Multi‐Scale Rate‐ and Roughness‐Dependent Frictional Constitutive Law and Dynamic Earthquake Sequence Simulation

Abstract The physical mechanisms that govern the multi‐scale source properties of earthquakes, such as fracture energy scaling, where the dynamic energy dissipation of earthquakes scales with fault slip, remain debatable. We introduced the rate‐ and roughness‐dependent friction (RRF) law which accounts for the multi‐scale roughness evolution of the fault interface. To obtain the RRF formulation, we modernized the previously proposed slip‐ and time‐dependent friction law into the form of the rate‐and‐state friction (RSF) by adding the direct effect. We performed dynamic earthquake sequence simulations using the RRF and found that it produced the fracture energy scaling with slip, as inferred from observations. However, the RRF exhibits a restricted range of rate‐weakening, and the accompanying slow healing causes a significant and unrealistic afterslip in the seismically slipped area. In addition, the previous formulation required significant memory to include numerous state variables for computation. Therefore, we further modified the RRF by assuming a cut‐off slip rate for the rate dependency and by employing the selective sampling of state variables. The modified RRF reproduces the fracture energy scaling without generating unrealistic afterslip. However, the simulated roughness evolution did not align with the observed fault roughness, suggesting that the constitutive relationship between roughness and fault shear strength still requires refinement. Our results indicate that, while more accurate formulations may exist, incorporating multi‐scale effects into the constitutive law, an aspect that has largely been overlooked in previous studies of RSF, is an efficient way of reproducing the general characteristics of earthquake sequences spanning across a broad range of magnitudes.