1887
  1. Home
  2. A-Z Publications
  3. Geophysical Prospecting
  4. Volume 69, Issue 8
  5. Article
Volume 69, Issue 8-9
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

The accuracy of an explicit traveltime‐offset approximation affects the results of the velocity analysis that plays a crucial role in the seismic data processing. Seismic anisotropy is important to account for large offset and azimuth since it can provide detailed information comparing with the isotropic assumption. For the perturbation‐based method, different traveltime approximation forms result in different accuracy. It is necessary to find the optimal traveltime approximation for specific signs and magnitudes of the anellipticity and different offset ranges. In this paper, a series of perturbation‐based traveltime approximations from different acoustic assumptions and parameterizations are specified. The perturbation coefficients are derived from the corresponding acoustic eikonal equations. We test the accuracy of the defined perturbation approximations in four homogeneous transversely isotropic medium with vertical symmetry axis (VTI) medium with a different set of anisotropy parameters and one multilayered transversely isotropic medium with vertical symmetry axis medium. The sensitivity in anellipticity for different approximations is also analysed. We find that different approximation achieves different accuracy under the circumstance of specific offset range and the value of anellipticity. Therefore, the optimal approximation form with higher accuracy can be selected based on different offset ranges and the magnitudes of anellipticity.

© 2021 European Association of Geoscientists & Engineers © 2021 European Association of Geoscientists & Engineers
Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.13131
2021-10-08
2024-04-24

  • From This Site

    /content/journals/10.1111/1365-2478.13131
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Alkhalifah, T. (1998) Acoustic approximations for processing in transversely isotropic media. Geophysics, 63, 623–631.
     [Google Scholar]
  2. Alkhalifah, T. (2000) An acoustic wave equation for anisotropic media. Geophysics, 65, 1239–1250.
     [Google Scholar]
  3. Alkhalifah, T. (2011) Scanning anisotropy parameters in complex media. Geophysics, 76, U13–U22.
     [Google Scholar]
  4. Alkhalifah, T. (2013) Residual extrapolation operators for efficient wavefield construction. Geophysical Journal International, 193, 1027–1034.
     [Google Scholar]
  5. Alkhalifah, T. and Plessix, R.É. (2014) A recipe for practical full‐waveform inversion in anisotropic media: An analytical parameter resolution study. Geophysics, 79, R91–R101.
     [Google Scholar]
  6. Bachman, R.T. (1983) Elastic anisotropy in marine sedimentary rocks. Journal of Geophysical Research, 88, 539–545.
     [Google Scholar]
  7. Bachrach, R., Dvorkin, J. and Nur, A. (2000) Seismic velocities and Poisson's ratio of shallow unconsolidated sands. Geophysics, 65, 559–564.
     [Google Scholar]
  8. Bender, C.M. and Orszag, S.A. (1978) Advanced Mathematical Methods for Scientists and Engineers. McGraw‐Hill.
     [Google Scholar]
  9. Berryman, J., Grechka, V. and Berge, P. (1999) Analysis of Thomsen parameters for finely layered VTI media. Geophysical Prospecting, 47, 959–978.
     [Google Scholar]
  10. bin Waheed, U., Stovas, A. and Alkhalifah, T. (2017) Anisotropy parameter inversion in vertical axis of symmetry media using diffractions. Geophysical Prospecting, 65, 194–203.
     [Google Scholar]
  11. Dix, C.H. (1955) Seismic velocities from surface measurements. Geophysics, 20, 68–86.
     [Google Scholar]
  12. Fomel, S. (2004) On anelliptic approximations for qP velocities in VTI media. Geophysical Prospecting, 52, 247–259.
     [Google Scholar]
  13. Fomel, S. and Stovas, A. (2010) Generalized nonhyperbolic moveout approximation. Geophysics, 75, U9–U18.
     [Google Scholar]
  14. Fowler, P.J. (2003) Practical VTI approximations: a systematic anatomy. Journal of Applied Geophysics, 54, 347–367.
     [Google Scholar]
  15. Golikov, P. and Stovas, A. (2012) Accuracy comparison of nonhyperbolic moveout approximations for qP‐waves in VTI media. Journal of Geophysics and Engineering, 9, 428–432.
     [Google Scholar]
  16. Grechka, V. (2013) Ray‐direction velocities in VTI media. Geophysics, 78, F1‐ F5.
     [Google Scholar]
  17. Grechka, V., Tsvankin, I. and Cohen, J. (1999) Generalized Dix equation and analytic treatment of normal moveout velocity for anisotropic media. Geophysical Prospecting, 47, 117–148.
     [Google Scholar]
  18. Grechka, V., Zhang, L. and Rector, J. (2004) Shear waves in acoustic anisotropic media. Geophysics, 69, 576–582.
     [Google Scholar]
  19. Huang, X. and Greenhalgh, S. (2018) Linearized formulations and approximate solutions for the complex eikonal equation in orthorhombic media and applications of complex seismic traveltime. Geophysics, 83, C115–C136.
     [Google Scholar]
  20. Huang, X. and Greenhalgh, S. (2019) Traveltime approximation for strongly anisotropic media using the homotopy analysis method. Geophysical Journal International, 216, 1648–1664.
     [Google Scholar]
  21. Huang, X., Sun, J. and Greenhalgh, S. (2018) On the solution of the complex eikonal equation in acoustic VTI media: a perturbation plus optimization scheme. Geophysical Journal International, 214, 907–932.
     [Google Scholar]
  22. Ibanez‐Jacome, W., Alkhalifah, T. and Waheed, U. (2013) Effective orthorhombic anisotropic models for wavefield extrapolation. Geophysical Journal International, 198, 1653–1661.
     [Google Scholar]
  23. Jones, L. and Wang, H. (1981) Ultrasonic velocities in Cretaceous shales from the Williston basin. Geophysics, 46, 288–297.
     [Google Scholar]
  24. Koren, Z. and Ravve, I. (2006) Constrained Dix inversion. Geophysics, 71, R113–R130.
     [Google Scholar]
  25. Pestana, R. and Stoffa, P.L. (2010) Time evolution of the wave equation using rapid expansion method. Geophysics, 75, T121–T131.
     [Google Scholar]
  26. Ravve, I. and Koren, Z. (2010) Moveout approximation for horizontal transversely isotropic and vertical transversely isotropic layered medium. Part I: 1D ray propagation. Geophysical Prospecting, 58, 577–597.
     [Google Scholar]
  27. Ravve, I. and Koren, Z. (2017) Traveltime approximation in vertical transversely isotropic layered media. Geophysical Prospecting, 65, 1559–1581.
     [Google Scholar]
  28. Ravve, I. and Koren, Z. (2019) Directional derivatives of ray velocity in anisotropic elastic media. Geophysical Journal International, 216, 859–895.
     [Google Scholar]
  29. Ravve, I. and Koren, Z. (2021) Slowness vector vs. ray direction in polar anisotropic media. Geophysical Journal International, 225, 1725–1754.
     [Google Scholar]
  30. Sayers, C. (2004) Seismic anisotropy of shales: What determines the sign of Thomsen's delta parameter? SEG Annual Meeting, SEG‐2004‐0103.
  31. Stovas, A., Alkhalifah, T. and Waheed, U. (2020) Pure P‐ and S‐wave equations in transversely isotropic media. Geophysical Prospecting, 68, 2762–2769.
     [Google Scholar]
  32. Tsvankin, I., Gaiser, J., Grechka, V., Van Der Baan, M. and Thomsen, L. (2010) Seismic anisotropy in exploration and reservoir characterization: an overview. Geophysics, 75, 75A15–75A29.
     [Google Scholar]
  33. Wang, X. and Tsvankin, I. (2009) Estimation of interval anisotropy parameters using velocity‐independent layer stripping. Geophysics, 74, WB117–WB127.
     [Google Scholar]
  34. Xu, S., Stovas, A. and Alkhalifah, T. (2016) Estimation of the anisotropy parameters from imaging moveout of diving wave in a factorized VTI medium. Geophysics, 81, C139‐C150.
     [Google Scholar]
  35. Xu, S., Stovas, A. and Hao, Q. (2017) Perturbation‐based moveout approximations in anisotropic media. Geophysical Prospecting, 65,1218–1230.
     [Google Scholar]
  36. Xu, S., Stovas, A., Alkhalifah, T. and Mikada, H. (2020) New acoustic approximation for transversely isotropic media with a vertical symmetry axis. Geophysics, 85, C1–C12.
     [Google Scholar]
  37. Xu, S., Stovas, A. and Sripanich, Y. (2018) An anelliptic approximation for geometrical spreading in transversely isotropic and orthorhombic media. Geophysics, 83, C37–C47.
     [Google Scholar]
  38. Yilmaz, O. (2001) Seismic Data Analysis: Processing, Inversion, and Interpretation of Seismic Data. Investigations in geophysics, vol. 10. SEG.
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.13131
Loading
Perturbation‐based traveltime approximation for two acoustic assumptions in the transversely isotropic media with a vertical symmetry axis
Geophysical Prospecting 69, 1591 (2021); https://doi.org/10.1111/1365-2478.13131
/content/journals/10.1111/1365-2478.13131
/content/journals/10.1111/1365-2478.13131
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Anisotropy; Modelling; Numerical study; Seismics; Velocity analysis

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error