Water-Saturated Sandy Sediments

Abstract

In the baseline Biot model, both shear and compressional wave absorption is dominated by the viscous loss due to relative motion between the pore fluid and the solid particles. For the compressional wave, frequency dependence is close to the second power of frequency below the characteristic frequency. At higher frequencies, the attenuation follows the half-power of frequency. In practice, other factors, such as squirt flow at the grain contacts, combined with the unavoidable distribution in pore sizes, can produce a range of frequency dependencies. Compressional wave absorption is most sensitive to the presence of small amounts of gas. Most of the laboratory measurements are suspected of being biased by the presence of minute concentrations of gas of the order of 1–10 parts per million by volume. At even higher frequencies, when the grains and pores are no longer small compared to the wavelength, the effective medium assumption that underlies the Biot model breaks down. Multiple scattering dominates and absorption increases as the fourth power of frequency. The shear wave speed is controlled by the frame shear modulus. There is an increase in the shear speed at the contact squirt-flow relaxation frequency. The Biot slow wave, being highly attenuated, is difficult to detect. Its speed is a function of the frame bulk modulus. It is easily detected in water-saturated sintered glass beads, in which the frame moduli are high, but more difficult to detect in unconsolidated sand, which, in the absence of any confining pressure, has low frame moduli. Nevertheless, it cannot be ignored because it makes its presence felt as a significant loss mechanism in the reflection process.