Seismic inversion for grain size distribution in granular geohazards: combining theory and experiments

Seismic signals generated by granular geohazards (e.g. rock avalanches, debris flows) contain critical information for hazard assessment and early warning systems. A key challenge is the real-time inversion of grain size distribution (GSD), which governs flow dynamics and impact mechanisms. This study develops a novel high-frequency (≥1 Hz) seismic model for falling granular geohazards, combining elastic impact theory, Green’s function and energy dissipation from bed deformation and inter-granular collisions. Model validation is conducted through laboratory experiments involving single-grain impacts, dual-grain impacts and multi-grain assemblies with varying GSDs, supplemented by field observations. Results of single-grain impacts with diameter $d$ show that the centroid frequency (⁠$fcen$⁠), elastic energy (⁠$Wel$⁠) and total power spectral density (⁠$PSDT$⁠) of seismic signals scale proportionally with $d-0·5$⁠, $d5$⁠, $d3$⁠, respectively. These scaling laws are further supported by field observations. Comparative analysis of different GSDs reveals that conventional effective diameters exhibit limited correlations with seismic signal characteristics. In contrast, the newly proposed GSD parameter $GSDe$⁠, which incorporates fractal dimension (⁠$Df$⁠) and effective diameter, demonstrates robust and scale-independent relationships with seismic signals. The new theoretical model shows strong agreement with measured seismic signals, outperforming existing physical models in prediction accuracy. The findings provide a theoretical and practical framework for real-time GSD inversion from seismic signals, with direct applications in geohazard monitoring and mitigation strategies.