Correlation Properties in Worldwide and Synthetic Earthquake Networks
Abstract
In this work, we studied the correlation properties of seismic networks by analyzing the assortativity of worldwide and synthetic earthquake networks. We used data from the World Earthquake Catalog for the period from 2002 to 2016, considering earthquakes with magnitude thresholds 4.5 and 5.0. Shallow earthquakes (a depth of up to 70 km) and deep earthquakes (a depth greater than 70 km) were analyzed separately. Synthetic data were produced from simulations using a modified version of the Olami-Feder-Christensen model, which can reproduce several statistical characteristics of actual earthquakes. The study was carried out for two methodologies of connections between the network elements, where the correlation measures were calculated for all networks. The results for shallow earthquakes and synthetic data indicate: assortative correlation (locations with similar seismic activities tend to have a greater number of connections between them); mainshocks induce other mainshocks in both close and further away regions; the structure found has a type of “attracting dynamics”, where the places with a more intense seismic activity produce large numbers of connections in other locations around them. Deep earthquake networks are neutral and therefore do not have an explicit correlation type. Our findings agree with previous works for specific areas and contribute to better understand correlations between seismological regions.
Keywords
Full Text:
PDFReferences
Abe, S., and N. Suzuki, 2004a, Scale-free network of earthquakes: Europhysics Letters, 65, 4, 581–586, doi: 10.1209/epl/i2003-10108-1.
Abe, S., and N. Suzuki, 2004b, Small-world structure of earthquake network: Physica A, 337, 1-2, 357–362, doi: 10.1016/j.physa.2004.01.059.
Abe, S., and N. Suzuki, 2006a, Complex earthquake networks: Hierarchical organization and assortative mixing: Phys. Rev. E, 74, 2, 026113, doi: 10.1103/PhysRevE.74.026113.
Abe, S., and N. Suzuki, 2006b, Complex-network description of seismicity: Nonlin. Processes Geophys., 13, 2, 145–150, doi: 10.5194/npg-13-145-2006.
Abercrombie, R.E., 1996, The magnitude-frequency distribution of earthquakes recorded with deep seismometers at Cajon Pass, southern California: Tectonophysics, 261, 1–3, 1–7, doi: 10.1016/0040-1951(96)00052-2.
Ahmed, N., S. Ghazi, and P. Khalid, 2016, On the variation of b-value for Karachi region, Pakistan through Gumbel’s extreme distribution method: Acta Geod. Geophys., 51, 227–235, doi: 10.1007/s40328-015-0122-8.
Albert, R., and A.L. Barabási, 2000, Topology of evolving networks: local events and universality: Phys. Rev. Lett., 85, 5234, doi: 10.1103/PhysRevLett.85.5234.
Albert, R., and A.L. Barabási, 2002, Statistical mechanics of complex networks: Rev. Mod. Phys., 74, 47, doi: 10.1103/RevModPhys.74.47.
Albert, R., H. Jeong, and A.L. Barabási, 1999, Diameter of the world-wide web: Nature, 401, 6749, 130–131, doi: 10.1038/43601.
Baiesi, M., and M. Paczuski, 2004, Scale-free networks of earthquakes and aftershocks: Phys. Rev. E, 69, 6, 066106, doi: 10.1103/PhysRevE.69.066106.
Bak, P., and M. Paczuski, 1995, Complexity, contingency, and criticality: Proc. Natl. Acad. Sci., 92, 15, 6689–6696, doi: 10.1073/pnas.92.15.6689.
Bak, P., K. Christensen, L. Danon, and T. Scanlon, 2002, Unified scaling law for earthquakes: Phys. Rev. Lett., 88, 17, 178501, doi: 10.1103/PhysRevLett.88.178501.
Barabási, A.L, 2002, Linked: The New Science of Networks: Perseus, Cambridge, MA. 280 pp.
Barabási, A.L., and R. Albert, 1999, Emergence of scaling in random networks: Science, 286, 509–512, doi: 10.1126/science.286.5439.509.
Barabási, Al., and M. Pósfai, 2016, Network science: Cambridge University Press, Cambridge, UK. 475 pp.
Caruso, F., V. Latora, A. Pluchino, A. Rapisarda, and B. Tadi?, 2006, Olami-Feder-Christensen model on different networks: Eur. Phys. J. B., 50, 1, 243–247, doi: 10.1140/epjb/e2006-00110-5.
Catanzaro, M., G. Caldarelli, and L. Pietronero, 2004, Assortative model for social networks: Phys. Rev. E, 10, 3, 037101, doi: 10.1103/PhysRevE.70.037101.
Chorozoglou, D., E. Papadimitriou, and D. Kugiumtzis, 2019, Investigating small-world and scale-free structure of earthquake networks in Greece: Chaos Soliton. Fract., 122, 143–152, doi: 10.1016/j.chaos.2019.03.018.
Christensen, K., and Z. Olami, 1992a, Variation of the Gutenberg?Richter b values and nontrivial temporal correlations in a spring?block model for earthquakes: J. Geophys. Res., 97, 8729–8735, doi: 10.1029/92JB00427.
Christensen, K., and Z. Olami, 1992b, Scaling, phase transitions, and nonuniversality in a self-organized critical cellular-automaton model: Phys. Rev. A, 46, 4, 1829, doi: 10.1103/PhysRevA.46.1829.
Davidsen, J., and M. Paczuski, 2005, Analysis of the spatial distribution between successive earthquakes: Phys. Rev. Lett., 94, 4, 048501, doi: 10.1103/PhysRevLett.94.048501.
Dorogovtsev, S.N., and J.F. Mendes, 2003, Evolution of networks: From biological nets to the Internet and WWW: Oxford University Press, Oxford, UK. 280 pp.
Ebel, H., L. Mielsch, and S. Bornholdt, 2002, Scale-free topology of e-mail networks: Phys. Rev. E, 66, 3, 035103, doi: 10.1103/PhysRevE.66.035103.
Ferreira, D.S.R., A.R.R. Papa, and R. Menezes, 2014, Small world picture of worldwide seismic events: Physica A, 408, 170–180, doi: 10.1016/j.physa.2014.04.024.
Ferreira, D. S. R., A. R. R. Papa, and R. Menezes, 2015, On the agreement between small-world-like OFC model and real earthquakes: Phys. Lett. A, 379, 7, 669–675, doi: 10.1016/j.physleta.2014.12.023.
Ferreira, D., J. Ribeiro, A. Papa, and R. Menezes, 2018. Towards evidence of long-range correlations in shallow seismic activities: Europhysics Letters, 121, 5, 58003, doi: 10.1209/0295-5075/121/58003.
Ferreira, D.S.R., Ribeiro J., P.S. L. Oliveira, A.R. Pimenta, R.P. Freitas, and A.R.R. Papa, 2020, Long-range correlation studies in deep earthquakes global series: Physica A, 560, 125146, doi: 10.1016/j.physa.2020.125146.
Fiedler, B., S. Hainzl, G. Zöller, and M. Holschneider, 2018, Detection of Gutenberg-Richter b-value changes in earthquake time series: B. Seismol. Soc. Am., 108, 2778–2787, doi: 10.1785/0120180091.
Foster, J., D. Foster, P. Grassberger, and M. Paczuski, 2010, Edge direction and the structure of networks: P. Natl. A. Sci., 107, 24, 10815–10820, doi: 10.1073/pnas.0912671107.
Frohlich, C., 1989, The nature of deep-focus earthquakes: Annu. Rev. Earth Planet. Sci., 17, 1, 227–254, doi: 10.1146/annurev.ea.17.050189.001303.
Frohlich, C., 2006, Deep Earthquakes: Cambridge University Press, Cambridge, UK. 592 pp, doi: 10.1017/CBO9781107297562.
Gheibi, A., Safari, H., and M. Javaherian, 2017, The solar flare complex network: Astrophys. J., 847, 2, 115, doi: 10.3847/1538-4357/aa8951.
Grassberger, P., 1994, Efficient large-scale simulations of a uniformly driven system: Phys. Rev. E, 49, 3, 2436, doi: 10.1103/PhysRevE.49.2436.
Gutenberg, B., and C.F. Richter, 1942, Earthquake magnitude, intensity, energy, and acceleration: B. Seismol. Soc. Am., 32, 3, 163–191, doi: 10.1785/BSSA0320030163.
He, X., H. Zhao, W. Cai, Z. Liu, and S.-Z. Si, 2014, Earthquake networks based on space–time influence domain: Physica A, 407, 175–184, doi: 10.1016/j.physa.2014.03.093.
He, X., S.B.H. Shah, B. Wei, and Z. Liu, 2021, Comparison and Analysis of Network Construction Methods for Seismicity Based on Complex Networks: Complexity, Article ID 6691880, doi: 10.1155/2021/6691880.
Helmstetter, A., Y.Y. Kagan, and D.D. Jackson, 2005, Importance of small earthquakes for stress transfers and earthquake triggering: J. Geophys. Res. 110, B05S08, doi: 10.1029/2004JB003286.
Jeong, H., S.P. Mason, A.L. Barabási, and Z.N. Oltvai, 2001, Lethality and centrality in protein networks: Nature, 411, 6833, 41–42, doi: 10.1038/35075138.
Johnson, S., J. Torres, J. Marro, and M. Munoz, 2010, Entropic origin of disassortativity in complex networks: Phys. Rev. Lett., 104, 10, 108702, doi: 10.1103/physrevlett.104.108702.
Kagan, Y., and D. Jackson, 1991, Long-term earthquake clustering: Geophys. J. Int., 104, 1, 117–133, doi: 10.1111/j.1365-246X.1991.tb02498.x.
Kanamori H., and E.E. Brodsky, 2004, The physics of earthquakes: Rep. Prog. Phys., 67, 8, 1429, doi: 10.1088/0034-4885/67/8/R03.
Leon, D., J. Valdivia, and V. Bucheli, 2022, A revision of seismicity models based on complex systems and earthquake networks: J. Seismol., 26, 137–145, doi: 10.1007/s10950-021-10017-0.
Lotfi, N., and A.H. Darooneh, 2012, The earthquakes network: the role of cell size: Eur. Phys. J. B, 85, 23, doi: 10.1140/epjb/e2011-20623-x.
Marsan, D., and O. Lengliné, 2008, Extending earthquakes’ reach through cascading: Science, 319, 5866, 1076–1079, doi: 10.1126/science.1148783.
Mega, S., P. Allegrini, P. Grigolini, V. Latora, L. Palatella, A. Rapisarda, and S. Vinciguerra, 2003, Power-law time distribution of large earthquakes: Phys. Rev. Lett., 90, 18, 188501, doi: 10.1103/PhysRevLett.90.188501.
Newman, M.E., 2002, Assortative mixing in networks: Phys. Rev. Lett., 89, 20, 208701, doi: 10.1103/PhysRevLett.89.208701.
Newman, M.E., 2003, Mixing patterns in networks: Phys. Rev. E, 67, 2, 026126, doi: 10.1103/PhysRevE.67.026126.
Olami, Z., H.J.S. Feder, and K. Christensen, 1992, Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes: Phys. Rev. Lett., 68, 8, 1244, doi: 10.1103/PhysRevLett.68.1244.
O’Malley, R.T., D. Mondal, C. Goldfinger, and M.J. Behrenfeld, 2018, Evidence of systematic triggering at teleseismic distances following large earthquakes: Sci. Rep., 8, 1, 1–12, doi: 10.1038/s41598-018-30019-2.
Pastén, D., F. Torres, B. Toledo, V. Munoz, J. Rogan, and J.A. Valdivia, 2016, Time-Based Network Analysis Before and After the ???????? 8.3 Illapel Earthquake 2015 Chile: Pure Appl. Geophys., 173, 2267–2275, doi: 10.1007/s00024-016-1335-7.
Pastén, D., F. Torres, B. Toledo, V. Muñoz, J. Rogan, and J. Valdivia, 2018, Non-universal critical exponents in earthquake complex networks: Physica A, 491, 445–452, doi: 10.1016/j.physa.2017.09.064.
Pastor-Satorras, R., A. Vázquez, and A. Vespignani, 2001, Dynamical and correlation properties of the internet: Phys. Rev. Lett., 87, 25, 258701, doi: 10.1103/PhysRevLett.87.258701.
Peixoto, T.P., and C.P. Prado, 2006, Network of epicenters of the Olami-Feder-Christensen model of earthquakes: Phys. Rev. E, 74, 1, 016126, doi: 10.1103/PhysRevE.74.016126.
Piraveenan, M., M. Prokopenko, and A. Zomaya, 2010, Assortative mixing in directed biological networks: IEEE/ACM Trans. Comput. Biol. Bioinform., 9, 1, 66–78, doi: 10.1109/TCBB.2010.80.
Roberts, D., and D. Turcotte, 1998, Fractality and self-organized criticality of wars: Fractals, 6, 4, 351–357, doi: 10.1142/S0218348X98000407.
Spence, W., S.A. Sipkin, and G. L. Choy, 1989, Measuring the size of an earthquake: Earthquake Information Bulletin (USGS), 21, 1, 58–63.
Stein, S., 1999, The role of stress transfer in earthquake occurrence: Nature, 402, 605–609, doi: 10.1038/45144.
Telesca, L., and M. Lovallo, 2012, Analysis of seismic sequences by using the method of visibility graph: Europhysics Letters, 97, 5, 50002, doi: 10.1209/0295-5075/97/50002.
Tenenbaum, J.N., S. Havlin, and H.E. Stanley, 2012, Earthquake networks based on similar activity patterns: Phys. Rev. E, 86, 4, 046107, doi: 10.1103/PhysRevE.86.046107.
Toda, S., and S. Stein, 2020, Long?and short?term stress interaction of the 2019 Ridgecrest sequence and Coulomb?based earthquake forecasts: B. Seismol. Soc. Am., 110, 4, 1765–1780, doi: 10.1785/0120200169.
Tosi, P., V. De Rubeis, V. Loreto, and L. Pietronero, 2008, Space–time correlation of earthquakes: Geophys. J. Int., 173, 3, 932–941, doi: 10.1111/j.1365-246X.2008.03770.x.
Vázquez, A., R. Pastor-Satorras, and A. Vespignani, 2002, Large-scale topological and dynamical properties of the Internet: Phys. Rev. E, 65, 6, 066130, doi: 10.1103/PhysRevE.65.066130.
Watkins, N., G. Pruessner, S. Chapman, N. Crosby, and H. Jensen, 2016, 25 years of self-organized criticality: Concepts and controversies: Space Sci. Rev., 198, 1, 3–44, doi: 10.1007/s11214-015-0155-x.
Watts, D.J., and S.H. Strogatz, 1998, Collective dynamics of ‘small-world’ networks: Nature, 393, 440–442, doi: 10.1038/30918.
DOI: http://dx.doi.org/10.22564/brjg.v40i1.2134
This work is licensed under a Creative Commons Attribution 4.0 International License.
a partir do v.37n.4 (2019) até o presente
v.15n.1 (1997) até v.37n.3 (2019)
Brazilian Journal of Geophysics - BrJG
Sociedade Brasileira de Geofísica - SBGf
Av. Rio Branco 156 sala 2509
Rio de Janeiro, RJ, Brazil
Phone/Fax: +55 21 2533-0064
E-mail: editor@sbgf.org.br
Since 2022, the BrJG publishes all content under Creative Commons CC BY license. All copyrights are reserved to authors.