Effect of seismic coupling on the scaling of seismicity

Summary Based on the dynamical mass‐spring model proposed by Burridge & Knopoff (1967), the effects on seismicity and the scaling exponent (i.e. the b value) of the frequency‐magnitude relation due to the variation in the stiffness ratio s , defined as the ratio of the spring constant between two masses to that between a mass and the moving plate, are studied. A linearly velocity‐dependent friction law is taken to control the relative motion between a mass and the plate. The distribution of the breaking strengths of the system is considered to be a fractal function. Computational results show the strong dependence of the seismicity pattern and the scaling exponent upon the stiffness ratio s. The number of large events increases with s. For s < 20, the data points of both cumulative frequency and discrete frequency versus magnitude cannot be completely interpreted by a single line. For S > 120, only the delocalized events, for which all masses of the model slide almost simultaneously in a time span, are generated. For 20≤ s ≤120, the data points of frequency versus magnitude in a large magnitude range follow a power‐law function very well. The lower bound of the magnitude range is almost constant, but the upper bound increases with s. The b value of the cumulative frequency‐magnitude relation is smaller than that of the discrete frequency‐magnitude one especially for a large value of s. The b value of the power‐law function for 20≤ s ≤120 decreases with increasing s in the following forms: b ∼ s −2/3 for the cumulative frequencymagnitude relation and b ∼ −1/ 2 for the discrete frequency‐magnitude one. In addition, the variations in several other parameters of the friction law also lead to different b values, but the distributions of b versus s still follow the previously mentioned relations.