Dispersion and attenuation of acoustic waves in granular packings

Propagation of acoustic waves through granular and fluid-granular systems has many important geophysical and technology applications. A complete description should connect grain-scale loss mechanisms to functional forms for the frequency dependence of wave speed and attenuation coefficient, presumably via a wave equation derived from grain-scale forces. Dissipation at the grain scale may arise from lossy grain-grain contacts, frictional slips, or viscous damping from the interstitial fluid. Previous work for the acoustic properties of marine sediments has postulated partial differential equations (PDEs) based on different types of grain scale forces. However, these previous theoretical approaches neglect the nonlinear mechanical response of the packing itself, which is known to lead to an array of complex behavior. Here we use discrete element method (DEM) simulations to demonstrate that simple, pairwise granular forces in disordered granular packings lead to emergent scaling laws, particularly for the attenuation coefficient, that do not agree with PDE-based approaches. Our results demonstrate the necessity of considering the granular packing structure in formulating theories for acoustics of marine sediments and other granular systems.