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

Wang Fuchang　Jin Zhitong　Qian Xiaoshi　Ren Qingqing　Huo Zhenxiang

Abstract

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.

References

吕鹏, 丁志峰, 朱露培. 2011. 结合波形互相关的双差定位方法在2008年汶川地震余震序列中的应用［J］. 地震学报, 33(4)： 407——419.

万永革, 沈正康, 刁桂苓, 王福昌, 胡新亮, 盛书中. 2008. 利用小震分布和区域应力场确定大震断层面参数方法研究及其在唐山地震序列中的应用［J］. 地球物理学报, 51(3): 793——804.

万永革, 吴忠良, 周公威, 黄静. 2000. 根据震源的两个节面的走向角和倾角求滑动角［J］. 地震地磁观测与研究, 21(5): 26——30.

王福昌, 曹慧荣, 万永革. 2010. 线性Errors——in——Variables模型在确定汶川地震主震断层面中的应用［J］. 数理统计与管理, 29(3): 381——390.

王福昌, 万永革, 胡顺田. 2008. 粒子群算法在主震断层面参数估计中的应用［J］. 地震研究, 31(2): 149——153.

王鸣, 王培德. 1992. 1989年10月18日大同—阳高地震的震源机制和发震构造［J］. 地震学报, 23(6): 407——415.

于湘伟, 陈运泰, 张怀. 2010. 京津唐地区中小地震重新定位［J］. 地震学报, 32(3): 257——269.

张广伟, 雷建设, 谢富仁, 郭永霞, 兰丛欣. 2011. 华北地区小震精定位及构造意义［J］. 地震学报, 33(6): 699——714.

朱艾斓, 徐锡伟, 胡平, 周永胜, 林元武, 陈桂华, 甘卫军. 2005a. 首都圈地区小震重新定位及其在地震构造研究中的应用［J］. 地质评论, 51(3): 268——274. 

朱艾斓, 徐锡伟, 周永胜, 尹京苑, 甘卫军, 陈桂华. 2005b. 川西地区小震重新定位及其活动构造意义［J］. 地球物理学报, 48(3): 629——636.

Babu&scaron;ka R, van der Veen P J, Kaymak U. 2002. Improved covariance estimation for Guastafson——Kessel clustering［C］// IEEE International Conference on Fuzzy System. Honolulu, HI, USA: 1081——1085.

Bensaid A M, Hall G A, Bezdek J C, Clarke L, Silbiger M, Arrington J, Murtagh R. 1996. Validity——guided (re)clustering with applications to image segmentation［J］. IEEE Transactions on Fuzzy System, 4(2): 112——123.

Gustafson D E, Kessel W C. 1979. Fuzzy clustering with a fuzzy covariance matrix［C］// Proceedings of the IEEE CDC. San Diego California: 761——766.

Lin G. 2009. LSH: an earthquake relocation catalog using southern California pick and waveform data ［EB/OL］.［2011——11——11］. http://www.rsmas.miami.edu/personal/glin/LSH.html.

Lin G, Shearer P, Hauksson E. 2007. Applying a three——dimensional velocity model, waveform cross correlation, and cluster analysis to locate southern California seismicity from 1981 to 2005［J］. J Geophys Res, 112, B12309, doi:10.1029/2007JB004986.

Ouillon G, Ducorbier C, Sornette D. 2008. Automatic reconstruction of fault networks from seismicity catalogs: Three——dimensional optimal anisotropic dynamic clustering［J］. J Geophys Res, 113(B1): B01306.1——B01306.15.

Pal N R, Bezdek J C. 1995. On cluster validity for the fuzzy C——means model［J］. IEEE Transactions on Fuzzy Systems, 3(3): 370——379.

Schaff P D, Waldhauser F. 2005. Waveform cross——correlation——based differential travel——time measurements at the Northern California Seismic Network［J］. Bull Seism Soc Amer, 95(6): 2446——2461.

Steacy S, Nalbant S S, McCloskey J, Nostro C, Scotti O, Baumont D. 2005. Onto what planes should Coulomb stress perturbations be resolved?［J］. J Geophys Res, 110, B05S15, doi:10.1029/2004JB003356.

Waldhause F, Ellsworth W L. 2000. A double difference earthquake location algorithm: Method and application to the North Hayward fault, California［J］. Bull Seism Soc Amer, 90(6): 1353——1368.

Wan Y G, Shen Z K. 2010. Static Coulomb failure stress changes on faults caused by the 2008 M_W7.9 Wenchuan, China earthquake［J］. Tectonophysics, 491(1——4): 105——118.

Wang S T, Chung K F, Shen H B, Zhu R Q. 2004. Note on the relationship between probabilistic and fuzzy clustering［J］. Soft Computing, 8(5): 366——369.

Xie X L, Beni G. 1991. A validity measure for fuzzy clustering［J］. IEEE Trans PAMI, 13(8): 841——847.