AUTOMATON MODELS OF SEISMIC FRACTURE - CONSTRAINTS IMPOSED BY THE MAGNITUDE-FREQUENCY RELATION

To obtain an understanding of the ingredients required in a realistic model of fa t 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.