Shear waves and the discrepancy between perceived and ideal frequency power laws for sediment attenuation

Abstract

Inverse techniques based on data for long-range propagation in shallow water have recently inferred that the attenuation in certain marine sediments varies at low frequency as the 1.8 power. Idealized models predict the exponent to be exactly 2.0. The inverse inferences usually assume the bottom is a fluid, and this is ordinarily a good approximation, because the shear wave speed in bottom sediments is typically very small. Direct numerical simulation [J. M. Collis et al., Proc. Oceans 2007, Aberdeen (2007)] indicates that shear waves make a sufficient contribution to shallow water attenuation that could account for the small discrepancy in exponents. To better assess whether this is the case, the present paper analyzes the effect of shear waves on modal attenuation. The Pekeris model with a lower elastic half-space is used with the shear wave speed taken to be substantially less than the sound speed in water. The derived dispersion relation has complex roots for the horizontal wave number, and the imaginary part, found by a perturbation analysis, predicts that the shear wave contribution to the modal attenuation is proportional to the cube of the ratio of the shear wave to water sound wave speeds. [Work supported by ONR.]