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Complex zone of the ocean is often characterized by horizontal variations of environmental parameters(bathymetry, sound speed profile, bottom properties etc.), initiating redistribution of the sound field in horizontal plane, which is the so-called three-dimensional (3D) effect. Based on the adiabatic mode parabolic equation method, modeling of 3D effects is carried out, in which the eigenvalues and eigenfunctions are calculated by the standard normal mode model KRAKEN, and the amplitude corresponding to each mode is computed by the wide-angle parabolic equation model RAM. The present 3D model is very efficient and can give clear physical meaning, but it can be only applied to a waveguide whose properties vary gradually with horizontal range due to the adiabatic assumption between different modes. This model is then used to analyze the horizontal refraction caused by internal waves and by a coastal wedge. The numerical results show that there are several areas in the horizontal plane, corresponding to different structures of intensity distributions. Moreover, the redistribution of the sound field in horizontal plane depends on source frequency and mode number. Frequency and modal dependences lead to variations of spectrum, distortion of signal with some spectrum, and spatiotemporal fluctuations of the sound field.
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Keywords:
- three-dimensional sound propagation /
- adiabatic mode parabolic equation /
- internal waves /
- coastal slope
[1] Tappert F D 1977 Wave Propagation and Underwater Acoustics (New York: Springer) p224
[2] Collis J M, Siegmann W L, Jensen F B Zampolli M, Ksel E T, Collins M D 2008 J. Acoust. Soc. Am. 123 51
[3] Pierce A D 1965 J. Acoust Soc. Am. 37 19
[4] Evans R B 1983 J. Acoust Soc. Am. 74 188
[5] Zhang R H, Liu H, He Y, Akulichev V A 1994 Acta Acust. 19 408 (in Chinese) [张仁和, 刘红, 何怡, Akulichev V A 1994 声学学报 19 408]
[6] Yang C M, Luo W Y, Zhang R H, Qin J X 2013 Acta Phys. Sin. 62 094302 (in Chinese) [杨春梅, 骆文于, 张仁和, 秦继兴 2013 物理学报 62 094302]
[7] Godin O A 1998 J. Acoust. Soc. Am. 103 159
[8] Athanassoulis G A, Belibassakis K A, Mitsoudis D A Kampanis N A, Dougalis V A 2008 J. Comput. Acoust. 16 83
[9] Schmidt H, Glattetre J 1985 J. Acoust. Soc. Am. 78 2105
[10] Collins M D, Schmidt H, Siegmann W L 2000 J. Acoust. Soc. Am 107 1964
[11] Stephen R A 1988 Rev. Geophys. 26 445
[12] Thompson L L 2006 J. Acoust. Soc. Am. 119 1315
[13] Zampolli M, Tesei A, Jensen F B Malm N, Blottman III J B 2007 J. Acoust. Soc. Am. 122 1472
[14] Cornyn J J 1973 GRASS: A Digital-Computer Ray-tracing and Transmission-Loss-Prediction System (Washington, DC: Naval Research Laboratory) Technical Report 7621
[15] Porter M B, Bucker H P 1987 J. Acoust. Soc. Am. 82 1349
[16] Felsen L B 1981 J. Acoust. Soc. Am. 69 352
[17] Abawi A T, Kuperman W A, Collins M D 1997 J. Acoust. Soc. Am. 102 233
[18] Perkins J S, Baer R N 1982 . J. Acoust. Soc. Am. 72 515
[19] Marfurt K J 1984 Geophysics 49 533
[20] Baer R N 1981 . J. Acoust. Soc. Am. 69 70
[21] Chiu C S, Ehret L L 1990 Computational Acoustics II: Ocean-Acoustic Models and Supercomputing (Amsterdam: Elsevier) p182
[22] Luo W Y, Schmidt H 2009 J. Acoust. Soc. Am. 125 52
[23] Lee D, Botsea G, Siegmann W L 1992 J. Acoust. Soc. Am. 91 3192
[24] Piao S C 1999 Ph. D. Dissertation (Harbin: Harbin Engineering University) (in Chinese) [朴胜春 1999 博士学位论文(哈尔滨: 哈尔滨工程大学)]
[25] Jones R M, Riley J P, Georges T M 1986 HARPO: A Versatile Three-dimensional Hamiltonian Ray-tracing Program for Acoustic Waves in an Ocean with Irregular Bottom (Boulder, Colorado: Environmental Research Laboratories) Technical Report
[26] Collins M D 1993 J. Acoust. Soc. Am. 94 2269
[27] Peng Z H, Zhang R H 2005 Acta Acust. 30 97 (in Chinese) [彭朝晖, 张仁和 2005 声学学报 30 97]
[28] Fawcett J A, Dawson T W 1990 J. Acoust. Soc. Am. 88 1913
[29] Orris G J, Collins M D 1994 J. Acoust. Soc. Am. 96 1725
[30] Qin J X, Luo W Y, Zhang R H Yang C M 2013 Chin. Phys. Lett. 30 114301
[31] Katsnelson B G, Pereselkov S A 2000 Acoust. Phys. 46 684
[32] Katsnelson B G, Lynch J, Tshoidze A V 2007 Acoust. Phys. 53 611
[33] Porter M B 1991 The KRAKEN Normal Mode Program (La Spezia: SACLANT Undersea Research Centre) Technical Report SM-245
[34] Collins M D User's Guide for RAM Versions 1.0 and 1.0p. (Washington, DC: Naval Research Laboratory)
[35] Brekhovskikh L M, Lysanov Yu P 2003 Fundamentals of Ocean Acoustics (3rd Ed.) (New York: Springer-Verlag) pp149-158
[36] Collins M D 1993 J. Acoust. Soc. Am. 93 1736
[37] Collins M D 1992 J. Acoust. Soc. Am. 92 2069
[38] Katsnelson B G, Malykhin A Yu 2012 Acoust. Phys. 58 301
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[1] Tappert F D 1977 Wave Propagation and Underwater Acoustics (New York: Springer) p224
[2] Collis J M, Siegmann W L, Jensen F B Zampolli M, Ksel E T, Collins M D 2008 J. Acoust. Soc. Am. 123 51
[3] Pierce A D 1965 J. Acoust Soc. Am. 37 19
[4] Evans R B 1983 J. Acoust Soc. Am. 74 188
[5] Zhang R H, Liu H, He Y, Akulichev V A 1994 Acta Acust. 19 408 (in Chinese) [张仁和, 刘红, 何怡, Akulichev V A 1994 声学学报 19 408]
[6] Yang C M, Luo W Y, Zhang R H, Qin J X 2013 Acta Phys. Sin. 62 094302 (in Chinese) [杨春梅, 骆文于, 张仁和, 秦继兴 2013 物理学报 62 094302]
[7] Godin O A 1998 J. Acoust. Soc. Am. 103 159
[8] Athanassoulis G A, Belibassakis K A, Mitsoudis D A Kampanis N A, Dougalis V A 2008 J. Comput. Acoust. 16 83
[9] Schmidt H, Glattetre J 1985 J. Acoust. Soc. Am. 78 2105
[10] Collins M D, Schmidt H, Siegmann W L 2000 J. Acoust. Soc. Am 107 1964
[11] Stephen R A 1988 Rev. Geophys. 26 445
[12] Thompson L L 2006 J. Acoust. Soc. Am. 119 1315
[13] Zampolli M, Tesei A, Jensen F B Malm N, Blottman III J B 2007 J. Acoust. Soc. Am. 122 1472
[14] Cornyn J J 1973 GRASS: A Digital-Computer Ray-tracing and Transmission-Loss-Prediction System (Washington, DC: Naval Research Laboratory) Technical Report 7621
[15] Porter M B, Bucker H P 1987 J. Acoust. Soc. Am. 82 1349
[16] Felsen L B 1981 J. Acoust. Soc. Am. 69 352
[17] Abawi A T, Kuperman W A, Collins M D 1997 J. Acoust. Soc. Am. 102 233
[18] Perkins J S, Baer R N 1982 . J. Acoust. Soc. Am. 72 515
[19] Marfurt K J 1984 Geophysics 49 533
[20] Baer R N 1981 . J. Acoust. Soc. Am. 69 70
[21] Chiu C S, Ehret L L 1990 Computational Acoustics II: Ocean-Acoustic Models and Supercomputing (Amsterdam: Elsevier) p182
[22] Luo W Y, Schmidt H 2009 J. Acoust. Soc. Am. 125 52
[23] Lee D, Botsea G, Siegmann W L 1992 J. Acoust. Soc. Am. 91 3192
[24] Piao S C 1999 Ph. D. Dissertation (Harbin: Harbin Engineering University) (in Chinese) [朴胜春 1999 博士学位论文(哈尔滨: 哈尔滨工程大学)]
[25] Jones R M, Riley J P, Georges T M 1986 HARPO: A Versatile Three-dimensional Hamiltonian Ray-tracing Program for Acoustic Waves in an Ocean with Irregular Bottom (Boulder, Colorado: Environmental Research Laboratories) Technical Report
[26] Collins M D 1993 J. Acoust. Soc. Am. 94 2269
[27] Peng Z H, Zhang R H 2005 Acta Acust. 30 97 (in Chinese) [彭朝晖, 张仁和 2005 声学学报 30 97]
[28] Fawcett J A, Dawson T W 1990 J. Acoust. Soc. Am. 88 1913
[29] Orris G J, Collins M D 1994 J. Acoust. Soc. Am. 96 1725
[30] Qin J X, Luo W Y, Zhang R H Yang C M 2013 Chin. Phys. Lett. 30 114301
[31] Katsnelson B G, Pereselkov S A 2000 Acoust. Phys. 46 684
[32] Katsnelson B G, Lynch J, Tshoidze A V 2007 Acoust. Phys. 53 611
[33] Porter M B 1991 The KRAKEN Normal Mode Program (La Spezia: SACLANT Undersea Research Centre) Technical Report SM-245
[34] Collins M D User's Guide for RAM Versions 1.0 and 1.0p. (Washington, DC: Naval Research Laboratory)
[35] Brekhovskikh L M, Lysanov Yu P 2003 Fundamentals of Ocean Acoustics (3rd Ed.) (New York: Springer-Verlag) pp149-158
[36] Collins M D 1993 J. Acoust. Soc. Am. 93 1736
[37] Collins M D 1992 J. Acoust. Soc. Am. 92 2069
[38] Katsnelson B G, Malykhin A Yu 2012 Acoust. Phys. 58 301
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