Skip to main content
SpringerLink
Log in

Boundary integral method for calculating displacement fields in three-dimensional viscoelastic piecewise-homogeneous media. I. Fundamental solutions

  • Physics Of Elementary Particles And Field Theory
  • Published:
Russian Physics Journal Aims and scope

Abstract

The boundary integral method is applied to the construction of stationary fields of elastic displacements in three-dimensional viscoelastic media, consisting of homogeneous regions with curvilinear separation boundaries. As fundamental solutions we use the sum of solutions describing converging and diverging waves. It is shown that for a such selected fundamental solution it is possible to satisfy the boundary and radiation conditions of waves at infinity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. A. Aleksidze, Fundamental Functions in Approximate Solutions of Boundary Value Problems [in Russian], Nauka, Moscow (1991).

    Google Scholar 

  2. V. A. Babeshko, E. V. Glushkov, and Zh. F. Zinchenko, Dynamics of Inhomogeneous Linearly Elastic Media [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  3. K. D. Kleim-Musatov, Boundary Wave Theory and Its Applications in Seismology [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  4. V. D. Kupradze et al., Three-Dimensional Problems of the Mathematical Theories of Elasticity and Thermoelasticity, Nauka, Moscow (1976).

    Google Scholar 

  5. B. Bakamjian, in: Expanded Abstracts with Biographies, 62nd Annual Intern. SEG Meeting, New Orleans (1992), pp. 1232–1235.

  6. M. Bouchon and K. Aki, Bull. Seism. Soc. Am.,67, 259–277 (1977).

    Google Scholar 

  7. D. M. Boore, Meth. Comp. Phys.,11, 355–361 (1972).

    Google Scholar 

  8. V. Cherveny, I. A. Molotkov, and I. Pšenchik, The Ray Method in Seismology, Karlova University, Prague (1977).

    Google Scholar 

  9. V. Cherveny, Geophys. J. Roy. Astr. Soc.,73, 389–426 (1983).

    Google Scholar 

  10. X. Chen, Bull. Seism. Soc. Am.,80, 1696–1724 (1990).

    Google Scholar 

  11. L. Eskola, Geophysical Interpretation Using Integral Equations, Chapman & Hall, London (1992).

    Google Scholar 

  12. A. J. Haines, Geophys. J. Int.,95, 237–260 (1988).

    Google Scholar 

  13. F. Hron and B. G. Mihailenko, Bull. Seism. Soc. Am.,71, 1011–1029 (1981).

    Google Scholar 

  14. K. R. Kelly et al., Geophys. J. Int.,79, 351–369 (1976).

    Google Scholar 

  15. B. L. N. Kennett, Geophys. J. Roy. Astr. Soc.,63, 301–325 (1972).

    Google Scholar 

  16. B. L. N. Kennett, Geophys. J. Roy. Astr. Soc.,87, 313–331 (1986).

    Google Scholar 

  17. B. L. N. Kennett, K. Koketsu, and A. J. Haines, Geophys. J. Int.,103, 95–101 (1990).

    Google Scholar 

  18. K. D. Kleim-Musatov and A. M. Aizenberg, Geophys. J. Int.,99, 351–367 (1989).

    Google Scholar 

  19. D. Kosloff et al., Geophys. Prosp.,37, 383–394 (1989).

    Google Scholar 

  20. W. D. Smith, J. Comp. Phys.,15, 492–503 (1974).

    Google Scholar 

Download references

Authors
  1. V. Yu. Grechka
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Institute of Geophysics, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vyssikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 76–81, July, 1994.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grechka, V.Y. Boundary integral method for calculating displacement fields in three-dimensional viscoelastic piecewise-homogeneous media. I. Fundamental solutions. Russ Phys J 37, 662–666 (1994). https://doi.org/10.1007/BF00559200

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00559200

Keywords

Search

Navigation