Journal of Mathematical Sciences

, Volume 142, Issue 6, pp 2620–2629 | Cite as

Investigation of the wave field in an effective model of a layered elastic-fluid medium

  • L. A. Molotkov
  • M. N. Perekareva


For a medium that consists of alternating elastic and fluid layers, an effective model is constructed and investigated. This model is a special case of the Biot medium. The wave field is represented as Fourier and Mellin integrals. In the Mellin integral, the contour of integration is replaced by a stationary contour. In the expressions obtained, the order of integration is changed and the inner integral is calculated. The outer integral is equal to two residues. The corresponding poles are roots of two equations of fourth order. These roots lie on the right half-plane and may be complex or real. The representation obtained for the wave field is in agreement with the expressions derived by the Smirnov-Sobolev method. Bibliography: 8 titles.


Saddle Point Real Axis Observation Point Wave Field Phase Function 


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  1. 1.
    L. A. Molotkov, “Equivalence of periodic layered and transversely isotropic media,” Zap. Nauchn. Semin. LOMI, 89, 219–233 (1979).MathSciNetGoogle Scholar
  2. 2.
    L. A. Molotkov and A. V. Bakulin, “An effective model of a stratified solid-fluid medium as a special case of the Biot model,” Zap. Nauchn. Semin. POMI, 230, 172–195 (1995).Google Scholar
  3. 3.
    L. A. Molotkov and A. E. Khilo, “Investigation of single-and multiphase effective models describing periodic media,” Zap. Nauchn. Semin. POMI, 140, 105–122 (1984).Google Scholar
  4. 4.
    M. Schoenberg, “Wave propagating in alternating fluid and solid layers,” Wave Motion, 6, 303–320 (1984).MATHCrossRefGoogle Scholar
  5. 5.
    J. Plona, K. W. Winkler, and M. Schoenberg, “Acoustic waves in alternating fluid/solid layers,” J. Acoust. Soc. Amer., 81, No. 5, 1227–1234 (1987).CrossRefGoogle Scholar
  6. 6.
    L. A. Molotkov, Investigation of Wave Propagation in Porous and Fractured Media on the Basis of Effective Biot Models and Layered Media [in Russian], St.Petersburg (2001).Google Scholar
  7. 7.
    L. A. Molotkov, “On wave attenuation in the effective model describing porous and fractured media saturated by fluid,” Zap. Nauchn. Semin. POMI, 297, 216–229 (2003).Google Scholar
  8. 8.
    S. L. Sobolev, “Some questions in the theory of propagation of oscillations,” Chap. XII, in: Differential and Integral Equations of Mathematical Physics, F. Frank and P. Mises (eds.), Leningrad-Moscow (1937), pp. 468–617.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • L. A. Molotkov
    • 1
  • M. N. Perekareva
    • 2
  1. 1.St.Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia
  2. 2.St.Petersburg State Marine Technical UniversitySt.PetersburgRussia

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