Acoustical Physics

, Volume 64, Issue 2, pp 225–236 | Cite as

On the Method of Source Images for the Wedge Problem Solution in Ocean Acoustics: Some Corrections and Appendices

  • Jun Tang
  • P. S. Petrov
  • Shengchun Piao
  • S. B. Kozitskiy
Ocean Acoustics. Hydroacoustics


In this study the method of source images for the problem of sound propagation in a penetrable wedge [G. Deane and M. Buckingham, J. Acoust. Soc. Am. 93 (1993) 1319–1328] is revisited. This solution is very important three-dimensional (3D) benchmark in computational underwater acoustics, since a wedge bounded from above by the sea surface and overlying a sloping penetrable bottom is the simplest model of a shallow-sea waveguide near the coastline. The corrected formulae for the positions of the source images and bottom images are presented together with the explanation of their derivation. The problem of branch choice in the reflection coefficient is thoroughly discussed, and the corresponding explicit formulae are given. In addition, numerical validation of the proposed branch choice schemes and the resulting wedge problem solutions are presented. Finally, source images solution is computed for a series of examples with different ratios of shear and bulk moduli in the bottom. The interplay between the acoustic-elastic waves coupling and the horizontal refraction in the wedge is demonstrated.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. B. Deane and M. J. Buckingham, J. Acoust. Soc. Am. 93, 1319 (1993).ADSCrossRefGoogle Scholar
  2. 2.
    P. S. Petrov, The 3D Penetrable Wedge Solution of G. Deane and M. Buckingham (MATLAB Code) (2015). PenetrableWedge/. Accessed April 13, 2017.Google Scholar
  3. 3.
    J. Tang, Analytic Solution for the Elastic Penetrable Wedge-Shaped Ocean (MATLAB Code) (2017). 20wedge%20(elastic%20bottom). Accessed April 13, 2017.Google Scholar
  4. 4.
    P. S. Petrov and F. Sturm, J. Acoust. Soc. Am. 139, 1343 (2016).ADSCrossRefGoogle Scholar
  5. 5.
    Y.-T. Lin, T. F. Duda, and A. E. Newhall, J. Comput. Acoust. 21, 1250018 (2013).MathSciNetCrossRefGoogle Scholar
  6. 6.
    F. Sturm, J. Acoust. Soc. Am. 139, 263 (2016).ADSCrossRefGoogle Scholar
  7. 7.
    L. M. Brekhovskikh and Y. P. Lysanov, Fundamentals of Ocean Acoustics, 3rd ed. (Springer, New York, 2003).zbMATHGoogle Scholar
  8. 8.
    COMSOL Multiphysics Reference Manual 5.2 (COMSOL AB, Stockholm, 2015})Google Scholar
  9. 9.
    J. T. Goh, H. Schmidt, P. Gerstoft, and W. Seong, IEEE J. Oceanic Eng. 22, 226 (1997).CrossRefGoogle Scholar
  10. 10.
    F. B. Jensen, W. A. Kuperman, M. B. Porter and H. Schmidt, Computational Ocean Acoustics, 2nd ed. (Springer, New York, 2012).zbMATHGoogle Scholar
  11. 11.
    S. H. Schot, Hist. Math. 19, 385 (1992).MathSciNetCrossRefGoogle Scholar
  12. 12.
    V. M. Babich, N. V. Mokeeva, and B. A. Samokish, J. Commun. Technol. Electron. 57, 993 (2012).CrossRefGoogle Scholar
  13. 13.
    B. G. Katsnelson, V. G. Petnikov, and J. Lynch, Fundamentals of Shallow Water Acoustics (Springer, New York, 2012).CrossRefzbMATHGoogle Scholar
  14. 14.
    P. S. Petrov, S. V. Prants, and T. N. Petrova, Phys. Lett. A. 381, 1921 (2017).ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    M. Badiey, B. G. Katsnelson, Y.-T. Lin, and J. F. Lynch, J. Acoust. Soc. Am. 129, EL141 (2011).CrossRefGoogle Scholar
  16. 16.
    A. N. Rutenko, S. B. Kozitskii, and D. S. Manul’chev, Acoust. Phys. 61, 72 (2015).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • Jun Tang
    • 1
    • 2
  • P. S. Petrov
    • 3
    • 4
  • Shengchun Piao
    • 1
    • 2
  • S. B. Kozitskiy
    • 3
  1. 1.College of Underwater Acoustic EngineeringHarbin Engineering UniversityHarbinChina
  2. 2.Acoustic Science and Technology LaboratoryHarbin Engineering UniversityHarbinChina
  3. 3.Il’ichev Pacific Oceanological InstituteVladiostokRussia
  4. 4.Far Eastern Federal UniversityVladivostokRussia

Personalised recommendations