Investigating the Relationship Between Seismological and Topological Properties of Seismicity in Italy and Taiwan
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Pure and Applied Geophysics
Investigating the Relationship Between Seismological and Topological Properties of Seismicity in Italy and Taiwan LUCIANO TELESCA,1 CHIEN-CHIH CHEN,2 and MICHELE LOVALLO3 Abstract—This study investigates the relationship between the b value of the Gutenberg–Richter law and the so-called k–M slope, a topological parameters, derived from the visibility graph analysis, that recently has been gaining great attention in describing the time dynamics of seismicity. The relationship has been already found to be nearly linear for several seismic areas. In this paper, we investigate such relationship in two of the most seismically active areas of the world: Italy and Taiwan. Our findings indicate that the relationship between the Gutenberg–Richter b value and k–M slope is nearly linear with a slope of regression line of about 0.07. Furthermore, analysing the seismicity by using the directed visibility graph, the role of the aftershocks is evidenced by the value of two new parameters, defined as the difference and the ratio between the forward directed and the backward directed k–M slopes, which are higher for the whole catalogues than for the aftershock-depleted ones. Keywords: Visibility graph, seismicity, b-value, k–M slope.
1. Introduction Visibility graph analysis (Lacasa et al. 2008) has become a widely used statistical tool to get insight into the dynamics of time series in different research fields. By such method a time series is converted into a mathematical graph known as visibility graph. The values of the time series, which are represented by the nodes of the graph, are connected to each other on the basis of their reciprocal ‘‘visibility’’ established by
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00024-020-02470-8) contains supplementary material, which is available to authorized users. 1 Institute of Methodologies for Environmental Analysis, National Research Council, C. da S. Loja, 85050 Tito, PZ, Italy. E-mail: [email protected] 2 National Central University, Taoyuan, Taiwan. 3 ARPAB, 85100 Potenza, Italy.
proper geometrical relationships between the series’ values. This method had fruitful applications in economics (Zhang et al. 2018; Long 2013; Wang et al. 2012; Qian et al. 2010), weather forecasting (Jiang et al. 2016; Chen et al. 2014; Elsner et al. 2009), robotics and path planning (Masehian and AminNaseri 2004), medicine (Yu et al. 2017; Nilanjana et al. 2016; Zhu et al. 2012), geophysics and oceanography (Pierini et al. 2012; Telesca et al. 2012), etc. Recently, visibility graph has been more frequently applied in seismology, where the availability of ever increasing amount of seismic data, allows to investigate the existence of possible patterns in seismic occurrence through statistical methods. Furthermore, the characteristics of complex system that earthquakes show makes the use of complex systems methods, like the visibility graph, a ‘‘necessary choice’’ to deeply understand some features of the underlying
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