基于二维Burridge-Knopoff模型的地震长程相互作用模拟研究
Simulation study of earthquakes based on the two-dimensional Burridge-Knopoff model with the long-range interaction
摘要：
本文利用数值模拟方法，研究了具有块体间长程相互作用的二维弹簧-块体（Burridge-Knopoff）地震模型的时空相关性。从弹性理论导出的长程相互作用考虑了断层面附近弹性体的影响，当距离r为1/r^3时，长程相互作用减弱。与相应的短程模型的性能进行了比较研究。长期模型的地震时空相关性一般比短期模型的地震时空相关性弱。幅度分布表现出"近临界"行为，即，在宽的参数范围内，接近古登堡-里希特定律的幂律行为，其B值为B \simeq 0.55，对模型参数不敏感，这与2D短程模型和1D短程和长程模型的行为形成鲜明对比，在2D短程模型和1D短程和长程模型中，这种"近临界"行为仅通过微调模型参数来实现。与短程情况相反，长程模型的地震事件的平均应力降几乎与其震级无关，与观测结果一致。大地震往往伴随前震，伴随着甜甜圈般的平静作为其前兆，而它们几乎不伴随余震，在主震后观察到的地震相关性几乎可以忽略不计。
英文摘要：
Spatiotemporal correlations of the two-dimensional spring-block (Burridge-Knopoff) models of earthquakes with the long-range inter-block interactions are extensively studied by means of numerical computer simulations. The long-range interaction derived from an elasticd theory, which takes account of the effect of the elastic body adjacent to the fault plane, falls off with distance r as 1/r^3. Comparison is made with the properties of the corresponding short-range models studied earlier. Seismic spatiotemporal correlations of the long-range models generally tend to be weaker than those of the short-range models. The magnitude distribution exhibits a ``near-critical'' behavior, i.e., a power-law-like behavior close to the Gutenberg-Richter law, for a wide parameter range with its B-value, B\simeq 0.55, insensitive to the model parameters, in sharp contrast to that of the 2D short-range model and those of the 1D short-range and long-range models where such a ``near-critical'' behavior is realized only by fine-tuning the model parameters. In contrast to the short-range case, the mean stress-drop at a seismic event of the long-range model is nearly independent of its magnitude, consistently with the observation. Large events often accompany foreshocks together with a doughnut-like quiescence as their precursors, while they hardly accompany aftershocks with almost negligible seismic correlations observed after the mainshock.
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