Science China Earth Sciences

, Volume 61, Issue 4, pp 425–440 | Cite as

Azimuthally pre-stack seismic inversion for orthorhombic anisotropy driven by rock physics

Research Paper
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Abstract

Based on the long-wavelength approximation, a set of parallel vertical fractures embedded in periodic thin interbeds can be regarded as an equivalent orthorhombic medium. Rock physics is the basis for constructing the relationship between fracture parameters and seismic response. Seismic scattering is an effective way to inverse anisotropic parameters. In this study, we propose a reliable method for predicting the Thomsen’s weak anisotropic parameters and fracture weaknesses in an orthorhombic fractured reservoir using azimuthal pre-stack seismic data. First, considering the influence of fluid substitution in mineral matrix, porosity, fractures and anisotropic rocks, we estimate the orthorhombic anisotropic stiffness coefficients by constructing an equivalent rock physics model for fractured rocks. Further, we predict the logging elastic parameters, Thomsen’s weak parameters, and fracture weaknesses to provide the initial model constraints for the seismic inversion. Then, we derive the P-wave reflection coefficient equation for the inversion of Thomsen’s weak anisotropic parameters and fracture weaknesses. Cauchy-sparse and smoothing-model constraint regularization taken into account in a Bayesian framework, we finally develop a method of amplitude variation with angles of incidence and azimuth (AVAZ) inversion for Thomsen’s weak anisotropic parameters and fracture weaknesses, and the model parameters are estimated by using the nonlinear iteratively reweighted least squares (IRLS) strategy. Both synthetic and real examples show that the method can directly estimate the orthorhombic characteristic parameters from the azimuthally pre-stack seismic data, which provides a reliable seismic inversion method for predicting Thomsen’s weak anisotropic parameters and fracture weaknesses.

Keywords

Orthorhombic anisotropy Fractures Rock physics AVAZ inversion 

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Supplementary material

11430_2017_9124_MOESM1_ESM.pdf (383 kb)
Appendix A Linearized P-wave reflection coefficient of orthorhombic anisotropic characteristic parameters

References

  1. Alemie W, Sacchi M D. 2011. High-resolution three-term AVO inversion by means of a Trivariate Cauchy probability distribution. Geophysics, 76: R43–R55CrossRefGoogle Scholar
  2. Ba J. 2010. Wave propagation theory in double-porosity medium and experimental analysis on seismic responses (in Chinese). Sci China Earth Sci, 40: 1398–1409Google Scholar
  3. Bachrach R. 2015. Uncertainty and nonuniqueness in linearized AVAZ for orthorhombic media. Leading Edge, 34: 1048–1056CrossRefGoogle Scholar
  4. Bachrach R, Sengupta M, Salama A, Miller P. 2009. Reconstruction of the layer anisotropic elastic parameters and high-resolution fracture characterization from P-wave data: A case study using seismic inversion and Bayesian rock physics parameter estimation. Geophys Prospect, 57: 253–262CrossRefGoogle Scholar
  5. Backus G E. 1962. Long-wave elastic anisotropy produced by horizontal layering. J Geophys Res, 67: 4427–4440CrossRefGoogle Scholar
  6. Bakulin A, Grechka V, Tsvankin I. 2000a. Estimation of fracture parameters from reflection seismic data—Part I: HTI model due to a single fracture set. Geophysics, 65: 1788–1802CrossRefGoogle Scholar
  7. Bakulin A, Grechka V, Tsvankin I. 2000b. Estimation of fracture parameters from reflection seismic data—Part II: Fractured models with orthorhombic symmetry. Geophysics, 65: 1803–1817CrossRefGoogle Scholar
  8. Bakulin A, Grechka V, Tsvankin I. 2002. Seismic inversion for the parameters of two orthogonal fracture sets in a VTI background medium. Geophysics, 67: 292–299CrossRefGoogle Scholar
  9. Batzle M L, Han D H, Hofmann R. 2006. Fluid mobility and frequencydependent seismic velocity—Direct measurements. Geophysics, 71: N1–N9CrossRefGoogle Scholar
  10. Biot M A. 1956a. Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range. J Acoust Soc Am, 28: 168–178CrossRefGoogle Scholar
  11. Biot M A. 1956b. Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range. J Acoust Soc Am, 28: 179–191CrossRefGoogle Scholar
  12. Brown R J S, Korringa J. 1975. On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid. Geophysics, 40: 608–616CrossRefGoogle Scholar
  13. Buland A, Omre H. 2003. Bayesian linearized AVO inversion. Geophysics, 68: 185–198CrossRefGoogle Scholar
  14. Chapman M. 2009. Modeling the effect of multiple sets of mesoscale fractures in porous rock on frequency-dependent anisotropy. Geophysics, 74: D97–D103CrossRefGoogle Scholar
  15. Chen H Z, Yin X Y, Gao J H, Liu B Y, Zhang G Z. 2015. Seismic inversion for underground fractures detection based on effective anisotropy and fluid substitution. Sci China Earth Sci, 58: 805–814CrossRefGoogle Scholar
  16. Chen H Z, Zhang G Z, Ji Y X, Yin X Y. 2017. Azimuthal seismic amplitude difference inversion for fracture weakness. Pure Appl Geophys, 174: 279–291CrossRefGoogle Scholar
  17. Cheng C H. 1978. Seismic velocities in porous rocks: Direct and inverse problems. Dissertation for Doctoral Degree. Cambridge: Massachusetts Institute of TechnologyGoogle Scholar
  18. Cheng C H. 1993. Crack models for a transversely isotropic medium. J Geophys Res, 98: 675–684CrossRefGoogle Scholar
  19. Chichinina T, Obolentseva I, Gik L, Bobrov B, Ronquillo-Jarillo G. 2009. Attenuation anisotropy in the linear-slip model: Interpretation of physical modeling data. Geophysics, 74: WB165–WB176CrossRefGoogle Scholar
  20. Daubechies I, De Vore R, Fornasier M, Güntürk C S. 2010. Iteratively reweighted least squares minimization for sparse recovery. Comm Pure Appl Math, 63: 1–38CrossRefGoogle Scholar
  21. Downton J E, Roure B. 2015. Interpreting azimuthal Fourier coefficients for anisotropic and fracture parameters. Interpretation, 3: ST9–ST27CrossRefGoogle Scholar
  22. Dvorkin J, Nur A. 1993. Dynamic poroelasticity: A unified model with the squirt and the Biot mechanisms. Geophysics, 58: 524–533CrossRefGoogle Scholar
  23. Gassmann F. 1951. Uber die elastizitat poroser medien. Vier der Natur Gesellschaft in Zurich, 96: 1–23Google Scholar
  24. Gurevich B. 2003. Elastic properties of saturated porous rocks with aligned fractures. J Appl Geophys, 54: 203–218CrossRefGoogle Scholar
  25. Hornby B E, Schwartz L M, Hudson J A. 1994. Anisotropic effectivemedium modeling of the elastic properties of shales. Geophysics, 59: 1570–1583CrossRefGoogle Scholar
  26. Hsu C J, Schoenberg M. 1993. Elastic waves through a simulated fractured medium. Geophysics, 58: 964–977CrossRefGoogle Scholar
  27. Huang L, Stewart R R, Sil S, Dyaur N. 2015. Fluid substitution effects on seismic anisotropy. J Geophys Res-Solid Earth, 120: 850–863CrossRefGoogle Scholar
  28. Hudson J A. 1981. Wave speeds and attenuation of elastic waves in material containing cracks. Geophys J Int, 64: 133–150CrossRefGoogle Scholar
  29. Liu E, Martinez A. 2012. Seismic Fracture Characterization. Amsterdam: EAGE PublicationGoogle Scholar
  30. Mallick S, Craft K L, Meister L J, Chambers R E. 1998. Determination of the principal directions of azimuthal anisotropy from P-wave seismic data. Geophysics, 63: 692–706CrossRefGoogle Scholar
  31. Mavko G, Mukerji T, Dvorkin J. 2009. The Rock Physics Handbook Tools for Seismic Analysis of Porous Media. 2nd ed. New York: Cambridge University PressCrossRefGoogle Scholar
  32. Parra J O. 1997. The transversely isotropic poroelastic wave equation including the Biot and the squirt mechanisms: Theory and application. Geophysics, 62: 309–318CrossRefGoogle Scholar
  33. Pšenčík I, Martins J L. 2001. Properties of weak contrast PP reflection/transmission coefficients for weakly anisotropic elastic media. Studia Geophys Geod, 45: 176–199CrossRefGoogle Scholar
  34. Rüger A. 1996. Reflection coefficients and azimuthal AVO analysis in anisotropic media. Dissertation for Doctoral Degree. Golden: Colorado School of MinesGoogle Scholar
  35. Schoenberg M. 1980. Elastic wave behavior across linear slip interfaces. J Acoust Soc Am, 68: 1516–1521CrossRefGoogle Scholar
  36. Schoenberg M. 1983. Reflection of elastic waves from periodically stratified media with interfacial slip. Geophys Prospect, 31: 265–292CrossRefGoogle Scholar
  37. Schoenberg M, Helbig K. 1997. Orthorhombic media: Modeling elastic wave behavior in a vertically fractured earth. Geophysics, 62: 1954–1974CrossRefGoogle Scholar
  38. Shaw R K, Sen M K. 2004. Born integral, stationary phase and linearized reflection coefficients in weak anisotropic media. Geophys J Int, 158: 225–238CrossRefGoogle Scholar
  39. Shaw R K, Sen M K. 2006. Use of AVOA data to estimate fluid indicator in a vertically fractured medium. Geophysics, 71: C15–C24CrossRefGoogle Scholar
  40. Stolt R H, Weglein A B. 2012. Seismic Imaging and Inversion: Application of Linear Inverse Theory. New York: Cambridge University PressGoogle Scholar
  41. Tang X M. 2011. A unified theory for elastic wave propagation through porous media containing cracks—An extension of Biot’s poroelastic wave theory. Sci China Earth Sci, 54: 1441–1452CrossRefGoogle Scholar
  42. Thomsen L. 1986. Weak elastic anisotropy. Geophysics, 51: 1954–1966CrossRefGoogle Scholar
  43. Thomsen L. 1995. Elastic anisotropy due to aligned cracks in porous rock1. Geophys Prospect, 43: 805–829CrossRefGoogle Scholar
  44. Thomsen L. 2002. Understanding seismic anisotropy in exploration and exploitation. SEG 2010 Distinguished Instructor Short CourseCrossRefGoogle Scholar
  45. Tsvankin I. 1997. Anisotropic parameters and P-wave velocity for orthorhombic media. Geophysics, 62: 1292–1309CrossRefGoogle Scholar
  46. Wood A W. 1955. A Textbook of Sound. New York: McMillan CoGoogle Scholar
  47. Wu R S, Aki K. 1985. Scattering characteristics of elastic waves by an elastic heterogeneity. Geophysics, 50: 582–595CrossRefGoogle Scholar
  48. Xu S, White R E. 1995. A new velocity model for clay-sand mixtures. Geophys Prospect, 43: 91–118CrossRefGoogle Scholar
  49. Xue J, Gu H M, Cai C G. 2015. General fracture weaknesses for quasistatic porous fractured media (in Chinese). OGP, 50: 1146–1153Google Scholar
  50. Yang D H, Zhang Z J. 2000. Effects of the Biot and the squirt-flow coupling interaction on anisotropic elastic waves. Chin Sci Bull, 45: 2130–2138CrossRefGoogle Scholar
  51. Yang D H, Zhang Z J. 2002. Poroelastic wave equation including the Biot/squirt mechanism and the solid/fluid coupling anisotropy. Wave Motion, 35: 223–245CrossRefGoogle Scholar
  52. Yin X Y, Zong Z Y, Wu G C. 2014. Seismic wave scattering inversion for fluid factor of heterogeneous media. Sci China Earth Sci, 57: 542–549CrossRefGoogle Scholar
  53. Zhang G Z, Chen H Z, Wang Q, Yin X Y. 2013. Estimation of S-wave velocity and anisotropic parameters using fractured carbonate rock physics model (in Chinese). Chin J Geophys, 56: 1707–1715Google Scholar
  54. Zong Z Y, Yin X Y, Wu G C. 2012. Fluid identification method based on compressional and shear modulus direct inversion (in Chinese). Chin J Geophys, 55: 284–292CrossRefGoogle Scholar
  55. Zong Z Y, Yin X Y, Wu G C. 2015a. Complex seismic amplitude inversion for P-wave and S-wave quality factors. Geophys J Int, 202: 564–577CrossRefGoogle Scholar
  56. Zong Z Y, Yin X Y, Wu G C, Wu Z P. 2015b. Elastic inverse scattering for fluid variation with time-lapse seismic data. Geophysics, 80: WA61–WA67CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of GeosciencesChina University of Petroleum (East China)QingdaoChina
  2. 2.Laboratory for Marine Mineral ResourcesQingdao National Laboratory for Marine Science and TechnologyQingdaoChina

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