The physical mechanism (viscosity related) of low‐frequency acoustic wave attenuation in sandy/silty sediments.

Abstract

Considered saturated sediments contain diverse rock pebbles (characteristic size of 0.1 mm). The weight of higher pebbles holds lower pebbles in contact sufficiently that acoustically induced solid displacements vary slowly over several adjacent pebbles. Apart from contact areas, each is nearly surrounded by water at a nearly uniform pressure. An appropriate first approximation predicts that the elastic stress tensor in the pebbles is diagonal, with components equal to the negative of the acoustic pressure in the neighboring fluid. The assumptions of Mallock and Wood apply: the mass weighted local average velocity is proportional to the negative gradient of the pressure in the water. The no‐slip condition at the interfaces tends to force the water to move with the pebbles, but the finite viscosity allows the fluid at small distances from the interfaces to move at a different velocity than the pebbles. The apparent driving force for the oscillations of the interstitial water relative to the pebbles is associated with the inertia of the water and is proportional to the difference in densities. The derived approximate wave equation predicts attenuation proportional to frequency squared, proportional to the square of the difference of the densities, and inversely proportional to viscosity. The derived dimensionless proportionality constant is consistent with recent experiments.