Connecting the Viscous Grain-shearing Mechanism of Wave Propagation in Marine Sediments to Fractional Calculus

This study builds on Buckingham’s viscous grain-shearing (VGS) model ( Buckingham, 2007 ) which is a modification of the grain-shearing model proposed to explain wave propagation in saturated, unconsolidated granular materials. The material impulse response function derived from the VGS model is found similar to the power-law memory kernel of fractional calculus. The VGS model then gives two equations; a fractional-order wave equation for the compressional wave and a fractional diffusion-wave equation for the shear wave. The fractional-order in the wave equations is identified as the geo-acoustic parameters of the medium. The two time constants which alter the material behavior in low frequency regime are found to be dependent on the material parameters as well. Besides, the decrease of phase velocity with increasing frequency for low frequencies is observed for compressional waves which went unnoticed in the originally proposed VGS model. Most of the predictions from the fractional framework agree with the VGS model. The overall aim is to establish the fractional framework as a modeling tool which besides being computationally less complex has foundations deeply rooted in physics.