震源机制解谱聚类方法的研究及应用

Research and Application of Spectral Clustering Method for Focal Mechanism Solutions

摘要:

多参数、多维度的震源机制解很难通过直观观察或简单的对比分析来进行有效的类型划分。谱聚类是一种基于谱图理论的聚类方法,对震源机制解这类非线性可分数据具有良好的划分效果。本文尝试使用该方法对震源机制解进行聚类分析,采用最小旋转角为相似度矩阵,利用规范割集准则(Ncut)完成类型判别,以间隔统计量法(Gap statistic)确定聚类数的最优解,从而对海量的震源机制解数据进行快速准确的类型划分。本文不仅通过一组随机样本数据集验证了这种方法的可行性和可靠性,还分别以海城 M_S7.3 地震序列和川滇及周边地区的震源机制解集作为研究对象,验证了此方法的实用性。结果表明,该方法合理细分了区域内的震源机制解类型,不同类型解之间的差异性主要体现在受不同的区域构造背景控制,有利于区域地震活动性的研究。总体上看,基于震源机制解的谱聚类方法是区分震源机制解类型较为有效的方法,具有一定的实用价值。

Abstract:

The focal mechanism solutions,as a set of data with multiple dimensions,could be classified hardly by visual observation or simple comparative analysis. However,spectral clustering based on spectrogram theory has been approved to be well suited for nonlinear separable data,such as for focal mechanism solutions. In this paper,we attempted to use this method,that could cluster mass focal mechanisms fast and accurately by using the minimum rotation angle as the similarity matrix,to conduct Gap statistics for optimal numbers of clusters in order to normalize cut criterion(Ncut)for classification discrimination. We verified the feasibility and reliability of this method through a set of random data sets,as well as verified the practicality of this method through the focal mechanisms for Haicheng M_S7.3 earthquake sequences and Sichuan-Yunnan and its adjacent regions. The results showed that this new method reasonably subdivided the types of focal mechanisms and mechanism variations were strongly associated with corresponding hypocentral structure. In addition,this method has good applicability no matter for the focal mechanism solutions of a small area with a small amount of data or a large area with a large amount of data. In general,the spectral cluster analysis for focal mechanism solutions could serve as a method that has practical utility in determining the type of earthquake clusters.