Acoustic mode at low frequencies in marine sediments: Derivation from first principles using the method of homogenization

The original low-frequency Biot model factors into three characteristic modes, one being the acoustics mode, having only three significant aggregate parameters: apparent density and bulk modulus, and a numerical coefficient relating attenuation to ω2. This prediction, although from a heuristic multiparametered model, finds an independent basis in a modification of the derivation by Burridge and Keller [‘‘Poroelasticity equations derived from microstructure,’’ J. Acoust. Soc. Am. 70 1140–1146 (1981)] of the poroelasticity equations from microstructure, using only the equations of elasticity and of those for a fluid with viscosity, with no exotic mechanisms. The overall mathematical procedure is the method of homogenization. Isolation of the acoustic mode is achieved by introducing a reference velocity scale, cref, the intrinsic sound speed in the fluid alone, with the macroscopic length scale H taken as cref/ω. Mass densities of fluid and elastic media are assumed comparable, and the elastic modulus is assumed comparable to bulk modulus of fluid. The nature of sediments suggests that one needs two inner scales, the larger of which is a representative grain dimension, and the smaller of which is associated with the contact areas of adjacent grains caused by gravitational compression.