We study aftershock sequences of six major earthquakes in New Zealand, including the 2016 M7.8 Kaikaoura and 2016 M7.1 North Island earthquakes. For Kaikaoura earthquake, we assess the expected number of long-delayed large aftershocks of M5+ and M5.5+ in two periods, 0.5 and 3 years after the main shocks, using 75 days of available data. We compare results with obtained for other sequences using same 75-days period. We estimate the errors by considering a set of magnitude thresholds and corresponding periods of data completeness and consistency. To avoid overestimation of the expected rates of large aftershocks, we presume a break of slope of the magnitude–frequency relation in the aftershock sequences, and compare two models, with and without the break of slope. Comparing estimations to the actual number of long-delayed large aftershocks, we observe, in general, a significant underestimation of their expected number. We can suppose that the long-delayed aftershocks may reflect larger-scale processes, including interaction of faults, that complement an isolated relaxation process. In the spirit of this hypothesis, we search for symptoms of the capacity of the aftershock zone to generate large events months after the major earthquake. We adapt an algorithm EAST, studying statistics of early aftershocks, to the case of secondary aftershocks within aftershock sequences of major earthquakes. In retrospective application to the considered cases, the algorithm demonstrates an ability to detect in advance long-delayed aftershocks both in time and space domains. Application of the EAST algorithm to the 2016 M7.8 Kaikoura earthquake zone indicates that the most likely area for a delayed aftershock of M5.5+ or M6+ is at the northern end of the zone in Cook Strait.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
Aki, K. (1965). Maximum likelihood estimate of b in the formula log N = a − b M and its confidence limits. Bulletin of the Earthquake Research Institute, University of Tokyo, 43, 237–239.
Baranov, S. V., & Shebalin, P. N. (2016). Forecasting aftershock activity: 1. Adaptive estimates based on the Omori and Gutenberg–Richter laws. Izvestiya-Physics of the Solid Earth, 52(3), 413–431. doi:10.1134/S1069351316020038.
Baranov, S. V., & Shebalin, P. N. (2017). Forecasting aftershock activity: 2. Estimating the area prone to strong aftershocks. Izvestiya-Physics of the Solid Earth. doi:10.7868/S0002333717020028.
Bender, B. (1983). Maximum likelihood estimation of b-values for magnitude grouped data. Bulletin of the Seismological Society of America, 73, 831–851.
Cattania, C., Hainzl, S., Wang, L., Roth, F., & Enescu, B. (2014). Propagation of Coulomb stress uncertainties in physics-based aftershock models. Journal of Geophysical Research: Solid Earth, 119(10), 7846–7864.
Ekström, G., Nettles, M., & Dziewonski, A. M. (2012). The global CMT project 2004–2010: Centroid-moment tensors for 13,017 earthquakes. Physics of the Earth and Planetary Interiors, 200–201, 1–9. doi:10.1016/j.pepi.2012.04.002.
Gardner, J. K., & Knopoff, L. (1974). Is the sequence of earthquakes in southern California, with aftershocks removed, Poissonian? Bulletin of the Seismological Society of America, 64, 1363–1367.
Gerstenberger, M., & Rhoades, D. (2010). New Zealand earthquake forecast testing centre. Pure and Applied Geophysics, 167(8–9), 877–892.
Gerstenberger, M. C., Wiemer, S., Jones, L. M., & Reasenberg, P. A. (2005). Real-time forecasts of tomorrow’s earthquakes in California. Nature, 435, 328–331.
Gutenberg, B., & Richter, C. F. (1954). Seismicity of the Earth and associated phenomena (Vol. ix, p. 310). Princeton: Princeton University Press.
Hainzl, S. (2016). Rate-dependent incompleteness of earthquake catalogs. Seismological Research Letters, 96(2A), 337–344. doi:10.1785/0220150211.
Harte, D. S. (2014). An ETAS model with varying productivity rates. Geophysical Journal International, 198(1), 270–284.
Helmstetter, A., Kagan, Y. Y., & Jackson, D. D. (2006). Comparison of short-term and time-independent earthquake forecast models for southern California. Bulletin of the Seismological Society of America, 96(1), 90–106.
Holschneider, M., Narteau, C., Shebalin, P., Peng, Z., & Schorlemmeret, D. (2012). Bayesian analysis of the modified Omori law. Journal of Geophysical Research, 117, B05317. doi:10.1029/2011JB009054.
Narteau, C. (2007). Classification of seismic patterns in a hierarchical model of rupture: A new phase diagram for seismicity. Geophysical Journal International, 167, 710–722.
Narteau, C., Byrdina, S., Shebalin, P., & Schorlemmer, D. (2009). Common dependence on stress for the two fundamental laws of statistical seismology. Nature, 462(7273), 642–645.
Narteau, C., Shebalin, P., & Holschneider, M. (2005). Onset of the power law aftershock decay rate in Southern California. Geophysical Research Letters, 32, L22312. doi:10.1029/2005GL023951.
Narteau, C., Shebalin, P., & Holschneider, M. (2008). Loading rates in California inferred from aftershocks. Nonlinear Processes in Geophysics, 15, 245–263.
Ogata, Y. (1983). Estimation of the parameters in the modified Omori formula for aftershock frequencies by the maximum likelihood procedure. Journal of Physics of the Earth, 31, 115–124.
Omi, T., Ogata, Y., Hirata, Y., & Aihara, K. (2013). Forecasting large aftershocks within one day after the main shock. Scientific Reports. doi:10.1038/srep02218.
Omi, T., Ogata, Y., Shiomi, K., Enescu, B., Sawazaki, K., & Aihara, K. (2016). Automatic aftershock forecasting: A test using real-time seismicity data in Japan. Bulletin of the Seismological Society of America. doi:10.1785/0120160100.
Reasenberg, P. A., & Jones, L. M. (1989). Earthquake hazard after a mainshock in California. Science, 242(4895), 1173–1176.
Rhoades, D. A. (2013). Mixture models for improved earthquake forecasting with short-to-medium time-horizons. Bulletin of the Seismological Society of America, 103(4), 2203–2215. doi:10.1785/0120120233.
Rhoades, D. A., Christophersen, A., & Gerstenberger, M. C. (2016). Multiplicative earthquake likelihood models based on fault and earthquake data. Bulletin of the Seismological Society of America, 105(6). doi:10.1785/0120150080.
Rhoades, D. A., Gerstenberger, M. C., Christophersen, A., Zechar, J. D., Schorlemmer, D., Werner, M. J., et al. (2014). Regional earthquake likelihood models II: Information gains of multiplicative hybrids. Bulletin of the Seismological Society of America, 104(6), 3072–3083. doi:10.1785/0120140035.
Shebalin, P. N. (2004). Aftershocks as indicators of the state of stress in a fault system. Doklady Earth Sciences, 398, 978–982.
Shebalin, P., Narteau, C., & Holschneider, M. (2012). From alarm-based to rate-based earthquake forecast models. Bulletin of the Seismological Society of America, 102(1), 64–72.
Shebalin, P., Narteau, C., Holschneider, M., & Schorlemmer, D. (2011). Short-term earthquake forecasting using early aftershock statistics. Bulletin of the Seismological Society of America, 101(4), 297–312.
Shebalin, P. N., Narteau, C., Zechar, J. D., & Holschneider, M. (2014). Combining earthquake forecasts using differential probability gains. Earth, Planets and Space, 66(37), 1–14. doi:10.1186/1880-5981-66-37.
Steacy, S., Gerstenberger, M. C., Williams, C., Rhoades, D. A., & Christophersen, A. (2014). A new hybrid Coulomb/statistical model for forecasting aftershock rates. Geophysical Journal International, 196(2), 918–923.
Tormann, T., Enescu, B., Woessner, J., & Wiemer, S. (2015). Randomness of megathrust earthquakes implied by rapid stress recovery after the Japan earthquake. Nature Geosciences, 8, 152–158. doi:10.1038/ngeo2343.
Tsuboi, C. (1956). Earthquake energy, earthquake volume, aftershock area, and strength of the Earth’s crust. Journal of Physics of the Earth, 4, 63–66.
Utsu, T. (1961). A statistical study on the occurrence of aftershocks. Geophysical Magazine, 30, 521–605.
Vorobieva, I., Narteau, C., Shebalin, P., Beauducel, F., Nercessian, A., Clouard, V., et al. (2013). Multiscale mapping of completeness magnitude of earthquake catalogs. Bulletin of the Seismological Society of America, 103, 2188–2202. doi:10.1785/0120120132.
Vorobieva, I., Shebalin, P., & Narteau, C. (2016). Break of slope in earthquake size distribution and creep rate along the San Andreas Fault system. Geophysical Research Letters. doi:10.1002/2016GL069636.
Wang, L., Hainzl, S., Sinan Özeren, M., & Ben-Zion, Y. (2010). Postseismic deformation induced by brittle rock damage of aftershocks. Journal of Geophysical Research, 115, B10422. doi:10.1029/2010JB007532.
Wells, D. L., & Coppersmith, K. J. (1994). New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bulletin of the Seismological Society of America, 84(4), 974–1002.
Werner, M., Marzocchi, W., Taroni, M., Zechar, J., Gerstenberger, M., Liukis, M., et al. (2015). Retrospective evaluation of time-dependent earthquake forecasting models during the 2010–12 Canterbury, New Zealand, earthquake sequence. SECED 2015 Conference: Earthquake Risk and Engineering towards a Resilient World 9–10 July 2015, Cambridge UK. http://www.seced.org.uk/images/newsletters/WERNER,%20MARZOCCHI,%20et%20al.pdf.
Wiemer, S., & Wyss, M. (2000). Minimum magnitude of completeness in earthquake catalogs: Examples from Alaska, the western United States, and Japan. Bulletin of the Seismological Society of America, 90(4), 859–869.
This work was supported by Russian Science foundation, project No. 16-17-00093. We acknowledge the New Zealand GeoNet project and its sponsors EQC, GNS Science and LINZ, for providing data used in this study. We thank an anonymous reviewer for reading the paper and suggesting useful improvements.
About this article
Cite this article
Shebalin, P., Baranov, S. Long-Delayed Aftershocks in New Zealand and the 2016 M7.8 Kaikoura Earthquake. Pure Appl. Geophys. 174, 3751–3764 (2017). https://doi.org/10.1007/s00024-017-1608-9
- Kaikoura Earthquake
- Frequency-magnitude Relation
- Main Shock
- Aftershock Sequence
- Aftershock Zone