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A one-dimensional BK dynamical lattice model (Burridge and Knopoff, 1967) is applied to simulate earthquakes for the study of the scaling relation between frequency and rupture length of earthquakes. Velocity-dependent friction controls the motion of mass elements. The distribution of the breaking strengths (i.e., static friction) is considered to be a fractal function. Simulation results show that the fractal dimension of the distribution of the breaking strengths is a minor factor in affecting the scaling of frequency versus rupture length. A fast velocity-weakening process from static friction to dynamic friction and a slow velocity-hardening one from dynamic friction to static friction are appropriate for interpreting the scaling of the frequency-rupture length (FL) relation. The frictional drop rather than the level of the breaking strength affects the FL scaling. Hence, the friction drop ratio (g) which determines the minimum value of the dynamic frictional force, is an important factor in influencing the FL relation. Smaller g (which a large friction drop) leads to a smaller scaling exponent value in the regime of localized events than larger g (with a smaller friction drop). The stiffness ratio, which is defined as the ratio of the stiffness of the coil spring to that of the leaf spring of the model, is also a significant parameter affecting the FL distribution. Nevertheless, simulation results show that small s is unable to produce a ower-law FL relation.

On the Frequency Distribution of Rupture Lengths of Earthquakes Synthesized from a One-Dimensional Dynamical Lattice Model.