A possible mechanism of Omori-Utsu’s law through an example of the great Tangshan earthquake
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摘要: 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．
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关键词:
- 大森-宇津定律 /
- 开尔文地震震源体模型 /
- 有限元方法 /
- 唐山大地震
Abstract: This paper proposes a conceptual model of earthquake source body with Kelvin viscoelastic property to investigate the physical mechanism of Omori-Utsu’s law, supposing that tectonic stress field after main shock does not change with time and equivalent viscosity in the aftershock region is much lower than that of its outside in the period of total aftershock activity. This model can simulate aftershock sequence induced by post-seismic creep and stress readjustment, and the whole process including creep stopping, materials recovering to its elastic state, and faulting turning to stick state for next earthquake. Finite element method is used to calculate stress field evolution caused by a main shock and its aftershocks in the model with heterogeneous material properties. Further- more, the model and the method are used to simulate decay of the aftershock frequency of the 1976 MS7.8 Tangshan earthquake. The results show that the mechanism of Omori-Utsu’s law may be attributed to the stress changes caused by the creep of the fault and earthquake source body, which implies that aftershock frequency depends on the creep rate and decay time of the aftershocks is controlled by the equivalent viscosity. The lager the viscosity is, the longer the creep time or the aftershocks last. -
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图 1 开尔文黏弹性震源体概念模型
(a)材料模型和边界条件；(b)主震震源区局部放大图 图中DWE和DNS分别代表东西方向和南北方向的距离； 滚筒表示切向自由滑动而法向位移为零． 震源体是由3种材料组成，其材料力学性质分别用红色、 黄色和绿色代表． 红色区域表示主震震源区(包括主震断层和破坏区)，其中白色长线表示断层核，黑色短线表示震前小破裂(前震)； 蓝色表示震源体外的原岩区
Figure 1. Conceptual model of earthquake source body with Kelvin viscoelasticity
(a)Material properties and boundary conditions of the model；(b)Partial enlarged drawing of the main shock source region DWE and DNS are the distances in the N--S and E--W directions，respectively. The roll boundary denotes sliding in the tangential direction and no displacement in normal direction，respectively. The earthquake source body is composed of three regions with different material properties marked by the red，yellow and green. The red rectangular denotes the mainshock source region including mainshock fault and damaged zone，in which the white long line and black short lines mark the mainshock fault core and pre-seismic cracks(foreshocks); the blue marks the host rock region
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图 2 有限元模拟得到的主震后地震触发因子C的时空分布图
(a)主震后第1个月；(b)主震后第2个月；(c)主震后第3个月；(d)主震后第4个月； (e)主震后第6个月；(f)主震后第9个月；(g)主震后第36个月；(h)主震后第40个月模型尺寸为200 km×200 km. 白色区域表示地震触发因子C≥1，余震发生； 红色区域表示临近库仑破裂; 蓝色区域表示地震触发因子C=0，意味着之前已发生过余震
Figure 2. Temporal and spatial distribution of earthquake triggering factor C after the mainshock obtained by finite element modeling
(a)In the first month；(b)In the second month；(c)In the third month；(d)In the fourth month； (e)In the sixth month；(f)In the ninth month；(g)In the 36th month；(h)In the 40th month The region scale is 200 km×200 km. The white color denotes C≥1 implies aftershock occurrence； the red represents closing to Coulomb failure； the blue represents C=0 implies aftershock in the past
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图 3 1976年MS7.8唐山大地震之后6年的实际余震(MS>4.0)的时空分布图①
(a)第1年内;(b)第2年内；(c)第3年内；(d)第4年内；(e)第5年内；(f)第6年内 图中八角星为唐山大地震主震，圆圈表示其余震
Figure 3. Temporal and spatial distribution of aftershocks(MS>4.0)for the 1976 MS7.8 Tangshan earthquake
(a)In the first year；(b)In the second year；(c)In the third year；(d)In the fourth year；(e)In the fifth year；(f)In the sixth year Star denotes the Tangshan main shock，and the circles denote its aftershocks
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