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Attenuation analysis in coal based on a fractal viscoelastic model

  • Research Article - Solid Earth Sciences
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Abstract

Great attention has been focused on uncovering the physics of seismic wave attenuation in rocks in the past few decades. However, the contribution of different attenuation mechanisms on attenuation is not completely clear in coal. We use the fractal viscoelastic model to describe the P-wave attenuation in coal, and the model has a good approximation to the constant-Q model when choosing lower fractional order \(\alpha\). We experimentally measured attenuation in dry and water-saturated coal samples in the frequency range of 10–250 Hz, at room temperature, and approximately room pressure. Attenuation in the dry sample is frequency independent and the fractal viscoelastic model curves fit well with the data when \(\alpha =0.056\). For the partial water saturation cases, attenuation is frequency dependent, and the simple viscoelastic attenuation theory cannot describe the strong attenuation in seismic band; when water saturation is high (\(\ge 80\%\)), we need wave-induced fluid flow mechanism to explain the high \(Q^{-1}\) values. The final contribution of viscoelasticity to attenuation is about 63%, while the final contribution of wave-induced fluid flow mechanism to attenuation is about 37% in the test.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  • Adam L, Batzle M, Lewallen K et al (2009) Seismic wave attenuation in carbonates. J Geophys Res Solid Earth. https://doi.org/10.1029/2008JB005890

    Article  Google Scholar 

  • Azimi SA (1968) Impulse and transient characteristics of media with linear and quadratic absorption laws. Izvestiya. Phys Solid Earth 2(2):88–93

    Google Scholar 

  • Ba J, Xu W, Fu L et al (2017) Rock anelasticity due to patchy saturation and fabric heterogeneity: a double double-porosity model of wave propagation. J Geophys Res Solid Earth 122(3):1949–1976

    Article  Google Scholar 

  • Batzle ML, Han DH, Hofmann R (2006) Fluid mobility and frequency-dependent seismic velocity-direct measurements. Geophysics 71(1):N1–N9

    Article  Google Scholar 

  • Best AI, Priest JA, Clayton CR et al (2013) The effect of methane hydrate morphology and water saturation on seismic wave attenuation in sand under shallow sub-seafloor conditions. Earth Planet Sci Lett 368:78–87

    Article  CAS  Google Scholar 

  • Carcione J (1990) Wave propagation in anisotropic linear viscoelastic media: theory and simulated wavefields. Geophys J Int 101(3):739–750

    Article  Google Scholar 

  • Carcione J, Cavallini F, Mainardi F et al (2002) Time-domain seismic modeling of constant-q wave propagation using fractional derivatives. Pure Appl Geophys 159(7):1719–1736

    Article  Google Scholar 

  • Carcione J, Helbig K, Helle H (2003) Effects of pressure and saturating fluid on wave velocity and attenuation in anisotropic rocks. Int J Rock Mech Min Sci 40(3):389–403

    Article  Google Scholar 

  • Carcione JM, Picotti S (2006) P-wave seismic attenuation by slow-wave diffusion: effects of inhomogeneous rock properties. Geophys J Soc Explor Geophys 71(3):O1–O8

    Google Scholar 

  • Dvorkin JP, Mavko G (2006) Modeling attenuation in reservoir and nonreservoir rock. Lead Edge 25(2):194–197

    Article  Google Scholar 

  • Futterman Walter I (1962) Dispersive body waves. J Geophys Res 67(13):5279–5291

    Article  Google Scholar 

  • Gordon R, Davis L (1968) Velocity and attenuation of seismic waves in imperfectly elastic rock. J Geophys Res 73(12):3917–3935

    Article  Google Scholar 

  • Guo J, Gurevich B (2020) Effects of coupling between wave-induced fluid flow and elastic scattering on p-wave dispersion and attenuation in rocks with aligned fractures. J Geophys Res Solid Earth 125(3):e2019JB018685

    Article  Google Scholar 

  • Guo J, Gurevich B (2020) Frequency-dependent p wave anisotropy due to wave-induced fluid flow and elastic scattering in a fluid-saturated porous medium with aligned fractures. J Geophys Res Solid Earth 125(8):e2020JB020320

    Article  Google Scholar 

  • Guo J, Gurevich B, Chen X (2022) Dynamic SV-wave signatures of fluid-saturated porous rocks containing intersecting fractures. J Geophys Res Solid Earth 127(8):e2022JB024745

    Article  Google Scholar 

  • Guo J, Zhao L, Chen X et al (2022) Theoretical modelling of seismic dispersion, attenuation and frequency-dependent anisotropy in a fluid-saturated porous rock with intersecting fractures. Geophys J Int 230(1):580–606

    Article  Google Scholar 

  • Hestholm S (1998) 3-D finite-difference elastic wave modelling including surface topography. Geophysics 63(2):613–622

    Article  Google Scholar 

  • King MS, Marsden JR (2002) Velocity dispersion between ultrasonic and seismic frequencies in brine-saturated reservoir sandstones. Geophysics 67(1):254–258

    Article  Google Scholar 

  • Kjartansson Einar (1979) Constant q-wave propagation and attenuation. J Geophys Res 84(B9):4737

    Article  Google Scholar 

  • Komatitsch D, Liu Q, Tromp J et al (2004) Simulations of ground motion in the Los Angeles basin based upon the spectral-element method. Bull Seismol Soc Am 94(1):187–206

    Article  Google Scholar 

  • McDonal F, Angona F, Mills R et al (1958) Attenuation of shear and compressional waves in Pierre shale. Geophysics 23(3):421–439

    Article  Google Scholar 

  • Müller T, Gurevich B, Lebedev M (2010) Seismic wave attenuation and dispersion due to wave-induced flow at mesoscopic heterogeneities: a review. Geophysics 75(5):75A147-75A164

    Article  Google Scholar 

  • Picotti S, Carcione JM, Rubino JG et al (2010) A viscoelastic representation of wave attenuation in porous media. Comput Geosci 36(1):44–53

    Article  Google Scholar 

  • Pimienta L, Fortin J, Guéguen Y (2015) Bulk modulus dispersion and attenuation in sandstones. Geophysics 80(2):D111–D127

    Article  Google Scholar 

  • Pimienta L, Fortin J, Guéguen Y (2015) Bulk modulus dispersion and attenuation in sandstones. Geophysics 80(2):D111–D127

    Article  Google Scholar 

  • Rasolofosaon PN (2009) Unified phenomenological model for the mechanical behavior of rocks. Geophysics 74(5):WB107–WB116

    Article  Google Scholar 

  • Robertsson JO, Blanch JO, Symes WW (1994) Viscoelastic finite-difference modeling. Geophysics 59(9):1444–1456

    Article  Google Scholar 

  • Spencer JW Jr (1981) Stress relaxations at low frequencies in fluid-saturated rocks: attenuation and modulus dispersion. J Geophys Res Solid Earth 86(B3):1803–1812

    Article  Google Scholar 

  • Tisato N, Quintal B (2013) Measurements of seismic attenuation and transient fluid pressure in partially saturated Berea sandstone: evidence of fluid flow on the mesoscopic scale. Geophys J Int 195(1):342–351

    Article  Google Scholar 

  • White J (1975) Computed seismic speeds and attenuation in rocks with partial gas saturation. Geophysics 40(2):224–232

    Article  Google Scholar 

  • Xu T, McMechan GA (1995) Composite memory variables for viscoelastic synthetic seismograms. Geophys J Int 121(2):634–639

    Article  Google Scholar 

  • Yin H, Zhao J, Tang G et al (2017) Pressure and fluid effect on frequency-dependent elastic moduli in fully saturated tight sandstone. J Geophys Res Solid Earth 122(11):8925–8942

    Article  Google Scholar 

  • Yin H, Zhao J, Tang G et al (2017) Pressure and fluid effect on frequency-dependent elastic moduli in fully saturated tight sandstone. J Geophys Res Solid Earth 122(11):8925–8942

    Article  Google Scholar 

  • Zhao T, Zou G, Peng S et al (2023) Analysis of the viscoelasticity in coal based on the fractal theory. Geophysics 88(1):WA177–WA187

    Article  Google Scholar 

  • Zhu T, Carcione JM (2014) Theory and modelling of constant-q p-and s-waves using fractional spatial derivatives. Geophys J Int 196(3):1787–1795

    Article  Google Scholar 

  • Zhu T, Carcione JM, Harris JM (2013) Approximating constant-q seismic propagation in the time domain. Geophys Prospect 61(5):931–940

    Article  Google Scholar 

Download references

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Correspondence to Zou Guangui.

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We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

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Edited by Prof. Fengqiang Gong (ASSOCIATE EDITOR) / Prof. Ramón Zúñiga (CO-EDITOR-IN-CHIEF).

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Tailang, Z., Guangui, Z., Fei, G. et al. Attenuation analysis in coal based on a fractal viscoelastic model. Acta Geophys. (2024). https://doi.org/10.1007/s11600-024-01314-6

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