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Earthquake networks based on similar activity patterns
Phys. Rev. E 86, 046107 – Published 15 October, 2012
DOI: https://doi.org/10.1103/PhysRevE.86.046107
Abstract
Earthquakes are a complex spatiotemporal phenomenon, the underlying mechanism for which is still not fully understood despite decades of research and analysis. We propose and develop a network approach to earthquake events. In this network, a node represents a spatial location while a link between two nodes represents similar activity patterns in the two different locations. The strength of a link is proportional to the strength of the cross correlation in activities of two nodes joined by the link. We apply our network approach to a Japanese earthquake catalog spanning the 14-year period 1985–1998. We find strong links representing large correlations between patterns in locations separated by more than 1000 kilometers, corroborating prior observations that earthquake interactions have no characteristic length scale. We find network characteristics not attributable to chance alone, including a large number of network links, high node assortativity, and strong stability over time.
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References (45)
- Y. Y. Kagan and D. D. Jackson, J. Geophys. Res. 96, 419 (1991).
- D. Marsan, C. J. Bean, S. Steacy, and J. McCloskey, J. Geophys. Res. 105, 28081 (2000).
- B. Gutenberg and C. F. Richter, Bull. Seismol. Soc. Am. 34, 185 (1944).
- F. Omori, J. Coll. Sci., Imp. Univ. Tokyo 7, 111 (1894); see the recent work of M. Bottiglieri, L. de Arcangelis, C. Godano, and E. Lippiello, Phys. Rev. Lett. 104, 158501 (2010).
- T. Utsu, Geophys. Magazine 30, 521 (1961).
- T. Utsu, Y. Ogata, and R. S. Matsu'ura, J. Phys. Earth 43, 1 (1995).
- M. Bath, Tectonophysics 2, 483 (1965).
- Y. Y. Kagan and L. Knopoff, Geophys. J. R. Astron. Soc. 62, 303 (1980).
- D. Turcotte, Fractals and Chaos in Geology and Geophysics (Cambridge University Press, Cambridge, England, 1997).
- P. G. Okubo and K. J. Aki, J. Geophys. Res. 92, 345 (1987).
- T. Hirata, Pure Appl. Geophys. 131, 157 (1989).
- P. Bak, K. Christensen, L. Danon, and T. Scanlon, Phys. Rev. Lett. 88, 178501 (2002).
- A. Corral, Phys. Rev. E 68, 035102(R) (2003).
- R. Olsson, Geodynamics 27, 547 (1999).
- S. Abe and N. Suzuki, J. Geophys. Res. 108, 2113 (2003).
- S. Abe and N. Suzuki, Physica A 332, 533 (2004).
- S. Abe and N. Suzuki, Physica A 350, 588 (2005).
- S. Abe and N. Suzuki, Eur. Phys. J. B 59, 93 (2007).
- J. Davidsen, P. Grassberger, and M. Paczuski, Geophys. Res. Lett. 33, L11304 (2006); Phys. Rev. E 77, 066104 (2008).
- N. Lotfi and A. H. Darooneha, Eur. Phys. J. B 85, 23 (2012).
- D. Pastén, S. Abe, V. Muñoz, and N. Suzuki, arXiv:1005.5548v1.
- S. Abe, D. Pastén, and N. Suzuki, Physica A 390, 1343 (2011).
- M. Baiesi and M. Paczuski, Phys. Rev. E 69, 066106 (2004).
- V. N. Livina, S. Havlin, and A. Bunde, Phys. Rev. Lett. 95, 208501 (2005).
- E. Lippiello, L. de Arcangelis, and C. Godano, Phys. Rev. Lett. 100, 038501 (2008).
- S. Lennartz, V. N. Livina, A. Bunde, and S. Havlin, Europhys. Lett. 81, 69001 (2008).
- Available online at http://wwweic.eri.u-tokyo.ac.jp/CATALOG/junec/.
- A. Corral, Phys. Rev. Lett. 92, 108501 (2004).
- D. Sornette and L. Knopoff, Bull. Seismol. Soc. Am. 87, 789 (1997).
- J. Davidsen and C. Goltz, Geophys. Res. Lett. 31, L21612 (2004).
- The Gutenberg-Richter law states that the number of events in the catalog greater than a certain magnitude has an exponential dependence (i.e., , where and are empirically observed constants with typically ).
- P waves and S waves are the body waves which originate at an earthquake and travel through the earth. They are the primary means for locating an event. See K. E. Bullen and B. A. Bolt, An Introduction to the Theory of Seismology (Cambridge University Press, Cambridge, England, 1993).
- W. Lowrie, Fundamentals of Geophysics (Cambridge University Press, Cambridge, England, 2007), p. 98.
- D. L. Wells and K. H. Coppersmith, Bull. Seismol. Soc. Am. 84, 974 (1994).
- K. I. Konstantinoua, G. A. Papadopoulos, A. Fokaefs, and K. Orphanogiannaki, Tectonophysics 403, 95 (2005).
- K. Arora, A. Cazenave, E. R. Engdahl, R. Kind, A. Manglik, S. Roy, K. Sain, S. Uyeda, and H. K. Gupta, Encyclopedia of Solid Earth Geophysics, Volume 1 (Springer, New York, 2011), p. 213.
- M. E. J. Newman, Phys. Rev. Lett. 89, 208701 (2002).
- We note that this term is similar in appearance though distinct from the cumulative Benioff strain [43], the predictive power of which is hotly contested in geophysics [44,45]. However, our technique does not use this term to make predictive statements about any individual events in a specific location, but rather allows us to observe patterns in the similarity of behavior across different locations.
- To detrend the data, we obtain a best fit linear trend for each time series and subtract it from the series. We calculate the cross correlation between the detrended sequences.
- The adjacency matrix fully specifies a given network. denotes a link between node and node while denotes no link.
- W. Feller, An Introduction to Probability Theory and Its Applications, edited by J. B. Kadtke and A. Bulsara (AIP, Woodbury, NY, 1997).
- For comparison, we also carried out our analysis with other three signal definitions that we omit here. (1)‘Average magnitude”: , where is the magnitude of the event and is the total number of events occurring in the 90-day time window in the grid square . (2)‘Number of events”: , with the symbols as defined in (1). (3)‘Magnitude sum”: . All three of these alternative definitions fail to give results significantly better than the shuffled data that are robust with respect to the various adjustable parameters.
- D. D. Bowman, G. Ouillon, C. G. Sammis, A. Sornette, and D. Sornette, J. Geophys. Res. 103, 359 (1998).
- K. R. Felzer, T. W. Becker, R. E. Abercrombie, G. Ekstrom, and J. R. Rice, J. Geophys. Res. 107, 2190 (2002).
- J. L. Hardebeck, K. Felzer, and A. J. Michael, J. Geophys. Res. 113, B08310 (2008).