Acoustical Physics

, Volume 46, Issue 4, pp 479–487 | Cite as

Numerical modeling of the reflection coefficients for the plane sound wave reflection from a layered elastic bottom

  • M. S. Fokina
  • B. N. Fokin
Article

Abstract

The matrix method and its numerical realization are considered in calculating the complex reflection coefficients and refraction indices of plane sound waves for geoacoustic models of the ocean bottom in the form of homogeneous elastic (liquid) absorbing layers overlying an elastic halfspace. In calculating the reflection coefficients at high frequencies or in the presence of a large numbers of sedimentary layers, a passage from the Thomson-Haskell matrix approach to the Dunkin-Thrower computational scheme is performed. The results of test calculations are presented. With the aim of developing resonance methods for the reconstruction of the parameters of layered elastic media, the behavior of the frequency-angular dependences of the reflection coefficient are studied for various geoacoustic bottom models. The structure of the angular and frequency resonances of the reflection coefficients is revealed. The dependence of the structure (the position, width, and amplitude) of two types of resonances on the parameters of the layered bottom is considered.

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References

  1. 1.
    L. M. Brekhovskikh and O. A. Godin, Acoustics of Layered Media (Nauka, Moscow, 1989; Berlin, Springer, 1990).Google Scholar
  2. 2.
    W. M. Ewing, W. S. Jardetzky, and F. Press, Elastic Waves in Layered Media (McGraw-Hill, New York, 1957).Google Scholar
  3. 3.
    L. A. Molotkov, in Computational Methods in Geophysics (Radio i Svyaz’, Moscow, 1981).Google Scholar
  4. 4.
    L. A. Molotkov, The Matrix Method in the Theory of Wave Propagation in Elastic and Fluid Layered Media (Nauka, Leningrad, 1984).Google Scholar
  5. 5.
    M. M. Machevariani, V. V. Tyutekin, and A. P. Shkvarnikov, Akust. Zh. 17, 97 (1971) [Sov. Phys. Acoust. 17, 77 (1971)].Google Scholar
  6. 6.
    V. Yu. Prikhod’ko and V. V. Tyutekin, Akust. Zh. 32, 212 (1986) [Sov. Phys. Acoust. 32, 125 (1986)].ADSGoogle Scholar
  7. 7.
    V. N. Fokin and M. S. Fokina, Akust. Zh. 44, 676 (1998) [Acoust. Phys. 44, 585 (1998)].Google Scholar
  8. 8.
    N. R. Chapman, M. Musil, and M. J. Wilmut, Boll. Geofis. Teor. Appl. 40(1), 40 (1999).Google Scholar
  9. 9.
    M. Siderius and J. P. Hermand, J. Acoust. Soc. Am. 106, 637 (1999).ADSCrossRefGoogle Scholar
  10. 10.
    N. R. Chapman, D. E. Hanny, and K. M. M. Rohr, in Proceedings of the 3rd European Conference on Underwater Acoustics, 1996, Vol. 2, p. 613.Google Scholar
  11. 11.
    K. E. Hawker, J. Acoust. Soc. Am. 64, 548 (1978).ADSGoogle Scholar
  12. 12.
    S. R. Rutherford and K. E. Hawker, J. Acoust. Soc. Am. 63, 750 (1978).ADSCrossRefGoogle Scholar
  13. 13.
    H. E. Morris, J. Acoust. Soc. Am. 48, 1198 (1970).CrossRefGoogle Scholar
  14. 14.
    T. Akal and R. Stoll, J. Acoust. Soc. Am. 100, 2668 (1996).ADSCrossRefGoogle Scholar
  15. 15.
    R. Carbo, J. Acoust. Soc. Am. 101, 227 (1997).ADSGoogle Scholar
  16. 16.
    R. F. Keltie, J. Acoust. Soc. Am. 103, 1855 (1998).ADSCrossRefGoogle Scholar
  17. 17.
    A. I. Lavrentyev and S. I. Rokhlin, J. Acoust. Soc. Am. 102, 3467 (1997).ADSCrossRefGoogle Scholar
  18. 18.
    W. T. Thomson, J. Appl. Phys. 21, 89 (1950).MATHMathSciNetGoogle Scholar
  19. 19.
    N. A. Haskell, Bull. Seismol. Soc. Am. 43, 17 (1953).MathSciNetGoogle Scholar
  20. 20.
    I. W. Dunkin, Bull. Seismol. Soc. Am. 55, 335 (1965).Google Scholar
  21. 21.
    E. N. Thrower, J. Sound Vibr. 2, 210 (1965).CrossRefGoogle Scholar
  22. 22.
    P. J. Vidmar and T. L. Foreman, J. Acoust. Soc. Am. 66, 1830 (1979).ADSCrossRefGoogle Scholar
  23. 23.
    F. R. Gantmacher, The Theory of Matrices (Fizmatgiz, Moscow, 1966, 3rd ed.; Chelsea, New York, 1959).Google Scholar
  24. 24.
    A. Nagl, H. Überall, and W. R. Hoover, IEEE Trans. Geosci. Remote Sens. GE-20, 332 (1982).Google Scholar
  25. 25.
    G. Breit and E. P. Wigner, Phys. Rev. 49, 519 (1936).ADSGoogle Scholar
  26. 26.
    A. Nagl, H. Überall, and Yoo Kwang-Bock, in Inverse Problems (Inst. of Physics, Bristol, 1985), Vol. 1, p. 99.Google Scholar
  27. 27.
    R. Fiorito, W. Madigosky, and H. Überall, J. Acoust. Soc. Am. 66, 1857 (1979).ADSCrossRefGoogle Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2000

Authors and Affiliations

  • M. S. Fokina
    • 1
  • B. N. Fokin
    • 1
  1. 1.Institute of Applied PhysicsRussian Academy of SciencesNizhni NovgorodRussia

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