Determination of a Distributed Inhomogeneity in a Two-Layered Waveguide from Scattered Sound

  • Robert P. Gilbert
  • Christopher Mawata
  • Yongzhi Xu
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 5)


This paper considers the determination of a distributed inhomogeneity in a two-layered waveguide from scattered sound. Assuming that we know the acoustic properties of the waveguide, we determine the unknown inhomogeneity by sending in incident waves from point sourses in given locations, and detecting the total waves along a line. In this paper we consider the case that wavenumber k is small. In this case we obtain the representation, uniqueness, and existence of the direct scattering problem, and the uniqueness of inverse scattering problem. Numerical examples are also presented.


Scattering Problem Boundary Integral Equation Method Inverse Scattering Problem Scattered Sound Acoustic Waveguide 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Ahluwalia,D. and Keller, J.: Exact and asymptotic representations of the sound field in a stratified ocean in Wave Propagation and Underwater Acoustics, Lecture Notes in Physics 70, Springer, Berlin, 1977.Google Scholar
  2. [2]
    T. S. Angell, R. E. Kleinman, C. Rozier and D. Lesselier, Uniqueness and complete families for an acoustic waveguide problem, submitted to Wave Motion (1996).Google Scholar
  3. [3]
    P. Carrion and G. Boehm, Tomographie imaging of opaque and low-contrast objects in range—independent waveguides, J. Acoust. Soc. Am., 91, 1440 - 1446, (1992).CrossRefGoogle Scholar
  4. [4]
    Colton, David and Kress, Rainer: Inverse Acoustic and Electromagnetic Scattering Theory, Springer-Verlag, (1993).Google Scholar
  5. [5]
    Gilbert, R.P. and Xu, Y.: Generalized Herglotz functions and inverse scattering problems in finite depth oceans in Inverse Problems, SIAM, (1992).Google Scholar
  6. [6]
    Gilbert, R.P., Xu, Y.: An inverse problem for harmonic acoustics in stratified oceans, J. Math. Anal. Appt 17 (1) (1993), 121 - 137.Google Scholar
  7. [7]
    R. P. Gilbert and Y. Xu, The searnount problem, in SIAM special issue on the occasion of Prof. I. Stakgolds 70th birthday, Nonlinear Problems in Applied Mathematics, T. Angell et al. Eds., SIAM, Philadelphia, pp. 140 - 149, (1996).Google Scholar
  8. [8]
    Gilbert, R.P. and Zhongyan Lin: On the conditions foruniqueness and existence of the solution to an acoustic inverse problem: I Theory, J. computational Acoustics, Vol. 1, No. 2 (1993) 229 - 247CrossRefGoogle Scholar
  9. [9]
    Gilbert, R.P. and Zhongyan Lin: An acoustic inverse problem: Numerical experiments, J. Computational Acoustics,(to appear 1995 ).Google Scholar
  10. [10]
    F. B. Jensen, W. A. Iiuperman, M. B. Porter and H. Schmidt, COMPUTATIONAL OCEAN ACOUSTICS, AIP, New York, (1994).Google Scholar
  11. [11]
    D. Lesselier and B. Duchene, Wavefield inversion of objects in stratified environments. From backpropayation schemes to full solutions, in REVIEW OF RADIO SCIENCE 1993-1995, R. Stone, ed., Oxford U. Press, Oxford, pp. 235 - 268, 1996.Google Scholar
  12. [12]
    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., 96, 1703 - 1724, (1994).CrossRefGoogle Scholar
  13. [13]
    C. Rozier, D. Lesselier and T. Angell, Optimal shape reconstruction of a perfect target in shallow water, in PROC. 3RD EUROP. CONF. UNDERWATER ACOUSTICS, Heraklion (1996).Google Scholar
  14. [14]
    D. Rozier, D. Lesselier, T. Angell and R. Kleinman, Reconstruction of an impenetrable obstacle immersed in a shallow water acoustic waveguide,Google Scholar
  15. in Proc.Conf. Problemes Inverses Propagation ET Diffraction DONDES, Aix-les-Bains (1996).Google Scholar
  16. [15]
    C. Rozier, D. Lesselier, T. Angell and R. Kleinman, Shape retrieval of an obstacle immersed in shallow water from single frequency farfields using a complete family method, submitted to Inverse Probs. (1996).Google Scholar
  17. [16]
    Xu, Y.: Direct and Inverse Scattering in Shallow Oceans, Ph.D. Thesis, University of Delaware, 1990.Google Scholar
  18. [17]
    Y. Xu and Y. Yan, Boundary integral equation method for source localization with a continuous wave sonar, J. Acoust. Soc. Am. 92, 995 - 1002, (1992).CrossRefGoogle Scholar
  19. [18]
    Y. Xu, T. C. Poling and T. Brundage, Direct and inverse scattering of harmonic acoustic waves in an inhomoyeneous shallow ocean, in Computational Acoustics, D. Lee et al. Eds., IMACS 9], vol 2., North-Holland, Amsterdam, pp. 21 - 43, (1993).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Robert P. Gilbert
    • 1
  • Christopher Mawata
    • 2
  • Yongzhi Xu
    • 2
  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkUSA
  2. 2.Department of MathematicsUniversity of tennessee at ChattanoogaChattanoogaUSA

Personalised recommendations