1887
Volume 69, Issue 1
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

An important cause of seismic anisotropic attenuation is the interbedding of thin viscoelastic layers. However, much less attention has been devoted to layer‐induced anisotropic attenuation. Here, we derive a group of unified weighted average forms for effective attenuation from a binary isotropic, transversely isotropic‐ and orthorhombic‐layered medium in the zero‐frequency limit by using the Backus averaging/upscaling method and analyse the influence of interval parameters on effective attenuation. Besides the corresponding interval attenuation and the real part of stiffness, the contrast in the real part of the complex stiffness is also a key factor influencing effective attenuation. A simple linear approximation can be obtained to calculate effective attenuation if the contrast in the real part of stiffness is very small. In a viscoelastic medium, attenuation anisotropy and velocity anisotropy may have different orientations of symmetry planes, and the symmetry class of the former is not lower than that of the latter. We define a group of more general attenuation‐anisotropy parameters to characterize not only the anisotropic attenuation with different symmetry classes from the anisotropic velocity but also the elastic case. Numerical tests reveal the influence of interval attenuation anisotropy, interval velocity anisotropy and the contrast in the real part of stiffness on effective attenuation anisotropy. Types of effective attenuation anisotropy for interval orthorhombic attenuation and interval transversely isotropic attenuation with a vertical symmetry (vertical transversely isotropic attenuation) are controlled only by the interval attenuation anisotropy. A type of effective attenuation anisotropy for interval TI attenuation with a horizontal symmetry (horizontal transversely isotropic attenuation) is controlled by the interval attenuation anisotropy and the contrast in the real part of stiffness. The type of effective attenuation anisotropy for interval isotropic attenuation is controlled by all three factors. The magnitude of effective attenuation anisotropy is positively correlated with the contrast in the real part of the stiffness. Effective attenuation even in isotropic layers with identical isotropic attenuation is anisotropic if the contrast in the real part of stiffness is non‐zero. In addition, if the contrast in the real part of stiffness is very small, a simple linear approximation also can be performed to calculate effective attenuation‐anisotropy parameters for interval anisotropic attenuation.

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2020-12-12
2021-01-18
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References

  1. Backus, G.E. (1962) Long‐wave elastic anisotropy produced by horizontal layering. Journal of Geophysical Research, 67(11), 4427–4440.
    [Google Scholar]
  2. Bakulin, A. (2003) Intrinsic and layer‐induced vertical transverse isotropy. Geophysics, 68(5), 1708–1713.
    [Google Scholar]
  3. Bakulin, A. and Grechka, V. (2003) Effective anisotropy of layered media. Geophysics, 68(6), 1817–1821.
    [Google Scholar]
  4. Behura, J. and Tsvankin, I. (2009) Estimation of interval anisotropic attenuation from reflection data. Geophysics, 74(6), A69–A74.
    [Google Scholar]
  5. Bos, L., Dalton, D.R., Slawinski, M.A. and Stanoev, T. (2017) On Backus average for generally anisotropic layers. Journal of Elasticity, 127(2), 179–196.
    [Google Scholar]
  6. Carcione, J.M. (1992) Anisotropic Q and velocity dispersion of finely layered media. Geophysical Prospecting, 40(7), 761–783.
    [Google Scholar]
  7. Carcione, J.M. (2014) Wave fields in real media: Wave propagation in anisotropic, anelastic, porous and electromagnetic media. Handbook of Geophysical Exploration: Seismic Exploration, 3rd edition, Amsterdam: Elsevier.
    [Google Scholar]
  8. Carter, A.J., Torres Caceres, V.A., Duffaut, K. and Stovas, A. (2020) Velocity‐attenuation model from check‐shot drift trends in North Sea well data. Geophysics, 85(2), D65–D74.
    [Google Scholar]
  9. Chichinina, T., Sabinin, V. and Ronquillo‐Jarillo, G. (2006) QVOA analysis: P‐wave attenuation anisotropy for fracture characterization. Geophysics, 71(3), C37–C48.
    [Google Scholar]
  10. Hao, Q. and Alkhalifah, T. (2017a) An acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis. Geophysics, 82(1), C9–C20.
    [Google Scholar]
  11. Hao, Q. and Alkhalifah, T. (2017b) An acoustic eikonal equation for attenuating orthorhombic media. Geophysics, 82(4), WA67–WA81.
    [Google Scholar]
  12. Hao, Q. and Greenhalgh, S. (2019) The generalized standard‐linear‐solid model and the corresponding viscoacoustic wave equations revisited. Geophysical Journal International, 219(3), 1939–1947.
    [Google Scholar]
  13. Hao, Q., Waheed, U. and Alkhalifah, T. (2019) P‐wave complex‐valued traveltimes in homogenous attenuating transversely isotropic media. Geophysical prospecting, 67, 2402–2413.
    [Google Scholar]
  14. Kumar, D. (2013) Applying Backus averaging for deriving seismic anisotropy of a long‐wavelength equivalent medium from well‐log data. Journal of Geophysics and Engineering, 10(5), 055001.
    [Google Scholar]
  15. Liu, E., Crampin, S., Queen, J.H and Rizer, W.D. (1993) Velocity and attenuation anisotropy caused by microcracks and macrofractures in a multiazimuth reverse VSP. Canadian Journal of Exploration Geophysics, 29(1), 177–188.
    [Google Scholar]
  16. MacBeth, C. (1999) Azimuthal variation in P‐wave signatures due to fluid flow. Geophysics, 64(4), 1181–1192.
    [Google Scholar]
  17. Parra, J.O. and Hackert, C. (2002) Wave attenuation attributes as flow unit indicators. The Leading Edge, 21(6), 564–572.
    [Google Scholar]
  18. Pointer, T., Liu, E. and Hudson, J.A. (2000) Seismic wave propagation in cracked porous media. Geophysical Journal International, 142(1), 199–231.
    [Google Scholar]
  19. Prasad, M. and Nur, A. (2003) Velocity and attenuation anisotropy in reservoir rocks. SEG Technical Program Expanded Abstracts, 1652–1655.
    [Google Scholar]
  20. Schoenberg, M. and Muir, F. (1989) A calculus for finely layered anisotropic media. Geophysics, 54(5), 581–589.
    [Google Scholar]
  21. Shapiro, S.A. and Kneib, G. (1993) Seismic attenuation by scattering: Theory and numerical results. Geophysical Journal International, 114(2), 373–391.
    [Google Scholar]
  22. Shekar, B. and Tsvankin, I. (2012) Anisotropic attenuation analysis of crosshole data generated during hydraulic fracturing. The Leading Edge, 31(5), 588–593.
    [Google Scholar]
  23. Stovas, A. and Ursin, B. (2003) Reflection and transmission responses of layered transversely isotropic viscoelastic media. Geophysical Prospecting, 51(5), 447–447–477.
    [Google Scholar]
  24. Stovas, A. and Roganov, Y. (2010) Scattering versus intrinsic attenuation in periodically layered media. Journal of Geophysics and Engineering, 7(2), 135–142.
    [Google Scholar]
  25. Tao, G. and King, M.S. (1990) Shear‐wave velocity and Q anisotropy in rocks: A laboratory study. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 27(5), 353–361.
    [Google Scholar]
  26. Thomsen, L. (1986) Weak elastic anisotropy. Geophysics, 51(10), 1954–1966.
    [Google Scholar]
  27. Tisato, N. and Quintal, B. (2014) Laboratory measurements of seismic attenuation in sandstone: Strain versus fluid saturation effects. Geophysics, 79(5), WB9–WB14.
    [Google Scholar]
  28. Tsvankin, I. (1997) Anisotropic parameters and P‐wave velocity for orthorhombic media. Geophysics, 62(4), 1292–1309.
    [Google Scholar]
  29. Vavryčuk, V. (2009) Weak anisotropy‐attenuation parameters. Geophysics, 74(5), WB203–WB213.
    [Google Scholar]
  30. Zhubayev, A., Houben, M.E., Smeulders, D.M. and Barnhoorn, A. (2016) Ultrasonic velocity and attenuation anisotropy of shales. Whitby, United Kingdom. Geophysics, 81(1), D45–D56.
    [Google Scholar]
  31. Zhu, Y. and Tsvankin, I. (2006) Plane‐wave propagation in attenuative transversely isotropic media. Geophysics, 71(2), T17–T30.
    [Google Scholar]
  32. Zhu, Y. and Tsvankin, I. (2007) Plane‐wave attenuation anisotropy in orthorhombic media. Geophysics, 72(1), D9–D19.
    [Google Scholar]
  33. Zhu, Y., Tsvankin, I., Dewangan, P. and Wijk, K.V. (2007) Physical modeling and analysis of P‐wave attenuation anisotropy in transversely isotropic media. Geophysics, 72(1), D1–D7.
    [Google Scholar]
  34. Zhu, Y., Tsvankin, I. and Vasconcelos, I. (2007) Effective attenuation anisotropy of thin‐layered media. Geophysics, 72(5), D93–D106.
    [Google Scholar]
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