1887
Volume 63, Issue 3
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

For pre‐stack phase‐shift migration in homogeneous isotropic media, the offset‐midpoint travel time is represented by the double‐square‐root equation. The travel time as a function of offset and midpoint resembles the shape of Cheops’ pyramid. This is also valid for transversely isotropic media with a vertical symmetry axis. In this study, we extend the offset‐midpoint travel‐time pyramid to the case of 2D transversely isotropic media with a tilted symmetry axis. The P‐wave analytical travel‐time pyramid is derived under the assumption of weak anelliptical property of the tilted transverse isotropy media. The travel‐time equation for the dip‐constrained transversely isotropic model is obtained from the depth‐domain travel‐time pyramid. The potential applications of the derived offset‐midpoint travel‐time equation include pre‐stack Kirchhoff migration, anisotropic parameter estimation, and travel‐time calculation in transversely isotropic media with a tilted symmetry axis.

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2014-12-07
2024-03-28
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References

  1. AlkhalifahT.1998. Acoustic approximations for seismic processing in transversely isotropic media. Geophysics63, 623–631.
    [Google Scholar]
  2. AlkhalifahT.2000a. An acoustic wave equation for anisotropic media. Geophysics65, 1239–1250.
    [Google Scholar]
  3. AlkhalifahT.2000b. The offset‐midpoint traveltime pyramid in transversely isotropic media. Geophysics65, 1316–1325.
    [Google Scholar]
  4. AlkhalifahT. and SavaP.2010. A transversely isotropic medium with a tilted symmetry axis normal to the reflector. Geophysics75, A19–A24.
    [Google Scholar]
  5. AlkhalifahT. and SavaP.2011. Migration using a transversely isotropic medium with symmetry normal to the reflector dip. International Journal of Geophysics, Article ID 530106, : 10.1155/2011/530106 online.
    [Google Scholar]
  6. BenderC.M. and OrszagS.A.1978. Advanced Mathematical Methods for Scientists and Engineers. McGraw‐Hill.
    [Google Scholar]
  7. ChapmanC.H. and MillerD.E.1996. Velocity sensitivity in transversely isotropic media. Geophysical Prospecting44, 525–549.
    [Google Scholar]
  8. ClaerboutJ.1985. Imaging the Earth's Interior. Blackwell Science Inc.
    [Google Scholar]
  9. DellS., PronevichA., KashtanB. and GajewskiD.2013. Diffraction traveltime approximation for general anisotropic media. Geophysics78, WC15–WC23.
    [Google Scholar]
  10. GolikovP. and StovasA.2012a. Traveltime parameters in a tilted elliptical isotropic media. Geophysical Prospecting60, 433–443.
    [Google Scholar]
  11. GolikovP. and StovasA.2012b. Traveltime parameters in tilted transversely isotropic media. Geophysics77, A19–A24.
    [Google Scholar]
  12. MoserT.J. and HowardC.B.2008. Diffraction imaging in depth. Geophysical Prospecting56, 627–641.
    [Google Scholar]
  13. StovasA. and AlkhalifahT.2012. A tilted transversely isotropic slowness surface approximation. Geophysical Prospecting61, 568–573.
    [Google Scholar]
  14. ThomsenL.1986. Weak elastic anisotropy. Geophysics51, 1954–1966.
    [Google Scholar]
  15. TsvankinI. and ThomsenL.1994. Nonhyperbolic reflection moveout in anisotropic media. Geophysics59, 1290–1304.
    [Google Scholar]
  16. TsvankinI.2001. Seismic signatures and analysis of reflection data in anisotropic medium, 1st ed.: Elsevier Science Publishing Company, Inc.
  17. WaheedU., AlkhalifahT. and StovasA.2013. Diffraction traveltime approximation for TI media with an inhomogeneous background. Geophysics78, WC103–WC111.
    [Google Scholar]
  18. YilmazO. 2001. Seismic data analysis, Processing, Inversion and Interpretation of Seismic Data: Vol. I. SEG, Tulsa, USA.
  19. ZhouB. and GreenhalghS.2008. Velocity sensitivity of seismic body waves to the anisotropic parameters of a TTI‐medium. Journal of Geophysics and Engineering5, 245–255.
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): Anisotropy; Migration; Modelling; Travel time

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