Transport in Porous Media

, Volume 83, Issue 1, pp 233–256

An Asymptotic Model of Seismic Reflection from a Permeable Layer


    • Lawrence Berkeley National Laboratory
  • Gennady Goloshubin
    • University of Houston
Open AccessArticle

DOI: 10.1007/s11242-010-9533-8


Analysis of compression wave propagation in a poroelastic medium predicts a peak of reflection from a high-permeability layer in the low-frequency end of the spectrum. An explicit formula expresses the resonant frequency through the elastic moduli of the solid skeleton, the permeability of the reservoir rock, the fluid viscosity and compressibility, and the reservoir thickness. This result is obtained through a low-frequency asymptotic analysis of Biot’s model of poroelasticity. A review of the derivation of the main equations from the Hooke’s law, momentum and mass balance equations, and Darcy’s law suggests an alternative new physical interpretation of some coefficients of the classical poroelasticity. The velocity of wave propagation, the attenuation factor, and the wave number are expressed in the form of power series with respect to a small dimensionless parameter. The absolute value of this parameter is equal to the product of the kinematic reservoir fluid mobility and the wave frequency. Retaining only the leading terms of the series leads to explicit and relatively simple expressions for the reflection and transmission coefficients for a planar wave crossing an interface between two permeable media, as well as wave reflection from a thin highly permeable layer (a lens). Practical applications of the obtained asymptotic formulae are seismic modeling, inversion, and attribute analysis.


Hooke’s law Darcy’s law Poroelasticity Low frequency Permeability Asymptotic analysis Seismic imaging


This study has been performed at Lawrence Berkeley National Laboratory (LBNL) of the U.S. Department of Energy (DOE) under Contract No. DE-AC02-05CH11231, and at the University of Houston. It has been partially supported by DOE grant DE-FC26-04NT15503, the UCOil Consortium, and the Reservoir Quantification Laboratory at the University of Houston. The authors are thankful to Dr. Steven Pride and Dr. Andrea Cortis of LBNL for reviewing an early version of the manuscript and for critical remarks and suggestions. The authors also acknowledge with gratitude the critical remarks and suggestions by the anonymous reviewers, which have helped to significantly improve the presentation.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Copyright information

© The Author(s) 2010