Abstract
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.
Highlights
There is no doubt that modern seismology still seeks improvements in the formulation of models to properly describe the physical processes occurring during faulting, in order to be able to explain the causes of the emission of the seismic waves and to predict the occurrence of earthquakes
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 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
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 and reduce the inter–event time
Summary
There is no doubt that modern seismology still seeks improvements in the formulation of models to properly describe the physical processes occurring during faulting, in order to be able to explain the causes of the emission (and the propagation) of the seismic waves and to predict the occurrence of earthquakes. The pioneering experiments performed by Dieterich [1978] and Ruina [1983] has been followed by several others, culminated in the so–called high velocity rotary shear experiments [see, among others, Sone and Shimamoto, 2009] All these results highlighted the fact that the pivotal quantity which controls the physics of the system (and the evolution of a natural fault) is represented by the scale length. This quantity — sometime invoked, improperly, as critical distance — basically represents the amount of cumulative slip that the system develops during the breakdown phase, i.e., during the portion of the coseismic stage during which the fault traction degrades from the yield level to the kinetic one This scale length is reported as characteristic slip–weakening distance (denoted by the symbol d0) in the framework of the slip–dependent governing model, such as the canonical, linear slip– weakening model postulated by Andrews [1976], or as the scale length L (or Dc as preferred by experimentalists) within the context of the rate– and state–dependent friction laws [Ruina, 1983 and references therein). By adopting a mass–spring model to solve the elastodynamic problem (see section 3) we incorporate these models in various formulations of rate‐ and state‐dependent friction laws, in order to explore the role of time‐variable L in the entire cycle of a natural fault (see sections 4 and 5)
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