Impulse Backscattering in Granular Beds: Introducing a Toy Model

Abstract

Impulses efficiently propagate into nominally dry granular beds and backscatter from buried inclusions in such beds may be potentially exploited to image shallow buried objects (SBOs). However, reliable imaging of SBOs requires ``cleaning up'' of surface vibrations, and, in addition to 3D particle dynamics simulations, a phenomenological model to parameterize the bed surface may be useful for field applications. We introduce a 1D mean-field-like toy model with two parameters that allows one to model surface vibrations, is consistent with experiments in a granular bed, and can help estimate the approximate signal transmission properties of the bed.