Science China Earth Sciences

, Volume 62, Issue 5, pp 798–811 | Cite as

Bayesian seismic inversion for estimating fluid content and fracture parameters in a gas-saturated fractured porous reservoir

  • Xinpeng Pan
  • Guangzhi ZhangEmail author
Research Paper


Understanding the effects of in situ fluid content and fracture parameters on seismic characteristics is important for the subsurface exploration and production of fractured porous rocks. The ratio of normal-to-shear fracture compliance is typically utilized as a fluid indicator to evaluate anisotropy and identify fluids filling the fractures, but it represents an underdetermined problem because this fluid indicator varies as a function of both fracture geometry and fluid content. On the bases of anisotropic Gassmann’s equation and linear-slip model, we suggest an anisotropic poroelasticity model for fractured porous reservoirs. By combining a perturbed stiffness matrix and asymptotic ray theory, we then construct a direct relationship between the PP-wave reflection coefficients and characteristic parameters of fluids (P- and S-wave moduli) and fractures (fracture quasi-weaknesses), thereby decoupling the effects of fluid and fracture properties on seismic reflection characterization. By incorporating fracture quasi-weakness parameters, we propose a novel parameterization method for elastic impedance variation with offset and azimuth (EIVOA). By incorporating wide-azimuth observable seismic reflection data with regularization constraints, we utilize Bayesian seismic inversion to estimate the fluid content and fracture parameters of fractured porous rocks. Tests on synthetic and real data demonstrate that fluid and fracture properties can be reasonably estimated directly from azimuthal seismic data and the proposed approach provides a reliable method for fluid identification and fracture characterization in a gas-saturated fractured porous reservoir.


Fluid parameters Fracture parameters Fractured porous reservoir Poroelasticity theory Bayesian seismic inversion 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The work was supported by the National Natural Science Foundation of China (Grant No. 41674130), the National Science and Technology Major Project (Grant No. 2016ZX05002-005).


  1. Ba J. 2010. Wave propagation theory in double-porosity medium and experimental analysis on seismic responses (in Chinese). Sci Sin Phys Mech Astron, 40: 1398–1409Google Scholar
  2. Ba J, Xu W, Fu L Y, Carcione J M, Zhang L. 2017. Rock anelasticity due to patchy saturation and fabric heterogeneity: A double double-porosity model of wave propagation. J Geophys Res-Solid Earth, 118: 1949–1976Google Scholar
  3. 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
  4. Bakulin A, Grechka V, Tsvankin I. 2000. Estimation of fracture parameters from reflection seismic data—Part I: HTI model due to a single fracture set. Geophysics, 65: 1788–1802CrossRefGoogle Scholar
  5. Batzle M L, Han D H, Hofmann R. 2006. Fluid mobility and frequencydependent seismic velocity—Direct measurements. Geophysics, 71: 1–9CrossRefGoogle Scholar
  6. Biot M A. 1956. Theory of propagation of elastic waves in a fluid-saturated porous solid—I. Low-frequency range. J Acoust Soc Am, 28: 168–178CrossRefGoogle Scholar
  7. Biot M A, Willis D G. 1957. The elastic coeff cients of the theory of consolidation. J Appl Mech, 15: 594–601Google Scholar
  8. 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
  9. Buland A, Omre H. 2003. Bayesian linearized AVO inversion. Geophysics, 68: 185–198CrossRefGoogle Scholar
  10. Chapman M. 2009. Modeling the effect of multiple sets of mesoscale fractures in porous rock on frequency-dependent anisotropy. Geophysics, 74: D97–D103CrossRefGoogle Scholar
  11. 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
  12. Connolly P. 1999. Elastic impedance. Leading Edge, 18: 438–452CrossRefGoogle Scholar
  13. Downton J E, Roure B. 2015. Interpreting azimuthal Fourier coefficients for anisotropic and fracture parameters. Interpretation, 3: ST9–ST27CrossRefGoogle Scholar
  14. Dvorkin J, Nur A. 1993. Dynamic poroelasticity: A unified model with the squirt and the Biot mechanisms. Geophysics, 58: 524–533CrossRefGoogle Scholar
  15. Gassmann F. 1951. Über die elastizität poröser medien. Vier der Natur Gesellschaft Zürich, 96: 1–23Google Scholar
  16. Grana D, Della Rossa E. 2010. Probabilistic petrophysical-properties estimation integrating statistical rock physics with seismic inversion. Geophysics, 75: 21–37CrossRefGoogle Scholar
  17. Gurevich B. 2003. Elastic properties of saturated porous rocks with aligned fractures. J Appl Geophys, 54: 203–218CrossRefGoogle Scholar
  18. Han D H, Batzle M L. 2004. Gassmann’s equation and fluid-saturation effects on seismic velocities. Geophysics, 69: 398–405CrossRefGoogle Scholar
  19. 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
  20. Hudson J A. 1981. Wave speeds and attenuation of elastic waves in material containing cracks. Geophys J Int, 64: 133–150CrossRefGoogle Scholar
  21. Hudson J A, Pointer T, Liu E. 2001. Effective-medium theories for fluidsaturated materials with aligned cracks. Geophys Prospect, 49: 509–522CrossRefGoogle Scholar
  22. Liu E, Martinez A. 2012. Seismic Fracture Characterization. Netherlands: EAGE PublicationGoogle Scholar
  23. Liu F P, Meng X J, Wang Y M, Shen G Q, Yang C C. 2010. Jacobian matrix for the inversion of P- and S-wave velocities and its accurate computation method. Sci China Earth Sci, 54: 647–654CrossRefGoogle Scholar
  24. Martins J L. 2006. Elastic impedance in weakly anisotropic media. Geophysics, 71: D73–D83CrossRefGoogle Scholar
  25. Mavko G, Bandyopadhyay K. 2009. Approximate fluid substitution for vertical velocities in weakly anisotropic VTI rocks. Geophysics, 74: D1–D6CrossRefGoogle Scholar
  26. Mavko G, Mukerji T, Dvorkin J. 2009. The Rock Physics Handbook. Cambridge: Cambridge University PressCrossRefGoogle Scholar
  27. Pan X, Zhang G, Chen H, Yin X. 2017a. McMC-based nonlinear EIVAZ inversion driven by rock physics. J Geophys Eng, 14: 368–379CrossRefGoogle Scholar
  28. Pan X, Zhang G, Chen H, Yin X. 2017b. McMC-based AVAZ direct inversion for fracture weaknesses. J Appl Geophys, 138: 50–61CrossRefGoogle Scholar
  29. Pan X, Zhang G, Yin X. 2017c. Azimuthally anisotropic elastic impedance inversion for fluid indicator driven by rock physics. Geophysics, 82: C211–C227CrossRefGoogle Scholar
  30. Pan X, Zhang G. 2018. Model parameterization and PP-wave amplitude versus angle and azimuth (AVAZ) direct inversion for fracture quasiweaknesses in weakly anisotropic elastic media. Surv Geophys, 39: 937–964CrossRefGoogle Scholar
  31. Pan X P, Zhang G Z, and Yin X Y. 2018a. Seismic scattering inversion for anisotropy in heterogeneous orthorhombic media (in Chinese). Chin J Geophys, 61: 267–283Google Scholar
  32. Pan X P, Zhang G Z, and Yin X Y. 2018b. Probabilistic seismic inversion for reservoir fracture and petrophysical parameters driven by rockphysics models (in Chinese). Chin J Geophys, 61: 683–696Google Scholar
  33. Pan X P, Zhang G Z, Yin X Y. 2018c. Azimuthally pre-stack seismic inversion for orthorhombic anisotropy driven by rock physics. Sci China Earth Sci, 61: 425–440CrossRefGoogle Scholar
  34. 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
  35. Rüger A. 1997. P-wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry. Geophysics, 62: 713–722CrossRefGoogle Scholar
  36. Russell B H, Hedlin K, Hilterman F J, Lines L R. 2003. Fluid-property discrimination with AVO: A Biot-Gassmann perspective. Geophysics, 68: 29–39CrossRefGoogle Scholar
  37. Russell B H, Gray D, Hampson D P. 2011. Linearized AVO and poroelasticity. Geophysics, 76: C19–C29CrossRefGoogle Scholar
  38. Schoenberg M. 1980. Elastic wave behavior across linear slip interfaces. J Acoust Soc Am, 68: 1516–1521CrossRefGoogle Scholar
  39. Schoenberg M. 1983. Reflection of elastic waves from periodically stratified media with interfacial slip. Geophys Prospect, 31: 265–292CrossRefGoogle Scholar
  40. Schoenberg M, Sayers C M. 1995. Seismic anisotropy of fractured rock. Geophysics, 60: 204–211CrossRefGoogle Scholar
  41. 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
  42. Shaw R K, Sen M K. 2006. Use of AVOA data to estimate fluid indicator in a vertically fractured medium. Geophysics, 71: 15–24CrossRefGoogle Scholar
  43. Sil S, Sen M K, Gurevich B. 2011. Analysis of fluid substitution in a porous and fractured medium. Geophysics, 76: WA157–WA166CrossRefGoogle Scholar
  44. Stolt R H, Weglein A B. 1985. Migration and inversion of seismic data. Geophysics, 50: 2458–2472CrossRefGoogle Scholar
  45. 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
  46. Thomsen L. 1986. Weak elastic anisotropy. Geophysics, 51: 1954–1966CrossRefGoogle Scholar
  47. Thomsen L. 1995. Elastic anisotropy due to aligned cracks in porous rock. Geophys Prospect, 43: 805–829CrossRefGoogle Scholar
  48. Thomsen L. 2002. Understanding seismic anisotropy in exploration and exploitation. SEG 2010 Distinguished Instructor Short CourseGoogle Scholar
  49. Whitcombe D N. 2002. Elastic impedance normalization. Geophysics, 67: 60–62CrossRefGoogle 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. Yin X Y, Zong Z Y, Wu G C. 2015. Research on seismic fluid identification driven by rock physics. Sci China Earth Sci, 58: 159–171CrossRefGoogle Scholar
  54. Zeng Q, Guo Y, Jiang R, Ba J, Ma H, Liu J. 2017. Fluid sensitivity of rock physics parameters in reservoirs: Quantitative analysis. J Seismic Explor, 26: 125–140Google Scholar
  55. Zhang G Z, Chen H Z, Wang Q, and 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
  56. Zong Z Y, Yin X Y, and Wu G C. 2012. Fluid identification method based on compressional and shear modulus direct iinversion (in Chinese). Chin J Geophys, 55: 284–292CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

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

Personalised recommendations