Earthquake pattern analysis using subsequence time series clustering

In this paper, a subsequence time-series clustering algorithm is proposed to identify the strongly coupled aftershocks sequences and Poissonian background activity from earthquake catalogs of active regions. The proposed method considers the inter-event time statistics between the successive pair of events for characterizing the nature of temporal sequences and observing their relevance with earthquake epicenters and magnitude information simultaneously. This approach categorizes the long-earthquake time series into the finite meaningful temporal sequences and then applies the clustering mechanism to the selective sequences. The proposed approach is built on two phases: (1) a Gaussian kernel-based density estimation for finding the optimal subsequence of given earthquake time-series, and (2) inter-event time (Δt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta t$$\end{document}) and distance-based observation of each subsequence for checking the presence of highly correlated aftershock sequences (hot-spots) in it. The existence of aftershocks is determined based on the coefficient of variation (COV). A sliding temporal window on Δt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta t$$\end{document} with earthquake’s magnitude M is applied on the selective subsequence to filter out the presence of time-correlated events and make the meaningful time stationary Poissonian subsequences. This proposed approach is applied to the regional Sumatra-Andaman (2000–2021) and worldwide ISC-GEM (2000–2016) earthquake catalog. Simulation results indicate that meaningful subsequences (background events) can be modeled by a homogeneous Poisson process after achieving a linear cumulative rate and time-independent λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document} in the exponential distribution of Δt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta t$$\end{document}. The relations COVa(T)>COVo(T)>(COVb(T)≈1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$COV_{a}(T)>COV_{o}(T)> (COV_{b}(T)\approx 1)$$\end{document} and COVa(d)>COVo(d)>COVb(d)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$COV_{a}(d)>COV_{o}(d)>COV_{b}(d)$$\end{document} are achieved for both studied catalogs. Comparative analysis justifies the competitive performance of the proposed approach to the state-of-art approaches and recently introduced methods.