On pore-fluid viscosity and the wave properties of saturated granular materials including marine sediments

The grain-shearing (GS) theory of wave propagation in a saturated granular material, such as a marine sediment, is extended to include the effects of the viscosity of the molecularly thin layer of pore fluid separating contiguous grains. An equivalent mechanical system consisting of a saturating, strain-hardening dashpot in series with a Hookean spring represents the intergranular interactions. Designated the VGS theory, the new model returns dispersion curves that differ mildly from those of the GS theory at lower frequencies, below $10kHz$⁠, where effects due to the viscosity of the pore fluid may be non-negligible. At higher frequencies, the VGS dispersion curves approach those of the GS theory asymptotically. The VGS theory is shown to match the SAX99 dispersion curves reasonably well over the broad frequency band of the measurements, from 1 to $400kHz$⁠. This includes the frequency regime between 1 and $10kHz$ occupied by Schock’s chirp sonar data, where the viscosity of the pore fluid appears to have a discernible effect on the dispersion curves.