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Forecasting Aftershock Activity: 5. Estimating the Duration of a Hazardous Period

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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.

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REFERENCES

  1. ANSS Comprehensive Earthquake Catalog (ComCat). https://earthquake.usgs.gov/data/comcat/. Cited November 18, 2018.

  2. 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

  3. 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.

    Article  Google Scholar 

  4. 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.

    Article  Google Scholar 

  5. 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.

    Article  Google Scholar 

  6. Båth, M., Lateral inhomogeneities in the upper mantle, Tectonophysics, 1965, vol. 2, pp. 483–514.

    Article  Google Scholar 

  7. Bender, B., Maximum likelihood estimation of b values for magnitude grouped data, Bull. Seismol. Soc. Am., 1983, vol. 73, no. 3, pp. 831–851.

    Google Scholar 

  8. 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.

  9. 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

    Article  Google Scholar 

  10. 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

    Article  Google Scholar 

  11. 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.

  12. 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.

    Google Scholar 

  13. Gutenberg, B. and Richter, C.F., Seismicity of the Earth and Associated Phenomena, 2nd ed., Princeton: Princeton Univ., 1954.

    Google Scholar 

  14. 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

    Article  Google Scholar 

  15. 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

    Article  Google Scholar 

  16. 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

    Article  Google Scholar 

  17. 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.

  18. 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

    Article  Google Scholar 

  19. 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

    Article  Google Scholar 

  20. 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.

  21. 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

    Article  Google Scholar 

  22. 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.

    Article  Google Scholar 

  23. Ogata, Y., Statistical models for standard seismicity and detection of anomalies by residual analysis, Tectonophysics, 1989, vol. 169, pp. 159–174.

    Article  Google Scholar 

  24. Ogata, Y., Seismicity analysis through point-process modeling; a review., Pure Appl. Geophys., 1999, vol. 155, pp. 471–508.

    Article  Google Scholar 

  25. Reasenberg, P., Second-order moment of Central California Seismicity, 1969–1982, J. Geophys. Res. Solid Earth, 1985, vol. 90, no. B7, pp. 5479–5495.

    Article  Google Scholar 

  26. 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

    Article  Google Scholar 

  27. 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

  28. 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.

    Article  Google Scholar 

  29. Seismologicheskii byulleten’ Kavkaza za 1971–1986 (Seismological Bulletin of the Caucasus for 1971–1986), Tbilisi: Metsniereba, 1972.

  30. 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

    Article  Google Scholar 

  31. 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.

  32. 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

    Article  Google Scholar 

  33. 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

  34. 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.

    Article  Google Scholar 

  35. 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.

    Article  Google Scholar 

  36. 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.

    Google Scholar 

  37. 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.

    Article  Google Scholar 

  38. 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.

  39. 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

  40. 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

    Article  Google Scholar 

  41. 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

    Article  Google Scholar 

  42. 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

    Article  Google Scholar 

  43. Utsu, T.A., Statistical study on the occurrence of aftershocks, Geophys. Mag., 1961, vol. 30, pp. 521–605.

    Google Scholar 

  44. 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.

    Article  Google Scholar 

  45. 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

    Article  Google Scholar 

  46. 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

    Article  Google Scholar 

  47. 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

    Article  Google Scholar 

  48. 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

    Article  Google Scholar 

  49. 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

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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.

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Correspondence to P. N. Shebalin or S. V. Baranov.

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Translated by M. Nazarenko

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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

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