Temporal pattern in Corinth rift seismicity revealed by visibility graph analysis

The investigation of complex time series properties through graph theoretical tools was greatly benefited from the recently developed method of visibility graph (VG) which acts as a hub between nonlinear dynamics, graph theory and time series analysis. In this work, earthquake time series, a representative example of a complex system, was studied by using VG method. The examined time series extracted from the Corinth rift seismic catalogue. By using a sliding window approach the temporal evolution of exponent γ of the degree distribution was studied. It was found that the time period of the most significant event (seismic swarm after major earthquake) in the examined seismic catalogue coincides with the time period where the exponent γ presents its minimum.

[1]  Luciano Telesca,et al.  Visibility Graph Analysis of the 2003–2012 Earthquake Sequence in the Kachchh Region of Western India , 2015, Pure and Applied Geophysics.

[2]  Yue Yang,et al.  Complex network-based time series analysis , 2008 .

[3]  Zhongke Gao,et al.  Visibility graph analysis of fluid flow signals , 2012, 2012 IEEE Fifth International Conference on Advanced Computational Intelligence (ICACI).

[4]  Vladimír Plicka,et al.  EFFICIENCY OF INDIVIDUAL CRL STATIONS IN SEISMIC MONITORING OF THE WESTERN GULF OF CORINTH , 2009 .

[5]  Luciano Telesca,et al.  Visibility graph approach to the analysis of ocean tidal records , 2012 .

[6]  Ping Li,et al.  Extracting hidden fluctuation patterns of Hang Seng stock index from network topologies , 2007 .

[7]  Filippos Vallianatos,et al.  Non-extensivity and long-range correlations in the earthquake activity at the West Corinth rift (Greece) , 2013 .

[8]  B. Luque,et al.  Horizontal visibility graphs: exact results for random time series. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Alejandro Ramírez-Rojas,et al.  Investigating the time dynamics of seismicity by using the visibility graph approach: Application to seismicity of Mexican subduction zone , 2013 .

[10]  Alejandro Ramirez-Rojas,et al.  Relationship between the Frequency Magnitude Distribution and the Visibility Graph in the Synthetic Seismicity Generated by a Simple Stick-Slip System with Asperities , 2014, PloS one.

[11]  Lucas Lacasa,et al.  Visibility Algorithms: A Short Review , 2012 .

[12]  Shijie Yan,et al.  Time Series Analysis Based on Visibility Graph Theory , 2015, 2015 7th International Conference on Intelligent Human-Machine Systems and Cybernetics.

[13]  Jeffery R. Westbrook,et al.  A Functional Approach to External Graph Algorithms , 1998, Algorithmica.

[14]  Z. Shao.  Network analysis of human heartbeat dynamics , 2010 .

[15]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[16]  Luciano Telesca,et al.  Precursory signatures in the visibility graph analysis of seismicity: An application to the Kachchh (Western India) seismicity , 2015 .

[17]  Michael Small,et al.  Complex network approach to characterize the statistical features of the sunspot series , 2013, 1307.6280.

[18]  Nicholas V. Sarlis,et al.  Scale-specific order parameter fluctuations of seismicity in natural time before mainshocks , 2011 .

[19]  Luciano Telesca,et al.  Analysis of seismic sequences by using the method of visibility graph , 2012 .

[20]  Masashi Kamogawa,et al.  Minimum of the order parameter fluctuations of seismicity before major earthquakes in Japan , 2013, Proceedings of the National Academy of Sciences.

[21]  S. Strogatz.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering , 1995 .

[22]  Jonathan F. Donges,et al.  Visibility graph analysis of geophysical time series: Potentials and possible pitfalls , 2012, Acta Geophysica.

[23]  Stefan Thurner,et al.  Directed Network Representation of Discrete Dynamical Maps , 2007, International Conference on Computational Science.

[24]  J. C. Nuño,et al.  The visibility graph: A new method for estimating the Hurst exponent of fractional Brownian motion , 2009, 0901.0888.

[25]  Lucas Lacasa,et al.  From time series to complex networks: The visibility graph , 2008, Proceedings of the National Academy of Sciences.

[26]  A. Deschamps,et al.  A microseismic study in the western part of the Gulf of Corinth (Greece): implications for large‐scale normal faulting mechanisms , 1996 .

[27]  Wei-Xing Zhou,et al.  Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence , 2009, 0905.1831.

[28]  Luciano Telesca,et al.  Visibility graph analysis of wind speed records measured in central Argentina , 2012 .

[29]  Eamonn J. Keogh,et al.  Segmenting Time Series: A Survey and Novel Approach , 2002 .

[30]  Lucas Lacasa,et al.  Description of stochastic and chaotic series using visibility graphs. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[32]  M Small,et al.  Detecting chaos in pseudoperiodic time series without embedding. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Michael Small,et al.  Long-term changes in the north-south asymmetry of solar activity: a nonlinear dynamics characterization using visibility graphs , 2014 .

[34]  Luciano Telesca,et al.  Visibility graph analysis of 2002–2011 Pannonian seismicity , 2014 .

[35]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[36]  Mehran Ahmadlou,et al.  Global organization of functional brain connectivity in methamphetamine abusers , 2013, Clinical Neurophysiology.

[37]  Vincenzo Lapenna,et al.  Multiresolution wavelet analysis of earthquakes , 2004 .

[38]  J. Drakopoulos,et al.  A revised and extended earthquake catalogue for Greece since 1900 , 1989 .

[39]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[40]  E. Macau,et al.  Searching chaos and coherent structures in the atmospheric turbulence above the Amazon forest , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[41]  Norbert Marwan,et al.  The geometry of chaotic dynamics — a complex network perspective , 2011, 1102.1853.

[42]  M Small,et al.  Complex network from pseudoperiodic time series: topology versus dynamics. , 2006, Physical review letters.

[43]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[44]  B. Gutenberg,et al.  Frequency of Earthquakes in California , 1944, Nature.

[45]  L. Lacasa.  Comment on the existence of a long range correlation in the geomagnetic disturbance storm time (Dst) index , 2012 .

[46]  Filippos Vallianatos,et al.  Multiresolution wavelets and natural time analysis before the January–February 2014 Cephalonia (Mw6.1 & 6.0) sequence of strong earthquake events , 2015 .

[47]  Zhi-Qiang Jiang,et al.  Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices , 2009, 0910.2524.

[48]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[49]  L. Amaral,et al.  Duality between Time Series and Networks , 2011, PloS one.

[50]  Vincent S. Tseng,et al.  A novel two-level clustering method for time series data analysis , 2010, Expert Syst. Appl..

[51]  A. Turner,et al.  From Isovists to Visibility Graphs: A Methodology for the Analysis of Architectural Space , 2001 .

[52]  Leila De Floriani,et al.  Visibility Algorithms on Triangulated Digital Terrain Models , 1994, Int. J. Geogr. Inf. Sci..

[53]  Filippos Vallianatos,et al.  Temporal patterns in southern Aegean seismicity revealed by the multiresolution wavelet analysis , 2007 .

[54]  Tomás Lozano-Pérez,et al.  An algorithm for planning collision-free paths among polyhedral obstacles , 1979, CACM.

[55]  U. Bhalla,et al.  Emergent properties of networks of biological signaling pathways. , 1999, Science.

[56]  J. Kurths,et al.  Complex network approach for recurrence analysis of time series , 2009, 0907.3368.

[57]  Na Wang,et al.  Visibility graph analysis on quarterly macroeconomic series of China based on complex network theory , 2012 .

[58]  Pascal Bernard,et al.  Local perturbations in the western rift of Corinth (Greece) caused by the 2011 Mw 9 Tohoku earthquake: joint observation of strain, water-level and seismic signals , 2013 .

[59]  M. Newman,et al.  The structure of scientific collaboration networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[60]  L. Guzmán-Vargas,et al.  Earthquake magnitude time series: scaling behavior of visibility networks , 2013 .

[61]  J. Hopfield,et al.  From molecular to modular cell biology , 1999, Nature.

[62]  Muhammad Sahimi,et al.  Mapping stochastic processes onto complex networks , 2009 .

[63]  Jürgen Kurths,et al.  Recurrence networks—a novel paradigm for nonlinear time series analysis , 2009, 0908.3447.