浅海波导中目标声散射特性研究
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摘要
浅海，作为水下活动中具有重要战略地位的区域，日益受到人们的关注。本文主要是对浅海波导中目标声散射问题进行研究。
在理论分析中，采用了F.Ingenito简正波展开法和N.C.Makris波数积分法，给出了浅海波导中目标散射场的简正波展开解和波数积分解的推导过程，并对两种求解方法进行了比较，发现了两者间的许多相似性和内在统一性。
在数值计算中，首先对目标散射场的简正波展开解和波数积分解分别实现了数值计算。对简正波展开解的数值计算得到了较满意的结果；在对波数积分解数值计算时，采用了FFP技术，同时探讨了目标散射场波数积分解积分核函数随水平波数的变化特点，为今后改进目标散射场波数积分解数值计算方法，采用非等间隔的波数采样法，提供了依据。
最后，利用简正波展开解对各种浅海波导条件下的目标散射场进行了系统计算，展开了对浅海波导中目标散射特性的探讨。讨论了绝对硬和绝对软两种球状目标，在理想波导情况、不同波导厚度情况，以及不同海底介质特性、不同海水介质特性，不同海水声速分布特性等各种情况下的目标散射特性。通过分析发现：浅海波导中目标散射场具有明显的相干特性；相干距离起点随着波导厚度的增大而增远；在r-φ水平平面上，目标散射场随距离强弱相间；在r-z垂直平面上，目标散射场形成了明显的相干波束；当声速为均匀等声速剖面时，目标散射场在波导中呈现出较好的对称性；当声速剖面为负梯度分布时，目标散射场在波导中形成的波束有向下弯曲的明显特征；当声速剖面为正梯度分布时，目标散射场在波导中形成的波束呈现向上弯曲的特征。
The shallow water, as an important region in underwater activities, is drawing more and more attention. In this paper, the scattering of an object submerged in a shallow water waveguide is discussed.The normal mode formulation developed by F. Ingenito and the spectral formulation by N. C. Makris for calculating the scattered field of an object submerged in a waveguide are adopted , and the detailed derivations of the modal formula and the spectral formula of the scattered field from the original Kirchhoff's integral equation are given. Through comparison, the similarity and unity of the two deriving method is discussed..The two formulations are then numerically implemented for calculating the scattered field of an object submerged in a shallow water waveguide. The modal formulation is successfully implemented. In the implementation of the spectral formulation, the FFP technology is used to avoid the mixing-up effect introduced by discretization, the core function of wave number integrals of the scattered field is discussed and some interesting properties are detected, and the improvement scheme for the implementation of the spectral formulation is proposed.Finally, the scattered fields of rigid and soft spheres submerged in a shallow water waveguide with different waveguide conditions, such as various boundary conditions, different depths of the waveguide, various media properties, different sound speed profiles, are computed by the modal formula. The scattering characteristics of an object submerged in a shallow water waveguide are then revealed. The coherence of the scattered field is founded. The property that the beginning range of the coherence becomes far with the increasing of the depth of the waveguide isobserved. In the r-φ horizontal slice, the scattered fields alternate with the highand low SPL; in the r-z vertical slice, the scattered fields form obvious coherent wave beams, which turn to the low sound velocity when there is a certain sound profile and show good symmetry in waveguide when the sound velocity is constant.
在理论分析中，采用了F.Ingenito简正波展开法和N.C.Makris波数积分法，给出了浅海波导中目标散射场的简正波展开解和波数积分解的推导过程，并对两种求解方法进行了比较，发现了两者间的许多相似性和内在统一性。
在数值计算中，首先对目标散射场的简正波展开解和波数积分解分别实现了数值计算。对简正波展开解的数值计算得到了较满意的结果；在对波数积分解数值计算时，采用了FFP技术，同时探讨了目标散射场波数积分解积分核函数随水平波数的变化特点，为今后改进目标散射场波数积分解数值计算方法，采用非等间隔的波数采样法，提供了依据。
最后，利用简正波展开解对各种浅海波导条件下的目标散射场进行了系统计算，展开了对浅海波导中目标散射特性的探讨。讨论了绝对硬和绝对软两种球状目标，在理想波导情况、不同波导厚度情况，以及不同海底介质特性、不同海水介质特性，不同海水声速分布特性等各种情况下的目标散射特性。通过分析发现：浅海波导中目标散射场具有明显的相干特性；相干距离起点随着波导厚度的增大而增远；在r-φ水平平面上，目标散射场随距离强弱相间；在r-z垂直平面上，目标散射场形成了明显的相干波束；当声速为均匀等声速剖面时，目标散射场在波导中呈现出较好的对称性；当声速剖面为负梯度分布时，目标散射场在波导中形成的波束有向下弯曲的明显特征；当声速剖面为正梯度分布时，目标散射场在波导中形成的波束呈现向上弯曲的特征。
The shallow water, as an important region in underwater activities, is drawing more and more attention. In this paper, the scattering of an object submerged in a shallow water waveguide is discussed.The normal mode formulation developed by F. Ingenito and the spectral formulation by N. C. Makris for calculating the scattered field of an object submerged in a waveguide are adopted , and the detailed derivations of the modal formula and the spectral formula of the scattered field from the original Kirchhoff's integral equation are given. Through comparison, the similarity and unity of the two deriving method is discussed..The two formulations are then numerically implemented for calculating the scattered field of an object submerged in a shallow water waveguide. The modal formulation is successfully implemented. In the implementation of the spectral formulation, the FFP technology is used to avoid the mixing-up effect introduced by discretization, the core function of wave number integrals of the scattered field is discussed and some interesting properties are detected, and the improvement scheme for the implementation of the spectral formulation is proposed.Finally, the scattered fields of rigid and soft spheres submerged in a shallow water waveguide with different waveguide conditions, such as various boundary conditions, different depths of the waveguide, various media properties, different sound speed profiles, are computed by the modal formula. The scattering characteristics of an object submerged in a shallow water waveguide are then revealed. The coherence of the scattered field is founded. The property that the beginning range of the coherence becomes far with the increasing of the depth of the waveguide isobserved. In the r-φ horizontal slice, the scattered fields alternate with the highand low SPL; in the r-z vertical slice, the scattered fields form obvious coherent wave beams, which turn to the low sound velocity when there is a certain sound profile and show good symmetry in waveguide when the sound velocity is constant.
引文
[1] Rayleigh, Lord. The Theory of sound. Dover, 1945.
[2] 何祚镛，赵玉芳．声学理论基础，国防工业山版社．(1981)．
[3] G. J. Burke et al, An integro-differential equation approach to acoustic scattering from fluid-immersed elastic bodies, J. Comput. Phys. , 1997, 10: 22-39.
[4] P. C. Waterman, New formulation of acoustic scattering. J. Acoust. Soc. Am., 1969, 45: 1417.
[5] J. H. Su, V. V. Varadan, V. K. Varadan, Acoustic wave scattering by a finite elastic cylinder in water. J. Acoust. Soc. Am., 1980, 68: 686.
[6] S. K. Numrick, V. V. Varadan, V. K. Varadan, Scattering of acoustic waves by finite elastic cylinder immersed in water. J. Acoust. Soc. Am. , 1981, 70: 1407.
[7] J. T. Hunt et al, A finite element approach to acoustic scattering from elastic structures, J. Acoust. Soc. Am. , 1974, 55: 269.
[8] G. T. Schuster and L. G. Smith, "Modeling scatterers embedded in a plane-layered media by a hybrid Haskell-Thomson and boundary integral equation method," J. Acoust. Soc. Am. , 1985, 78: 1387-1394.
[9] 汤渭霖，奇异点展开法(SEM)与共振散射理论(RST)之间的联系，声学学报，1991，16：199-208．
[10] 汤渭霖，可分离变量水下弹性体的纯弹性共振散射，声学学报，1995，20(6)：456-465．
[11] 刘国利、汤渭霖，平面声波斜入射到水中无限长圆柱壳体的纯弹性共振散射，声学学报，1996，21(5)：805-814．
[12] 徐贵英、丁玮、阎宜生、赵俊渭、赵日吕，双基地声呐目标特性实验研究，西北工业大学学报，1997，15(3)：476-481．
[13] 赵俊渭、 丁玮、阎宜生、赵日吕、王荣庆、王之程，收发分置水下目标散射特性的实验研究，声学学报，1997，22(2)：123-131．
[14] 张小凤、赵俊渭、王荣庆、韩静，双基地声呐散射声场的建模与仿真，系统仿真学报，2002，14(5)：562-565．
[15] 杨士莪，沉底和掩埋水雷探测的基础研究论文集，中科院东海研究站，1991，pp．6-23．
[16] 王鸿振、郭梵，声场声信息国家重点实验室年报Ⅰ，声学研究所，1991，pp．293-298．
[17] 徐海亭、涂哲民，声学学报，1995，20：26-32．
[18] 布列霍夫斯基赫，《分层介质中的波》，第二版，科学出版社，1985．
[19] R. H. Hackman and G. S. Sammelmann, Acoustic Scattering in an Inhomogeneous Waveguide: Theory. J. Acoust. Soc. Am. 1986, 80: 1447-1458.
[20] R. H. Hackman and G. S. Sammelmann, Multiple scattering analysis for a target in an ocean waveguide. J. Acoust. Soc. Am. 1988, 84: 1813-1825.
[21] A. Bostrom, Wave Motion 2, 167-184 (1980).
[22] G. V. Norton, and M. F. Werby, J. Appl. Phys., 1991, 70: 4101-4112.
[23] Yu. A. Kravtsov, V. M. Kuz' kin, and V. G. Petnikov, Sov. Phys. Acoust. 1984, 30: 199-202.
[24] F. Ingenito, Scattering from an object in a stratified medium. J. Acoust. Soc. Am. 1987, 82: 2051-2059.
[25] M. D. Collins and M. F. Werby, A parabolic equation model for scattering in the ocean. J. Acoust. Soc. Am: 1989, 85: 1895-1902.
[26] J. S. Perkins, W. A. Kuperman, K. D. Heaney, and G. T. Murphy, Scattering from an object in a three-dimensional ocean. Proceedings of the 20th Annual International Meeting of the Technical Cooperation Subgroup, Subgroup G, Technical Panel 9, October 1991.
[27] J. S. Perkins, W. A. Kuperman, L. E. Tinker, and G. T. Murphy, Active matched field processing. J. Acoust. Soc. Am., 1992, 91: 2366.
[28] N. C. Makris, F. Ingenito, and W. A. Kuperman, Detection of a submerged object insonified by surface noise in an ocean waveguide. J. Acoust. Soc. Am., 1994, 96: 1703-1724.
[29] N. C. Makris and D. H. Cato, Acoustic tracking of non-vocalizing whales usig the scattered field of vocalizing whales, in Proceedings of the Australian Acoustical Society, Sydney, Australia, 1994.
[30] N. C. Makris, A spectral approach to 3-D object sattering in layered media applied to scattering from submerged spheres. J. Acoust. Soc. Am., 1998, 104:2105-2113;1999, 106:518(Erratum).
[31] N. C. Makris and P. Ratilal, A unified model for reverberation and submerged object scattering in a stratified ocean waveguide. J. Acoust. Soc. Am. , 2001,109:909-941 .
[32] Purnima Ratilal and Nicholas C. Makris, Extinction theorem for object scattering in a stratified medium, J. Acoust. Soc. Am., 2001, 110(6):2924-2945.
[33] Purnima Ratilal, Yisan Lai, and Nicholas C. Makris, Validity of the sonar equation and Babinet' s principle for scattering in a stratified medium. J. Acoust. Soc. Am., 2002, 112(5), Pt. 1:1797-1816.
[34] Jensen E B., W. A. Kuperman M. B. Porter. H. Scbmidt 著 张润中，唐宗瑜译 《计算海洋声学》杭州：中国船舶重工集团公司 七一五研究所，2000，pp179-181．
[35] P．M．莫尔斯，K．U．英格特，《理论声学》，第一版，北京：科学出版社，1984，pp395．
[36] Yu. A. Kravtsov, V. M. Kuz'kin, and V. G. Petnikov, Sov. Phys. Acoust., 1984, 30:199-202.
[37] M. Abromovitz and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Gaithersburg, MD, 1964, Applied Mathematics Series 55, P.437.
[38] 同文献[35], pp153-160.
[39] F. R. DiNapoli and R. B. Deavenport, Theoretical and numerical Green's function solution in a plane layered medium, J. Acoust. Soc. Am., 1980, 67:92-105.
[40] J. J. Bowman, T. B. A. Senior, and P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes, 1969, (North-Holland, Amsterdam).
[2] 何祚镛，赵玉芳．声学理论基础，国防工业山版社．(1981)．
[3] G. J. Burke et al, An integro-differential equation approach to acoustic scattering from fluid-immersed elastic bodies, J. Comput. Phys. , 1997, 10: 22-39.
[4] P. C. Waterman, New formulation of acoustic scattering. J. Acoust. Soc. Am., 1969, 45: 1417.
[5] J. H. Su, V. V. Varadan, V. K. Varadan, Acoustic wave scattering by a finite elastic cylinder in water. J. Acoust. Soc. Am., 1980, 68: 686.
[6] S. K. Numrick, V. V. Varadan, V. K. Varadan, Scattering of acoustic waves by finite elastic cylinder immersed in water. J. Acoust. Soc. Am. , 1981, 70: 1407.
[7] J. T. Hunt et al, A finite element approach to acoustic scattering from elastic structures, J. Acoust. Soc. Am. , 1974, 55: 269.
[8] G. T. Schuster and L. G. Smith, "Modeling scatterers embedded in a plane-layered media by a hybrid Haskell-Thomson and boundary integral equation method," J. Acoust. Soc. Am. , 1985, 78: 1387-1394.
[9] 汤渭霖，奇异点展开法(SEM)与共振散射理论(RST)之间的联系，声学学报，1991，16：199-208．
[10] 汤渭霖，可分离变量水下弹性体的纯弹性共振散射，声学学报，1995，20(6)：456-465．
[11] 刘国利、汤渭霖，平面声波斜入射到水中无限长圆柱壳体的纯弹性共振散射，声学学报，1996，21(5)：805-814．
[12] 徐贵英、丁玮、阎宜生、赵俊渭、赵日吕，双基地声呐目标特性实验研究，西北工业大学学报，1997，15(3)：476-481．
[13] 赵俊渭、 丁玮、阎宜生、赵日吕、王荣庆、王之程，收发分置水下目标散射特性的实验研究，声学学报，1997，22(2)：123-131．
[14] 张小凤、赵俊渭、王荣庆、韩静，双基地声呐散射声场的建模与仿真，系统仿真学报，2002，14(5)：562-565．
[15] 杨士莪，沉底和掩埋水雷探测的基础研究论文集，中科院东海研究站，1991，pp．6-23．
[16] 王鸿振、郭梵，声场声信息国家重点实验室年报Ⅰ，声学研究所，1991，pp．293-298．
[17] 徐海亭、涂哲民，声学学报，1995，20：26-32．
[18] 布列霍夫斯基赫，《分层介质中的波》，第二版，科学出版社，1985．
[19] R. H. Hackman and G. S. Sammelmann, Acoustic Scattering in an Inhomogeneous Waveguide: Theory. J. Acoust. Soc. Am. 1986, 80: 1447-1458.
[20] R. H. Hackman and G. S. Sammelmann, Multiple scattering analysis for a target in an ocean waveguide. J. Acoust. Soc. Am. 1988, 84: 1813-1825.
[21] A. Bostrom, Wave Motion 2, 167-184 (1980).
[22] G. V. Norton, and M. F. Werby, J. Appl. Phys., 1991, 70: 4101-4112.
[23] Yu. A. Kravtsov, V. M. Kuz' kin, and V. G. Petnikov, Sov. Phys. Acoust. 1984, 30: 199-202.
[24] F. Ingenito, Scattering from an object in a stratified medium. J. Acoust. Soc. Am. 1987, 82: 2051-2059.
[25] M. D. Collins and M. F. Werby, A parabolic equation model for scattering in the ocean. J. Acoust. Soc. Am: 1989, 85: 1895-1902.
[26] J. S. Perkins, W. A. Kuperman, K. D. Heaney, and G. T. Murphy, Scattering from an object in a three-dimensional ocean. Proceedings of the 20th Annual International Meeting of the Technical Cooperation Subgroup, Subgroup G, Technical Panel 9, October 1991.
[27] J. S. Perkins, W. A. Kuperman, L. E. Tinker, and G. T. Murphy, Active matched field processing. J. Acoust. Soc. Am., 1992, 91: 2366.
[28] N. C. Makris, F. Ingenito, and W. A. Kuperman, Detection of a submerged object insonified by surface noise in an ocean waveguide. J. Acoust. Soc. Am., 1994, 96: 1703-1724.
[29] N. C. Makris and D. H. Cato, Acoustic tracking of non-vocalizing whales usig the scattered field of vocalizing whales, in Proceedings of the Australian Acoustical Society, Sydney, Australia, 1994.
[30] N. C. Makris, A spectral approach to 3-D object sattering in layered media applied to scattering from submerged spheres. J. Acoust. Soc. Am., 1998, 104:2105-2113;1999, 106:518(Erratum).
[31] N. C. Makris and P. Ratilal, A unified model for reverberation and submerged object scattering in a stratified ocean waveguide. J. Acoust. Soc. Am. , 2001,109:909-941 .
[32] Purnima Ratilal and Nicholas C. Makris, Extinction theorem for object scattering in a stratified medium, J. Acoust. Soc. Am., 2001, 110(6):2924-2945.
[33] Purnima Ratilal, Yisan Lai, and Nicholas C. Makris, Validity of the sonar equation and Babinet' s principle for scattering in a stratified medium. J. Acoust. Soc. Am., 2002, 112(5), Pt. 1:1797-1816.
[34] Jensen E B., W. A. Kuperman M. B. Porter. H. Scbmidt 著 张润中，唐宗瑜译 《计算海洋声学》杭州：中国船舶重工集团公司 七一五研究所，2000，pp179-181．
[35] P．M．莫尔斯，K．U．英格特，《理论声学》，第一版，北京：科学出版社，1984，pp395．
[36] Yu. A. Kravtsov, V. M. Kuz'kin, and V. G. Petnikov, Sov. Phys. Acoust., 1984, 30:199-202.
[37] M. Abromovitz and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Gaithersburg, MD, 1964, Applied Mathematics Series 55, P.437.
[38] 同文献[35], pp153-160.
[39] F. R. DiNapoli and R. B. Deavenport, Theoretical and numerical Green's function solution in a plane layered medium, J. Acoust. Soc. Am., 1980, 67:92-105.
[40] J. J. Bowman, T. B. A. Senior, and P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes, 1969, (North-Holland, Amsterdam).