Acta Geophysica

, Volume 67, Issue 6, pp 1515–1523 | Cite as

Statistical properties of complex network for seismicity using depth-incorporated influence radius

  • Xuan HeEmail author
  • Luyang Wang
  • Hongbo Zhu
  • Zheng Liu
Research Article - Solid Earth Sciences


In recent years, seismic time series has been used to construct complex network models in order to describe the seismic complexity. The effect of the factor focal depth has been elided in some of these models. In this paper, we aim to construct a new complex network model for seismicity by considering depth factor from the earthquake catalog and investigate the statistical properties of the network. Since the networks have been proved to be scale-free and small-world properties, the new network models should be studied whether the properties have changed. The results show that the new network model by considering depth factor is still scale-free and small-world. However, it is found that its average degree is smaller than the original network. The clustering coefficient increases at the year including mainshocks. The assortativity coefficient, which demonstrates preferential attachment of nodes, is positive and shows consistent pattern when main shocks occur.


Complex network Seismicity Focal depth Assortative mixing 



This work has been supported by National Natural Science Foundation of China (NSFC) (Grant Nos. 61806048, 61771121), the Fundamental Research Funds for the Central Universities (Grant No. N171903002), the Open Program of Neusoft Research of Intelligent Healthcare Technology, Co. Ltd. (Grant No. NRIHTOP1802). The authors thank SCSN (Southern California Seismic Network) for providing the seismic data of the study area.


  1. Abe S, Suzuki N (2004a) Scale-free network of earthquakes. EPL (Europhys Lett) 65(4):581CrossRefGoogle Scholar
  2. Abe S, Suzuki N (2004b) Small-world structure of earthquake network. Phys A Stat Mech Appl 337(1–2):357–362CrossRefGoogle Scholar
  3. Abe S, Suzuki N (2006) Complex earthquake networks: hierarchical organization and assortative mixing. Phys Rev E 74(2):026113CrossRefGoogle Scholar
  4. Abe S, Suzuki N (2009a) Determination of the scale of coarse graining in earthquake networks. EPL (Europhys Lett) 87(4):48008CrossRefGoogle Scholar
  5. Abe S, Suzuki N (2009b) Scaling relation for earthquake networks. Phys A Stat Mech Appl 388(12):2511–2514CrossRefGoogle Scholar
  6. Abe S, Pastén D, Muñoz V, Suzuki N (2011) Universalities of earthquake-network characteristics. Chin Sci Bull 56(34):3697–3701CrossRefGoogle Scholar
  7. Abe S, Suzuki N (2012a) Aftershocks in modern perspectives: complex earthquake network, aging, and non-markovianity. Acta Geophys 60(3):547–561CrossRefGoogle Scholar
  8. Abe S, Suzuki N (2012b) Universal law for waiting internal time in seismicity and its implication to earthquake network. EPL (Europhys Lett) 97(4):49002CrossRefGoogle Scholar
  9. Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74(1):47CrossRefGoogle Scholar
  10. Albert R, Jeong H, Barabási AL (1999) Diameter of the world-wide web. Nature 401(6749):130–131CrossRefGoogle Scholar
  11. Baiesi M, Paczuski M (2004) Scale-free networks of earthquakes and aftershocks. Phys Rev E 69(6):066106CrossRefGoogle Scholar
  12. Bak P, Christensen K, Danon L, Scanlon T (2002) Unified scaling law for earthquakes. Phys Rev Lett 88(17):178501CrossRefGoogle Scholar
  13. Båth M, Duda SJ (1963) Strain release in relation to focal depth. Geofis Pura E Appl 56(1):93–100CrossRefGoogle Scholar
  14. Borgatti SP, Mehra A, Brass DJ, Labianca G (2009) Network analysis in the social sciences. Science 323(5916):892–895CrossRefGoogle Scholar
  15. Chorozoglou D, Papadimitriou E, Kugiumtzis D (2019) Investigating small-world and scale-free structure of earthquake networks in Greece. Chaos Solitons Fractals 122:143–152CrossRefGoogle Scholar
  16. Crucitti P, Latora V, Marchiori M, Rapisarda A (2004) Error and attack tolerance of complex networks. Phys A Stat Mech Appl 340(1–3):388–394CrossRefGoogle Scholar
  17. Daoyi X (2001) The network features of large earthquake occurrence and some words on the debate of earthquake prediction. Earth Sci Front 8(2):211–216Google Scholar
  18. Dorogovtsev SN, Goltsev AV, Mendes JFF (2006) K-core organization of complex networks. Phys Rev Lett 96(4):040601CrossRefGoogle Scholar
  19. Ferreira DS, Ribeiro J, Papa AR, Menezes R (2014) Towards evidences of long-range correlations in seismic activity. Physics, arXiv preprint arXiv:1405.0307
  20. Gardner LK, Knopoff L (1974) Is the sequence of earthquakes in southern California, with aftershocks removed, poissonian. Bull Seismol Soc Am 64(5):1363–1367Google Scholar
  21. Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci 99(12):7821–7826CrossRefGoogle Scholar
  22. Gutenberg B, Richter CF (1936) Magnitude and energy of earthquakes. Science 83(2147):183–185CrossRefGoogle Scholar
  23. Gutenberg B, Richter CF (1941) Seismicity of the earth. Geological Society of America No. 34: 1–126Google Scholar
  24. Gutenberg B (1956) The energy of earthquakes. Q J Geol Soc 112(1–4):1–14CrossRefGoogle Scholar
  25. He X, Zhao H, Cai W, Liu Z, Si SZ (2014) Earthquake networks based on space–time influence domain. Phys A Stat Mech Appl 407:175–184CrossRefGoogle Scholar
  26. He X, Zhao H, Cai W, Li GG, Pei FD (2015) Analyzing the structure of earthquake network by k-core decomposition. Phys A Stat Mech Appl 421:34–43CrossRefGoogle Scholar
  27. Jeong H, Mason SP, Barabási AL, Oltvai ZN (2001) Lethality and centrality in protein networks. Nature 411(6833):41–42CrossRefGoogle Scholar
  28. Lotfi N, Darooneh AH (2012) The earthquakes network: the role of cell size. Eur Phys J B 85(1):23CrossRefGoogle Scholar
  29. Lotfi N, Darooneh AH, Rodrigues FA (2018) Centrality in earthquake multiplex networks. Chaos Interdiscip J Nonlinear Sci 28(6):063113CrossRefGoogle Scholar
  30. Manighetti I, Campillo M, Sammis C, Mai PM, King G (2005) Evidence for self-similar, triangular slip distributions on earthquakes: implications for earthquake and fault mechanics. J Geophys Res Solid Earth 110:B05302CrossRefGoogle Scholar
  31. Newman MEJ (2002) Assortative mixing in networks. Phys Rev Lett 89(20):208701CrossRefGoogle Scholar
  32. Newman MEJ (2003) Mixing patterns in networks. Phys Rev E 67(2):026126CrossRefGoogle Scholar
  33. Omori F (1895) On the after-shocks of earthquakes. J College Sci Imp Univ Japan 7:111–200Google Scholar
  34. Persh SE, Houston H (2004) Strongly depth-dependent aftershock production in deep earthquakes. Bull Seismol Soc Am 94(5):1808–1816CrossRefGoogle Scholar
  35. Rezaei S, Moghaddasi H, Darooneh AH (2018) Preferential attachment in evolutionary earthquake networks. Phys A Stat Mech Appl 495:172–179CrossRefGoogle Scholar
  36. Rezaei S, Moghaddasi H, Darooneh AH, Zare M (2019a) Forecasting earthquakes by hybrid model of pattern informatic and pagerank methods. Bull Seismol Soc Am. CrossRefGoogle Scholar
  37. Rezaei S, Moghaddasi H, Darooneh AH (2019b) PageRank: an alarming index of probable earthquake occurrence. Chaos Interdiscip J Nonlinear Sci 29(6):063114CrossRefGoogle Scholar
  38. Stein RS (1999) The role of stress transfer in earthquake occurrence. Nature 402(6762):605CrossRefGoogle Scholar
  39. Vespignani A (2003) Evolution thinks modular. Nat Genet 35(2):118CrossRefGoogle Scholar
  40. Virkar Y, Clauset A (2014) Power-law distributions in binned empirical data. Ann Appl Stat 8(1):89–119CrossRefGoogle Scholar
  41. Wang X, Liu PLF (2006) An analysis of 2004 Sumatra earthquake fault plane mechanisms and Indian ocean tsunami. J Hydraul Res 44(2):147–154CrossRefGoogle Scholar
  42. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393(6684):440CrossRefGoogle Scholar
  43. Xie ZM (2011) Network topology and network dynamical behavior of seismicity. Technol Earthq Disaster Prev 6(1):1–17Google Scholar
  44. Zhang Y, Zhao H, He X, Pei FD, Li GG (2016) Bayesian prediction of earthquake network based on space–time influence domain. Phys A Stat Mech Appl 445:138–149CrossRefGoogle Scholar
  45. Zhou S, Mondragón RJ (2004) Accurately modeling the internet topology. Phys Rev E 70(6):066108CrossRefGoogle Scholar

Copyright information

© Institute of Geophysics, Polish Academy of Sciences & Polish Academy of Sciences 2019

Authors and Affiliations

  1. 1.School of Sino-Dutch Biomedical and Information EngineeringNortheastern UniversityShenyangChina
  2. 2.Neusoft Research of Intelligent Healthcare Technology, Co. Ltd.ShenyangChina
  3. 3.School of Computer Science and EngineeringNortheastern UniversityShenyangChina

Personalised recommendations