Extension of the multiplicative cascade model for descriptions of frequency regime of strong earthquakes: application to regional seismicity of Southeast Asia
Category: 16-2UDC 550.34
M.V. Rodkin(1), Ngo Thi Lu(2), L.M. Labuntsova(3)
(1) International Institute of Earthquake Prediction Theory and Mathematical Geophysics RAS, Moscow, Russia
(2) Institute of Geophysics, Vietnam Academy of Science and Technology, Hanoi, Vietnam
(3) Geophysical Center RAS, Moscow, Russia
Abstract. It is known that the ordinary Gutenberg–Richter law of earthquake recurrence can be modeled within the scheme of multiplicative cascade in which the seismic regime is treated as a sequence of a large number of episodes of avalanche-like relaxation, randomly occurring on the set of metastable subsystems. It is shown that this model can simulate such well known regularities in the seismic regime as a decrease in b-value in connection with the strong earthquakes occurrence, Omori law of aftershock number decay, the existence of the foreshock activity and the seismic cycle. We propose here the extension of the schema by adding of nonlinear terms in the kinetic equation of the multiplicative cascade to describe the effect of “bending down” of the graph of strong earthquake recurrence and the possibility of occurrence of characteristic earthquakes. The results are compared with data on seismicity of the Southeast Asia and the physical conditions of occurrence of characteristic earthquakes are discussed.
Keywords: earthquake statistics, multiplicative cascade model, bend down of the distribution law of earthquakes, characteristic earthquakes.
References
Bak P., Tang C. and Wiesenfeld K., Self-organised criticality, Phys. Rev. A., 1988, vol. 38, pp. 364–374.
Faenza L., Hainzl S. and Scherbaum F., Statistical analysis of the Central-Europe seismicity, Tectonophysics, 2009, vol. 470, pp. 195–204.
Gasperini P. and Lolli B., Correlation between the parameters of the aftershock rate equation: implications for the forecasting of future sequences, Phys. Earth Planet. Inter, 2006, vol. 156, no. 1–2, pp. 41–58.
Golitsyn G.S., The place of the Gutemberg-Richter law among other statistical laws of nature, in Problemy dinamiki litosfery i seismichnosti. Vychislitel’naya Seismologiya (Problems of lithosphere dynamics and seismicity. Computational seismology), vol. 32, Moscow: Nauka, 2001, pp. 138–161.
Grigorian S.S., On the mechanism of earthquake generation and meaning of empiric seismic correlations. Dokl. Akad. Nauk SSSR, 1988, vol. 299, no. 6. pp. 1094–1101.
Kagan Y.Y., Universality of the seismic moment-frequency relation, Pure Appl Geophys., 1999, vol. 155, no. 2–4, pp. 537–573.
Lu N.T., Gatinsky Y.G. and Kondorskaia N.V., Seismicity and recent geokinematics of Southeastern Asia. Doklady Earth Sciences, 2000, vol. 374, no. 7. pp. 1153–1157.
Myachkin V.I., Kostrov B.V., Sobolev G.A. and Shamina O.G., Earthquake source physics fundamentals and earthquake precursors, in Fizika ochaga zemletryaseniya (Earthquake source physics), Moscow: Nauka, 1975, pp. 6–29.
Ngo T.L., Estimation of seismological potential of Vietnam territory according to combination of geological, geophysical and seismic data, in Proekt mezhdunarodnogo nauchnogo sotrudnichestva po Soglasheniyu mezhdu V’etnamskoy akademiey nauk i tekhnologiy i Rossiyskoy akademiey nauk (2008–2010). Svodnyy otchet (Project of international scientific collaboration by Convention between Vietnam academy of sciences and technologies and Russian Academy of Sciences (2008–2010). General report), Hanoi, 2011, 163 p.
Ogata Y., Space–time point-process models for earthquake occurrence, Ann. Inst. Statis. Math., 1998, vol. 50, pp. 379–402.
Ogata Y., Statistical models for earthquake occurrence and residual analysis for point processes, J. Am. Stat. Assoc., 1988, vol. 83, pp. 9–27.
Pisarenko V. and Rodkin M., Heavy-Tailed Distributions in Disaster Analysis, in Advances in Natural and Technological Hazards Research, vol. 30. Dordrecht-Heidelberg-London-New York: Springer, 2010. DOI: 10.1007/978-90-481-9171-0
Pisarenko V. and Rodkin M., Statistical Analysis of Natural Disasters and Related Losses, in Springer Briefs in Earth Sciences. Dordrecht-Heidelberg-London-New York: Springer, 2013. DOI: 10.1007/978-3-319-01454-8
Pisarenko V.F. and Rodkin M.V., Heavy-Tailed Distributions in Disaster Analysis, in Vychislitel’naya Seismologiya (Computational seismology), vol. 38, Moscow: GEOS, 2007, 240 p.
Pisarenko V.F., Rodkin M.V. and Rukavishnikova T.A., Estimation of the probability of strongest seismic disasters based on the extreme value theory. Izv. Phys. Solid Earth, 2014, vol. 50, no. 3, pp. 89–103. DOI: 10.1134/S1069351314030070
Rodkin M.V. and Shatakhtsyan A.R., Statistical analysis of catalogs of large and superlarge ore deposits: empirical regularities and their interpretation. Geoinformatika, 2013, no. 4. pp. 25–32.
Rodkin M.V., Alternative to SOC concept-model of seismic regime as a set of episodes of random avalanche-like releases occurring on a set of metastable subsystems. Izv. Phys. Solid Earth, 2011, vol. 47, no. 10. pp.18–26. DOI: 10.1134/S1069351311100107
Rodkin M.V., Gvishiani A.D. and Labuntsova L.M., Models of generation of power laws of distribution in the processes of seismicity and in formation of oil fields and ore deposits, Russian Journal of Earth Sciences, 2008, vol. 10, no. 5, ES5004. DOI: 10.2205/2007ES000282
Sadovsky M.A. (Ed.), Diskretnye svoistva geofizicheskoy sredy (Discrete Properties of Geophysical Medium), Moscow: Nauka, 1989, 176 p.
Sobolev G.A. and Ponomarev A.V., Fizika zemletryasenii i prekursory (Physics of earthquakes and precursors), Moscow: Nauka, 2003, 270 p.
Sobolev G.A., The earthquake predictability concept based on seismicity dynamics under triggering impact, in Ekstremal'nye prirodnye yavleniya i katastrofy. T. 1. Ocenka i puti snizheniya negativnykh posledstviy ekstremal'nykh prirodnykh yavleniy (Extreme natural phenomena and catastrophes, vol. 1 Assessment and ways to mitigation of negative consequences of extreme natural phenomena), Moscow: IPE RAS, 2010, pp. 15–43.
Sornette D., Critical Phenomena in Natural Sciences, Berlin: Springer, 2000, 450 p.
Turcotte D.L., Seismicity and self-organized criticality, Phys. Earth Planet. Inter., 1999, vol. 111, pp. 275–293.
Ulomov V.I. and Bogdanov M.I., A new set of the seismic zoning maps of the Russian Federation (GSZ-2012). Inzhenernye Izyskaniya, 2013, no. 8. pp. 30–39.