Skip to main content

Numerical Algorithm of Seismic Wave Propagation and Seismic Attenuation Estimation in Anisotropic Fractured Porous Fluid-Saturated Media

  • Conference paper
  • First Online:
Computational Science and Its Applications – ICCSA 2021 (ICCSA 2021)

Abstract

We present a numerical algorithm of seismic wave propagation in anisotropic fractured fluid-saturated porous media and estimation of seismic attenuation. The algorithm is based on numerical solution of anisotropic Biot equations of poroelasticity. We use finite-difference approximation of Biot equations on the staggered grid. We perform a set of numerical experiments of wave propagation in fractured media. Fractures in the media are connected and filled with anisotropic material providing wave induced fluid flow within connected fractures. Numerical estimations of inverse quality factor demonstrate the effect of fracture-filling material anisotropy on seismic wave attenuation.

The work is supported by Mathematical Center in Akademgorodok, the agreement with Ministry of Science and High Education of the Russian Federation number 075-15-2019-1613.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Berenger, J.P.: A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114(2), 185–200 (1994)

    Article  MathSciNet  Google Scholar 

  2. Biot, M.A.: Theory of propagation of elastic waves in fluid-saturated porous solid. I. Low-frequency range. J. Acoust. Soc. Am. 28, 168–178 (1956)

    Article  MathSciNet  Google Scholar 

  3. Carcione, J.M., Morency, C., Santos, J.E.: Computational poroelasticity – a review. Geophysics 75(5), 75A229–75A243 (2010)

    Google Scholar 

  4. Cheng, A.H.D.: Material coefficients of anisotropic poroelasticity. Int. J. Rock Mech. Min. Sci. 342, 199–205 (1997)

    Article  Google Scholar 

  5. Guo, J., Rubino, J.G., Glubokovskikh, S., Gurevich, B.: Effects of fracture intersections on seismic dispersion: theoretical predictions versus numerical simulations. Geophys. Prospect. 65(5), 1264–1276 (2017)

    Article  Google Scholar 

  6. Huang, F., et al.: The first post-injection seismic monitor survey at the Ketzin pilot CO\(_2\) storage site: results from time-lapse analysis. Geophysical Prospect. 66(1), 62–84 (2018)

    Article  Google Scholar 

  7. Hunziker, J., et al.: Seismic attenuation and stiffness modulus dispersion in porous rocks containing stochastic fracture networks. J. Geophys. Res. Solid Earth 123(1), 125–143 (2018)

    Article  Google Scholar 

  8. Kong, L., Gurevich, B., Zhang, Y., Wang, Y.: Effect of fracture fill on frequency-dependent anisotropy of fractured porous rocks. Geophys. Prospect. 65(6), 1649–1661 (2017)

    Article  Google Scholar 

  9. Lisitsa, V., Podgornova, O., Tcheverda, V.: On the interface error analysis for finite difference wave simulation. Comput. Geosci. 14(4), 769–778 (2010)

    Article  Google Scholar 

  10. Lisitsa, V.: Optimal discretization of PML for elasticity problems. Electron. Trans. Numer. Anal. 30, 258–277 (2008)

    MathSciNet  MATH  Google Scholar 

  11. Martin, R., Komatitsch, D., Ezziani, A.: An unsplit convolutional perfectly matched layer improved at grazing incidence for seismic wave propagation in poroelastic media. Geophysics 73(4), T51–T61 (2008)

    Article  Google Scholar 

  12. Marty, N.C.M., Hamm, V., Castillo, C., Thiery, D., Kervevan, C.: Modelling waterrock interactions due to long-term cooled-brine reinjection in the dogger carbonate aquifer (paris basin) based on in-situ geothermal well data. Geothermics 88, 101899 (2020)

    Article  Google Scholar 

  13. Masson, Y.J., Pride, S.R.: Finite-difference modeling of Biot’s poroelastic equations across all frequencies. Geophysics 75(2), N33–N41 (2010)

    Article  Google Scholar 

  14. Mavko, G., Mukerj, T., Dvorkin, J.: The Rock Physics Handbook, 2nd edn. Cambridge University Press, Cambridge (1999)

    Google Scholar 

  15. Menke, H.P., Reynolds, C.A., Andrew, M.G., Pereira Nunes, J.P., Bijeljic, B., Blunt, M.J.: 4D multi-scale imaging of reactive flow in carbonates: assessing the impact of heterogeneity on dissolution regimes using streamlines at multiple length scales. Chem. Geol. 481, 23–37 (2018)

    Article  Google Scholar 

  16. Moczo, P., Kristek, J., Galis, M.: The Finite-Difference Modelling of Earthquake Motion: Waves and Ruptures. Cambridge University Press, Cambridge (2014)

    Book  Google Scholar 

  17. Muller, T.M., Gurevich, B., Lebedev, M.: Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks – a review. Geophysics 75(5), 75A147–75A164 (2010)

    Google Scholar 

  18. Novikov, M.A., Lisitsa, V.V., Bazaikin, Y.V.: Wave propagation in fractured porous media with different percolation length of fracture systems. Lobachevskii J. Math. 41(8), 1533–1544 (2020)

    Article  MathSciNet  Google Scholar 

  19. Rubino, J.G., Muller, T.M., Guarracino, L., Milani, M., Holliger, K.: Seismoacoustic signatures of fracture connectivity. J. Geophys. Res. Solid Earth 119(3), 2252–2271 (2014)

    Article  Google Scholar 

  20. Salaun, N., et al.: High-resolution 3D seismic imaging and refined velocity model building improve the image of a deep geothermal reservoir in the Upper Rhine Graben. Lead. Edge 39(12), 857–863 (2020)

    Article  Google Scholar 

  21. Samarskii, A.A.: The Theory of Difference Schemes. (Pure and Applied Mathematics), vol. 240. CRC Press, Bosa Roca (2001)

    Book  Google Scholar 

  22. Tran, N.: Simulated annealing technique in discrete fracture network inversion: optimizing the optimization. Comput. Geosci. 11, 249–260 (2007)

    Article  Google Scholar 

  23. Virieux, J.: P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method. Geophysics 51(4), 889–901 (1986)

    Article  Google Scholar 

  24. Xu, C., Dowd, P.: A new computer code for discrete fracture network modelling. Comput. Geosci. 36(3), 292–301 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mikhail Novikov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Novikov, M., Lisitsa, V., Khachkova, T., Reshetova, G., Vishnevsky, D. (2021). Numerical Algorithm of Seismic Wave Propagation and Seismic Attenuation Estimation in Anisotropic Fractured Porous Fluid-Saturated Media. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science(), vol 12949. Springer, Cham. https://doi.org/10.1007/978-3-030-86653-2_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-86653-2_32

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86652-5

  • Online ISBN: 978-3-030-86653-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics