Skip to main content
SpringerLink
Log in

Some properties on far-field pattern of scattering by penetrable obstacle in ocean waveguide

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

This paper is concerned with 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. The sets of solutions to the transmission problem are 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 are determined. These properties are important in investigating inverse transmission problems in an ocean waveguide.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

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.

    Article  MATH  MathSciNet  Google Scholar 

  2. Kirsch A. Properties of far-field operator in acoustic scattering[J]. Math Meth Appl Sci, 1989, 11:773–787.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  4. Colton D, Kress R. Inverse acoustic and electromagnetic scattering theory[M]. 2nd Edition. Berlin: Springer, 1998.

    Google Scholar 

  5. Colton D, Coyle C, Monk P. Recent developments in inverse acoustic scattering theory[J]. SIAM Rev, 2000, 42(3):369–414.

    Article  MATH  MathSciNet  Google Scholar 

  6. Miao Guoping, You Yunxiang, Liu Yingzhong. A numerical method for shape reconstruction problem in acoustic scattering[J]. Inverse Problems in Engineering, 2000, 8(3):229–249.

    Article  Google Scholar 

  7. You Yunxiang, Miao Guoping, Liu Yingzhong. A numerical method for an inverse transmission problem[J]. Inverse Problems, 2001, 17(3):421–435.

    Article  MATH  MathSciNet  Google Scholar 

  8. You Yunxiang, Miao Guoping, Liu Yingzhong. 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, 2:29–42.

    MATH  MathSciNet  Google Scholar 

  9. You Yunxiang, Miao Guoping, Liu Yingzhong. 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.

    Article  Google Scholar 

  10. You Yunxiang, Yap F F, Miao Guoping. A numerical method for the inverse impedance obstacle problem[J]. ACTA Acustica United with Acustica, 2002, 88(1):1–13.

    Google Scholar 

  11. You Yunxiang, Miao Guoping. Numerical method for the shape reconstruction of a hard target[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(10):1233–1244.

    Article  MATH  MathSciNet  Google Scholar 

  12. You Yunxiang, Miao Guoping. A fast algorithm for visualizing multiple three dimensional objects using near field acoustic measurements[J]. Acta Physica Sinica, 2001, 50(6):1103–1109 (in Chinese).

    Google Scholar 

  13. You Yunxiang, Miao Guoping, Liu Yingzhong. A fast method for acoustic imaging of multiple three-dimensional objects[J]. J Acoust Soc Am, 2000, 108(1):31–37.

    Article  Google Scholar 

  14. You Yunxiang, Miao Guoping, Liu Yingzhong. 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.

    MathSciNet  Google Scholar 

  15. You Yunxiang, Miao Guoping. An indicator sampling method for solving the inverse acoustic scattering problem from penetrable obstacles[J]. Inverse Problems, 2002, 18(3):859–880.

    Article  MATH  MathSciNet  Google Scholar 

  16. You Yunxiang, Miao Guoping. Acoustic far-field inversion of three dimensional penetrable objects by an indicator sampling method[J]. Acta Physica Sinica, 2002, 51(9):2038–2050 (in Chinese).

    Google Scholar 

  17. Hackman R H, Sammelmann G S. Multiple-scattering analysis for a target in an oceanic waveguide[ J]. J Acoust Soc Am, 1988, 84:1813–1825.

    Article  Google Scholar 

  18. Sarkassian A. Multiple scattering effects when scattering from a target in a bounded medium[J]. J Acoust Soc Am, 1994, 96(5):3137–3144.

    Article  Google Scholar 

  19. Gilbert R P, Xu Yongzhi. Dense sets and the projection theorem for acoustic harmonic waves in a homogeneous finite-depth ocean[J]. Math Meth Appl Sci, 1990, 12:69–76.

    Article  MathSciNet  Google Scholar 

  20. Gilbert R P, Xu Yongzhi. The propagation problem and far-field patterns in a stratified finitedepth ocean[J]. Math Meth Appl Sci, 1990, 12:199–208.

    Article  MATH  MathSciNet  Google Scholar 

  21. Xu Yongzhi. Radition condition and scattering problem for time-harmonic acoustic waves in a stratified medium with a nonstratified inhomogeneous[J]. IMA J Appl Math, 1995, 54(1):9–29.

    Article  MATH  MathSciNet  Google Scholar 

  22. Xu Yongzhi. 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, 18:51–66.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Pan Wen-feng  (潘文峰) & Li Zhuo-qiu  (李卓球)

  2. School of Naval Architecture and Ocean Engineering, Shanghai Jiaotong University, Shanghai, 200030, P. R. China

    You Yun-xiang  (龙云祥) & Miao Guo-ping  (谬国平)

Authors
  1. Pan Wen-feng  (潘文峰)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. You Yun-xiang  (龙云祥)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Miao Guo-ping  (谬国平)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Li Zhuo-qiu  (李卓球)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pan Wen-feng  (潘文峰).

Additional information

Communicated by HUANG Yong-nian

Project supported by the National Natural Science Foundation of China (No. 10672128), the Doctor Foundation of Wuhan University of Technology (No. 471-38650238), and the Undergraduate Innovative Foundation of Wuhan University of Technology (No. A145)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pan, Wf., You, Yx., Miao, Gp. et al. Some properties on far-field pattern of scattering by penetrable obstacle in ocean waveguide. Appl. Math. Mech.-Engl. Ed. 29, 239–250 (2008). https://doi.org/10.1007/s10483-008-0211-y

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-008-0211-y

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation