Some reflections on Buckingham’s viscous grain shearing model

Sediment geoacoustic properties are of considerable interest for commercial, industrial, and naval applications. In order to make geoacoustic inferences from acoustic data, the practitioner must choose a sediment acoustics model. The ‘Hamilton model’ is the most common, which assumes a frequency-independent sound speed, density, and an attenuation varying linearly with frequency, f¹. Buckingham’s Viscous Grain Shearing (VGS) model offers a practical alternative with important benefits. For example, since it obeys causality, it provides fundamental bounds to the parameter space that the Hamilton model does not. Furthermore, if the acoustic data are sufficiently informative, the model provides insight into the frequency dependence of sound speed and attenuation. The central physics in VGS are expressed in high-level (material impulse response) functions, which consider both viscous and friction loss mechanisms and lead to attenuation varying between f^1/2 to f¹ to f². Geoacoustic inference from seabed reflection measurements using the VGS model provides insight into the frequency dependence of naturally occurring marine sediments, i.e., admixtures of clay, silt, sand. At present, the VGS model is likely the most general (causal) sediment acoustics model, i.e., can reasonably treat the broadest range of sediment fabrics. [Research supported by the ONR Ocean Acoustics Program.]