1887
Volume 67 Number 9
  • E-ISSN: 1365-2478
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Abstract

ABSTRACT

Degeneracies of the slowness surfaces of shear (and compressional) waves in low‐symmetry anisotropic media (such as orthorhombic), known as point singularities, pose difficulties during modelling and inversion, but can be potentially used in the latter as model parameter constraints. I analyse the quantity and spatial arrangement of point singularities in orthorhombic media, as well as their relation to the overall strength of velocity anisotropy. A classification scheme based on the number and spatial distribution of singularity directions is proposed. In orthorhombic models (where the principal shear moduli are smaller than the principal compressional moduli), point singularities can only be arranged in three distinct patterns, and media with the theoretical minimum (0) and maximum (16) number of singularities are not possible. In orthorhombic models resulting from embedding vertical fractures in transversely isotropic background, only two singularity distributions are possible, in contrast to what was previously thought. Although the total number of singularities is independent of the overall anisotropy strength, for general (non‐) orthorhombic models, different spatial distributions of singularities become more probable with increasing magnitude of anisotropy.

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2019-05-30
2020-08-10
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References

  1. AlshitsV. and LotheJ.1979. Elastic waves in triclinic crystals. II. Topology of polarization fields and some general theorems. Soviet Physics, Crystallography24, 393–398. Originally in Russian, 1978, Crystallography, 24, 683–693.
    [Google Scholar]
  2. BakulinA., GrechkaV. and TsvankinI.2000. Estimation of fracture parameters for reflection seismic data; Part II, Fractured models with orthorhombic symmetry. Geophysics65, 1803–1817.
    [Google Scholar]
  3. BoulangerP. and HayesM.1998. Acoustic axes for elastic waves in crystals: theory and applications. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences454, 2323–2346.
    [Google Scholar]
  4. BrownR. J., CrampinS., GallantE. V. and VestrumR. W.1993. Modelling shear‐wave singularities in an orthorhombic medium. Canadian Society of Exploration Geophysicists, a special issue on papers presented at the Fifth International Workshop on Seismic Anisotropy 29, 276–284.
    [Google Scholar]
  5. CrampinS.1981. A review of wave motion in anisotropic and cracked elastic‐media. Wave Motion3, 343–391.
    [Google Scholar]
  6. CrampinS.1991. Effects of point singularities on shear‐wave propagation in sedimentary basins. Geophysical Journal International107, 531–543.
    [Google Scholar]
  7. GrechkaV.2015. Shear‐wave group‐velocity surfaces in low‐symmetry anisotropic media. Geophysics80, C1–C7.
    [Google Scholar]
  8. GrechkaV.2017. Algebraic degree of a general group‐velocity surface. Geophysics82, WA45–WA53.
    [Google Scholar]
  9. GrechkaV. and YaskevichS.2014. Azimuthal anisotropy in microseismic monitoring: A Bakken case study. Geophysics79, KS1–KS12.
    [Google Scholar]
  10. GrechkaV. Y. and ObolentsevaI. R.1993. Geometrical structure of shear wave surfaces near singularity directions in anisotropic media. Geophysical Journal International115, 609–616.
    [Google Scholar]
  11. IvanovY. and StovasA.2017. S‐wave singularities in tilted orthorhombic media. Geophysics82, WA11–WA21.
    [Google Scholar]
  12. IvanovY. and StovasA.2018. Occurrence of the Point Singularities in Orthorhombic Media. 80th EAGE Conference and Exhibition, We B 10. EAGE, Extended Abstracts.
  13. JainA., OngS. P., HautierG., ChenW., RichardsW. D., DacekS., et al. 2013. Commentary: The Materials Project: a materials genome approach to accelerating materials innovation. APL Materials1, 011002.
    [Google Scholar]
  14. JongM. d., ChenW., AngstenT., JainA., NotestineR., GamstA., et al. 2015. Charting the complete elastic properties of inorganic crystalline compounds. Scientific Data2, sdata20159.
    [Google Scholar]
  15. KhatkevichA. G.1977. Classification of crystals by acoustic properties. Soviet Physics, Crystallography22, 701–705.
    [Google Scholar]
  16. MusgraveM. J. P.1981. On an elastodynamic classification of orthorhombic media. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences374, 401–429.
    [Google Scholar]
  17. MusgraveM. J. P.1985. Acoustic axes in orthorhombic media. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences401, 131–143.
    [Google Scholar]
  18. RanganathanS. I. and Ostoja‐StarzewskiM.2008. Universal elastic anisotropy index. Physical Review Letters101, 055504.
    [Google Scholar]
  19. SchoenbergM.1980. Elastic wave behavior across linear slip interfaces. The Journal of the Acoustical Society of America68, 1516–1521.
    [Google Scholar]
  20. SchoenbergM. and HelbigK.1997. Orthorhombic media: modeling elastic wave behavior in a vertically fractured earth. Geophysics62, 1954–1974.
    [Google Scholar]
  21. ShuvalovA. L.1998. Topological features of the polarization fields of plane acoustic waves in anisotropic media. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences454, 2911–2947.
    [Google Scholar]
  22. ThomsenL.1986. Weak elastic anisotropy. Geophysics51, 1954–1966.
    [Google Scholar]
  23. TsvankinI.1997. Anisotropic parameters and P‐wave velocity for orthorhombic media. Geophysics62, 1292–1309.
    [Google Scholar]
  24. VavryčukV.1999. Properties of S waves near a kiss singularity: a comparison of exact and ray solutions. Geophysical Journal International138, 581–589.
    [Google Scholar]
  25. VavryčukV.2001. Ray tracing in anisotropic media with singularities. Geophysical Journal International145, 265–276.
    [Google Scholar]
  26. VavryčukV.2003a. Behavior of rays near singularities in anisotropic media. Physical Review B67, 054105.
    [Google Scholar]
  27. VavryčukV.2003b. Parabolic lines and caustics in homogeneous weakly anisotropic solids. Geophysical Journal International152, 318–334.
    [Google Scholar]
  28. VavryčukV.2005. Acoustic axes in triclinic anisotropy. The Journal of the Acoustical Society of America118, 647–653.
    [Google Scholar]
  29. VavryčukV.2013. Inversion for weak triclinic anisotropy from acoustic axes. Wave Motion50, 1271–1282.
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): Anisotropy , Attenuation , Numerical study and Theory
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