Acoustic wave propagation in composite fluid‐saturated media

Abstract

Biot’s linear model of stress‐wave propagation in a fluid‐saturated elastic framework is combined with a linear theoretical description of an inelastic frame to describe fluid‐saturated media in terms of a composite model. The composite model, the Constant Q (CQ) model, assumes an inelastic frame with frequency‐dependent complex elastic moduli and results in a frame response that is causal with Q exactly independent of frequency. The influence of frame inelasticity on the composite‐model Type I (compression), Type II, and shear‐wave attenuation response is found to be greatest for high and low frequencies, considering a frequency range of [Formula: see text]. The model is most sensitive to variations in permeability and pore‐size parameter for both attenuation and phase‐velocity responses. Parameter variations showed little effect on shear‐wave attenuation for a fine to course sand‐size frame matrix, indicating a fluid mechanism is responsible for the influence seen in Type I and Type II attenuations. The CQ model results fit the experimentally measured values of Type I attenuation and velocity for a fully saturated fine‐grained frame material (clay‐silt size grains) and a fully saturated coarse‐grained frame material (fine to coarse sand‐size grains). For Type I velocity, the experimentally observed dispersion clearly distinguishes the CQ model as superior to composite models that include a nondispersive frame, since such models predict very little dispersion due only to interpore fluid mechanisms.