大森-宇津定律的一种可能机制——以唐山大地震为例

In order to explore the physical mechanism of the Omori - Utsu law, under the assumptions that the equivalent viscosity in the aftershock area is much lower than that outside it and the tectonic stress field remains basically unchanged during the entire aftershock activity time interval, this paper proposes a conceptual model of a Kelvin viscoelastic seismic source body. This model can be used to simulate the aftershock sequence triggered by fault creep and stress adjustment in the source area after the main shock, as well as the entire process of the end of aftershocks after the creep stops, the medium returning to an elastic state, the fault relocking and accumulating for the next earthquake. The finite element method can be used to calculate the stress field caused by the main shock and each aftershock in the inhomogeneous viscoelastic seismic source body model and its evolution process over time. On this basis, the conceptual model of the Kelvin viscoelastic seismic source body and the finite element method are used to simulate the aftershock sequence of the 1976 Tangshan Ms7.8 earthquake. The results show that the empirical Omori - Utsu law can be explained by the Kelvin viscoelastic source body model, which means that the frequency of aftershock attenuation depends on the creep rate; the duration of the aftershock sequence is controlled by the viscosity of the source body, that is, the greater the viscosity, the longer the creep time and the longer the duration of aftershocks.

为了探讨大森-宇津定律的物理机制，本文在余震区等效黏度远低于其外部，且构造应力场在整个余震活动时间间隔内基本保持不变的假设条件下，提出了一个开尔文黏弹性地震震源体概念模型。该模型可用于模拟主震后断层蠕变和震源区应力调整触发的余震序列以及蠕变停止后余震终结、介质恢复到弹性状态、断层重新闭锁和积累下一次地震的整个过程。有限元方法可用来计算非均匀黏弹性地震震源体模型中主震和每次余震所引起的应力场及其随时间的演化过程。在此基础上，采用开尔文黏弹性地震震源体概念模型和有限元方法模拟了1976年唐山Ms7.8地震余震序列。结果表明：经验的大森-宇津定律可以用开尔文黏弹性震源体模型来解释，这意味着余震衰减的频度取决于蠕变的速率；余震序列持续时间受控于震源体的黏度，即黏度越大，蠕变时间越长，余震持续的时间也就越长。