由余震分布确定大地震子断层及其参数的模糊聚类方法

大地震的破裂过程一般涉及多个断层的活动, 发震断层并非是单一断层平面, 而是由多个断层平面组合而成． 利用成丛小震发生在断层面附近的原则, 假定震源点围绕子断层面中心服从三维正态分布, 使用GK模糊聚类方法结合主成分分析给出了一种可以重构活动断层网络三维空间结构的新方法.该方法首先对全部震源点目录使用GK模糊聚类方法得到它的划分矩阵, 再利用划分矩阵及合适的阈值, 剔除离群震源点, 提取出平面型分布的子类, 最后对每个子类在三维正态分布的假设下确定断层面分布的95%置信矩形断层区域位置、 走向角和倾向角参数.当给定地震目录事件后, 可以给出符合假设的一系列最优断层面区域, 每个子断层由它的中心位置、 长度、 宽度、 走向角和倾角所刻画.为检验新方法的性能, 先进行计算机仿真, 结果显示算法可成功地重建模拟地震目录的断层部分.最后将新方法用于南加州兰德斯(Landers)地震部分余震精确定位数据中, 得到的重建结果与已知的研究结果比较吻合, 说明了新方法的有效性. 

Fuzzy clustering analysis in determining sub-faults of large earthquakes based on aftershock distribution

A large earthquake rupture process generally involves several fault motions and the major fault is usually a combination of multiple fault planes. Assuming aftershocks concentrating in the center of fault planes and obeying three-dimensional (3-D) normal distribution, we reconstructed a 3-D structure of the active part of a fault network by using a new fuzzy clustering and principal component analysis. Firstly, the partition matrix of the spatial locations of all earthquakes is obtained by GK fuzzy clustering analysis; then, based on the partition matrix and appropriate threshold values, the data outliers are deleted and the planar clusters are obtained； finally, the 95% confidence limits of the rectangular fault plane region, the fault strike and dip are determined by assuming the cluster obeying 3-D normal distribution. When the seismic events are given, the optimal spatial fault segments can be obtained by this new method. Each of the fault segments is fully characterized by its central location, length, width, strike and dip angle. In our computer simulation study, this method was successfully applied in extracting fault planes constructed from synthetic earthquake catalogs. We also applied the new method to the determination of the fault plane from the aftershock sequence of Landers earthquake in southernCalifornia. The reconstructed plane segments fully agree with the faults already known on geological maps or with the blind faults appearing to be quite clear.