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Integer and fractional-order entropy analysis of earthquake data series

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Abstract

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

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Acknowledgments

The authors acknowledge the International Seismological Centre (ISC) for the data (http://www.isc.ac.uk/).

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Authors and Affiliations

  1. Institute of Mechanical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    António M. Lopes

  2. Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072, Porto, Portugal

    J. A. Tenreiro Machado

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Correspondence to António M. Lopes.

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Lopes, A.M., Tenreiro Machado, J.A. Integer and fractional-order entropy analysis of earthquake data series. Nonlinear Dyn 84, 79–90 (2016). https://doi.org/10.1007/s11071-015-2231-x

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