Publication Cover
Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 5
90
Views
1
CrossRef citations to date
0
Altmetric
Articles

Time-harmonic acoustic wave scattering in an ocean with depth-dependent sound speed

&
Pages 978-999 | Received 02 Feb 2015, Accepted 29 Apr 2015, Published online: 21 May 2015

References

  • Buchanan J, Gilbert R, Wirgin A, Xu Y. Marine acoustics: direct and inverse problems. Philadelphia: SIAM; 2004.
  • Buckingham MJ. Ocean-acoustic propagation models. J. Acoustique. 1992;06:223–287.
  • Sauter S, Schwab C. Boundary element methods. New York (NY): Springer; 2011.
  • Arens T, Gintides D, Lechleiter A. Variational formulations for scattering in a three-dimensional acoustic waveguide. Math. Methods Appl. Sci. 2008;31:821–847.
  • Arens T, Gintides D, Lechleiter A. Direct and inverse medium scattering in a 3d homogeneous planar waveguide. SIAM J. Appl. Math. 2011;71:753–772.
  • Jensen FB, Kuperman WA, Porter MB, Schmidt H. Computational ocean acoustics. New York (NY): Springer; 2011. doi:10.1007/978-1-4419-8678-8.
  • Ahluwalia DS, Keller JB. Exact and asymptotic representations of the sound field in a stratified ocean. Lect. Notes Phys. 1977;70:14–85.
  • Ames WF, Lee D. Current development in the numerical treatment of ocean acoustic propagation. Appl. Numer. Math. 1987;3:25–47.
  • Xu Y. The propagating solutions and far-field patterns for acoustic harmonic waves in a finite depth ocean. Appl. Anal. 1990;35:129–151.
  • Gilbert RP, Xu Y. The propagation problem and far-field patterns in a stratified finite-depth ocean. Math. Methods Appl. Sci. 1990;12:199–208.
  • Xu Y. Scattering of acoustic wave by obstacle in stratified medium. Pitman research notes in mathematics. Essex: Longman Science & Technology; 1992.
  • Gilbert RP, Xu Y. The coefficient problem for a shallow ocean with an unknown inhomogeneity and an elastic seabed. Appl. Anal. 1996;63:77–86.
  • Bayliss A, Goldstein CI, Turkel E. The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics. Comput. Math. Appl. 1985;11:655–665. Special issue computational ocean acoustics.
  • Dushaw BD, Worcester PF, Cornuelle BD, Howe BM. On equations for the speed of sound in seawater. J. Acoust. Soc. Am. 1993;93:255–275.
  • Gilbert RP, Lin Z. Acoustic field in a shallow, stratified ocean with a poro-elastic seabed. Z. Angew. Math. Mech. 1997;77:677–688.
  • Lechleiter A, Rienmüller T. Time-harmonic acoustic wave scattering in an ocean with depth-dependent sound speed. Technical report. Universität Bremen; 2015.
  • McLean WCH. Strongly elliptic systems and boundary integral equations. Cambridge: Cambridge University Press; 2000.
  • Kato T. Perturbation theory for linear operators. 2nd ed. Berlin: Springer-Verlag; 1995. Reprint of the edition 1980.
  • Levitan BM, Sargsyan IS. Some problems in the theory of a Sturm--Liouville equation. Russian Math. Surv. 1960;15:1–96.
  • Kirsch A. An introduction to the mathematical theory of inverse problems. New York (NY): Springer; 2011.
  • Colton DL, Kress R. Inverse acoustic and electromagnetic scattering theory. 3rd ed. New York (NY): Springer; 2012.
  • Claeys X, Haddar H. Scattering from infinite rough tubular surfaces. Math. Methods Appl. Sci. 2007;30:389–414.
  • Mujica J. Complex analysis in Banach spaces: holomorphic functions and domains of holomorphy in finite and infinite dimensions. Amsterdam: North-Holland; 1985.
  • Abramowitz M, Stegun IA. Handbook of mathematical functions: with formulas, graphs, and mathematical tables. New York (NY): Dover Publications; 1964.
  • Cruz A, Sesma J. Zeros of the Hankel function of real order and of its derivative. Math. Comp. 1982;39:639–645.
  • Jerison D, Kenig CE. Unique continuation and absence of positive eigenvalues for the Schrödinger operator. Ann. Math. 1985;121:463–488.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.