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

Abstract

ABSTRACT

Fractures in elastic media add compliance to a rock in the direction normal to the fracture strike. Therefore, elastic wave velocities in a fractured rock will vary as a function of the energy propagation direction relative to the orientation of the aligned fracture set. Anisotropic Thomson–Haskell matrix Rayleigh‐wave equations for a vertically transverse isotropic media can be used to model surface‐wave dispersion along the principal axes of a vertically fractured and transversely isotropic medium. Furthermore, a workflow combining first‐break analysis and azimuthal anisotropic Rayleigh‐wave inversion can be used to estimate P‐wave and S‐wave velocities, Thomsen's , and Thomsen's along the principal axes of the orthorhombic symmetry. In this work, linear slip theory is used to map our inversion results to the equivalent vertically fractured and transversely isotropic medium coefficients. We carried out this inversion on a synthetic example and a field example. The synthetic data example results show that joint estimation of S‐wave velocities with Thomsen's parameters and along normal and parallel to the vertical fracture set is reliable and, when mapped to the corresponding vertically fractured and transversely isotropic medium, provides insight into the fracture compliances. When the inversion was carried out on the field data, results indicated that the fractured rock is more compliant in the azimuth normal to the visible fracture set orientation and that the normal fracture compliance to tangential fracture compliance ratio is less than half, which implies some cementation may have occurred along the fractures. Such an observation has significant implications when modelling the transport properties of the rock and its strength. Both synthetic and field examples show the potential of azimuthal anisotropic Rayleigh‐wave inversion as the method can be further expanded to a more general case where the vertical fracture set orientation is not known .

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12840
2019-07-22
2024-04-24
Loading full text...

Full text loading...

References

  1. AdamJ.M.C. and LebedevS.2012. Azimuthal anisotropy beneath southern Africa from very broad‐band surface‐wave dispersion measurements. Geophysical Journal International191, 155–174.
    [Google Scholar]
  2. CrampinS.1984. Anisotropy in exploration seismics. First Break02, 19–21.
    [Google Scholar]
  3. DeschampsF., LebedevS., MeierT. and TrampertJ.2008. Azimuthal anisotropy of Rayleigh‐wave phase velocities in the east‐central United States. Geophysical Journal International173, 827–843.
    [Google Scholar]
  4. DuijndamA.J.W.1988. Bayesian estimation in seismic inversion. Part I.: principles. Geophysical Prospecting36, 878–898.
    [Google Scholar]
  5. FotiS., SambuilliL., SoccoV.L. and StrobbiaC.2003. Experiments of joint acquisition of seismic refraction and surface wave data. Near Surface Geophysics01, 119–129.
    [Google Scholar]
  6. GardnerL.1967. The delay‐time method. Seismic Refraction Prospecting, General Series. Society of Exploration Geophysicists337–361.
    [Google Scholar]
  7. GilbertF. and BackusG.E.1966. Propagator matrices in elastic wave and vibration problems. Geophysics31, 326–332.
    [Google Scholar]
  8. GoferE., BachrachR. and MarcoS.2017a. Anisotropic surface‐wave characterization of granular media. Geophysics82, MR191–MR200.
    [Google Scholar]
  9. GoferE., BachrachR. and MarcoS.2017b. Considerations for Anisotropic Surface‐Wave Inversion. SEG Technical Program Expanded Abstracts2627–2631.
    [Google Scholar]
  10. GravesR.W.1996. Simulating seismic wave propagation in 3D elastic media using staggered‐grid finite differences. Bulletin of the Seismological Society of America86, 1091–1106.
    [Google Scholar]
  11. HaskellN.A.1953. The dispersion of surface wave on multilayered media. Bulletin of the Seismological Society of America43, 17–34.
    [Google Scholar]
  12. HobdayC. and WorthingtonM.H.2012. Field measurements of normal and shear fracture compliance. Geophysical Prospecting60, 488–499.
    [Google Scholar]
  13. KachanovM.1980. Continuum model of medium with cracks. Journal of Engineering Mechanics Division106, 1039–1051.
    [Google Scholar]
  14. LevanderA.R.1988. Fourth‐order finite‐difference P‐SV seismograms. Geophysics53, 1425–1436.
    [Google Scholar]
  15. MillerD.E. and SpencerC.1994. An exact inversion for anisotropic moduli from phase slowness data. Journal of Geophysical Research‐Solid Earth99, 21651–21657.
    [Google Scholar]
  16. MontagnerJ.P. and NatafH.C.1986. A simple method for inverting the azimuthal anisotropy of surface waves. Journal of Geophysical Research91, 511–520.
    [Google Scholar]
  17. RavennaM. and LebedevS.2018. Bayesian inversion of surface‐wave data for radial and azimuthal shear‐wave anisotropy, with applications to central Mongolia and west‐central Italy. Geophysical Journal International213, 278–300.
    [Google Scholar]
  18. SayersC.M. and EbromD.A.1997. Seismic traveltime analysis for azimuthally anisotropic media: theory and experiment. Geophysics62, 1570–1582.
    [Google Scholar]
  19. SayersC.M. and KachanovM.1991. A simple technique for finding effective elastic constants of cracked solids for arbitrary crack orientation statistics. International Journal of Solids and Structures27, 671–680.
    [Google Scholar]
  20. SayersC.M. and KachanovM.1995. Microcrack‐induced elastic wave anisotropy of brittle rocks. Journal of Geophysical Research100, 4149–4156.
    [Google Scholar]
  21. SayersC.M., Dahi TaleghaniA. and AdachiJ.2009. The effect of mineralization on the ratio of normal to tangential compliance of fractures. Geophysical Prospecting57, 439–446.
    [Google Scholar]
  22. SchoenbergM. and HelbigK.1997. Orthorhombic media: modeling elastic wave behavior in a vertically fractured earth. Geophysics62, 1954–1974.
    [Google Scholar]
  23. SchoenbergM. and SayersC.M.1995. Seismic anisotropy of fractured rock. Geophysics60, 204–211.
    [Google Scholar]
  24. SimonsF., van der HilstR., MontagnerJ. and ZielhuisA.2002. Multimode Rayleigh wave inversion for shear wave speed heterogeneity and azimuthal anisotropy of the Australian upper mantle. Geophysical Journal International151, 738–754.
    [Google Scholar]
  25. SmithM.L. and DahlenF.A.1973. The azimuthal dependence of love and Rayleigh wave propagation in a slightly anisotropic medium. Journal of Geophysical Research78, 3321–3333.
    [Google Scholar]
  26. SoccoL.V., FotiS. and BoieroD.2010. Surface‐wave analysis for building near‐surface velocity models — established approaches and new perspectives. Geophysics75, 75A83–75A102.
    [Google Scholar]
  27. TsvankinI.1997. Anisotropic parameters and P‐wave velocity for orthorhombic media. Geophysics62, 1292.
    [Google Scholar]
  28. XiaJ., MillerR.D. and ParkC.B.1999. Estimation of near‐surface shear‐wave velocity by inversion of Rayleigh waves. Geophysics64, 691.
    [Google Scholar]
  29. YangY. and ForsythD.W.2006. Rayleigh wave phase velocities, small‐scale convection, and azimuthal anisotropy beneath Southern California. Journal of Geophysical Research: Solid Earth111, 1–20.
    [Google Scholar]
  30. YaoH.2015. A method for inversion of layered shear wavespeed azimuthal anisotropy from Rayleigh wave dispersion using the neighborhood algorithm. Earthquake Science28, 59–69.
    [Google Scholar]
  31. ZhangY., SayersC.M. and AdachiJ.2008. The use of effective medium theories for seismic wave propagation and fluid flow in fractured reservoirs under applied stress. SEG technical program expanded abstracts, 3713–3716.
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12840
Loading
/content/journals/10.1111/1365-2478.12840
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Anisotropy; Fractures; Surface wave inversion

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