Some Properties on the Far-Field Pattern of Scattering by a Penetrable Obstacle in an Ocean Waveguide

PAN Wen-feng; YOU Yun-xiang; MIAO Guo-ping; LI Zhuo-qiu

Volume 29 Issue 2

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Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(2): 217-227

PAN Wen-feng, YOU Yun-xiang, MIAO Guo-ping, LI Zhuo-qiu. Some Properties on the Far-Field Pattern of Scattering by a Penetrable Obstacle in an Ocean Waveguide[J]. Applied Mathematics and Mechanics, 2008, 29(2): 217-227.

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Some Properties on the Far-Field Pattern of Scattering by a Penetrable Obstacle in an Ocean Waveguide

1.
School of Science, Wuhan University of Technology, Wuhan 430070, P. R. China;

Received Date: 2007-08-14
Rev Recd Date: 2008-01-03
Publish Date: 2008-02-15

Abstract

Abstract

The properties of propagation far-field patterns corresponding to the scattering of time harmonic acoustic waves by a bounded penetrable obstacle in an ocean waveguide were concerned with.The sets of solutions to the transmission problem were constructed such that the restriction of these solutions to the boundary of the penetrable obstacle is dense in a Hilbert space.Then conditions under which a set of propagation far-field patterns is complete in a Hilbert space were determined.These properties are important in investigating inverse transmission problems in an ocean waveguide.
- oceanic waveguide,
- penetrable object,
- far-field pattern,
- completeness,
- denseness

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References

[1]	Colton D,Kirsch A. Dense sets and far-field patterns in acoustic wave propagation[J].SIAM J Math Anal,1984,15(5):996-1009. doi: 10.1137/0515076
[2]	Kirsch A. Properties of far-field operator in acoustic scattering[J].Math Meth Appl Sci,1989,11(9):773-787. doi: 10.1002/mma.1670110604
[3]	Colton D,Monk P.The inverse scattering problem for time-harmonic acoustic waves in a penetrable medium[J].J Mech Appl Math,1987,40(2):189-212. doi: 10.1093/qjmam/40.2.189
[4]	Colton D, Kress R.Inverse Acoustic and Electromagnetic Scattering Theory[M].2nd Ed.Berlin:Springer,1998.
[5]	Colton D, Coyle C, Monk P.Recent developments in inverse acoustic scattering theory[J].SIAM Rev,2000,42(3):369-414. doi: 10.1137/S0036144500367337
[6]	MIAO Guo-ping, YOU Yun-xiang, LIU Ying-zhong.A numerical method for shape reconstruction problem in acoustic scattering[J].Inverse Problems in Engineering,2000,8(3):229-249. doi: 10.1080/174159700088027729
[7]	YOU Yun-xiang, MIAO Guo-ping, LIU Ying-zhong. A numerical method for an inverse transmission problem[J].Inverse Problems,2001,17(3):421-435. doi: 10.1088/0266-5611/17/3/304
[8]	YOU Yun-xiang, MIAO Guo-ping, LIU Ying-zhong. A numerical method for solving the limited aperture problem in three-dimensional inverse obstacle scattering[J].International Journal of Nonlinear Science and Numerical Simulation,2001，2(1):29-42.
[9]	YOU Yun-xiang, MIAO Guo-ping, LIU Ying-zhong. The numerical solution of the three dimensional inverse obstacle scattering problem for point source generated wave fields[J].Inverse Problems in Engineering,2002,10(3):215-233. doi: 10.1080/10682760290024454
[10]	YOU Yun-xiang, Yap F F,MIAO Guo-ping.A numerical method for the inverse impedance obstacle problem[J].Acta Acustica United With Acustica,2002,88(1):1-13.
[11]	尤云祥，缪国平.刚性目标形状反演的一种非线性最优化方法[J].应用数学和力学，2003,24(10):1090-1100.
[12]	尤云祥, 缪国平.用近场声学测量信息可视化多个三维障碍物的一种快速算法[J].物理学报,2001,50(6):1103-1109.
[13]	YOU Yun-xiang, MIAO Guo-ping, LIU Ying-zhong. A fast method for acoustic imaging of multiple three-dimensional objects[J].J Acoust Soc Am,2000,108(1):31-37.[JP3]. YOU Yun-xiang, MIAO Guo-ping, LIU Ying-zhong. A simple method for visualizing multiple three dimensional objects from near field data with point source excitation[J].Acta Acustica,2001,87(1):1-10. doi: 10.1121/1.429441
[15]	YOU Yun-xiang,MIAO Guo-ping.An indicator sampling method for solving the inverse acoustic scattering problem from penetrable obstacles[J].Inverse Problems,2002,18(3):859-880. doi: 10.1088/0266-5611/18/3/321
[16]	尤云祥, 缪国平. 三维可穿透目标远场声波反演的一种指示器样本方法[J].物理学报,2002,51(9):2038-2050.
[17]	Hackman R H, Sammelmann G S.Multiple-scattering analysis for a target in an oceanic waveguide[J].J Acoust Soc Am,1988,84(5):1813-1825. doi: 10.1121/1.397148
[18]	Sarkassian A. Multiple scattering effects when scattering from atarget in a bounded medium[J].J Acoust Soc Am,1994,96(5):3137-3144. doi: 10.1121/1.411251
[19]	Gilbert R P, XU Yong-zhi. Dense sets and the projection theorem for acoustic harmonic waves in a homogeneous finite-depth ocean[J].Math Meth Appl Sci,1990,12(1):69-76. doi: 10.1002/mma.1670120105
[20]	Gilbert R P, XU Yong-zhi. The propagation problem and far-field patterns in a stratified finite-depth ocean[J].Math Meth Appl Sci，1990,12(2):199-208. doi: 10.1002/mma.1670120303
[21]	XU Yong-zhi. Radiation condition and scattering problem for time-harmonic acoustic waves in a stratified medium with a non-stratified inhomogeneous[J].IMA J Appl Math,1995,54(1):9-29. doi: 10.1093/imamat/54.1.9
[22]	XU Yong-zhi. Reciprocity relations and completeness of far-field pattern vectors for obstacle scattering of acoustic wave in a stratified medium[J].Math Meth Appl Sci,1995,18(1):51-66. doi: 10.1002/mma.1670180104

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