Abstract
We investigate the structural properties of a spatio-temporal network of earthquake events that incorporates magnitude information between the connected events. The network creates temporally directed links from an origin event towards a later event if it breaks the record closest distance from the origin among all the events in the catalog so far. Additionally, the links are conditionally classified based on the magnitude difference between connected events: “up” (“down”) connections point from a weaker (stronger) to a stronger (weaker) event. Using earthquake records from the Philippines from 1973 to 2012 and southern California from 1982 to 2012, we observe that the out-degree distributions show slight deviations from the corresponding Poisson distribution of the same mean. The space and time separations of connected earthquakes both show power-law regimes, suggesting spatio-temporal (self-)organization. More importantly, the conditional distributions of “up” and “down” connections in space, time, and network structure point to a higher likelihood of a stronger event triggering a nearby weaker event for the first few connections, as in the case of aftershocks. The results are captured by a sandpile-based model where a small but finite probability of preferentially targeting the most susceptible grid site is introduced. Our analysis, coupled with the discrete model analog, provides a quantitative picture of the spatio-temporal and magnitude organization of seismicity beyond just the successive events. The technique may be extended to further characterize similar long-period earthquake records to yield a more complete picture of the underlying processes involved in seismicity.
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References
Abe S, Suzuki N (2007) Dynamical evolution of clustering in complex network of earthquakes. Eur Phys J B 59(1):93–97. https://doi.org/10.1140/epjb/e2007-00259-3
Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Modern Phys 74(1):47. https://doi.org/10.1103/RevModPhys.74.47
Baiesi M, Paczuski M (2004) Scale-free networks of earthquakes and aftershocks. Phys Rev E 69(6):066106. https://doi.org/10.1103/PhysRevE.69.066106
Bak P, Tang C (1989) Earthquakes as a self-organized critical phenomenon. J Geophys Res 94:15635–15637. https://doi.org/10.1029/JB094iB11p15635
Bak P, Christensen K, Danon L, Scanlon T (2002) Unified scaling law for earthquakes. Phys Rev Lett 88:178501. https://doi.org/10.1103/PhysRevLett.88.178501
Batac RC (2016) Statistical properties of the immediate aftershocks of the 15 October 2013 magnitude 7.1 earthquake in Bohol, Philippines. Acta Geophys 64(1):15–25. https://doi.org/10.1515/acgeo-2015-0054
Batac RC, Kantz H (2014) Observing spatio-temporal clustering and separation using interevent distributions of regional earthquakes. Nonlinear Processes Geophys 21(4):735–744. https://doi.org/10.5194/npg-21-735-2014
Batac RC, Paguirigan AA Jr, Tarun AB, Longjas AG (2017) Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes. Nonlinear Processes Geophys 24(2):179–187. https://doi.org/10.5194/npg-24-179-2017
Davidsen J, Baiesi M (2016) Self-similar aftershock rates. Phys Rev E 94(2):022314. https://doi.org/10.1103/PhysRevE.94.022314
Davidsen J, Paczuski M (2005) Analysis of the spatial distribution between successive earthquakes. Phys Rev Lett 94:048501. https://doi.org/10.1103/PhysRevLett.94.048501
Davidsen J, Grassberger P, Paczuski M (2006) Earthquake recurrence as a record breaking process. Geophys Res Lett 33(11):L11304. https://doi.org/10.1029/2006GL026122
Davidsen J, Grassberger P, Paczuski M (2008) Networks of recurrent events, a theory of records, and an application to finding causal signatures in seismicity. Phys Rev E 77(6):066104. https://doi.org/10.1103/PhysRevE.77.066104
Efstathiou A, Tzanis A, Vallianatos F (2017) On the nature and dynamics of the seismogenetic systems of North California, USA: an analysis based on non-extensive statistical physics. Phys Earth Planet Inter 270:46–72. https://doi.org/10.1016/j.pepi.2017.06.010
Frohlich C, Davis SD (1993) Teleseismic b values; or, much ado about 10. J Geophys Res Solid Earth 98(B1):631–644. https://doi.org/10.1029/92JB01891
Gu C, Schumann AY, Baiesi M, Davidsen J (2013) Triggering cascades and statistical properties of aftershocks. J Geophys Res Solid Earth 118:4278–4295. https://doi.org/10.1002/jgrb.50306
Gutenberg B, Richter CF (1954) Seismicity of the earth and associated phenomena, 2nd edn. Princeton University Press, Princeton
Hayakawa M, Hobara Y (2010) Current status of seismoelectromagnetics for short-term earthquake prediction. Geomatics Nat Hazards Risk 1(2):115–155. https://doi.org/10.1080/19475705.2010.486933
Helmstetter A, Kagan YY, Jackson DD (2005) Importance of small earthquakes for stress transfers and earthquake triggering. J Geophys Res 110(B5):2156–2202. https://doi.org/10.1029/2004JB003286
Ito K, Matsuzaki M (1990) Earthquakes as self-organized critical phenomena. J Geophys Res 95:6853–6860. https://doi.org/10.1029/JB095iB05p06853
Jagla EA (2013) Forest-fire analogy to explain the b value of the Gutenberg-Richter law for earthquakes. Phys Rev Lett 111(23):238501. https://doi.org/10.1103/PhysRevLett.111.238501
Keilis-Borok V, Soloviev AA (eds) (2013) Nonlinear dynamics of the lithosphere and earthquake prediction. Springer Science and Business Media, Berlin
Landes FP, Lippiello E (2016) Scaling laws in earthquake occurrence: disorder, viscosity, and finite size effects in Olami-Feder-Christensen models. Phys Rev E 53:051001. https://doi.org/10.1103/PhysRevE.93.051001
Livina VN, Havlin S, Bunde A (2005) Memory in the occurrence of earthquakes. Phys Rev Lett 95(20):208501. https://doi.org/10.1103/PhysRevLett.95.208501
Marekova E (2014) Analysis of the spatial distribution between successive earthquakes occurred in various regions in the world. Acta Geophys 62(6):1262–1282. https://doi.org/10.2478/s11600-014-0234-5
Narteau C, Byrdina S, Shebalin P, Schorlemmer D (2009) Common dependence on stress for the two fundamental laws of statistical seismology. Nature 462:642–645. https://doi.org/10.1038/nature08553
Olami Z, Feder HJS, Christensen K (1992) Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes. Phys Rev Lett 68(8):1244. https://doi.org/10.1103/PhysRevLett.68.1244
PDE (1973-2012), Preliminary determination of epicentres catalogue. http://earthquake.usgs.gov/earthquakes/eqarchives/epic. Last access: December 2012
Saichev A, Sornette D (2006) “Universal” distribution of interearthquake times explained. Phys Rev Lett 97(7):078501. https://doi.org/10.1103/PhysRevLett.97.078501
SCEDC (1982-2012), Southern California earthquake data center. http://www.data.scec.org/eq-catalogs/date_mag_loc.php, last access: December 2012
Schoenball M, Davatzes NC, Glen JM (2015) Differentiating induced and natural seismicity using space-time-magnitude statistics applied to the Coso Geothermal field. Geophys Res Lett 42(15):6221–6228. https://doi.org/10.1002/2015GL064772
Scholz CH (2015) On the stress dependence of the earthquake b value. Geophys Res Lett 42(5):1399–1402. https://doi.org/10.1002/2014GL062863
Schorlemmer D, Wiemer S, Wyss M (2005) Variations in earthquake-size distribution across different stress regimes. Nature 437:539–542. https://doi.org/10.1038/nature04094
Spada M, Tormann T, Wiemer S, Enescu B (2013) Generic dependence of the frequency-size distribution of earthquakes on depth and its relation to the strength profile of the crust. Geophys Res Lett 40:709–714. https://doi.org/10.1029/2012GL054198
Tarun AB, Paguirigan AA, Batac RC (2015) Spatiotemporal recurrences of sandpile avalanches. Phys A 436:293–300. https://doi.org/10.1016/j.physa.2015.05.016
Telesca L (2007) Time-clustering of natural hazards. Nat Hazards 40(3):593–601. https://doi.org/10.1007/s11069-006-9023-z
Touati S, Naylor M, Main IG (2009) Origin and nonuniversality of the earthquake interevent time distribution. Phys Rev Lett 102(16):168501. https://doi.org/10.1103/PhysRevLett.102.168501
Tzanis A, Vallianatos F, Efstathiou A (2013) Multidimensional earthquake frequency distributions consistent with non-extensive statistical physics: the interdependence of magnitude, interevent time and interevent distance in North California. Bulletin Geol. Soc. Greece 47(3):1326–1337. https://doi.org/10.12681/bgsg.10914
Zaliapin I, Ben-Zion Y (2013a) Earthquake clusters in southern California I: identification and stability. J Geophys Res 118:2847–2864. https://doi.org/10.1002/jgrb.50179
Zaliapin I, Ben-Zion Y (2013b) Earthquake clusters in southern California II: classification and relation to physical properties of the crust. J Geophys Res 118:2865–2877. https://doi.org/10.1002/jgrb.50178
Zaliapin I, Ben-Zion Y (2015) Artefacts of earthquake location errors and short-term incompleteness on seismicity clusters in southern California. Geophys J Int 202:1949–1968. https://doi.org/10.1093/gji/ggv259
Zaliapin I, Gabrielov A, Keilis-Borok V, Wong H (2008) Clustering analysis of seismicity and aftershock identification. Phys Rev Lett 101:018501. https://doi.org/10.1103/PhysRevLett.101.018501
Acknowledgements
The authors thank A.B. Tarun, A.A. Paguirigan Jr., and A.G. Longjas for useful preliminary discussions. D.C.B. is supported by a scholarship from the Department of Science and Technology (DOST) Science Education Institute (SEI).
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Janer, C.D., Biton, D.C. & Batac, R.C. Incorporating space, time, and magnitude measures in a network characterization of earthquake events. Acta Geophys. 65, 1153–1166 (2017). https://doi.org/10.1007/s11600-017-0100-3
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DOI: https://doi.org/10.1007/s11600-017-0100-3