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.