Numerical Investigation of Wave Scattering in Granular Media: Grain-Scale Inversion and the Role of Boundary Effects

TL;DR

This paper uses discrete element simulations to study wave scattering in granular media, evaluating how boundary effects influence the accuracy of microstructural property inversion based on the radiative transfer equation.

Contribution

It introduces a DEM-based approach to model wave scattering at grain scale and assesses boundary effects on RTE-based inversion accuracy.

Findings

DEM accurately reproduces wavefields in granular media

RTE-based inversion can recover grain-scale properties

Boundary reflections cause significant inversion errors

Abstract

Seismic coda waves, once regarded as noise, are now recognized as key indicators of wave scattering in seismograms. Aki (1969) first proposed that these waves result from small-scale heterogeneities in the Earth's interior, spurring research into their interpretation and applications. Coda waves are now known to carry valuable information about subsurface heterogeneity, making the study of scattering essential for understanding complex geological structures. Wave scattering in unconsolidated granular media is especially relevant to planetary regoliths, such as those on the Moon and Mars. The radiative transfer equation (RTE) provides a theoretical framework to link scattering behavior to microstructural properties like grain size, coordination number, and porosity. However, the RTE assumes an infinite medium, a condition rarely met in real settings, emphasizing the need to evaluate how boundary effects influence scattering and inversion accuracy. This study uses the discrete element method (DEM) to simulate elastic wave propagation and scattering in granular media. Unlike traditional numerical methods, DEM explicitly models grain-scale interactions and dynamic behavior, capturing detailed wavefield features shaped by microstructural heterogeneity and boundary conditions. By applying the RTE framework, we invert scattered wave energy to estimate microstructural parameters and analyze the impact of absorbing (infinite) and rigid (finite) boundary conditions on inversion results. The findings show that DEM accurately reproduces wavefields in granular media and that RTE-based inversion can effectively recover grain-scale properties. However, boundary reflections significantly distort the wavefield and lead to notable errors in inversion outcomes.