二维Burridge-Knopoff地震模型中的震间时间统计
Interoccurrence time statistics in the two-dimensional Burridge-Knopoff earthquake model
摘要：
我们已经数值研究了所谓的interocurrence时间或等待时间，即，连续地震之间的时间间隔，基于二维（2-D）弹簧块（Burridge-Knopoff）模型，选择速度弱化属性作为本构摩擦定律。通过调整断层的刚度和摩擦特性这两个动力学参数，讨论了频率分布和互现时间累积分布的统计特性。我们优化这些模型参数，重现自然界中的intercurrence时间统计，频率和累积分布可以描述的幂律和Zipf-Mandelbrot型幂律，分别。在最佳情况下，古登堡-里克特定律的b值和波传播速度比与实际地震的结果一致。随着震级阈值的增大，地震间隔时间分布趋于指数分布。因此，除了小震级地震外，地震的时间序列是一个泊松过程，这是在自然界中观察到的。我们发现，由二维BK（原）模型导出的地震间时间统计量能有效地再现真实地震的统计量，因此，从地震间时间统计量的角度来看，该模型是一个符合实际的模型。
英文摘要：
We have numerically investigated statistical properties of the so-called interoccurrence time or the waiting time, i.e., the time interval between successive earthquakes, based on the two-dimensional (2-D) spring-block (Burridge-Knopoff) model, selecting the velocity-weakening property as the constitutive friction law. The statistical properties of frequency distribution and the cumulative distribution of the interoccurrence time are discussed by tuning the dynamical parameters, namely, a stiffness and frictional property of a fault. We optimize these model parameters to reproduce the interoccurrence time statistics in nature; the frequency and cumulative distribution can be described by the power law and Zipf-Mandelbrot type power law, respectively. In an optimal case, the b-value of the Gutenberg-Richter law and the ratio of wave propagation velocity are in agreement with those derived from real earthquakes. As the threshold of magnitude is increased, the interoccurrence time distribution tends to follow an exponential distribution. Hence it is suggested that a temporal sequence of earthquakes, aside from small-magnitude events, is a Poisson process, which is observed in nature. We found that the interoccurrence time statistics derived from the 2-D BK (original) model can efficiently reproduce that of real earthquakes, so that the model can be recognized as a realistic one in view of interoccurrence time statistics.
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