Pure and Applied Geophysics

, Volume 176, Issue 1, pp 1–23 | Cite as

Aftershock Sequences of the Recent Major Earthquakes in New Zealand

  • Vladimir G. KossobokovEmail author
  • Anastasia K. Nekrasova
Part of the following topical collections:
  1. NZ-2016


The three clusters of the epicenters of the nine recent (1993–2018) earthquakes of magnitude 7.0 or larger in New Zealand are located in three different tectonic environments of the Australia–Pacific Plate boundary, including the southern part of the Kermadec Trench (showing rapid westward subduction), the oblique collision zone between the Pacific Plate and Indo-Australian Plate with the dominant Alpine Fault (showing right-lateral strike-slip movement), and the Puysegur Trench (showing eastward oblique subduction). From the viewpoint of the unified scaling law for earthquakes (USLE), these regions are characterized by different levels of seismic rate (A), earthquake magnitude exponent (B), and fractal dimension of epicenter loci (C). The recent major earthquakes exemplify different scenarios of aftershock sequences in terms of either the dynamics of interevent time (τ) or the USLE control parameter (η = τ × 10B×(5−M) × LC), where τ is the time interval between two successive earthquakes, M is the magnitude of the second one, and L is the distance between them. We find the existence, in the long term, of different, intermittent levels of rather steady seismic activity characterized by near-constant values of mean η (〈η〉), which, in the mid-term, switch between one another at times of critical transitions, including those associated with all but one magnitude 7.0 or larger earthquake. At such a transition, seismic activity may follow different scenarios with interevent time scaling of different kinds. Evidently, although these results based on analysis of an individual series do not support the presence of universality in seismic energy release, they provide constraints on modeling realistic seismic sequences for earthquake physicists and supply decision-makers with information for improving local seismic hazard assessments.


Unified scaling law for earthquakes strong earthquakes sequences of associated earthquakes background seismic activity self-organized nonlinear dynamical system control parameter of a system 



The authors acknowledge the New Zealand GeoNet project and its sponsors EQC, GNS Science, and LINZ, for providing data used in this study. Thanks to the anonymous reviewers for their comments and suggestions, which helped to clarify our claims and conclusions. The study was supported by the Russian Science Foundation (grant no. 16-17-00093).


  1. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723. Scholar
  2. Bak, P., Christensen, K., Danon, L., & Scanlon, T. (2002). Unified scaling law for earthquakes. Physical Review Letters, 88, 178501–178504.CrossRefGoogle Scholar
  3. Ben-Zion, Y. (2008). Collective behavior of earthquakes and faults: Continuum-discrete transitions, progressive evolutionary changes, and different dynamic regimes. Revues of Geophysics, 46(4), RG4006. Scholar
  4. Christensen, K., Danon, L., Scanlon, T., & Bak, P. (2002). Unified scaling law for earthquakes. Proceedings of the National Academy of Sciences, 99(suppl 1), 2509–2513. Scholar
  5. ComCat (2017). ANSS Comprehensive earthquake catalog (ComCat). Accessed 1 Jan 2018.
  6. Davies, G. F. (1999). Dynamic earth: Plates. Plumes, and mantle convection. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  7. Davis, C., Keilis-Borok, V., Kossobokov, V., & Soloviev, A. (2012). Advance prediction of the March 11, 2011 Great East Japan Earthquake: A missed opportunity for disaster preparedness. International Journal of Disaster Risk Reduction, 1, 17–32. Scholar
  8. Di Giacomo, D., & Bormann, P. (2011). Earthquake energy. In H. Gupta (Ed.), Encyclopedia of solid earth geophysics (pp. 233–236). New York: Springer.CrossRefGoogle Scholar
  9. Dobrovolsky, I. P., Zubkov, S. I., & Miachkin, V. I. (1979). Estimation of the size of earthquake preparation zones. Pure and Applied Geophysics, 117(5), 1025–1044. Scholar
  10. Fry, B., Bannister, S. C., Beavan, R. J., Bland, L., Bradley, B. A., Cox, S. C., et al. (2009). The M W 7.6 Dusky Sound earthquake of 2009: Preliminary report. Bulletin of the New Zealand Society for Earthquake Engineering, 43(1), 24–40.Google Scholar
  11. Gabrielov, A., Newman, W. I., & Turcotte, D. L. (1999). An exactly soluble hierarchical clustering model: Inverse cascades, self-similarity, and scaling. Physical Review E, 60, 5293–5300.CrossRefGoogle Scholar
  12. Gardner, J., & Knopoff, L. (1974). Is the sequence of earthquakes in S California with aftershocks removed Poissonian? Bulletin of the Seismological Society of America, 64(5), 1363–1367.Google Scholar
  13. GeoNet (2018) GeoNet quake search. Accessed 1 Jan 2018.
  14. Gledhill, K., Ristau, J., Reyners, M., Fry, B., & Holden, C. (2010). The Darfield (Canterbury) earthquake of September 2010: Preliminary seismological report. Bulletin of the New Zealand National Society for Earthquake Engineering, 43(4), 215–221.Google Scholar
  15. Goda, K., Yasuda, T., Mori, N., & Maruyama, T. (2016). New scaling relationships of earthquake source parameters for stochastic Tsunami simulation. Coastal Engineering Journal, 58(3), 1650010-1–1650010-40. Scholar
  16. Gutenberg, R., & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34, 185–188.Google Scholar
  17. Gutenberg, B., & Richter, C. F. (1954). Seismicity of the earth (2nd ed.). Princeton: Princeton University Press.Google Scholar
  18. Hamling, I. J., Hreinsdóttir, S., Clark, K., Elliott, J., Liang, C., Fielding, E., et al. (2017). Complex multifault rupture during the 2016 M w 7.8 Kaikōura earthquake, New Zealand. Science, 356(6334), eaam7194. Scholar
  19. Harte, D., & Vere-Jones, D. (1999). Differences in coverage between the PDE and New Zealand local earthquake catalogs. New Zealand Journal of Geology and Geophysics, 42, 237–253.CrossRefGoogle Scholar
  20. Kagan, Y. Y. (2003). Accuracy of modern global catalogs. Physics of the Earth and Planetary Interiors, 135, 173–209.CrossRefGoogle Scholar
  21. Kaiser, A., Holden, C., Beavan, J., Beetham, D., Benites, R., Celentano, A., et al. (2012). The M w 6.2 Christchurch earthquake of February 2011: preliminary report. New Zealand Journal of Geology and Geophysics, 55(1), 67–90.CrossRefGoogle Scholar
  22. Kanamori, H., & Brodsky, E. H. (2001). The physics of earthquakes. Physics Today, 54, 34–40.CrossRefGoogle Scholar
  23. Kanamori, H., & Cipar, J. J. (1974). Focal process of the great Chilean Earthquake May 22, 1960. Physics of the Earth and Planetary Interiors, 9(2), 128–136. Scholar
  24. Keilis-Borok, V. I. (1990). The lithosphere of the Earth as a nonlinear system with implications for earthquake prediction. Reviews of Geophysics, 28(1), 19–34.CrossRefGoogle Scholar
  25. Kossobokov, V. G., Lepreti, F., & Carbone, V. (2008). Complexity in sequences of solar flares and earthquakes. Pure and Applied Geophysics, 165, 761–775. Scholar
  26. Kossobokov, V. G., & Mazhkenov, S. A. (1994). On similarity in the spatial distribution of seismicity. In D. K. Chowdhury (Ed.), Computational seismology and geodynamics, 1 (pp. 6–15). Washington DC: AGU, The Union.Google Scholar
  27. Kossobokov, V., & Nekrasova, A. (2012). Global seismic hazard assessment program maps are erroneous. Seismic Instruments, 48(2), 162–170. Scholar
  28. Kossobokov, V. G., & Nekrasova, A. A. (2017). Characterizing aftershock sequences of the recent strong earthquakes in Central Italy. Pure and Applied Geophysics, 174, 3713–3723. Scholar
  29. Kossobokov, V., Peresan, A., & Panza, G. F. (2015a). Reality check: seismic hazard models you can trust. EOS, 96(13), 9–11.Google Scholar
  30. Kossobokov, V., Peresan, A., & Panza, G. F. (2015b). On operational earthquake forecast and prediction problems. Seismological Research Letters, 86(2), 287–290. Scholar
  31. Lay, T., Kanamori, H., Ammon, C. J., Nettles, M., Ward, S. N., Aster, R. C., et al. (2005). The great Sumatra-Andaman earthquake of 26 December 2004. Science, 308(5725), 1127–1133. Scholar
  32. Mignan, A. (2015). Modeling aftershocks as a stretched exponential relaxation. Geophysical Research Letters, 42, 9726–9732. Scholar
  33. Nekrasova, A. K., & Kosobokov, V. G. (2005). Temporal variations in the parameters of the Unified Scaling Law for Earthquakes in the eastern part of Honshu Island (Japan). Doklady Earth Sciences, 405, 1352–1356.Google Scholar
  34. Nekrasova, A., Kossobokov, V. (2002). Generalizing the Gutenberg-Richter scaling law. EOS Trans. AGU, 83(47), Fall Meet. Suppl., Abstract NG62B-0958.Google Scholar
  35. Nekrasova, A. K., & Kossobokov, V. G. (2016). Unified scaling law for earthquakes in Crimea and Northern Caucasus. Doklady Earth Sciences, 470(2), 1056–1058.CrossRefGoogle Scholar
  36. Nekrasova, A., Kossobokov, V. G., Parvez, I. A., & Tao, X. (2015). Seismic hazard and risk assessment based on the unified scaling law for earthquakes. Acta Geodaetica et Geophysica, 50(1), 21–37. Scholar
  37. Nekrasova, A., Kossobokov, V., Peresan, A., Aoudia, A., & Panza, G. F. (2011). A multiscale application of the unified scaling law for earthquakes in the Central Mediterranean Area and Alpine Region. Pure and Applied Geophysics, 168, 297–327. Scholar
  38. Nekrasova, A., Kossobokov, V., Peresan, A., & Magrin, A. (2014). The comparison of the NDSHA, PSHA seismic hazard maps and real seismicity for the Italian territory. Natural Hazards, 70(1), 629–641. Scholar
  39. Okubo, P., & Aki, K. (1987). Fractal geometry in the San Andreas fault system. Journal of Geophysical Research Atmospheres, 92(B1), 345–356. Scholar
  40. Omori, F. (1894). On the after-shocks of earthquakes. Journal of the College of Science, Imperial University of Tokyo, 7, 111–200.Google Scholar
  41. Panza, G., Kossobokov, V. G., Peresan, A., & Nekrasova, A. (2014). Chapter 12. Why are the standard probabilistic methods of estimating seismic hazard and risks too often wrong? In M. Wyss & J. Shroder (Eds.), Earthquake hazard, risk, and disasters (pp. 309–357). London: Elsevier.CrossRefGoogle Scholar
  42. Parvez, I. A., Nekrasova, A., & Kossobokov, V. (2014). Estimation of seismic hazard and risks for the Himalayas and surrounding regions based on Unified Scaling Law for Earthquakes. Natural Hazards, 71(1), 549–562. Scholar
  43. Reyners, M., Eberhart-Phillips, D., & Martin, S. (2013). Prolonged Canterbury earthquake sequence linked to widespread weakening of strong crust. Nature Geoscience, 7, 34–37. Scholar
  44. Simons, M., Minson, S. E., Sladen, A., Ortega, F., Jiang, J., Owen, S. E., et al. (2011). The 2011 magnitude 9.0 Tohoku-Oki earthquake: mosaicking the megathrust from seconds to centuries. Science, 332, 1421–1425. Scholar
  45. Smirnov, N. (1948). Table for estimating the goodness of fit of empirical distributions. Annals of Mathematical Statistics, 19, 279–281. Scholar
  46. Stirling, M., McVerry, G., Gerstenberger, M., Litchfield, N., Van Dissen, R., Berryman, K., et al. (2012). National seismic hazard model for New Zealand: 2010 update. Bulletin of the Seismological Society of America, 102(4), 1514–1542. Scholar
  47. Storcheus, A. V. (2011). Calculating the seismic energy of earthquakes and explosions. Journal of Volcanology and Seismology, 5, 341–350. Scholar
  48. Turcotte, D. L. (1997). Fractals and chaos in geology and geophysics (2nd ed.). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  49. Utsu, T., & Ogata, Y. (1997). Statistical analysis of seismicity. In J. H. Healy, V. I. Keilis-Borok, & W. H. K. Lee (Eds.), Algorithms for earthquake statistics and prediction (Vol. 6, pp. 13–94). El Cerrito: IASPEI Software Library, Seismological Society of America.Google Scholar
  50. Utsu, T., Ogata, Y., & Matsu’ura, R. S. (1995). The centenary of the Omori formula for a decay law of aftershock activity. Journal of Physics of the Earth, 43(1), 1–33.CrossRefGoogle Scholar
  51. Wells, D., & Coppersmith, K. (1994). New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bulletin of the Seismological Society of America, 84, 974–1002.Google Scholar
  52. Werner, M. J., & Sornette, D. (2008). Magnitude uncertainties impact seismic rate estimates, forecasts, and predictability experiments. Journal of Geophysical Research, 113, B08302. Scholar
  53. Wyss, M., Nekrasova, A., & Kossobokov, V. (2012). Errors in expected human losses due to incorrect seismic hazard estimates. Natural Hazards, 62(3), 927–935. Scholar
  54. Zaliapin, I., & Ben-Zion, Y. (2016). A global classification and characterization of earthquake clusters. Geophysical Journal International, 207, 608–634.CrossRefGoogle Scholar
  55. Zaliapin, I., Gabrielov, A., Keilis-Borok, V., & Wong, H. (2008). Clustering analysis of seismicity and aftershock identification. Physical Review Letters, 101, 018501. Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Institute of Earthquake Prediction Theory and Mathematical Geophysics, RASMoscowRussian Federation
  2. 2.Geophysical Center, RASMoscowRussian Federation
  3. 3.Institut de Physique du Globe de ParisParisFrance
  4. 4.International Seismic Safety OrganizationArsitaItaly

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