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对弹性半空间中的几个含有不连续断层系的三维弹性连续介质模型,在沿单元垂直走滑断层发生的滑动过程进行了数值模拟。模型的几何形状和所使用的边界条件大致与圣安德烈斯断层中部的情形相符合。数值模拟综合考虑了脆性形变和蠕动变形。断层带的总形变率为蠕变率和摩擦滑动率之和。脆性断层的性质由破裂段(数值单元)的不同地震应力降的分布来给定。所假设的分布描述了两种理想化的情形,它们分别对应于不同断层滑动的极限状态:(1)以大尺度范围为特征的强无序状态,表示不成熟的断层带及扩展空间域。(2)相对有序的状态,以小尺度范围为特征,表示成熟的完全滑动断层。假定断层的蠕变特性在所有的情形中都相同,并且是用蠕滑速率与应力的幂次律关系来刻画的。利用这种脆性蠕变过程和模型参数可以得到一个在12.5km 深度含有“脆性-延性”过渡带的应力-深度剖面,以及一个在1857年地震破裂西北65km 处存在有“脆性-蠕变”过渡带的沿走向的应力剖面。模拟的震源空间分布在统计意义上与观测数据相类似。结果表明,断层强烈不均匀性的特征尺度范围会在断层系统的地震响应中显著表现出来。若尺度范围小,则会使震级-频度分布接近于特征地震分布,在时间上会导致如地震空区说所预言的大地震的准周期分布。而大尺度范围的地震活动性符合古登堡-里克特的震级-频度关系以及大地震的随机或是成簇的时间分布特征。数值模拟的结果表明,各种形式的震级-频度关系以及地震时间分布的统计特征都可以通过表征断层带不均匀性的尺度范围统一起来。这可以通过借助一个给定的断层带或是岩石层的结构特征给出一个清晰的物理解释,并且得到地震及断层观测资料的支持。在一些模拟中,小地震的震级-频度关系曲线明显低于自相似的古登堡-里克特关系曲线。这说明在构造加载过程中,小地震通过平滑应力的长波成分,为大地震的发生创造了条件。这一过程是通过与小地震的大量断裂有关的短波应力的消失过程来完成的。大地震的大尺度破裂的发生正好导致与上述长、短波应力的平滑与消失变化相反的过程。
Several 3D elastic continuum models with discontinuous faults in elastic half-space are numerically simulated in the sliding process along the vertical strike-slip faults. The geometry of the model and the boundary conditions used roughly correspond to those in the middle of the San Andres Fault. The numerical simulation considers the brittle deformation and creep deformation synthetically. The total deformation rate of fault zone is the sum of creep rate and frictional slip rate. The nature of the brittle fault is given by the distribution of the different seismic stress drops in the fractured segments (numerical units). The hypothetical distribution describes two idealized cases, which correspond to the limit states of different fault slips, respectively: (1) Strongly disordered states characterized by large-scale ranges represent immature fault zones and extended spatial domains. (2) The relatively ordered state, characterized by small scale ranges, represents a mature complete slip fault. It is assumed that the fault’s creep behavior is the same in all cases and is characterized by the power law of creep rate versus stress. Using this brittle creep process and model parameters, a stress-depth profile with a “brittle-ductile” transition zone at a depth of 12.5 km and a “brittle-creep” transition at 65 km northwest of the 1857 earthquake rupture can be obtained Belt along the direction of the stress profile. The simulated source spatial distribution is statistically similar to the observed data. The results show that the characteristic scale range of strong inhomogeneity of faults is obviously shown in the seismic response of fault system. If the scale is small, the magnitude-frequency distribution will be close to the characteristic seismic distribution, which will lead to the quasi-periodic distribution of large earthquakes as foreseen by the seismic areas. The large-scale range of seismicity is consistent with the magnitude-frequency relationship of Gutenberg-Richter as well as the random or clustered time distribution of large earthquakes. Numerical simulations show that various forms of magnitude-frequency relationships and statistical features of seismic time distributions can be unified by characterizing the extent of fault zone heterogeneity. This provides a clear physical explanation by means of the structural features of a given fault zone or rock formation and is supported by seismic and fault observations. In some simulations, the magnitude-frequency curve of small earthquakes is significantly lower than that of the self-similar Gutenberg-Rickett curve. This shows that during the process of tectonic loading, the small earthquakes create the conditions for the occurrence of major earthquakes by smoothing long-wave components. This process is accomplished through the disappearance of the shortwave stress associated with the large number of minor earthquakes. The occurrence of large-scale rupture of a large earthquake just leads to the opposite of the smooth and disappearing change of the long and short wave stress mentioned above.