An acoustic model of a laminar sand bed

It was postulated that a laminar sand bed may be modeled as an ensemble of randomly layered Biot media. The thickness of each layer was approximately half a grain diameter. The porosity variations in the vertical direction were matched to the mean and standard deviation of that of a structure of packed spherical grains. The effect of large-scale lateral variations in porosity was simulated by performing a coherent ensemble average of the acoustic output from several realizations of the randomly layered medium. The medium parameters were chosen to represent water-saturated sand. Specifically, the sand bed was modeled as bounded by a homogeneous water halfspace above, and a homogeneous poroelastic halfspace of equal average porosity below. Reflected and transmitted signals were computed. Coherent and random components of the reflected signal were calculated. The coherent parts were directly related to the reflected and the transmitted waves. Results showed significant differences between the modeled sand be...