scholar
[49] Haskell N A 1953 Bull. Seismol. Soc. Am. 43 86Google Scholar
[50] Knopoff L A 1964 Bull. Seismol. Soc. Am. 54 431Google Scholar
[51] Randall M J 1967 Bull. Seismol. Soc. Am. 57 1299Google Scholar
[52] Lowe M J S 1995 IEEE T. Ultrason. Ferr. 42 525Google Scholar
[53] Yu L Y, Tian Z H 2015 Nondestruct. Test. Eva. 3 1Google Scholar
[54] Press F, Harkrider D G, Seafeldt C A 1961 Bull. Seismol. Soc. Am. 51 495Google Scholar
[55] Thrower E N 1965 J. Sound Vib. 2 210Google Scholar
[56] Watson T H 1970 Bull. Seismol. Soc. Am. 60 161Google Scholar
[57] Fred, Schwab 1970 Bull. Seismol. Soc. Am. 60 1491Google Scholar
[58] Schwab F A, Knopoff L 1972 Methods in Computational Physics: Advances in Research and Applications (Vol. 11) (New York: Academic Press) pp87–180
[59] Mal A K, Kundu T 1987 Review of Progress in Quantitative NDE (Vol. 6) (New York: Springer US) pp109–116
[60] M. J. S. Lowe 1993 Ph. D. Dissertation (London: University of London)
[61] Barshinger J N, Rose J L 2004 IEEE T. Ultrason. Ferr. 51 1547Google Scholar
[62] 刘增华, 何存富, 吴斌 2005 无损检测 27 225Google Scholar
Liu Z H, He C F, Wu B 2005 Non Destructive Testing 27 225Google Scholar
[63] 龚家元 2010 硕士学位论文(哈尔滨: 哈尔滨工程大学)
Gong J Y 2010 M. S. Dissertation (Harbin: Harbin Engineering University) (in Chinese)
[64] 马丁一, 张宇翔, 谢志南, 高家辉, 殷敬伟 2019 声学技术 4 479
Ma D Y, Zhang Y X, Xie Z N, Gao J H, Yin J W 2019 Technic. Acoustics 4 479
[65] 赵凤文 1991 哈尔滨船舶工程学院学报 2 110
Zhao S W 1991 J. Harbin Engineer. Univ. 2 110
[66] Adamou A T I, Craster R V 2004 J. Acoust. Soc. Am. 116 1524Google Scholar
[67] Karpfinger F, Gurevich B, Bakulin A 2008 J. Acoust. Soc. Am. 124 859Google Scholar
[68] Karpfinger F, Valero H P, Gurevich B, Bakulin A, Sinha B 2010 Geophysics 75 H19Google Scholar
[69] 王献忠, 吴卫国, 庞福振, 孔祥韶 2015 振动与冲击 34 13Google Scholar
Wang X Z, Wu W G, Pang F Z, Kong X S 2015 J. Vibrat. Shock 34 13Google Scholar
[70] Zharnikov T V, Syresin D E, Hsu C J 2013 J. Acoust. Soc. Am. 134 1739Google Scholar
[71] Quintanilla F H, Lowe M, Craster R 2015 AIP Conf. Proc. 1650 739Google Scholar
[72] Sinha, B K, Tiersten H F 1981 J. Appl. Phys. 52 7196Google Scholar
[73] Jen C K, Safaai-Jazi A, Farnell W G 1986 IEEE T. Ultrason. Ferr. 33 634Google Scholar
[74] Porter M B, Reiss E L 1985 J. Acoust. Soc. Am. 77 S13Google Scholar
[75] Brazier-Smith P R, Scott J F M 1991 J. Sound Vib. 145 503Google Scholar
[76] 何世平, 汤渭霖, 范军 2005 声学学报 30 249Google Scholar
He S P, Tang W L, Fan J 2005 Acta Acustica 30 249Google Scholar
[77] Ivansson S 1992 J. Acoust. Soc. Am. 89 1894Google Scholar
[78] Wang N Wang H Z 2010 J. Comput. Acoust. 18 159Google Scholar
[79] Wang H Z, Wang N, Gao D Z 2012 J. Acoust. Soc. Am. 131 1047Google Scholar
[80] Mccammon D F, Mcdaniel S T 1985 J. Acoust. Soc. Am. 77 499Google Scholar
[81] Ewing M, Crary A P, Jr A M T 1934 Physics 5 165Google Scholar
[82] Crary, A P 1954 EOS Transact. Am. Geophys. Union 35 293Google Scholar
[83] Hunkins K 1960 J. Geophys. Res. 65 3459Google Scholar
[84] Schwartz J 1970 Revue Decologie Et De Biologie. Du. Sol. 354
[85] Timco G W, Frederking R M W 1996 Cold Reg. Sci. Technol. 24 1Google Scholar
[86] Cox G F, Weeks W F 1988 Army Cold Regions Research & Engineering Laboratory Crrel Report 88 13
[87] Eicken H, Krouse H R, Kadko D, Perovich D K 2002 J. Geophys. Res. 107 8046Google Scholar
[88] Cox G F N Weeks W F 1974 J. Glaciol. 13 109Google Scholar
[89] Johnston M Timco G W 2002 Proceedings of the 16 th IAHR International Symposium on Ice 2 194
[90] Ackley S F, Hibler W D, Kugzruk F K, Kovacs A, Weeks W F 1974 Oceans IEEE 1 109Google Scholar
[91] Andreas E L, Lange M A, Ackley S F, Wadhams P 1993 J. Geophys. Res-Oceans 98 12Google Scholar
[92] Mcphee M G 2002 J. Geophys. Res-Oceans 107 11Google Scholar
[93] Adolphs U 1999 J. Geophys. Res-Oceans 104 13Google Scholar
[94] Robinson N J, Stevens C L, McPhee M G 2017 Geophys. Res. Lett. 44 1814Google Scholar
[95] Ech-Cherif El-Kettani M, F Luppé, Guillet A 2004 Ultrasonics 42 807Google Scholar
[96] Johnston M, Masterson D, Wright B 2009 Proceedings 20 th POAC Conference 9 120
[97] Marical P, Ech-Cherif El-Kettani M, Predoi M V 2007 Ultrasonics 47 1Google Scholar
[98] Ech-Cherif El-Kettani M, Marical P, Hamitouche Z 2009 IEEE T. Ultrason. Ferr. 56 2023Google Scholar
[99] Oliver J, Crary A P, Cotell R 1954 EOS Transact. Am. Geophys. Union 35 282Google Scholar
[100] Sutherland G Rabault J 2016 J. Geophys. Res-Oceans 121 1984Google Scholar
[101] Marsan D, Weiss J, Larose E, Métaxian J 2012 J. Acoust. Soc. Am. 131 80Google Scholar
[102] Marsan D, Weiss J, Moreau L, Gimbert F, Doble M, Larose E, Grangeon J 2019 J. Acoust. Soc. Am. 145 1600Google Scholar
[103] Moreau L, Lachaud C, Thery R, Predoi M V, Marsan D, Larose E, Weiss J, Montagnat M 2017 J. Acoust. Soc. Am. 142 2873Google Scholar
[104] Moreau L, Boué P, Serripierri A, Weiss J, Hollis D, Pondaven I, Vial B, Garambois S, Larose É, Helmstetter A, Stehly L, Hillers G, Gilbert O 2020 J. Geophys. Res-Oceans 125
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