[S-SS10] Fault Rheology and Earthquake Physics

[SSS10-15] Does fracture energy of small earthquakes scale with slip or slip squared?

*Sae Watanabe¹, Kazuki Masuda, Yoshihiro Kaneko¹ (1.Kyoto University)

Keywords:earthquake source scaling, fracture energy, dynamic rupture simulation, hierarchal patch structure

Understanding earthquake rupture growth processes and the resulting seismic radiation is essential for advancing earthquake source physics and mitigating seismic hazards. While scaling laws of source parameters provide critical insights into the physical processes driving rupture, existing physics-based models cannot fully explain these scaling relations. This study tests the hypothesis that spontaneous dynamic rupture models, incorporating hierarchical patches of fracture energy (Gc) within a slip-weakening friction framework, can reproduce several well-established scaling laws. To achieve this, we integrate a renormalization procedure into two- and three-dimensional dynamic rupture models using the spectral element method, enabling efficient simulations of multi-scale rupture processes. Earthquakes ranging from magnitude M2 to M6 are simulated to quantify source parameter scaling laws, including seismic moment, source duration, magnitude-frequency distributions, moment growth, fracture energy, stress drop, and scaled energy. We further explore how varying input friction parameters influences these scaling relationships. Our results show that modeled stress drops and scaled energy remain constant across magnitudes, and most scaling laws derived from the simulations are consistent with observational inferences. However, modeled fracture energy scales linearly with mean slip, contrary to earlier observational studies suggesting a quadratic relationship. Parameter sensitivity analysis shows that changes in input parameters do not significantly impact the fracture energy–slip scaling trends. After reanalyzing observational data, we show that biases in estimating fracture energy and mean slip have influenced prior conclusions. Applying corrections based on dynamic rupture models leads to revised fracture energy scaling that exhibits a linear relationship with mean slip across 10 orders of magnitude. These findings have important implications for understanding the energy budget of small and large earthquakes and the mechanisms governing rupture growth on natural faults.