Abstract
Seismic data is difficult to analyze and classical mathematical tools reveal strong limitations in exposing hidden relationships between earthquakes. In this paper, we study earthquake phenomena in the perspective of complex systems. Global seismic data, covering the period from 1962 up to 2011 is analyzed. The events, characterized by their magnitude, geographic location and time of occurrence, are divided into groups, either according to the Flinn-Engdahl (F-E) seismic regions of Earth or using a rectangular grid based in latitude and longitude coordinates. Two methods of analysis are considered and compared in this study. In a first method, the distributions of magnitudes are approximated by Gutenberg-Richter (G-R) distributions and the parameters used to reveal the relationships among regions. In the second method, the mutual information is calculated and adopted as a measure of similarity between regions. In both cases, using clustering analysis, visualization maps are generated, providing an intuitive and useful representation of the complex relationships that are present among seismic data. Such relationships might not be perceived on classical geographic maps. Therefore, the generated charts are a valid alternative to other visualization tools, for understanding the global behavior of earthquakes.
Highlights
Earthquakes are caused by a sudden release of elastic strain energy accumulated between the surfaces of tectonic plates
We present the main mathematical tools adopted in this study, namely G-R distributions, mutual information and clustering analysis
The events are divided into the fifty groups corresponding to the Flinn-Engdahl (F-E) regions of Earth [58,59], which correspond to seismic zones usually used by seismologists for localizing earthquakes (Table 1)
Summary
Earthquakes are caused by a sudden release of elastic strain energy accumulated between the surfaces of tectonic plates. Earthquakes reveal self-similarity and absence of characteristic length-scale in magnitude, space and time, caused by the complex dynamics of Earth’s tectonic plates [9,10]. The mutual information is adopted as a measure of similarity between events in the distinct regions In both cases, clustering analysis and visualization maps are adopted as an intuitive and useful representation of the complex relationships among seismic events. The generated maps are evidenced as a valid alternative to standard visualization tools, for understanding the global behavior of earthquakes. Bearing these ideas in mind, this paper is organized as follows: in Section 2, we give a brief review of the techniques used.
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