A low-frequency asymptotic model of seismic reflection from a high-permeability layer

Analysis of compression wave propagation through a high-permeability layer in a homogeneous poroelastic medium predicts a peak of reflection 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 the Biot's model of poroelasticity. A new physical interpretation of some coefficients of the classical poroelasticity is a result of the derivation of the main equations from the Hooke's law, momentum and mass balance equations, and the Darcy's law. 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 latter is equal to the product of the kinematic reservoir fluid mobility, an imaginary unit, and the frequency of the signal. 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). The practical implications of the theory developed here are seismic modeling, inversion, and attribute analysis