Dispersion and attenuation of acoustic guided waves in layered fluid-filled porous media

Abstract

The analysis of acoustic wave propagation in fluid-filled porous media based on Biot and homogenization theories has been adapted to calculate dispersion and attenuation of guided waves trapped in low-velocity layered media. Constitutive relations, the balance equation, and the generalized Darcy law of the modified Biot theory yield a coupled system of differential equations which governs the wave motion in each layer. The displacement and stress fields satisfy the boundary conditions of continuity of displacements and tractions across each interface, and the radiation condition at infinity. To avoid precision problems caused by the growing exponential in individual matrices for large wave numbers, the global matrix method was implemented as an alternative to the traditional propagation approach to determine the periodic equations. The complex wave numbers of the guided wave modes were determined using a combination of two-dimensional bracketing and minimization techniques. The results of this work indicate that the acoustic guided wave attenuation is sensitive to the in situ permeability. In particular, the attenuation changes significantly as the in situ permeability of the low-velocity layer is varied at the frequency corresponding to the minimum group velocity (Airy phase). Alternatively, the attenuation of the wave modes are practically unaffected by those permeability variations in the layer at the frequency corresponding to the maximum group velocity.