To obtain an understanding of the ingredients required in a realistic model of fault dynamics, we have constructed a number of models for the initiation and propagation of seismic fractures on a planar fault. The models are all of the cellular automaton‐type and fall into two broad categories which can be subdivided into 40 different classes. They differ in whether the fracture propagates as a crack or as a partial stress drop model; whether they are loaded homogenously or randomly; whether or not the models are asperity models; whether the characteristic time associated to the initiation of fracture is short or long; and whether or not the dynamic variable (e.g., stress or energy) is conserved on the fault plane. We restrict ourselves to the question whether models are capable of reproducing a Gutenberg‐Richter power‐law decay of event frequency with fracture dimensions, irrespective of the b value. We find that very few models can generate a power law which extends to all sizes, although more models can generate power laws that cover a broad range of sizes. Of these, only a few exhibit acceptable scaling behavior with system size. We conclude that, within the class of models studied, only a reduced subset of partial stress drop models is acceptable for the modeling of seismic fault dynamics.
A model for dynamic steady state friction between two rough surfaces is developed in which the transfer of momentum from the horizontal to the vertical direction by collisions between asperities on opposing surfaces leads to a friction law which is independent of the detailed mechanism of energy dissipation. For nonfractal surfaces the model applies above a lower critical velocity which increases exponentially with smoothness. At high velocities there is velocity weakening and, as the smoothness of the surfaces increases, the velocity dependence rapidly approaches the experimentally observed logarithmic dependence, in agreement with phenomenological state variable friction laws. For fractallike surfaces the model applies over the whole velocity range above V = 0, showing velocity strengthening at low velocities and velocity weakening at high velocities, implying the existence of a stick‐sliplike instability.
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