1887
Volume 69, Issue 3
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Wave‐induced pore‐fluid flows are recognized as an important cause of seismic‐wave attenuation at frequencies below 1 kHz within heterogeneous rocks. By using Lagrangian continuum mechanics, wave‐induced pore‐fluid flow mechanisms can be classified strictly on the basis of macroscopic non‐Biot's material properties. In this classification, type I and II wave‐induced pore‐fluid flows are identified by local internal deformations being elastically coupled with either the whole Biot's rock or only with its pore fluid, respectively. Type III wave‐induced pore‐fluid flow is defined as a mixture of types I and II. For all types of wave‐induced pore‐fluid flows, the model predicts all rock properties observed in rock‐deformation experiments, such as the frequency‐dependent poroelastic moduli. The observed attenuation peaks and effective moduli can be used to invert for new, non‐Biot's material properties of porous rock. In data examples, we focus on the pore‐fluid coupled (type II) wave‐induced pore‐fluid flow mechanism and compare it to a previous analysis of type I. Non‐Biot's elastic and viscous rock properties are inverted for by fitting the effective drained bulk moduli measured in two previously published experiments: (1) with real sandstone including two saturating fluids and multiple confining pressures, and (2) a numerical experiment with heterogeneous sandstone containing mesoscopic‐ and microscopic‐scale wave‐induced pore‐fluid flows. Compared with a previous study of type I wave‐induced pore‐fluid flow, the data‐fitting method is improved by focusing on attenuation peaks and additional points in the observed spectra. For both of these experiments, both type I and II interpretations yield accurate fitting of the observed attenuation and dispersion spectra. Combinations of type I and II models (type III) yield a broad variety of acceptable mechanical models. This ambiguity of inversion shows that the different types of wave‐induced pore‐fluid flows cannot be differentiated in conventional attenuation/dispersion experiments. However, these WIFF types are physically meaningful and lead to rigorous equations of rock deformation that can be used in many applications.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.13003
2021-02-12
2021-03-07
Loading full text...

Full text loading...

References

  1. Ba, J., Xu, W., Fu, L.Y., Carcione, J.M. and Zhang, L. (2017) Rock anelasticity due to patchy saturation and fabric heterogeneity: a double double‐porosity model of wave propagation. Journal of Geophysical Research, Solid Earth B, 122, 1–28.
    [Google Scholar]
  2. Biot, M.A. (1956) Theory of propagation of elastic waves in a fluid‐saturated porous solid. I. Low‐frequency range. Journal of the Acoustical Society of America, 28(2), 168–178.
    [Google Scholar]
  3. Blanch, J.O., Robertsson, J.O.A. and Symes, W.W. (1995) Modeling of a constant Q: methodology and algorithm for an efficient and optimally inexpensive viscoelastic technique. Geophysics, 60, 176–184.
    [Google Scholar]
  4. Bourbié, T., Coussy, O. and Zinszner, B. (1987) Acoustics of Porous Media. Paris, France: Editions Technip.
    [Google Scholar]
  5. Carcione, J.M., Cavallini, F., Mainardi, F. and Hanyga, A. (2002) Time‐domain seismic modeling of constant‐Q wave propagation using fractional derivatives. Pure and Applied Geophysics, 159, 1719–1736.
    [Google Scholar]
  6. Carcione, J. and Gurevich, B. (2011) Differential form and numerical implementation of Biot's poroelasticity equations with squirt dissipation. Geophysics, 76, N55–N64.
    [Google Scholar]
  7. Chapman, M., Zatcepin, S.V. and Crampin, S. (2002) Derivation of a microstructural poroelastic model. Geophysical Journal International, 151, 427–451.
    [Google Scholar]
  8. Coulman, T., Deng, W. and Morozov, I.B. (2013) Models of seismic attenuation measurements in the laboratory. Canadian Journal of Exploration Geophysics, 38, 51–67.
    [Google Scholar]
  9. Deng, W. and Morozov, I.B. (2019) Macroscopic mechanical properties of porous rock with one saturating fluid. Geophysics, 84, MR223–MR239.
    [Google Scholar]
  10. Deng, W. and Morozov, I.B. (2016) Solid viscosity of fluid‐saturated porous rock with squirt flows at seismic frequencies. Geophysics, 81(4), D395–D404.
    [Google Scholar]
  11. Deng, W. and Morozov, I.B. (2018) Mechanical interpretation and generalization of the Cole–Cole model in viscoelasticity. Geophysics, 83(6), MR345–MR352.
    [Google Scholar]
  12. Dvorkin, J. and Nur, A. (1993) Dynamic poroelasticity: a unified model with the squirt and the Biot mechanisms. Geophysics, 58, 524–533.
    [Google Scholar]
  13. Gurevich, B., Makarynska, D., Paula, O.B. and Pervukhina, M. (2010) A simple model for squirt‐flow dispersion and attenuation in fluid‐saturated granular rocks. Geophysics, 75(6), N109–N120.
    [Google Scholar]
  14. Guo, J., Rubino, J.G., Barbosa, N.D., Glubokovskikh, S. and Gurevich, B. (2018a) Seismic dispersion and attenuation in saturated porous rocks with aligned fractures of finite thickness: theory and numerical simulations – Part 1: P‐wave perpendicular to the fracture plane. Geophysics, 83(1), WA49–WA62.
    [Google Scholar]
  15. Guo, J., Rubino, J.G., Barbosa, N.D., Glubokovskikh, S. and Gurevich, B. (2018b) Seismic dispersion and attenuation in saturated porous rocks with aligned fractures of finite thickness: theory and numerical simulations – Part 2: Frequency‐dependent anisotropy. Geophysics, 83(1), WA63–WA71.
    [Google Scholar]
  16. Holliger, K. and Goff, J. (2003) A generalized model for the 1/f‐scaling nature of seismic velocity fluctuations. In: Goff, J. and Holliger, K. (Eds) Heterogeneity in the Crust and the Upper Mantle – Nature, Scaling, and Seismic Properties. Kluwer Academic/Plenum Scientific Publishers, pp. 131–154.
    [Google Scholar]
  17. Jakobsen, M. and Chapman, M. (2009) Unified theory of global flow and squirt flow in cracked porous media. Geophysics, 74(2), WA65−WA76.
    [Google Scholar]
  18. Johnston, D.H., Toksöz, M. and Timur, A. (1979) Attenuation of seismic waves in dry and saturated rocks: II. Mechanisms. Geophysics,44(4), 691–711.
    [Google Scholar]
  19. Landau, L. and Lifshitz, E. (1986) Course of Theoretical Physics. Volume 7. Theory of Elasticity (3rd English edition). Butterworth‐Heinemann.
    [Google Scholar]
  20. Mavko, G. and Jizba, D. (1991) Estimating grain‐scale fluid effects on velocity dispersion in rocks. Geophysics, 56(12), 1940–1949.
    [Google Scholar]
  21. Morozov, I.B. and Baharvand Ahmadi, A. (2015) Taxonomy of Q. Geophysics, 80(1), T41–T49.
    [Google Scholar]
  22. Morozov, I.B. and Deng, W. (2016) Macroscopic framework for viscoelasticity, poroelasticity, and wave‐induced fluid flows—Part 1: General linear solid. Geophysics, 81(1), L1–L13.
    [Google Scholar]
  23. Morozov, I.B. and Deng, W. (2018a) Inversion for Biot‐consistent material properties in subresonant oscillation experiments with fluid‐saturated porous rock. Geophysics, 83(2), MR67–MR79.
    [Google Scholar]
  24. Morozov, I.B. and Deng, W. (2018b) Elastic potential and pressure dependence of elastic moduli in fluid‐saturated rock with double porosity. Geophysics, 83(4), MR231–MR244.
    [Google Scholar]
  25. Müller, T., Gurevich, B. and Lebedev, M. (2010) Seismic wave attenuation and dispersion resulting from wave‐induced flow in porous rock – a review. Geophysics, 75, 75A147–75A164.
    [Google Scholar]
  26. Murphy, W.F., Winkler, K.W. and Kleinberg, R.L. (1986) Acoustic relaxation in sedimentary rocks, dependence on grain contacts and fluid saturation. Geophysics, 51, 757–766.
    [Google Scholar]
  27. Pimienta, L., Fortin, J. and Guéguen, Y. (2015) Experimental study of Young's modulus dispersion and attenuation in sandstones. Geophysics, 80(5), L57–L72.
    [Google Scholar]
  28. Pride, S.R. and Berryman, J.G. (2003) Linear dynamics of double‐porosity and dual‐permeability materials. I. Governing equations and acoustic attenuation. Physical Review E, 68, 036603.
    [Google Scholar]
  29. Ricker, N. (1941) A note on the determination of the viscosity of shale from the measurement of wavelet breadth. Geophysics, 6, 254–258.
    [Google Scholar]
  30. Rubino, J. and Holliger, K. (2013) Research note: seismic attenuation due to wave‐induced fluid flow at microscopic and mesoscopic scales. Geophysical Prospecting, 61, 882–889.
    [Google Scholar]
  31. Sahay, P.N. (2008) On the Biot slow S‐wave. Geophysics, 73(4), N19–N33.
    [Google Scholar]
  32. Song, Y., Hu, H. and Rudnicki, J.W. (2016a) Shear properties of heterogeneous fluid‐filled porous media with spherical inclusions. International Journal of Solids and Structures, 83, 154–168.
    [Google Scholar]
  33. Song, Y., Hu, H., Rudnicki, J.W. and Duan, Y. (2016b) Dynamic transverse shear modulus for a heterogeneous fluid‐filled porous solid containing cylindrical inclusions. Geophysical Journal International, 206, 1677–1694.
    [Google Scholar]
  34. Tisato, N. and Quintal, B. (2013) Measurements of seismic attenuation and transient fluid pressure in partially saturated Berea sandstone: evidence of fluid flow on the mesoscopic scale. Geophysical Journal International, 195, 342–351.
    [Google Scholar]
  35. Toksöz, M.N., Johnston, D.H. and Timur, A. (1979) Attenuation of seismic waves in dry and saturated rocks: I. Laboratory measurements. Geophysics, 41(4), 681–690.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.13003
Loading
/content/journals/10.1111/1365-2478.13003
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Attenuation , Inversion , Parameter estimation , Rock physics and Theory
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error