Pure and Applied Geophysics

, Volume 173, Issue 7, pp 2267–2275 | Cite as

Time-Based Network Analysis Before and After the \(M_w\)  8.3 Illapel Earthquake 2015 Chile

  • Denisse Pastén
  • Felipe Torres
  • Benjamín Toledo
  • Víctor Muñoz
  • José Rogan
  • Juan Alejandro Valdivia
Part of the following topical collections:
  1. Illapel, Chile, Earthquake on September 16th, 2015


A complex network analysis of the seismic activity in the central zone of Chile is made, where each node corresponds to a location, where a seism occurs. The \(M_w =\) 8.3 Illapel earthquake (16 September 2015) is included in the data set studied. Assuming a self-similar data network, the value of the power law characteristic exponent \(\gamma\) for the link probability distribution of the directed network and the value of the power law characteristic exponent \(\delta\) for the cumulative distribution of the betweenness centrality are studied, before and after the earthquake. Both exponents have a different values before and after the earthquake when the network is built with cell size of 5 \(\times\) 5 \(\times\) 5 km, but there is no difference when the cell size is 10 \(\times\) 10 \(\times\) 10 km. The exponents were evaluated for the data set with the total number of seismic events and for three cutoffs in magnitude. There is not much variation when applying the cutoff. Variations of both exponents are found when both subsets, before and after the main event, are compared, suggesting that the topological features of the complex network of seisms are modified by major events.


Complex networks Illapel Earthquake 



This work was supported by the Fondo Nacional de Investigaciones Científicas y Tecnológicas (FONDECyT) under grants No 1130272 and No 1120599 (JR), No 1150718 (JAV), No 1130273 (BT), No 1121144 and 1161711 (VM), and No 1150806 (FT). We thank the support of CEDENNA through “Financiamiento Basal para Centros Científicos y Tecnológicos de Excelencia” FB0807 (FT, JR, JAV). We also thank financial support of project Anillo Conicyt Pia ACT1405 (JR, VM, JAV). DP wants to thank Sandeep Kumar for his valuable help.


  1. S. Abe, N. Suzuki, Scale-free network of earthquakes. Europhys. Lett. 65(4), 581–586 (2004)Google Scholar
  2. S. Abe, D. Pastén, N. Suzuki, Finite data-size scaling of clustering in eartquake networks. Physica A 390, 7 (2010)Google Scholar
  3. S. Abe, D. Pastén, V. Muñoz, N. Suzuki, Universalities of earthquake-network characteristics. Chinese Science Bulletin 56, 34 (2011)Google Scholar
  4. S. Abe, N. Suzuki, Complex-network description of seismicity. Nonlinear Proc. Geophys. 13, 145–150 (2006)Google Scholar
  5. B. Aguilar-SanJuan, L.G. Vargas, Earthquake magnitude time series: scaling behavior of visibility networks. Eur. Phys. J. B 86, 454 (2013)Google Scholar
  6. R. Albert, H. Jeong, L. Barabasi, Diameter of the world wide web. Nature 401, 130–131 (1999)Google Scholar
  7. U. Alon, Biological networks: the tinkerer as engineer. Science 301, 1866–1867 (2003)Google Scholar
  8. M. Baiesi, M. Paczuski, Scale-free networks of earthquakes and aftershoks. Phys. Rev. E 69, 066106 (2004)Google Scholar
  9. Z. Bar-Joseph, G.K. Gerber, T.I. Lee, N.J. Rinaldi, J.Y. Yoo, F. Robert, D.B. Gordon, E. Fraenkel, T.S. Jaakkloa, R.A. Young, D.K. Gifford., Computational discovery of gene modules and regulatory networks 21, 1337–1342 (2003)Google Scholar
  10. A.-L. Barabási, Z.N. Oltvai, Network biology: understanding the cell’s functional organization. Nature Reviews Genetics 5, 101–113 (2004)Google Scholar
  11. A.-L. Barabási, R. Albert, H. Jeong, Scale-free characteristics of random networks: the topology of the world-wide web. Phys. A 281, 69–77 (2000)Google Scholar
  12. M. Barthelemy, Betweenness centrality in large complex networks. Eur. Phys. J. B 38, 163–168 (2004)Google Scholar
  13. D. Centola, The spread behavior in an online social network experiment. Science 329, 1194–1197 (2010)Google Scholar
  14. L. da F. Costa, F.A. Rodrigues, G. Travieso, P.R.V. Boas, Characterization of complex networks: A survey of measurements. Advances in Physics 56, 167–242 (2005)Google Scholar
  15. S.N. Dorogovtsev, J.F.F. Mendes, Evolution of Networks, vol. 1, 1st edn. (Oxford University Press, New York, 2003), p. 264Google Scholar
  16. S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes, Critical phenomena in complex networks 80, 1275–1335 (2008)Google Scholar
  17. R. Germano, A.P.S. de Moura, Traffic of particles in complex networks. Phys. Rev. E 74, 036117 (2006)Google Scholar
  18. H.O. Ghaffari, R.P. Young, Acoustic-friction networks and the evolution of precursor rupture fronts in laboratory earthquakes. Sci. Rep. 3(1799), 1–6 (2013)Google Scholar
  19. M.L. Goldstein, S.A. Morris, G.G. Yen, Problems with fiiting to the power-law distribution. Eur. Phys. J. B 41, 255–258 (2004)Google Scholar
  20. A. Gruzd, B. Wellman, Y. Takhteyev, Imagining twitter as an imagined community. American Behavioral Scientist 55(10), 1294–1318 (2011)Google Scholar
  21. M. Kitsak, S. Havlin, G. Paul, M. Riccaboni, F. Pammolli, H.E. Stanley, Betweenness centrality of fractal and nonfractal scale-free model networks and tests on real networks. Phys. Rev. E 75(056115), 1–8 (2007)Google Scholar
  22. L. Lacasa, B. Luque, J. Luque, J.C. Nuño, The visibility graph: A new method for estimating the hurst exponent of fractional brownian motion. A Lett. Jour. Explor. the Front. of Phys. 86(30001), 1–5 (2009)Google Scholar
  23. M.E.J. Newman, Assortative mixing in networks. Phys. Rev. Lett. 89(20), 208701 (2002)Google Scholar
  24. M.E.J. Newman, A measure of betweenness centrality based on random walks. Social Networks 27, 39–54 (2005)Google Scholar
  25. M.E.J. Newman, M. Girvan, Finding and evaluating community structure in networks. Phys. Rev. E 69(026113), 1–15 (2004)Google Scholar
  26. G. Palla, I. Derényi, I. Farkas, T. Vicsek, Uncovering the overlapping community structure of complex networks in nature and society. Nature 435, 814–818 (2005)Google Scholar
  27. L. Telesca, M. Lovallo, Analysis of seismic sequences by using the method of visibility graph 97, 50002–1500024 (2012)Google Scholar

Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Denisse Pastén
    • 1
    • 2
  • Felipe Torres
    • 1
    • 3
  • Benjamín Toledo
    • 1
  • Víctor Muñoz
    • 1
  • José Rogan
    • 1
    • 3
  • Juan Alejandro Valdivia
    • 1
    • 3
  1. 1.Departamento de Física, Facultad de CienciasUniversidad de ChileSantiagoChile
  2. 2.AG2E, Advanced Mining Technology Center, Facultad de Ciencias Físicas y MatemáticasUniversidad de ChileSantiagoChile
  3. 3.Centro para la Nanociencia y la NanotecnologíaLos AndesChile

Personalised recommendations