A three-parameter dispersion relationship for Biot's fast compressional wave in a marine sediment.

When the bulk and shear moduli of the mineral frame are set to zero, the full Biot theory of wave propagation in a porous medium such as a marine sediment reduces to Williams' "effective density fluid" (EDF) model [J. Acoust. Soc. Am. 110, 2276-2281 (2001)]. Although eight material variables appear in the EDF model, it is in fact tightly constrained, possessing just three degrees of freedom: the phase speeds in the limits of low and high frequency, c0 and c∞, respectively, and a transition frequency, fT, separating the low- and high-frequency regimes. In this paper, an algebraic approximation to the EDF model is formulated, which is termed the "modified viscous fluid" (MVF) model, involving only the three parameters (c0, c∞, fT). Expressions are developed for (c0, c∞, fT) in terms of the eight material properties; and a comparison of the MVF and EDF dispersion curves is performed, showing that they are essentially identical at all frequencies. Apart from its computational simplicity, the MVF model provides insight into the effect of each material parameter on the shape of the dispersion curves. For instance, the transition frequency scales as the ratio of the pore-fluid viscosity to the permeability, but neither the viscosity nor the permeability affects the limiting phase speeds c0 and c∞. [ABSTRACT FROM AUTHOR]