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

Seismic coda waves, once dismissed as mere noise, are now recognized as critical signatures of wave scattering in seismograms. In 1969, Aki proposed that these waves originate from small-scale heterogeneities within the Earth’s interior, sparking a new research focused on their interpretation and application. Subsequent studies have demonstrated that coda waves carry rich information about subsurface heterogeneity, making investigating scattering phenomena essential for probing complex geological structures. Wave propagation and scattering in unconsolidated granular media are particularly relevant for understanding the seismic behavior of planetary regoliths, such as those found on the Moon and Mars. The energy-based radiative transfer equation (RTE) offers a theoretical framework to quantitatively relate scattering characteristics to microstructural properties, including grain size, coordination number, and porosity. However, the RTE assumes an infinite medium, an assumption rarely satisfied in realistic scenarios, underscoring the need to evaluate how boundary effects influence wave scattering and inversion accuracy. This study leverages the discrete element method (DEM) to simulate elastic wave propagation and scattering in granular media. Unlike conventional numerical approaches, DEM explicitly models grain-scale interactions, including contact forces and dynamic behavior, enabling detailed resolution of wavefield features shaped by microstructural heterogeneity and boundary geometry. Using the RTE framework, we invert scattered wave energy to estimate microstructural parameters and assess the effects of absorbing (infinite) and rigid (finite) boundary conditions on inversion performance. The results show that DEM effectively reproduces wavefields in granular media and that RTE-based inversion is a feasible approach for retrieving grain-scale properties. However, boundary reflections significantly distort the wavefield, leading to substantial errors in the inversion outcomes. This research provides new insights into wave scattering in granular materials and offers theoretical guidance for designing and interpreting seismic experiments in planetary regolith environments.