Acoustical Physics

, Volume 57, Issue 4, pp 529–541 | Cite as

Estimation of hydro-fracture parameters by analysis of tube waves at vertical seismic profiling

  • G. A. Maksimov
  • A. V. Derov
  • B. M. Kashtan
  • M. Yu. Lazarkov
Acoustics of Structurally Inhomogeneous Solid Media. Geological Acoustics


The problem on tube wave excitation in a well intersected by a finite-size fluid-filled crack under action of external seismic wave is considered. This situation appears at vertical seismic profiling (VSP) in the presence of hydro-fracture intersecting the borehole. A heterogeneous integral-differential equation for the fluid pressure field in fracture is derived in the long-wave approximation by the fracture opening. Stitching of the solution for pressure in fracture with that for tube waves in a well allows to calculate the amplitude and shape of generated tube waves. Numerical computations that under action of the external seismic field the crack edges excite a strongly dispersive mode of a thin fluid layer which can be used for estimation of linear fracture size on the basis of VSP technique.


primary and secondary tube waves fracture waves effective wave equation 3D simulation verification 


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  1. 1.
    W. B. Beydoun, C. H. Cheng, and M. N. Toksoz, J. Geophys. Res. B 90, 4557 (1985).ADSCrossRefGoogle Scholar
  2. 2.
    X. M. Tang and C. H. Cheng, Geophys. Res. 94, 7567 (1989).ADSCrossRefGoogle Scholar
  3. 3.
    B. E. Hornby, D. L. Johnson, K. W. Winkler, and R. A. Plumb, Geophys. 54, 1274 (1989).CrossRefGoogle Scholar
  4. 4.
    S. Kostek, D. L. Johnson, K. W. Winkler, and B. E. Horby, Geophys. 63, 809 (1998).CrossRefGoogle Scholar
  5. 5.
    F. Henry, J. T. Fokkema, and C. J. de Pater, in Proceedings of the EAGE 64th Conference and Exhibition (2002), p. 143.Google Scholar
  6. 6.
    A. V. Derov and G. A. Maksimov, Akust. Zh. 48, 331 (2002) [Acoust. Phys. 48, 284 (2002)].Google Scholar
  7. 7.
    A. M. Ionov, Geophys. Prospect 55, 71 (2007).ADSCrossRefGoogle Scholar
  8. 8.
    W. L. Medlin and D. P. Schmitt, JPT, 239 (1994).Google Scholar
  9. 9.
    R. W. Paige, L. R. Murray, and J. D. M. Roberts, SPE Product. Facil., 7 (1995).Google Scholar
  10. 10.
    T. W. Patzek and A. De, J. Petrol. Sci. Eng. 25, 59 (2000).CrossRefGoogle Scholar
  11. 11.
    J. Groenenboom and J. Falk, Geophysics 65, 612 (2000).ADSCrossRefGoogle Scholar
  12. 12.
    J. Groenenboom and D. B. van Dam, Geophysics 65, 603 (2000).ADSCrossRefGoogle Scholar
  13. 13.
    A. M. Ionov and G. A. Maximov, Geophys. Int. 124, 888 (1996).ADSCrossRefGoogle Scholar
  14. 14.
    A. V. Derov and G. A. Maksimov, in Proceedings of the 16th Session of Russian Acoustic Society (GEOS, Moscow, 2005), Vol. 1, pp. 324–327.Google Scholar
  15. 15.
    A. V. Derov and G. A. Maksimov, Tekhnol. Seismorazv. 4, 60 (2008).Google Scholar
  16. 16.
    P. V. Krauklis, Prikl. Mat. Mekh. 26, 1111 (1962).Google Scholar
  17. 17.
    V. Ferrazini and K. Aki, J. Geophys. Res. B 92, 9215 (1987).ADSCrossRefGoogle Scholar
  18. 18.
    G. A. Maksimov and A. M. Ionov, Akust. Zh. 44, 510 (1998) [Acoust. Phys. 44, 437 (1998)].Google Scholar
  19. 19.
    A. V. Derov, G. A. Maksimov, and M. Yu. Lazar’kov, in Proceedings of the 20th Session of Russian Acoustic Society (GEOS, Moscow, 2008), Vol. 1, pp. 265–268.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • G. A. Maksimov
    • 1
  • A. V. Derov
    • 1
  • B. M. Kashtan
    • 2
  • M. Yu. Lazarkov
    • 2
  1. 1.Andreev Acoustic InstituteMoscowRussia
  2. 2.St. Petersburg State UniversitySt. PetersburgRussia

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