基于Dieterich地震发生率模型分析前震成因的力学机制

前震是地震前兆观测中的一个重要物理量，前震的研究对地震预测的发展尤为重要，前震序列的典型特征包括加速发生的小震与古登堡-里克特定律（Gutenberg-Richter Law）中的b值变小.本文在Dieterich提出的地震发生率模型的基础上，探讨前震发生的力学成因机制及前震-主震-余震时域演化特征.模型分析结果表明，前震震源区断层及其断层周边剪应力加载速率的变化可能是前震发生及地震发生率变化的一个关键原因.由于前震震源区次级断层之间剪应力加载速率受来自主震成核过程中断层自加速滑移的影响升高，从而可导致这些次级断裂的加速失稳，即加速前震的发生.当震源区内由前震所产生的静态应力扰动不可忽略时，应力扰动和主震成核的共同作用也可对后续前震发生率产生影响.当正向应力扰动出现时，后续的前震序列的地震发生率会出现陡增，随后其地震发生率逐渐下降.而当负向应力扰动出现时，地震发生率会出现陡降，然后再次逐渐上升.基于Kostrov模型，本文得到了剪应力加载速率与古登堡-里克特定律中b值的关系式，结果表明前震序列中b值的减小与前震区内的剪应力加载速率的上升有关.

Analysis of the mechanism of foreshocks base on Dieterich seismicity model

Anomalous seismic activities such as an increase of seismicity rate or quiescence in a given region are often observed before moderate to large earthquakes. These increased earthquake events are usually called foreshocks and their occurrences may be represented by a reliable precursory pattern for the development of short-term earthquake prediction. The statistical features of foreshocks can be interpreted in terms of the Dieterich's seismic triggering model and are represented as a standard foreshock-mainshock-aftershock model. The typical characteristics of the foreshock series may include a significant acceleration of seismicity before mainshock with moderate to large magnitudes and an apparent decrease of the b-value given by Gutenberg-Richter law. In this study, we have investigated the triggering mechanisms of foreshocks and their temporal evolution features related to foreshock-mainshock-aftershock based on the Dieterich seismicity model. Using a piecewise approach in time domain, we have derived the analytical and approximate solutions to foreshock's activity patterns, which include earthquake swarm and Omori type's aftershock decay. Our results indicate that the shear stressing rate increase near the foreshock nucleation zones may be a key reason for a significant increase in seismicity rate preceding a mainshock. Such kind of stressing rate increase could be contributed from the accelerating fault slip motion on the mainshock's nucleation zone. Furthermore, when the static stress change caused by foreshocks with larger magnitude cannot be ignored, both of static stress perturbation and stressing rate change could influence the seismicity pattern related to the subsequence foreshock sequence. Numerical tests indicate that, during a short time interval with a much higher stressing rate, a positive static stress perturbation will cause an abrupt seismicity rate increase, and then followed by a rapid decreased seismicity rate as time increases. Otherwise, with a negative static stress perturbation, the seismicity rate will decrease first, and increases rapidly later on. In addition, we also obtain an approximate relationship between shear stressing rate and b-value. The results also indicate that a decrease of the b-value in the foreshock sequence is directly associated with the shear stressing rate increase.