The Variations of Characteristic Scale Length of Friction Evolution Affect Earthquake Dynamics

Within a fault governing model the characteristic scale length is one of the most relevant physical parameters because it accounts for the so–called fracture energy (density) of the system, its dynamics, the time during which the accumulated stress is released and the seismic waves are excited, the amount of slip developed during an instability event. Friction laboratory experiments reveal that it is not a material property, but that it changes with the sliding velocity. We propose two rather different analytical models to fit laboratory evidence and we incorporate them into a fault model able to simulate repeated earthquakes in the framework of various formulations of rate and state friction. We demonstrate that temporal variations of the scale length do not prevent the system to reach its limit cycle, but they systematically reduce the magnitude of the expected event (both in term of developed slip, and thus seismic moment, and released stress) and also reduce the inter–event time (recurrence interval). Depending on the friction model, the system can penetrate into the stable regime and can either continue the accelerating phase toward to failure or decelerate and abort instability.