Skip to main content
Log in

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

  • Research Paper
  • Published:
Science China Earth Sciences Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ba J. 2010. Wave propagation theory in double-porosity medium and experimental analysis on seismic responses (in Chinese). Sci Sin Phys Mech Astron, 40: 1398–1409

    Google Scholar 

  • 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: 1949–1976

    Google Scholar 

  • 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: 253–262

    Article  Google Scholar 

  • 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: 1788–1802

    Article  Google Scholar 

  • Batzle M L, Han D H, Hofmann R. 2006. Fluid mobility and frequencydependent seismic velocity—Direct measurements. Geophysics, 71: 1–9

    Article  Google Scholar 

  • 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: 168–178

    Article  Google Scholar 

  • Biot M A, Willis D G. 1957. The elastic coeff cients of the theory of consolidation. J Appl Mech, 15: 594–601

    Google Scholar 

  • 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: 608–616

    Article  Google Scholar 

  • Buland A, Omre H. 2003. Bayesian linearized AVO inversion. Geophysics, 68: 185–198

    Article  Google Scholar 

  • Chapman M. 2009. Modeling the effect of multiple sets of mesoscale fractures in porous rock on frequency-dependent anisotropy. Geophysics, 74: D97–D103

    Article  Google Scholar 

  • 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: 805–814

    Article  Google Scholar 

  • Connolly P. 1999. Elastic impedance. Leading Edge, 18: 438–452

    Article  Google Scholar 

  • Downton J E, Roure B. 2015. Interpreting azimuthal Fourier coefficients for anisotropic and fracture parameters. Interpretation, 3: ST9–ST27

    Article  Google Scholar 

  • Dvorkin J, Nur A. 1993. Dynamic poroelasticity: A unified model with the squirt and the Biot mechanisms. Geophysics, 58: 524–533

    Article  Google Scholar 

  • Gassmann F. 1951. Über die elastizität poröser medien. Vier der Natur Gesellschaft Zürich, 96: 1–23

    Google Scholar 

  • Grana D, Della Rossa E. 2010. Probabilistic petrophysical-properties estimation integrating statistical rock physics with seismic inversion. Geophysics, 75: 21–37

    Article  Google Scholar 

  • Gurevich B. 2003. Elastic properties of saturated porous rocks with aligned fractures. J Appl Geophys, 54: 203–218

    Article  Google Scholar 

  • Han D H, Batzle M L. 2004. Gassmann’s equation and fluid-saturation effects on seismic velocities. Geophysics, 69: 398–405

    Article  Google Scholar 

  • Huang L, Stewart R R, Sil S, Dyaur N. 2015. Fluid substitution effects on seismic anisotropy. J Geophys Res-Solid Earth, 120: 850–863

    Article  Google Scholar 

  • Hudson J A. 1981. Wave speeds and attenuation of elastic waves in material containing cracks. Geophys J Int, 64: 133–150

    Article  Google Scholar 

  • Hudson J A, Pointer T, Liu E. 2001. Effective-medium theories for fluidsaturated materials with aligned cracks. Geophys Prospect, 49: 509–522

    Article  Google Scholar 

  • Liu E, Martinez A. 2012. Seismic Fracture Characterization. Netherlands: EAGE Publication

    Google Scholar 

  • 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: 647–654

    Article  Google Scholar 

  • Martins J L. 2006. Elastic impedance in weakly anisotropic media. Geophysics, 71: D73–D83

    Article  Google Scholar 

  • Mavko G, Bandyopadhyay K. 2009. Approximate fluid substitution for vertical velocities in weakly anisotropic VTI rocks. Geophysics, 74: D1–D6

    Article  Google Scholar 

  • Mavko G, Mukerji T, Dvorkin J. 2009. The Rock Physics Handbook. Cambridge: Cambridge University Press

    Book  Google Scholar 

  • Pan X, Zhang G, Chen H, Yin X. 2017a. McMC-based nonlinear EIVAZ inversion driven by rock physics. J Geophys Eng, 14: 368–379

    Article  Google Scholar 

  • Pan X, Zhang G, Chen H, Yin X. 2017b. McMC-based AVAZ direct inversion for fracture weaknesses. J Appl Geophys, 138: 50–61

    Article  Google Scholar 

  • Pan X, Zhang G, Yin X. 2017c. Azimuthally anisotropic elastic impedance inversion for fluid indicator driven by rock physics. Geophysics, 82: C211–C227

    Article  Google Scholar 

  • 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: 937–964

    Article  Google Scholar 

  • 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: 267–283

    Google Scholar 

  • 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: 683–696

    Google Scholar 

  • 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: 425–440

    Article  Google Scholar 

  • Parra J O. 1997. The transversely isotropic poroelastic wave equation including the Biot and the squirt mechanisms: Theory and application. Geophysics, 62: 309–318

    Article  Google Scholar 

  • Rüger A. 1997. P-wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry. Geophysics, 62: 713–722

    Article  Google Scholar 

  • Russell B H, Hedlin K, Hilterman F J, Lines L R. 2003. Fluid-property discrimination with AVO: A Biot-Gassmann perspective. Geophysics, 68: 29–39

    Article  Google Scholar 

  • Russell B H, Gray D, Hampson D P. 2011. Linearized AVO and poroelasticity. Geophysics, 76: C19–C29

    Article  Google Scholar 

  • Schoenberg M. 1980. Elastic wave behavior across linear slip interfaces. J Acoust Soc Am, 68: 1516–1521

    Article  Google Scholar 

  • Schoenberg M. 1983. Reflection of elastic waves from periodically stratified media with interfacial slip. Geophys Prospect, 31: 265–292

    Article  Google Scholar 

  • Schoenberg M, Sayers C M. 1995. Seismic anisotropy of fractured rock. Geophysics, 60: 204–211

    Article  Google Scholar 

  • Shaw R K, Sen M K. 2004. Born integral, stationary phase and linearized reflection coefficients in weak anisotropic media. Geophys J Int, 158: 225–238

    Article  Google Scholar 

  • Shaw R K, Sen M K. 2006. Use of AVOA data to estimate fluid indicator in a vertically fractured medium. Geophysics, 71: 15–24

    Article  Google Scholar 

  • Sil S, Sen M K, Gurevich B. 2011. Analysis of fluid substitution in a porous and fractured medium. Geophysics, 76: WA157–WA166

    Article  Google Scholar 

  • Stolt R H, Weglein A B. 1985. Migration and inversion of seismic data. Geophysics, 50: 2458–2472

    Article  Google Scholar 

  • 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: 1441–1452

    Article  Google Scholar 

  • Thomsen L. 1986. Weak elastic anisotropy. Geophysics, 51: 1954–1966

    Article  Google Scholar 

  • Thomsen L. 1995. Elastic anisotropy due to aligned cracks in porous rock. Geophys Prospect, 43: 805–829

    Article  Google Scholar 

  • Thomsen L. 2002. Understanding seismic anisotropy in exploration and exploitation. SEG 2010 Distinguished Instructor Short Course

    Google Scholar 

  • Whitcombe D N. 2002. Elastic impedance normalization. Geophysics, 67: 60–62

    Article  Google Scholar 

  • 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: 2130–2138

    Article  Google Scholar 

  • Yang D H, Zhang Z J. 2002. Poroelastic wave equation including the Biot/Squirt mechanism and the solid/fluid coupling anisotropy. Wave Motion, 35: 223–245

    Article  Google Scholar 

  • 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: 542–549

    Article  Google Scholar 

  • Yin X Y, Zong Z Y, Wu G C. 2015. Research on seismic fluid identification driven by rock physics. Sci China Earth Sci, 58: 159–171

    Article  Google Scholar 

  • 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: 125–140

    Google Scholar 

  • 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: 1707–1715

    Google Scholar 

  • 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: 284–292

    Article  Google Scholar 

Download references

Acknowledgements

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).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Guangzhi Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pan, X., Zhang, G. Bayesian seismic inversion for estimating fluid content and fracture parameters in a gas-saturated fractured porous reservoir. Sci. China Earth Sci. 62, 798–811 (2019). https://doi.org/10.1007/s11430-018-9284-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11430-018-9284-2

Keywords

Navigation