Abstract
Continuing the series of publications on aftershock hazard assessment, we consider the problem of estimating the time interval after a strong earthquake that is prone to aftershocks which may pose an independent hazard. The distribution model of this quantity, which depends on three parameters of the Omori–Utsu law, is constructed. With the appropriate averaged parameter estimates, the model fairly closely fits the real (empirical) distributions of this quantity on the global and regional scale. A key parameter in the model is the expected number of aftershocks of a given magnitude. This number broadly varies from earthquake-to-earthquake, which determines the wide confidence variant of the estimates based on the averaged parameters. Therefore, for forecasting the duration of the hazardous aftershock-prone period, we propose to use two variants of the estimates. The first variant is based only on the averaged parameter estimates for the region under study and on the value of the magnitude of the earthquake. This variant is applicable immediately after a strong earthquake. The second variant employs information about the aftershocks that occurred during the first few hours after an earthquake, which improves the forecast considerably.
Similar content being viewed by others
REFERENCES
ANSS Comprehensive Earthquake Catalog (ComCat). https://earthquake.usgs.gov/data/comcat/. Cited November 18, 2018.
Baiesi, M. and Paczuski, M., Scale-free networks of earthquakes and aftershocks, Phys. Rev. E:, 2004, vol. 69, no. 6. https://doi.org/10.1103/PhysRevE.69.066106
Baranov, S.V. and Shebalin, P.N., Forecasting aftershock activity: 3. Båth’s dynamic law, Izv., Phys. Solid Earth. 2018, vol. 54, no. 6, pp. 926–932.
Baranov, S.V. and Shebalin, P.N., Global statistics of aftershocks following large earthquakes: independence of times and magnitudes, J. Volcanol. Seismol., 2019, vol. 19, no. 2, pp. 124–130.
Baranov, S.V., Pavlenko, V.A., and Shebalin, P.N., Forecasting aftershock activity: 4. Estimating the maximum magnitude of future aftershocks, Izv., Phys. Solid Earth, 2019, vol. 55, no. 4, pp.548–562.
Båth, M., Lateral inhomogeneities in the upper mantle, Tectonophysics, 1965, vol. 2, pp. 483–514.
Bender, B., Maximum likelihood estimation of b values for magnitude grouped data, Bull. Seismol. Soc. Am., 1983, vol. 73, no. 3, pp. 831–851.
Caucasus Earthquake Catalog of the Geophysical Survey of the Russian Academy of Sciences. ftp://ftp.gsras.ru/pub/ Teleseismic_Catalog/Caucasus-catalog-EQ.xlsx. Cited November 19, 2018.
Cocco, M., Hainzl, S., Catalli, F., Enescu, B., Lom-bardi, A.M., and Woessner, J., Sensitivity study of forecasted aftershock seismicity based on Coulomb stress calculation and rate- and state-dependent frictional response, J. Geophys. Res., 2010, vol. 115, B05307. https://doi.org/10.1029/2009JB006838
Dieterich, J.H., A constitutive law for rate of earthquake production and its application to earthquake clustering, J. Geophys. Res., 1994, vol. 99, no. B2, pp. 2601–2618. https://doi.org/10.1029/93JB02581
Earthquake Catalog compiled by the Baikal Branch of the Geophysical Survey of the Russian Academy of Sciences. http://seis-bykl.ru/modules.php?name=Data&da=1. Cited November 19, 2018.
Gardner, J.K. and Knopoff, L., Is the sequence of earthquakes in Southern California, with aftershocks removed, Poissonian?, Bull. Seismol. Soc. Am., 1974, vol. 64, no. 5, pp. 1363–1367.
Gutenberg, B. and Richter, C.F., Seismicity of the Earth and Associated Phenomena, 2nd ed., Princeton: Princeton Univ., 1954.
Hainzl, S., Christophersen, A., Rhoades, D., and Harte, D., Statistical estimation of the duration of aftershock sequences, Geophys. J. Int., 2016, vol. 205, no. 2, pp. 1180–1189. https://doi.org/10.1093/gji/ggw075
Helmstetter, A., Kagan, Y.Y., and Jackson, D.D., Comparison of short-term and time-independent earthquake forecast models for Southern California, Bull. Seismol. Soc. Am., 2006, vol. 96, no. 1, pp. 90–106. https://doi.org/10.1785/0120050067
Holschneider, M., Narteau, C., Shebalin, P., Peng, Z., and Schorlemmer, D., Bayesian analysis of the modified Omori law, J. Geophys. Res., 2012, vol. 117, B05317. https://doi.org/10.1029/2011JB009054
Kamchatka and Commander Islands Earthquake Catalog (1962 to present) of the Geophysical Survey of the Russian Academy of Sciences. http://www.emsd.ru/sdis/earthquake/catalogue/catalogue.php. Cited November 11, 2018.
Marsan, D. and Helmstetter, A., How variable is the number of triggered aftershocks?, J. Geophys. Res. Solid Earth, 2017, vol. 122, pp. 5544–5560. https://doi.org/10.1002/2016JB013807
Marsan, D. and Lengline, O., A new estimation of the decay of aftershock density with distance to the mainshock, J. Geophys. Res. Solid Earth, 2010, vol. 115, B09302. https://doi.org/10.1029/2009JB007119
Molchan, G.M. and Dmitrieva, O.E., Identification of aftershocks: a review and new approaches, in Vychislitel’naya Seismologiya (Computational Seismology), Moscow: Nauka, 1991, vol. 24, pp. 19–50.
Molchan, G.M. and Dmitrieva, O.E., Aftershock identification: methods and new approaches, Geophys. J. Int., 1992, vol. 109, pp. 501–516. https://doi.org/10.1111/j.1365-246X.1992.tb00113.x
Narteau, C., Byrdina, S., Shebalin, P., and Schorlemmer, D., Common dependence on stress for the two fundamental laws of statistical seismology, Nature, 2009, vol. 462, no. 2, pp. 642–645.
Ogata, Y., Statistical models for standard seismicity and detection of anomalies by residual analysis, Tectonophysics, 1989, vol. 169, pp. 159–174.
Ogata, Y., Seismicity analysis through point-process modeling; a review., Pure Appl. Geophys., 1999, vol. 155, pp. 471–508.
Reasenberg, P., Second-order moment of Central California Seismicity, 1969–1982, J. Geophys. Res. Solid Earth, 1985, vol. 90, no. B7, pp. 5479–5495.
Reasenberg, P.A. and Jones, L.M., Earthquake hazard after a mainshock in California, Science, 1989, vol. 242, no. 4895, pp. 1173–1176. https://doi.org/10.1126/science.243.4895.1173
Saichev, A. and Sornette, D., Distribution of the largest aftershocks in branching models of triggered seismicity: theory of the universal Båth law, Phys. Rev. E, 2005, vol. 71, no. 5, pp. 056127-1– 056127-11. https://doi.org/10.1103/PhysRevE.71.056127
Schorlemmer, D., Gerstenberger, M., Wiemer, S., Jackson, D.D., and Rhoades, D.A., Earthquake likelihood model testing, Seismol. Res. Lett, 2007, vol. 78, pp. 17–29.
Seismologicheskii byulleten’ Kavkaza za 1971–1986 (Seismological Bulletin of the Caucasus for 1971–1986), Tbilisi: Metsniereba, 1972.
Shcherbakov, R., Zhuang, J., and Ogata, Y., Constraining the magnitude of the largest event in a foreshock-mainshock-aftershock sequence, Geophys. J. Int., 2018, vol. 212, pp. 1–13. https://doi.org/10.1093/gji/ggx407
Shebalin, P.N., Mathematical methods of analysis and forecast of earthquake aftershocks: the need to change the paradigm, Chebyshevskii Sb., 2018, vol. 19, no. 4(68), pp. 227–242.
Shebalin, P. and Baranov, S., Long-delayed aftershocks in New Zealand and the 2016 M7.8 Kaikoura earthquake, Pure Appl. Geophys., 2017, vol. 174, no. 10, pp. 3751–3764. https://doi.org/10.1007/s00024-017-1608-9
Shebalin, P. and Narteau, C., Depth dependent stress revealed by aftershocks, Nat. Commun., 2017, vol. 8, no. 1317. https://doi.org/10.1038/s41467-017-01446-y
Shebalin, P., Narteau, C., Holschneider, M., and Zechar, J., Combining earthquake forecast models using differential probability gains, Earth, Planets Space, 2014, vol. 66, pp. 1–14.
Shebalin, P.N., Baranov, S.V., and Dzeboev, B.A., The law of the repeatability of the number of aftershocks, Dokl. Earth Sci., 2018, vol. 481, no. 1, pp. 963–966.
Smirnov, V.B., Prognostic anomalies of seismic regime. I. Technique for preparation of original data, Geofiz. Issled., 2009, vol. 10, no. 2, pp. 7–22.
Smirnov, V.B., Ponomarev, A.V., Bernar, P., and Patonin, A.V., Regularities in transient modes in the seismic process according to the laboratory and natural modeling, Izv., Phys. Solid Earth, 2010, vol. 46, no. 2, pp. 17–49.
Solov’ev, S.L. and Solov’eva, O.N., Exponential distribution of the total number of future shocks of an earthquake and the depth decay of its mean value, Izv. Akad. Nauk SSSR, Ser. Geofiz., 1962, no. 12, pp. 1685–1694.
Sornette, D. and Helmstetter, A., Occurrence of finite-time-singularity in epidemic models of rupture, earthquakes and starquakes, Phys. Rev. Lett., 2002, vol. 89, no. 15, pp. 158 501-1–158 501-4. https://doi.org/10.1103/PhysRevLett.89.158501
Stein, S. and Liu, M., Long aftershock sequences within continents and implications for earthquake hazard assessment, Nature, 2009, vol. 462, pp. 87–89 https://doi.org/10.1038/nature08502
Tahir, M., Grasso, J.-R., and Amorèse, D., The largest aftershock: how strong, how far away, how delayed?, Geophys. Rev. Lett., 2002, vol. 39, L04301. https://doi.org/10.1029/2011GL050604
Toda, S. and Stein, R.S., Why aftershock duration matters for probabilistic seismic hazard assessment, Bull. Seismol. Soc. Am., 2018, vol. 108, no. 3A, pp. 1414–1426. https://doi.org/10.1785/0120170270
Utsu, T.A., Statistical study on the occurrence of aftershocks, Geophys. Mag., 1961, vol. 30, pp. 521–605.
Vorobieva, I., Narteau, C., Shebalin, P., Beauducel, F., Nercessian, F., Clouard, V., and Bouin, M.P., Multiscale mapping of completeness magnitude of earthquake catalogs, Bull. Seismol. Soc. Am., 2013, vol. 103, pp. 2188–2202.
Zaliapin, I. and Ben-Zion, Y., Earthquake clusters in Southern California I: identification and stability, J. Geophys. Res.: Solid Earth, 2013, vol. 118, no. 6, pp. 2847–2864. https://doi.org/10.1002/jgrb.50178
Zaliapin, I. and Ben-Zion, Y., A global classification and characterization of earthquake clusters, Geophys. J. Int., 2016, vol. 207, no. 1, pp. 608–634. https://doi.org/10.1093/gji/ggw300
Zaliapin, I., Gabrielov, A., Keilis-Borok, V., and Wong, H., Clustering analysis of seismicity and aftershock identification, Phys. Rev. Lett., 2008, vol. 101, no. 1, pp. 1–4. https://doi.org/10.1103/PhysRevLett.101.018501
Zhuang, J., Ogata, Y., and Vere-Jones, D., Stochastic declustering of space-time earthquake occurrences, J. Am. Stat. Assoc., 2002, vol. 97, pp. 369–380. https://doi.org/10.1198/016214502760046925
Zhuang, J., Ogata, Y., and Vere-Jones, D., Analyzing earthquake clustering features by using stochastic reconstruction, J. Geophys. Res., 2004, vol. 109, no. B05301. https://doi.org/10.1029/2003JB002879
ACKNOWLEDGMENTS
We are grateful to the two anonymous reviewers for their valuable comments.
Funding
This research was supported by the Russian Ministry of Science and Education under project no. 14.W03.31.0033 and by the Russian Foundation for Basic Research under project no. 17-05-00749 in partial fulfillment of state contracts nos. АААА-А19-119011490127-6 and 0152-2019-0010.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Translated by M. Nazarenko
Rights and permissions
About this article
Cite this article
Shebalin, P.N., Baranov, S.V. Forecasting Aftershock Activity: 5. Estimating the Duration of a Hazardous Period. Izv., Phys. Solid Earth 55, 719–732 (2019). https://doi.org/10.1134/S1069351319050112
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1069351319050112