Advertisement

Surveys in Geophysics

, Volume 39, Issue 5, pp 937–964 | Cite as

Model Parameterization and PP-Wave Amplitude Versus Angle and Azimuth (AVAZ) Direct Inversion for Fracture Quasi-Weaknesses in Weakly Anisotropic Elastic Media

  • Xinpeng Pan
  • Guangzhi Zhang
Article
  • 52 Downloads

Abstract

Homogeneous isotropic or vertically transverse isotropic rocks containing a single set of aligned, vertical fractures exhibits an effective long-wavelength horizontally transverse isotropy (HTI) or orthorhombic anisotropy. The estimation for properties of subsurface fractures has significant application in characterization of naturally fractured rocks. The purpose of this work is to demonstrate an approach of amplitude versus angle and azimuth (AVAZ) direct inversion for fracture characterization utilizing the observable wide-azimuth seismic reflection data in weakly anisotropic elastic media. The simplest single fracture system is HTI model. Much attention has been devoted to the weak-contrast and weak-anisotropy HTI model due to its significance for reservoir characterization. Treating the fractures as linear-slip interfaces, we begin with the derivation for perturbations of stiffness matrix at a planar weak-contrast interface separating two weakly anisotropic HTI half-spaces that share the same fracture normal, as a function of background elastic moduli and fracture parameters. Using the perturbation matrix and scattering function, we then derive a linearized PP-wave reflection coefficient of a weakly HTI medium in terms of P- and S-wave moduli, density, and fracture weaknesses, which builds a linearized relationship between the fracture parameters and reflection coefficient with the priority calculation for the azimuth of fracture normal based on the least square ellipse fitting method. Finally, we reformulate the reflectivity caused by weakness differences to parameterize the weaknesses for the so-called quasi-weaknesses and propose a method of Bayesian AVAZ direct inversion in seismic detection of subsurface fractures. Cauchy and Gaussian probability distribution are used for the a priori information of model parameters and the likelihood function, and the maximum a posteriori estimate of quasi-weaknesses is reasonably estimated with the nonlinear iteratively reweighted least squares algorithm. Synthetic and real data illustrate the applicability of the proposed AVAZ inversion method in fracture characterization.

Keywords

Bayesian AVAZ inversion Horizontally transverse isotropy and orthorhombic anisotropy Fracture quasi-weaknesses Maximum a posteriori estimate 

Notes

Acknowledgements

We would like to express our gratitude to the sponsorship of National Natural Science Foundation of China (41674130, U1562215), and National Basic Research Program of China (2014CB239201), National Grand Project for Science and Technology (2016ZX05027004-001, 2016ZX05002005-09HZ), and the Fundamental Research Funds for the Central Universities for their funding in this research. We also thank Alexey Stovas and another anonymous reviewer for their constructive suggestions.

References

  1. Bachrach R, Sengupta M, Salama A (2009) Reconstruction of the layer anisotropic elastic parameter 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
  2. 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
  3. 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
  4. Downton J (2005) Seismic parameter estimation from AVO inversion. Ph.D. Thesis, University of CalgaryGoogle Scholar
  5. Downton JE, Roure B (2015) Interpreting azimuthal Fourier coefficients for anisotropic and fracture parameters. Interpretation 3:ST9-ST27CrossRefGoogle Scholar
  6. Gassmann F (1951) Über die elastizität poröser medien. Vier. der Natur. Gesellschaft Zürich 96:1–23Google Scholar
  7. Gray D, Todorovic-Marinic D (2004) Fracture detection using 3D azimuthal AVO. CSEG Rec 29:5–8Google Scholar
  8. Hampson DP, Russell BH, Bankhead B (2005) Simultaneous inversion of pre-stack seismic data. SEG Tech Progr Expand Abstr 2005:1633–1637Google Scholar
  9. Hill R (1952) The elastic behavior of crystalline aggregate. Proc Phys Soc 65:349–354CrossRefGoogle Scholar
  10. Hsu CJ, Schoenberg M (1993) Elastic waves through a simulated fractured medium. Geophysics 58:964–977CrossRefGoogle Scholar
  11. Ikelle LT (1996) Amplitude variations with azimuths (AVAZ) inversion based on linearized inversion of common azimuthal sections, chapter 19. In: Fjaer E, Holt R, Rathore JS (eds) Seismic anisotropy. SEG, Tulsa, pp 601–644CrossRefGoogle Scholar
  12. Ikelle LT (1997) Parameterization of AVAZ (amplitude variation with azimuth) inversion. J Seism Explor 6:19–34Google Scholar
  13. Liu E, Martinez A (2012) Seismic fracture characterization: concepts and practical applications. EAGE Publication, AmsterdamGoogle Scholar
  14. Mallick S, Craft KL, Meister LJ, Chambers RE (1998) Determination of the principal directions of azimuthal anisotropy from P-wave seismic data. Geophysics 63:692–706CrossRefGoogle Scholar
  15. Mavko G, Mukerji T, Dvorkin J (2009) The rock physics handbook. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  16. Mesdag P (2016) A new approach to quantitative azimuthal inversion for stress and fracture detection: 86th annual international meeting, SEG, expanded abstracts, pp 357–361Google Scholar
  17. Narr W, Schechter WS, Thompson L (2006) Naturally fractured reservoir characterization. SPE Publication, New YorkGoogle Scholar
  18. Pan X, Zhang G, Chen H, Yin X (2017a) McMC-based AVAZ direct inversion for fracture weaknesses. J Appl Geophys 138:50–61CrossRefGoogle Scholar
  19. Pan X, Zhang G, Yin X (2017b) Azimuthally anisotropic elastic impedance inversion for fluid indicator driven by rock physics. Geophysics 82:C211–C227CrossRefGoogle Scholar
  20. Pan X, Zhang G, Yin X (2018) Azimuthal seismic amplitude variation with offset and azimuth inversion in weakly anisotropic media with orthorhombic symmetry. Surv Geophys 39:99–123CrossRefGoogle Scholar
  21. Pšenčik I, Gajewski D (1998) Polarization, phase velocity and NMO velocity of qP waves in arbitrary weakly anisotropic media. Geophysics 63:1754–1766CrossRefGoogle Scholar
  22. Pšenčik I, Martins JL (2001) Properties of weak contrast PP reflection/transmission coefficients for weakly anisotropic elastic media. Studia Geophysica et Geodaetica 45:176–199CrossRefGoogle Scholar
  23. Pšenčik I, Vavryčuk V (1998) Weak contrast PP-wave displacement R/T coefficients in weakly anisotropic elastic media. Pure Appl Geophys 151:699–718CrossRefGoogle Scholar
  24. Rüger A (1997) P-wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry. Geophysics 62:713–722CrossRefGoogle Scholar
  25. Rüger A (1998) Variation of P-wave reflectivity with offset and azimuth in anisotropic media. Geophysics 63:935–947CrossRefGoogle Scholar
  26. Sacchi MD, Ulrych TJ (1995) High-resolution velocity gathers and offset space reconstruction. Geophysics 60:1169–1177CrossRefGoogle Scholar
  27. Scales JA, Smith ML (1994) Introductory geophysical inverse theory. Samizdat Press, GoldenGoogle Scholar
  28. Schoenberg M (1980) Elastic wave behavior across linear slip interfaces. J Acoust Soc Am 68:1516–1521CrossRefGoogle Scholar
  29. Schoenberg M, Douma J (1988) Elastic-wave propagation in media with parallel fractures and aligned cracks. Geophys Prospect 36:571–590CrossRefGoogle Scholar
  30. Schoenberg M, Helbig K (1997) Orthorhombic media: modeling elastic wave behavior in a vertically fractured earth. Geophysics 62:1954–1957CrossRefGoogle Scholar
  31. Schoenberg M, Protazio J (1990) ‘Zoeppritz’ rationalized and generalized to anisotropy. J Acoust Soc Am 88:S46Google Scholar
  32. Schoenberg M, Sayers CM (1995) Seismic anisotropy of fractured rock. Geophysics 60:204–211CrossRefGoogle Scholar
  33. Shaw RK, Sen MK (2004) Born integral, stationary phase and linearized reflection coefficients in weak anisotropic media. Geophys J Int 158:225–238CrossRefGoogle Scholar
  34. Shaw RK, Sen MK (2006) Use of AVOA data to estimate fluid indicator in a vertically fractured medium. Geophysics 71:C15–C24CrossRefGoogle Scholar
  35. Thomsen L (1986) Weak elastic anisotropy. Geophysics 51:1954–1966CrossRefGoogle Scholar
  36. Thomsen L (2007) Understanding seismic anisotropy in exploration and exploitation: 2002 SEG/EAGE distinguished instructor short course [M]. Society of Exploration GeophysicistsGoogle Scholar
  37. Tsvankin L (1996) P-wave signatures and notation for transversely isotropic media: an overview. Geophysics 61:467–483CrossRefGoogle Scholar
  38. Tsvankin L, Grechka V (2011) Seismology of azimuthally anisotropic media and seismic fracture characterization. SEG Publication, New YorkCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

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