Skip to main content
Log in

Reflection and refraction of plane harmonic waves at an interface between elastic solid and porous solid saturated by viscous liquid

  • Published:
pure and applied geophysics Aims and scope Submit manuscript

Abstract

A general solution of Biot's field equations governing small motions of a porous solid saturated by viscous liquid is employed to study the reflection and refraction at the interface between an elastic solid and a liquid-saturated porous solid. The incident wave is assumed to be plane and homogeneous, propagating through the isotropic elastic solid. The poroelastic solid is considered to be a dissipative one. Amplitude and energy ratios are computed numerically for a particular model. With first-order corrections for the porosity of solid and viscosity of liquid, the limiting cases of low and high frequencies are computed.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Abramowtiz, M., andStegun, I. A.,Handbook of Mathematical Functions (Dover Publications, New York 1965).

    Google Scholar 

  • Achenbach, J. D.,Wave Propagation in Elastic Solids (North-Holland Publishing Company 1973).

  • Biot, M. A. (1956),The Theory of Propagation of Elastic Waves in Fluid-saturated Porous Solid, J. Acoust. Soc. Am.28, 168–191.

    Google Scholar 

  • Biot, M. A. (1962),Mechanics of Deformation and Acoustic Propagation in Porous Media, J. Appl. Phys.33, 1482–1498.

    Google Scholar 

  • Borcherdt, R. D. (1982),Reflection-refraction of General P- and Type-I S-Waves in Elastic and Anelastic Solids, Geophys. J. R. Astr. Soc.70, 621–638.

    Google Scholar 

  • Bullen, K. E.,An Introduction to the Theory of Seismology (Cambridge University Press 1963).

  • Burridge, R., andVargas, C. A. (1979),The Fundamental Solution in Dynamic Poroelasticity, Geophys. J. R. Astr. Soc.58, 51–90.

    Google Scholar 

  • Costley, R. D., andBedford, A. (1988),An Experimental Study of Acoustic Waves in Saturated Glass Beads, J. Acoust. Soc. Am.83, 2165–2174.

    Google Scholar 

  • Deresiewicz, H., andRice, J. T. (1962),The Effect of Boundaries on Wave Propagation in a Liquid Filled Porous Solid: III. Reflection of Plane Waves at Free Boundaries, Bull. Seismol. Soc. Am.52, 595–626.

    Google Scholar 

  • Deresiewicz, H., andSkalak, R. (1963),On Uniqueness in Dynamic Poroelasticity, Bull. Seismol. Soc. Am.53, 783–789.

    Google Scholar 

  • Dunn, K. J. (1986),Acoustic Attenuation in Fluid-saturated Porous Cylinders at Low Frequencies, J. Acoust. Soc. Am.79, 1709–1721.

    Google Scholar 

  • Fatt, I. (1959),Biot-Willis Elastic Coefficients for a Sandstone, J. Appl. Mech.26, 296–297.

    Google Scholar 

  • Hajra, S., andMukhopadhyay, A. (1982),Reflection and Refraction of Seismic Waves Incident Obliquely at the Boundary of Liquid-saturated Porous Solid, Bull. Seismol. Soc. Am.72, 1509–1533.

    Google Scholar 

  • Yamamoto, T., andTurgut, A. (1988),Acoustic Wave Propagation through Porous Media with Arbitrary Pore Size Distributions, J. Acoust. Soc. Am.83, 1744–1751.

    Google Scholar 

  • Yew, C. H., andJogi, P. N. (1976),Study of Wave Motions in Fluid-saturated Porous Rocks, J. Acousis Soc. Am.60, 2–8.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sharma, M.D., Gogna, M.L. Reflection and refraction of plane harmonic waves at an interface between elastic solid and porous solid saturated by viscous liquid. PAGEOPH 138, 249–266 (1992). https://doi.org/10.1007/BF00878898

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00878898

Key words

Navigation