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Journal of Mathematical Sciences

, Volume 175, Issue 6, pp 651–671 | Cite as

Boundary layer method in the problem of far propagation of surface SV-waves

  • N. Ya. Kirpichnikova
  • A. S. Kirpichnikova
Article
  • 25 Downloads

The SV polarized wave field is investigated in an elastic gradient layer of constant width. A point source is situated on the boundary of the layer. Rigid contact conditions are assumed to be valid on the boundary between the layer and an elastic half-space. It is shown that the interference field in the principal approximation far from the source does not depend on the relation between the phase velocity and the transversal and longitudinal velocities in the half-space. Bibliography: 11 titles.

Keywords

Russia Boundary Layer Point Source Phase Velocity Wave Field 
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References

  1. 1.
    C. Stephens and B. L. Isacks, “Toward an understading of Sn: normal modes of Love waves in an oceanic structure,” Bull. Seism. Soc. Amer., 67, No. 1, 69–78 (1977).Google Scholar
  2. 2.
    P. V. Krauklis, N. V. Zepelev, and L. A. Krauklis, “On the asymptotic approach to the wave distant propagation problem,” J. Sov. Math., 50, No. 4, 1761–1769 (1990).CrossRefGoogle Scholar
  3. 3.
    M. A. Leontovich and V. A. Fock, “Solution of the problem of propagation of electromagnetic waves along the earth’s surface by the method of parabolic equations,” J. Exper. Theor. Phys., 16, No. 7, 557–573 (1946).MathSciNetGoogle Scholar
  4. 4.
    R. N. Buchal and J. B. Keller, “Boundary layer problems in diffraction theory,” J. Comm. Pure Appl. Math., 13, No. 1, 85–114 (1960).MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    V. M. Babich and N. Ya. Kirpichnikova, The Boundary-Layer Method in Diffraction Problems, Springer-Verlag (1974).Google Scholar
  6. 6.
    D. L. Anderson and S. B. Archambeau, “The anelasticite of the earth,” J. Geophys. Res., 69, 2071–2084 (1964).CrossRefGoogle Scholar
  7. 7.
    L. M. Brehovskih, “Surface waves in a solid which are confined by the curvature of the boundary,” Akust. J. AN SSSR, 13, 541–555 (1967).Google Scholar
  8. 8.
    I. V. Muhina and I. A. Molotkov, “Propagation of Rayleigh waves in an elastic half-space which is inhomogeneous with respect to two coordinates,” Izv. Akad. Nauk SSSR, Ser. Fiz. Zemli, No.4, 3–8 (1967).Google Scholar
  9. 9.
    N. Ya. Kirpichnikova, “Propagation of surface waves concentrated near rays in an inhomogeneous elastic body of arbitrary shape,” Trudy Mat. Inst. Steklov, CXV, No. 1, 114–130 (1971).Google Scholar
  10. 10.
    N. Ya. Kirpichnikova and V. B. Philippov, “Behavior of surface waves at transition through a function line on the boundary of an elastic homogeneous isotropic body,” Zap. Nauchn. Semin. POMI, 230, 86–102 (1995).Google Scholar
  11. 11.
    N. Ya. Kirpichnikova, “Diffraction of surface SV-waves on the line of discontinuity of elastic parameters,” Zap. Nauchn. Semin. POMI, 342, 77–105 (2007).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.St.Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

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