1887
Volume 67, Issue 5
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Kinematical characteristics of reflected waves in anisotropic elastic media play an important role in the seismic imaging workflow. Considering compressional and converted waves, we derive new, azimuthally dependent, slowness‐domain approximations for the kinematical characteristics of reflected waves (radial and transverse offsets, intercept time and traveltime) for layered orthorhombic media with varying azimuth of the vertical symmetry planes. The proposed method can be considered an extension of the well‐known ‘generalized moveout approximation’ in the slowness domain, from azimuthally isotropic to azimuthally anisotropic models. For each slowness azimuth, the approximations hold for a wide angle range, combining power series coefficients in the vicinity of both the normal‐incidence ray and an additional wide‐angle ray. We consider two cases for the wide‐angle ray: a ‘critical slowness match’ and a ‘pre‐critical slowness match’ studied in Parts I and II of this work, respectively. For the critical slowness match, the approximations are valid within the entire slowness range, up to the critical slowness. For the ‘pre‐critical slowness match’, the approximations are valid only within the bounded slowness range; however, the accuracy within the defined range is higher. The critical slowness match is particularly effective when the subsurface model includes a dominant high‐velocity layer where, for nearly critical slowness values, the propagation in this layer is almost horizontal. Comparing the approximated kinematical characteristics with those computed by numerical ray tracing, we demonstrate high accuracy.

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2019-03-26
2024-03-29
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References

  1. AbediM. and StovasA.2018. Extended generalized nonhyperbolic moveout approximation. Geophysical Journal International, 216, 1428–1440.
    [Google Scholar]
  2. Al‐DajaniA., TsvankinI. and ToksozM. N.1998. Nonhyperbolic reflection moveout for azimuthally anisotropic media: 68th Annual International Meeting, SEG. Expanded Abstracts, 1479–1482.
  3. AlkhalifahT.1998. Acoustic approximations for processing in transversely isotropic media. Geophysics63, 623–631.
    [Google Scholar]
  4. AlkhalifahT.2000. The offset‐midpoint traveltime equation for transversely isotropic media. Geophysics65, 1316–1325.
    [Google Scholar]
  5. AlkhalifahT.2003. An acoustic wave equation for orthorhombic anisotropy. Geophysics68, 1169–1172.
    [Google Scholar]
  6. AlkhalifahT.2011. Scanning anisotropy parameters in complex media. Geophysics76, U13–U22.
    [Google Scholar]
  7. AlkhalifahT.2013. Traveltime approximations for inhomogeneous transversely isotropic media with a horizontal symmetry axis. Geophysical Prospecting61, 495–503.
    [Google Scholar]
  8. AlkhalifahT. and TsvankinI.1995. Velocity analysis for transversely isotropic media. Geophysics60, 1550–1566.
    [Google Scholar]
  9. BliasE.2013. Two‐interval high‐accuracy NMO approximation: 83rd Annual International Meeting, SEG. Expanded Abstracts, 4666–4671.
  10. ČervenýV.2001. Seismic Ray Theory. Cambridge University Press.
  11. ChapmanC.2004. Fundamentals of Seismic Wave Propagation. Cambridge University Press.
  12. CrampinS.1981. A review of wave motion in anisotropic and cracked elastic‐media. Wave Motion3, 343–391.
    [Google Scholar]
  13. CrampinS.1991. Effects of point singularities on shear‐wave propagation in sedimentary basins. Geophysical Journal International107, 531–543.
    [Google Scholar]
  14. FarraV. and PšenčíkI.2013a. Moveout approximations for P and SV waves in VTI media. Geophysics78, WC81–WC92.
    [Google Scholar]
  15. FarraV. and PšenčíkI.2013b. Moveout approximations for P and SV waves in dip‐constrained transversely isotropic media. Geophysics78, C53–C59.
    [Google Scholar]
  16. FarraV., PšenčíkI. and JílekP.2016. Weak‐anisotropy moveout approximations for P waves in homogeneous layers of monoclinic or higher anisotropy symmetries. Geophysics81, C17–C37.
    [Google Scholar]
  17. FarraV. and PšenčíkI.2017. Weak‐anisotropy moveout approximations for P‐waves in homogeneous TOR layers. Geophysics82, WA23–WA32.
    [Google Scholar]
  18. FomelS. and StovasA.2010. Generalized nonhyperbolic moveout approximation. Geophysics75, U9–U18.
    [Google Scholar]
  19. GereaC., NicoletisL. and GrangerP.2000. Multicomponent true‐amplitude anisotropic imaging. Anisotropy 2000, Fractures, Converted Waves, and Case Studies.
  20. GrechkaV. and TsvankinI.1998. Feasibility of non‐hyperbolic moveout inversion in transversely isotropic media. Geophysics63, 957–969.
    [Google Scholar]
  21. HakeH.1986. Slant stacking and its significance for anisotropy. Geophysical Prospecting34, 595–608.
    [Google Scholar]
  22. HaoQ. and StovasA.2016.P‐wave slowness surface approximation for tilted orthorhombic media. Geophysics81, C99–C112.
    [Google Scholar]
  23. HaoQ., StovasA. and AlkhalifahT.2016. The offset‐midpoint traveltime pyramid of P‐waves in homogeneous orthorhombic media. Geophysics81, C151–C162.
    [Google Scholar]
  24. HelbigK. and SchoenbergM.1987. Anomalous polarization of elastic waves in transversely isotropic media. Journal of the Acoustical Society of America81, 1235–1245.
    [Google Scholar]
  25. IvanovY. and StovasA.2016. Normal moveout velocity ellipse in tilted orthorhombic media. Geophysics81, C319–C336.
    [Google Scholar]
  26. IvanovY. and StovasA.2017. Traveltime parameters in tilted orthorhombic media. Geophysics82, C187–C200.
    [Google Scholar]
  27. KorenZ. and RavveI.2017a. Fourth‐order NMO velocity in elastic layered orthorhombic media, Part II: Offset‐azimuth domain. Geophysics82, C113–C132.
    [Google Scholar]
  28. KorenZ. and RavveI.2017b. Normal moveout coefficients for horizontally layered triclinic media. Geophysics82, WA119–WA145.
    [Google Scholar]
  29. KorenZ. and RavveI.2018. Slowness domain offset and traveltime approximations in layered vertical transversely isotropic media. Geophysical Prospecting66, 1070–1096.
    [Google Scholar]
  30. PechA., TsvankinI. and GrechkaV.2003. Quartic moveout coefficient: 3D description and application to tilted TI media. Geophysics68, 1600–1610.
    [Google Scholar]
  31. PechA. and TsvankinI.2004. Quartic moveout coefficient for a dipping azimuthally anisotropic layer. Geophysics69, 699–707.
    [Google Scholar]
  32. PšenčíkI. and FarraV.2017. Reflection moveout approximations for P‐waves in a moderately anisotropic homogeneous tilted transverse isotropy layer. Geophysics82, C175–C185.
    [Google Scholar]
  33. Ravve, I. and KorenZ.2017a. Fourth‐order NMO velocity in elastic layered orthorhombic media, Part I: Slowness‐azimuth domain. Geophysics82, C91–C111.
    [Google Scholar]
  34. RavveI. and KorenZ.2017b. Traveltime approximation in vertical transversely isotropic layered media. Geophysical Prospecting65, 1559–1581.
    [Google Scholar]
  35. SchoenbergM. and HelbigK.1997. Orthorhombic media: modeling elastic wave behavior in a vertically fractured earth. Geophysics62, 1954–1974.
    [Google Scholar]
  36. SripanichY. and FomelS.2015. On anelliptic approximations for qP velocities in transversely isotropic and orthorhombic media. Geophysics80, C89–C105.
    [Google Scholar]
  37. SripanichY. and FomelS.2016. Theory of interval traveltime parameter estimation in layered anisotropic media. Geophysics81, C253–C263.
    [Google Scholar]
  38. SripanichY., FomelS., StovasA. and HaoQ.2017. 3D generalized nonhyperbolic moveout approximation. Geophysics82, C49–C59.
    [Google Scholar]
  39. StovasA.2015. Azimuthally‐dependent kinematic properties of orthorhombic media. Geophysics80, C107–C122.
    [Google Scholar]
  40. StovasA.2017. Kinematic parameters of pure‐ and converted‐mode waves in elastic orthorhombic media. Geophysical Prospecting65, 426–452.
    [Google Scholar]
  41. StovasA. and AlkhalifahT.2012. A new traveltime approximation for TI media. Geophysics77, C37–C42.
    [Google Scholar]
  42. StovasA. and AlkhalifahT.2013. A tilted transversely isotropic slowness surface approximation. Geophysical Prospecting61, 568–573.
    [Google Scholar]
  43. StovasA. and FomelS.2012. Generalized nonelliptic moveout approximation in τ − p domain. Geophysics77, U23–U30.
    [Google Scholar]
  44. StovasA. and FomelS.2017. The modified generalized moveout approximation: a new parameter selection. Geophysical Prospecting65, 687–695.
    [Google Scholar]
  45. StovasA., MasmoudiN. and AlkhalifahT.2016. Application of perturbation theory for P‐wave Eikonal equation in orthorhombic media. Geophysics81, C309–C317.
    [Google Scholar]
  46. ThomsenL.1986. Weak elastic anisotropy. Geophysics51, 1954–1966.
    [Google Scholar]
  47. TsvankinI.1997. Anisotropic parameters and P‐wave velocity for orthorhombic media. Geophysics62, 1292–1309.
    [Google Scholar]
  48. TsvankinI.2012. Seismic Signatures and Analysis of Reflection Data in Anisotropic Media, 3rd edn. Society of Exploration Geophysicists.
    [Google Scholar]
  49. TsvankinI. and GrechkaV.2011. Seismology of Azimuthally Anisotropic Media and Seismic Fracture Characterization. Oklahoma: Society of Exploration Geophysicists.
    [Google Scholar]
  50. TsvankinI. and ThomsenL.1994. Nonhyperbolic reflection moveout in anisotropic media. Geophysics59, 1290–1304.
    [Google Scholar]
  51. VasconcelosI. and TsvankinI.2006. Nonhyperbolic moveout inversion of wide‐azimuth P‐wave data for orthorhombic media. Geophysical Prospecting54, 535–552.
    [Google Scholar]
  52. Xu, S. and Stovas, A.2018. Triplications on traveltime surface for pure and converted wave modes in elastic orthorhombic media. Geophysical Journal International215, 677–694.
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): Anisotropy; Modeling

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