A two-dimensional earthquake model which has two significant features is studied. In this model, the nucleation length is proportional to the final size of the earthquake and fault strength healing occurs at an exponential rate. The time evolution of the spatial average of the crust strength shows f-v fluctuations when the characteristic healing time τ is longer than a critical value τc. Furthermore we obtain a relation which is independent of the model parameters. Our results indicate that crust rigidity can be worked out from earthquake data statistics.
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