1887
Volume 65, Issue 6
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

The well‐known asymptotic fractional four‐parameter traveltime approximation and the five‐parameter generalised traveltime approximation in stratified multi‐layer transversely isotropic elastic media with a vertical axis of symmetry have been widely used for pure‐mode and converted waves. The first three parameters of these traveltime expansions are zero‐offset traveltime, normal moveout velocity, and quartic coefficient, ensuring high accuracy of traveltimes at short offsets. The additional parameter within the four‐parameter approximation is an effective horizontal velocity accounting for large offsets, which is important to avoid traveltime divergence at large offsets. The two additional parameters in the above‐mentioned five‐parameter approximation ensure higher accuracy up to a given large finite offset with an exact match at this offset. In this paper, we propose two alternative five‐parameter traveltime approximations, which can be considered extensions of the four‐parameter approximation and an alternative to the five‐parameter approximation previously mentioned. The first three short‐offset parameters are the same as before, but the two additional long‐offset parameters are different and have specific physical meaning. One of them describes the propagation in the high‐velocity layer of the overburden (nearly horizontal propagation in the case of very large offsets), and the other characterises the intercept time corresponding to the critical slowness that includes contributions of the lower velocity layers only. Unlike the above‐mentioned approximations, both of the proposed traveltime approximations converge to the theoretical (asymptotic) linear traveltime at the limit case of very large (“infinite”) offsets. Their accuracy for moderate to very large offsets, for quasi‐compressional waves, converted waves, and shear waves polarised in the horizontal plane, is extremely high in cases where the overburden model contains at least one layer with a dominant higher velocity compared with the other layers. We consider the implementation of the proposed traveltime approximations in all classes of problems in which the above‐mentioned approximations are used, such as reflection and diffraction analysis and imaging.

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2017-03-19
2024-03-29
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References

  1. AkiK. and RichardsP.2002. Quantitative Seismology, 2nd edn. University Science Books.
    [Google Scholar]
  2. Al‐DajaniA. and ToksozN.2001. Non‐hyperbolic Reflection Moveout for Orthorhombic Media. Earth Resources Laboratory, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA.
    [Google Scholar]
  3. AlkhalifahT.1997. Velocity analysis using nonhyperbolic moveout in transversely isotropic media. Geophysics62, 1839–1854.
    [Google Scholar]
  4. AlkhalifahT.2011. Scanning anisotropy parameters in complex media. Geophysics76, U13–U22.
    [Google Scholar]
  5. AlkhalifahT. and TsvankinI.1995. Velocity analysis for transversely isotropic media. Geophysics60, 1550–1566.
    [Google Scholar]
  6. BliasE.2009. Long‐offset NMO approximations for a layered VTI model. Model study. SEG annual meeting, Extended Abstracts, 3745–3748.
  7. CastleR.1988. Shifted hyperbola and normal moveout. 58th SEG meeting, Expanded Abstracts, 894–896.
  8. CastleR.1994. A theory of normal moveout. Geophysics59, 983–999.
    [Google Scholar]
  9. de BazelaireE.1988. Normal moveout revisited: inhomogeneous media and curved interfaces. Geophysics53, 143–157.
    [Google Scholar]
  10. DixC.H.1955. Seismic velocities from surface measurements. Geophysics20, 68–87.
    [Google Scholar]
  11. DoumaH. and CalvertA.2006. Nonhyperbolic moveout analysis in VTI media using rational interpolation. Geophysics71(3), D59–D71.
    [Google Scholar]
  12. DoumaH. and van der BaanM.2008. Rational interpolation of qP‐traveltimes for semblance‐based anisotropy estimation in layered VTI media. Geophysics73(4), D53–D62.
    [Google Scholar]
  13. FarraV. and PsencıkI.2013a. Moveout approximations for P and SV waves in VTI media. Geophysics78, WC81–WC92.
    [Google Scholar]
  14. FarraV. and PsencikI.2013b. Moveout approximations for P and SV waves in dip‐constrained transversely isotropic media. Geophysics78, C53–C59.
    [Google Scholar]
  15. FarraV. and PsencikI.2014. Moveout approximations for P waves in media of monoclinic and higher anisotropy symmetries. Seismic Waves in Complex 3‐D Structures24, 35–58.
    [Google Scholar]
  16. FarraV., PsencikI. and JilekP.2015. Weak‐anisotropy moveout approximations for P waves in homogeneous layers of monoclinic or higher anisotropy symmetries. Seismic Waves in Complex 3‐D Structures25, 51–92.
    [Google Scholar]
  17. FomelS.2004. On anelliptic approximations for qP velocities in VTI media. Geophysical Prospecting52, 247–259.
    [Google Scholar]
  18. FomelS. and StovasA.2010. Generalized nonhyperbolic moveout approximation. Geophysics75, U9–U18.
    [Google Scholar]
  19. GereaC.2001. Multicomponent prestack time‐imaging and migration‐based velocity analysis in transversely isotropic media. Ph.D. thesis, French Institute of Petroleum, France.
    [Google Scholar]
  20. GereaC., NicoletisL. and GrangerP.2000. Multicomponent true‐amplitude anisotropic imaging. 9th IWSA International Workshop on Seismic Anisotropy: Fractures, Converted Waves and Case Studies, Extended Abstracts.
    [Google Scholar]
  21. GrechkaV. and TsvankinI.1998. Feasibility of nonhyperbolic moveout inversion in transversely isotropic media. Geophysics63, 957–969.
    [Google Scholar]
  22. GrechkaV., TsvankinI. and CohenJ.1997. Generalized Dix equation and analytic treatment of normal‐moveout velocity for anisotropic media. SEG annual meeting, Expanded Abstracts, 1246–1249.
  23. HakeH., HelbigK. and MesdagC.1984. Three‐term Taylor series for t2−x2 curves of P‐ and S‐waves over layered transversely isotropic ground. Geophysical Prospecting32, 828–850.
    [Google Scholar]
  24. HaoQ. and StovasA.2015. Generalized moveout approximation for P–SV converted waves in vertically inhomogeneous transversely isotropic media with a vertical symmetry axis. Geophysical Prospecting. Early view.
    [Google Scholar]
  25. KorenZ. and RavveI.2015. Fourth‐order NMO velocity for compressional waves in layered orthorhombic media. 77th EAGE meeting, Extended Abstracts.
  26. LevinV. and ParkJ.1997. P‐SH conversions in a flat‐layered medium with anisotropy of arbitrary orientation. Geophysics Journal International131, 253–266.
    [Google Scholar]
  27. LiX. and YuanJ.1999. Converted‐wave moveout and parameter estimation for transverse isotropy. 61st EAGE meeting, Expanded Abstracts, Vol. I, 4–35.
  28. LiX. and YuanJ.2003. Converted‐wave moveout and conversion‐point equations in layered VTI media: theory and applications. Journal of Applied Geophysics54, 297–317.
    [Google Scholar]
  29. MalovichkoA.1978. A new representation of the traveltime curve of reflected waves in horizontally layered media. Applied Geophysics91, 47–53 (in Russian).
    [Google Scholar]
  30. RavveI. and KorenZ.2015. Long‐offset asymptotic moveout for compressional waves in layered orthorhombic media. 77th EAGE meeting, Extended Abstracts.
  31. RavveI. and KorenZ.2016. Long‐offset moveout approximation for VTI elastic layered media. 78th EAGE meeting, Extended Abstracts.
  32. SchoenbergM. and DayleyT.2003. qSV wavefront triplication in a transversely isotropic material. 73rd SEG meeting, Expanded Abstracts, 137–140.
  33. SenM. and MukherjeeA.2003. τp analysis in transversely isotropic media. Geophysical Journal International154, 647–658.
    [Google Scholar]
  34. SimmonsG. and WangH.1971. Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook. Massachusetts Institute of Technology Press.
    [Google Scholar]
  35. StewartR., GaiserJ., BrownR. and LawtonD.2002. Converted‐wave seismic exploration: methods. Geophysics67, 1348–1363.
    [Google Scholar]
  36. StewartR., GaiserJ., BrownR. and LawtonD.2003. Converted‐wave seismic exploration: applications. Geophysics68, 40–57.
    [Google Scholar]
  37. StovasA.2010. Generalized moveout approximation for qP‐ and qSV‐waves in a homogeneous transversely isotropic medium. Geophysics75, D79–D84.
    [Google Scholar]
  38. StovasA. and FomelS.2012. Generalized nonelliptic moveout approximation in τp domain. Geophysics77, U23–U30.
    [Google Scholar]
  39. TanerM. and KoehlerF.1969. Velocity spectra—digital computer derivation and applications of velocity functions. Geophysics34, 859–881. Errata 1971. Geophysics36, 787.
    [Google Scholar]
  40. ThomsenL.1986. Weak elastic anisotropy. Geophysics51, 1954–1966.
    [Google Scholar]
  41. ThomsenL.A.1999. Converted‐wave reflection seismology over inhomogeneous anisotropic media. Geophysics64, 678–690.
    [Google Scholar]
  42. TsvankinI.2001. Seismic Signatures and Analysis of Reflection Data in Anisotropic Media. Elsevier Science Ltd.
    [Google Scholar]
  43. TsvankinI. and ThomsenL.1994. Nonhyperbolic reflection moveout in anisotropic media. Geophysics59, 1290–1304.
    [Google Scholar]
  44. TygelM.1994. On the convergence of the NMO power series for a horizontally stratified medium. Russian Geology and Geophysics35, 124–132.
    [Google Scholar]
  45. TygelM., UrsinB. and StovasA.2007. Convergence of traveltime power series for a layered VTI medium. Geophysics72, D21–D28.
    [Google Scholar]
  46. UrsinB.1977. Seismic velocity estimation. Geophysical Prospecting25, 658–666.
    [Google Scholar]
  47. UrsinB. and StovasA.2006. Traveltime approximations for a layered transversely isotropic medium. Geophysics71, D23–D33.
    [Google Scholar]
  48. van der BaanM. and KendallJ. 2002. Estimating anisotropy parameters and traveltimes in the τp domain. Geophysics67, 1076–1086.
    [Google Scholar]
  49. van der BaanM. and KendallJ.2003. Traveltime and conversion‐point computations and parameter estimation in layered, anisotropic media by τp transform. Geophysics68, 210–224.
    [Google Scholar]
  50. VavryčukV.2004. Approximate conditions for the off‐axis triplication in transversely isotropic media. Studia Geophysica et Geodaetica48, 187–198.
    [Google Scholar]
  51. WaheedU., AlkhalifahT. and StovasA.2013. Diffraction traveltime approximation for TI media with an inhomogeneous background. Geophysics78, WC103–WC111.
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): layered media; traveltime approximation; vertical transverse isotropy

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