1887
Volume 65, Issue 2
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Existing and commonly used in industry nowadays, closed‐form approximations for a P‐wave reflection coefficient in transversely isotropic media are restricted to cases of a vertical and a horizontal transverse isotropy. However, field observations confirm the widespread presence of rock beds and fracture sets tilted with respect to a reflection boundary. These situations can be described by means of the transverse isotropy with an arbitrary orientation of the symmetry axis, known as tilted transversely isotropic media. In order to study the influence of the anisotropy parameters and the orientation of the symmetry axis on P‐wave reflection amplitudes, a linearised 3D P‐wave reflection coefficient at a planar weak‐contrast interface separating two weakly anisotropic tilted tranversely isotropic half‐spaces is derived. The approximation is a function of the incidence phase angle, the anisotropy parameters, and symmetry axes tilt and azimuth angles in both media above and below the interface. The expression takes the form of the well‐known amplitude‐versus‐offset “Shuey‐type” equation and confirms that the influence of the tilt and the azimuth of the symmetry axis on the P‐wave reflection coefficient even for a weakly anisotropic medium is strong and cannot be neglected. There are no assumptions made on the symmetry‐axis orientation angles in both half‐spaces above and below the interface. The proposed approximation can be used for inversion for the model parameters, including the orientation of the symmetry axes. Obtained amplitude‐versus‐offset attributes converge to well‐known approximations for vertical and horizontal transverse isotropic media derived by Rüger in corresponding limits. Comparison with numerical solution demonstrates good accuracy.

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2016-08-29
2021-07-30
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References

  1. AkiK. and RichardsP.G.1980. Quantitative Seismology: Theory and Methods. W.H. Freeman and Co. San Francisco, SA.
    [Google Scholar]
  2. AngererE., HorneS.A., GaiserJ.E., WaltersR., BagalaS. and VetriL.2002. Characterization of dipping fractures using Ps mode‐converted data. 72nd SEG meeting, Salt Lake City, USA, Expanded Abstracts, 1010–1013.
  3. AuldB.1973. Acoustic Fields and Waves in Solids, Vol.1. Wiley – Interscience.
    [Google Scholar]
  4. BehuraJ. and TsvankinI.2005. Small‐angle AVO response of PS‐waves in tilted TI media. 75th SEG meeting, Houston, USA, Expanded Abstracts, 206–209.
  5. BlangyJ.P.1994. AVO in transversely isotropic media: an overview. Geophysics59, 775–781.
    [Google Scholar]
  6. ChopraS. and CastagnaJ.2014. AVO, Investigations in Geophysics Vol. 16. Society of Exploration Geophysicists.
    [Google Scholar]
  7. GolikovP. and StovasA.2010. New weak‐contrast approximation for reflection coefficients in transversely isotropic media. Journal of Geophysics and Engineering7, 343–350.
    [Google Scholar]
  8. GrechkaV. and TsvankinI.2004. Characterization of dipping fractures in a transversely isotropic background. Geophysical Prospecting52, 1–10.
    [Google Scholar]
  9. IsaacJ. and LawtonD.2004. A practical method for estimating effective parameters of anisotropy from reflection seismic data. Geophysics69, 681–689.
    [Google Scholar]
  10. JechJ. and PsencikI.1989. First‐order perturbation method for anisotropic media. In: Workshop on Seismic Wave Propagation in Laterally Inhomogeneous Media, 13–18 June 1988, 369–376.
  11. JílekP.2002. Converted PS‐wave reflection coefficients in weakly anisotropic media. Pure and Applied Geophysics159, 1527–1562.
    [Google Scholar]
  12. MenschT. and RasolofosaonP.N.J.1997. Elastic‐wave velocities in anisotropic media of arbitrary symmetry; generalization of Thomsen's parameters epsilon, delta and gamma. Geophysical Journal International128, 43–64.
    [Google Scholar]
  13. Ps̆enc̆íkI. and MartinsJ.L.2001. Properties of weak contrast PP reflection/transmission coefficients for weakly anisotropic elastic media. Studia Geophysica et Geodetica45, 176–199.
    [Google Scholar]
  14. Ps̆enc̆íkI. and Vavryc̆ukV.1998. Weak contrast PP wave displacement R/T coefficients in weakly anisotropic elastic media. In: Geodynamics of lithosphere and Earth's Mantle: Seismic Anisotropy as a Record of the Past and Present Dynamic Processes, pp. 699–718.
  15. RügerA.1997. P‐wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry. Geophysics62, 713–722.
    [Google Scholar]
  16. RügerA.1998. Variation of P‐wave reectivity with offset and azimuth in anisotropic media. Geophysics63, 935–947.
    [Google Scholar]
  17. ShawR.K. and SenM.K.2004. Born integral, stationary phase and linearized reflection coefficients in weak anisotropic media. Geophysical Journal International158, 225–238.
    [Google Scholar]
  18. ShawR.K., SenM.K. and ChatterjeeA.B.2006. Estimation of dip of oblique fractures using AVOA analysis. In: 6th International Conference & Exposition on Petroleum Geophysics “Kolkata 2006”, pp. 377–281.
  19. ShueyR.1985. A simplification of the Zoeppritz equations. Geophysics50, 609–614.
    [Google Scholar]
  20. ThomsenL.1986. Weak elastic anisotropy. Geophysics51, 1954–1966.
    [Google Scholar]
  21. ThomsenL.1993. Weak anisotropic reflections. In: Offset Dependent Reflectivity (eds. Castagna and Backus). Society of Exploration Geophysicists, Tulsa, USA.
  22. TsvankinI.2012. Seismic Signatures and Analysis of Reection Data in Anisotropic Media, 3rd edn, Geophysical References Series. Society of Exploration Geophysicists.
    [Google Scholar]
  23. UrsinB. and HaugenG.U.1996. Weak‐contrast approximation of the elastic scattering matrix in anisotropic media. Pure and Applied Geophysics148, 685–714.
    [Google Scholar]
  24. Vavryc̆ukV.1999. Weak‐contrast reflection/transmission coefficients in weakly anisotropic elastic media: P‐wave incidence. Geophysical Journal International138, 553–562.
    [Google Scholar]
  25. Vavryc̆ukV. and Ps̆enc̆íkI.1998. PP‐wave reflection coefficients in weakly anisotropic elastic media. Geophysics63, 2129–2141.
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): Anistropy , AVA and TTI media
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