Theory of compressional and shear waves in fluidlike marine sediments

An unconsolidated, saturated marine sediment consists of a more or less loose assemblage of mineral grains in contact, with seawater in the interstices. It is postulated that the two-phase medium possesses no skeletal frame, implying that the elastic rigidity modulus of the material is zero. A theory of wave propagation in such a sediment is developed, in which the medium is treated as a fluid that supports a specific form of intergranular dissipation. Two important equations emerge from the analysis, one for compressional wave propagation and the second describing transverse disturbances. For the type of dissipation considered, which exhibits hysteresis or memory, the shear equation admits a wavelike solution, and is thus a genuine wave equation, even though the sediment shows no elastic rigidity. In effect, the medium possesses a “dissipative” rigidity, which is capable of supporting shear. This behavior is distinct from that of a viscous fluid, for which the shear equation is diffusionlike in character, giving rise to critically damped disturbances rather than propagating waves. The new theory predicts an attenuation coefficient for both compressional and shear waves that scales with the first power of frequency, in accord with published data. The wave theory is combined with a model of the mechanical properties of marine sediments to yield expressions relating the compressional and shear wave speeds to the grain size, the porosity, and the density of the medium. These expressions show compelling agreement with a number of measurements from the literature, representing a variety of sediment types ranging from clay to coarse sand.