1887
Volume 42 Number 7
  • E-ISSN: 1365-2478

Abstract

Abstract

Both approximate and exact formulations for the interaction of an incident elastic wave with a cased borehole are presented. In the approximate method, simple and explicit formulae are derived for the pressure in fluid at low frequencies. In the exact method, elastic potentials in each annulus are represented as a superposition of fundamental solutions to the Helmholtz equations. Continuity of displacements and stresses across layer boundaries are used to determine unknown coefficients. A global matrix algorithm is employed to compute simultaneously these coefficients in individual layers. Calculations show that, in cased boreholes, the borehole effects on downhole seismic measurements are more significant than in open boreholes. A strong resonance occurs in the fluid for SV‐wave incidence from a soft formation. This resonance is prominent even at very high frequencies because the tube‐wave velocity is raised well above the formation shear velocity by the steel pipe. At a particular angle of incidence of a plane P‐wave, the pressure in the fluid is near zero at low frequencies (the cased borehole screening phenomenon). For hard formations and frequencies above 1 kHz, the cased borehole influence on a downhole geophone measurement is significant, especially at grazing incidence. For soft formations, both the pressure in the fluid and the solid displacement on the borehole wall show strong dependence on frequency and angle of incidence, even at low frequencies.

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2006-04-28
2020-04-02
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References

  1. AlbrightJ.N. and JohnsonP.A.1990. Cross‐borehole observation of mode conversion from borehole Stoneley waves to channel waves at a coal layer. Geophysical Prospecting38, 607–620.
    [Google Scholar]
  2. BlairD.P.1984. Rise times of attenuated seismic pulse detected in both empty and fluid‐filled cylindrical boreholes. Geophysics49, 398–410.
    [Google Scholar]
  3. ChinR.C.Y., HedstromG.W. and ThigpenL.1984. Matrix methods in synthetic seismograms. Geophysical Journal of the Royal Astronomical Society77, 483–502.
    [Google Scholar]
  4. EsmersoyC.1984. Polarization analysis, rotation and velocity estimation in three component VSP. In: Vertical Seismic Profiling (eds M.N.Toksöz and R.R.Stewart ) 14B, pp. 236–255. Geophysical Press.
    [Google Scholar]
  5. GibsonR.L. and PengC.1994. Low and high frequency radiation from seismic sources in cased boreholes. Geophysics, in press.
    [Google Scholar]
  6. GreenfieldR.J.1978. Seismic radiation from a point source on the surface of cylindrical cavity. Geophysics43, 1071–1082.
    [Google Scholar]
  7. LeeM.W.1987. Particle displacement on the wall of a borehole from incident plane waves. Geophysics52, 1290–1296.
    [Google Scholar]
  8. LinesL., MillerM., TanH., ChambersR. and TreitelS.1993. Integrated interpretation of borehole and crosswell data from a west Texas field. The Leading Edge12, 13–16.
    [Google Scholar]
  9. LovellJ.R. and HornbyB.E.1990. Borehole coupling at sonic frequencies. Geophysics55, 806–814.
    [Google Scholar]
  10. MahrerK.D. and ZookB.J.1993. A field test of an electrodeless arc discharge, borehole seismic source. Geophysics58, 1558–1564.
    [Google Scholar]
  11. MarzettaT.L.1992. Inverse borehole coupling theory and its application to hydrophone vertical seismic profiling. 62nd SEG meeting, New Orleans, U.S.A. Expanded Abstracts, 145–147.
  12. MarzettaT.L. and SchoenbergM.1985. Tube waves in cased boreholes. 55th SEG meeting, Washington, U.S.A., Expanded Abstracts, 34–36.
  13. MatareseJ.R.1993. Nonlinear traveltime tomography . Ph.D. thesis, Massachusetts Institute of Technology.
  14. MeredithJ.A., ToksözM.N. and ChengC.H.1993. Secondary shear waves from source boreholes. Geophysical Prospecting41, 287–312.
    [Google Scholar]
  15. PengC.1993. Borehole effects on downhole seismic measurements . Ph. D. thesis. Massachusetts Institute of Technology.
  16. PengC., ChengC.H. and ToksözM.N.1993. Borehole effects on downhole seismic measurements. Geophysical Prospecting41, 883–912.
    [Google Scholar]
  17. RechtienR.D. and HambeckerK.L.1993. A high‐frequency sparker source for the borehole environment. Geophysics58, 660–669.
    [Google Scholar]
  18. SchaackM.V., Harris, J.M., RectorJ.W. and LazaratosS.K.1992. High resolution crosswell imaging of a west Texas carbonate reservoir: Part 2. wavefield analysis and tomography. 62nd SEG meeting, New Orleans, U.S.A., Expanded Abstracts, 40–44.
  19. SchmidtH. and TangoG.1986. Efficient global matrix appraoch to the computation of synthetic seismograms. Geophysical Journal of the Royal Astronomical Society84, 331–359.
    [Google Scholar]
  20. SchoenbergM.1986. Fluid and solid motion on the neighborhood of a fluid‐filled borehole due to the passage of a low frequency elastic plane wave. Geophysics51, 1191–1205.
    [Google Scholar]
  21. SchoenbergM., MarzettaT.L., AronJ. and PorterR.1981. Space‐time dependence of acoustic waves in a borehole. Journal of the Acoustical Society of America70, 1496–1507.
    [Google Scholar]
  22. TubmanK.1984. Full waveform acoustic logs in radially layered boreholes . Ph. D. thesis. Massachusetts Institute of Technology.
  23. WhiteJ.E.1953. Signals in a borehole due to plane waves in the solid. Journal of the Acoustical Society of America, 25, 906–915.
    [Google Scholar]
  24. WhiteJ.E.1983. Underground Sound: Application of Seismic Waves. Elsevier Science Publishing Co.
    [Google Scholar]
  25. WhiteJ.E. and WelshE.1988. Borehole coupling of seismic waves in a permeable solid. Geophysical Prospecting36, 417–429.
    [Google Scholar]
  26. ZhouC., CaiW., LuoY., SchusterG. and HassanzadehS.1993. High resolution crosswell imaging by seismic traveltime + waveform inversion. The Leading Edge12, 988–991.
    [Google Scholar]
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