The velocity ratio of water-saturated sediment derived from the Biot-Gassmann theory depends mainly on the Biot coefficient?a property of dry rock?for consolidated sediments
with porosity less than the critical porosity. With this theory, the shear moduli of dry sediments are the same as the shear moduli of water-saturated sediments. Because the velocity ratio depends on the Biot coefficient explicitly, Biot-Gassmann theory accurately predicts velocity ratios with respect to differential pressure for a given porosity. However, because the velocity ratio is weakly related to porosity, it is not appropriate to investigate the velocity ratio with respect to porosity (f).
A new formulation based on the assumption that the velocity ratio is a function of (1?f)n yields a velocity ratio that depends on porosity, but not on the Biot coefficient explicitly. Unlike the Biot-Gassmann theory, the shear moduli of water-saturated sediments depend not only on the Biot coefficient but also on the pore fluid. This nonclassical behavior of the shear modulus of water-saturated sediment is speculated to be an effect of interaction between fluid and the solid matrix, resulting in softening or hardening of the rock frame and an effect of velocity dispersion owing to local fluid flow. The exponent n controls the degree of softening/hardening of the formation. Based on laboratory data measured near 1 MHz, this theory is extended to include the effect of differential pressure
on the velocity ratio by making n a function of differential pressure and consolidation. However, the velocity dispersion and anisotropy are not included in the formulation.
Additional publication details
USGS Numbered Series
Velocity ratio and its application to predicting velocities