Slip-Weakening and Rate-Strengthening Friction Law for Shallow Layer Above the Seismogenic Zone
Accurate modeling of slip-rate time functions in the shallow portion above the seismogenic zone on a fault is essential for ground-motion prediction. Recent observations, such as those from the 2016 Kumamoto, central Kyushu, Japan, earthquake (MJMA 7.3), have revealed long-period ground motions and permanent displacements with long rise times near the surface fault, indicating that contributions of the shallow fault portion must be considered in addition to strong-motion generation areas within the deep seismogenic zone. In this study, we propose a friction law applicable to fault surfaces in an elastic medium, in which a slip-rate strengthening mechanism operates below a characteristic slip rate Vc, supplementing the standard slip-weakening law. Pure slip weakening is applied within the seismogenic zone, whereas the slip-rate strengthening branch is applied to the shallow fault portion above the seismogenic zone. Dynamic rupture simulations using a 3D elastic model with a shallow stress drop of 0 MPa demonstrate that the model incorporating slip-rate strengthening suppresses slip rates on the shallow layer and reduces peak ground velocity amplitudes within approximately 1 km of the surface fault compared with a purely slip-weakening model, despite producing nearly identical overall rupture propagation and seismic moments. Sensitivity analyses further show that δ, which is the incremental parameter of the rate-strengthening friction law, primarily controls peak slip rate through its influence on the effective fracture energy, whereas Vc mainly affects rupture duration, particularly the slip-termination phase. Although long Dc or negative stress drop has traditionally been used to mimic suppression of shallow slip rates, the proposed law more efficiently reproduces a gradual slip-rate onset, prolonged slip duration, and peak suppression, compared to friction laws without slip-rate dependence that have a similar effective fracture energy. The proposed friction formulation is simple to implement, computationally efficient, and useful for large-scale source-model exploration and applications in near-fault ground-motion prediction.