Elastic waves propagation through a liquid-saturated poroelastic interlayer based on the fractional viscoelastic BISQ model

References

• Bourbié T, Coussy O, Zinszner B. Acoustics of porous media. Paris: Gulf Publishing; 1987.
   Google Scholar
• Biot MA. Theory of propagation of elastic waves in a fluid-saturated porous solid: I: low-frequency range. J Acoust Soc Am. 1956;28(2):168–178.
   Web of Science ®Google Scholar
• Biot MA. Theory of propagation of elastic waves in a fluid-saturated porous solid: II: higher frequency range. J Acoust Soc Am. 1956;28(2):179–191.
   Web of Science ®Google Scholar
• Biot MA. Generalized theory of acoustic propagation in porous dissipative media. J Acoust Soc Am. 1962;34(9):1254–1264.
   Web of Science ®Google Scholar
• Biot MA. Mechanics of deformation and acoustic propagation in porous media. J Appl Phys. 1962;33(4):1482–1498.
   Web of Science ®Google Scholar
• Plona TJ. Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies. Appl Phys Lett. 1980;36(4):259–261.
   Web of Science ®Google Scholar
• Corapcioglu MY, Tuncay K. Propagation of waves in porous media. In: Corapcioglu MY, editor. Advances in porous media. Amsterdam: Elsevier; 1996. p. 361–440.
   Google Scholar
• Dvorkin J, Nur A. Dynamic poroelasticity: a unified model with the squirt and the Biot mechanisms. Geophysics. 1993;58(4):524–533.
   Web of Science ®Google Scholar
• Dvorkin J, Nolen-Hoeksema R, Nur A. The squirt-flow mechanism: macroscopic description. Geophysics. 1994;59(3):428–438.
   Web of Science ®Google Scholar
• Parra JO. The transversely isotropic poroelastic wave equation including the Biot and the squirt mechanisms: theory and application. Geophysics. 1997;62(1):309–318.
   Web of Science ®Google Scholar
• Parra JO. Poroelastic model to relate seismic wave attenuation and dispersion to permeability anisotropy. Geophysics. 2000;65(1):202–210.
   Web of Science ®Google Scholar
• Yang DH, Zhang ZJ. Effects of the Biot and the squirt-flow coupling interaction on anisotropic elastic waves. Chinese Sci Bull. 2000;45(23):2130–2138.
   Google Scholar
• Yang DH, Zhang ZJ. Poroelastic wave equation including the Biot/squirt mechanism and the solid/fluid coupling anisotropy. Wave Motion. 2002;35(3):223–245.
   Web of Science ®Google Scholar
• Diallo MS, Appel E. Acoustic wave propagation in saturated porous media: reformulation of the Biot/squirt flow theory. J Appl Geophys. 2000;44(4):313–325.
   Web of Science ®Google Scholar
• Nie JX, Yang DH, Yang HZ. A generalized viscoelastic Biot/squirt model for clay-bearing sandstones in a wide range of permeabilities. Appl Geophys. 2008;5(4):249–260.
   Web of Science ®Google Scholar
• Nie JX, Ba J, Yang DH, et al. BISQ model based on a Kelvin-Voigt viscoelastic frame in a partially saturated porous medium. Appl Geophys. 2012;9(2):213–222.
   Web of Science ®Google Scholar
• Liu JW, Yong WA. Stability analysis of the Biot/squirt models for wave propagation in saturated porous media. Geophys J Int. 2016;204:535–543.
   Web of Science ®Google Scholar
• Stoll R D, Kan T K. Reflection of acoustic waves at a water-sediment interface. J Acoust Soc Am. 1981;70(1):149–156.
   Web of Science ®Google Scholar
• Wu KY, Xue Q, Adler L. Reflection and transmission of elastic waves from a fluid-saturated porous solid boundary. J Acoust Soc Am. 1990;87(6):2349–2358.
   Web of Science ®Google Scholar
• Vashisth AK, Gogna ML. The effect of loose boundaries on wave propagation in a porous solid: reflection and refraction of seismic waves across a plane interface. Int J Solids Struct. 1993;30(18):2485–2499.
   Web of Science ®Google Scholar
• Sharma MD, Gogna ML. Reflection and refraction of plane harmonic waves at an interface between elastic solid and porous solid saturated by viscous liquid. Pure Appl Geophys. 1992;138(2):249–266.
   Web of Science ®Google Scholar
• Singh J, Tomar SK. Reflection and transmission of transverse waves at a plane interface between two different porous elastic solid half-spaces. Appl Math Comput. 2006;176:364–378.
   Web of Science ®Google Scholar
• Cui ZW, Wang KX. Influence of the squirt flow on reflection and refraction of elastic waves at a fluid/fluid-saturated poroelastic solid interface. Int J Eng Sci. 2003;41(18):2179–2191.
   Web of Science ®Google Scholar
• Wang J T, Jin F, Zhang C H. Reflection and transmission of plane waves at an interface of water/porous sediment with underlying solid substrate. Ocean Eng. 2013;63:8–16.
   Web of Science ®Google Scholar
• Lyu DD, Wang JT, Feng J, et al. Reflection and transmission of plane waves at a water-porous sediment interface with a double-porosity substrate. Transport Porous Med. 2014;103:25–45.
   Web of Science ®Google Scholar
• Chen WY, Wang ZH, Zhao K, et al. Reflection of acoustic wave from the elastic seabed with an overlying gassy poroelastic layer. Geophys J Int. 2015;203(1):213–227.
   Web of Science ®Google Scholar
• Feng SJ, Chen ZL, Chen HX. Reflection and transmission of plane waves at an interface of water/multilayered porous sediment overlying solid substrate. Ocean Eng. 2016;126:217–231.
   Web of Science ®Google Scholar
• Biot MA. Theory of stress-strain relations in anisotropic viscoelasticity and relaxation phenomena. J Appl Phys. 1954;25(11):1385–1391.
   Web of Science ®Google Scholar
• Stoll RD. Acoustic waves in ocean sediments. Geophysics. 1977;42(4):715–725.
   Web of Science ®Google Scholar
• Liu X, Greenhalgh S, Zhou B, et al. Effective Biot theory and its generalization to poroviscoelastic models. Geophys J Int. 2018;212(2):1255–1273.
   Web of Science ®Google Scholar
• Carcione JM, Ouiroga-Good G. Full frequency-range transient solution for compressional waves in a fluid-saturated viscoacoustic porous medium. Geophys Prospect. 1996;44(1):99–129.
   Web of Science ®Google Scholar
• Liu X, Greenhalgh S, Zhou B. Approximating the wave moduli of double porosity media at low frequencies by a single Zener or Kelvin-Voigt element. Geophys J Int. 2010;181(1):391–398.
   Web of Science ®Google Scholar
• Mainardi F. Fractional calculus and waves in linear viscoelasticity-an introduction to mathematical models. London: Imperial College Press; 2010.
   Google Scholar
• Bagley RL, Torvik PJ. On the fractional calculus model of viscoelastic behavior. J Rheol. 1986;30:133–155.
   Web of Science ®Google Scholar
• Podlubny I. Fractional differential equations. New York (NY): Academic Press; 1999.
   Google Scholar
• Tsiklauri D, Beresnev I. Properties of elastic waves in a Non-Newtonian (Maxwell) fluid-saturated porous medium. Transport Porous Med. 2003;53(1):39–50.
   Web of Science ®Google Scholar
• Cui ZW, Liu JX, Wang K X. Elastic waves in non-Newtonian (Maxwell) fluid-saturated porous media. Wave Random Complex. 2003;13(3):191–203.
   Web of Science ®Google Scholar
• Tsiklauri D, Beresnev I. Enhancement in the dynamic response of a viscoelastic fluid flowing through a longitudinally vibrating tube. Phys Rev E. 2001;63(4):046304.
   Web of Science ®Google Scholar
• Yin Y, Zhu KQ. Oscillating flow of a viscoelastic fluid in a pipe with the fractional Maxwell model. Appl Math Comput. 2006;173(1):231–242.
   Web of Science ®Google Scholar
• Schiessel H, Metzler R, Blumen A, et al. Generalized viscoelastic models: their fractional equations with solutions. J Phys A-Math Theor. 1995;28:6567–6584.
   Google Scholar