Journal of Seismology

, Volume 7, Issue 2, pp 145–153 | Cite as

The conditional probability of earthquake occurrence and the next large earthquake in Tokyo, Japan

  • Sergio G. Ferraes
Article

Abstract

The use of probability distribution ofrecurrence times as described by theexponential, Weibull and Rayleihgprobability densities form the core of theprobabilistic seismic prediction analysispresented in this paper. Using these threeprobabilistic models we derive threeformulas to calculate the conditionalprobability P(Δt|t) than an earthquakeevent will occur in the time interval (t, t+ Δt), provide that it has not occurredin the elapsed time t since the last largeearthquake (M ≥ 6.4) in the Tokyo area.This paper proposes a new method toestimate the time interval Δt foroccurrence of a new large earthquake inTokyo area. This time interval is measuredafter the elapsed time (t) since the lastlarge earthquake. To do this we use thethree formulas for the conditionalprobability P(Δt|t) and the criterionof the maximum conditional probability ofearthquake occurrence.Using a list of historical earthquakeswhich have occurred in the Tokyo area asgiven by Usami (1976, pp. 235–243), wefound that: (1) Using the exponentialmodel, it is estimated that a highlydamaging earthquake magnitude M ≥ 6.4, mayoccur before the year 2009.50, orequivalently before June 2009; (2) Usingthe Weibull model, it is estimated that thedamaging earthquake (M ≥ 6.4) may occurbefore the year 2129.80, or equivalentlybefore October 2129.

conditional probability of occurrence earthquake prediction exponential Japan maximum criterion probabilistic models Rayleigh Tokyo Weibull 

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References

  1. Benjamin, J.R. and Cornell, C.A., 1970, Probability, Statistic, and Decision for Civil Engineers, Mac Graw-Hill.Google Scholar
  2. Cooper, G.R. and McGillen, C.D., 1971, Probabilistic Methods for Signal and System Analysis, Holt, Rinehart and Winston, Inc.Google Scholar
  3. Cornell, C.A. and Winterstein, S.R., 1998, Temporal and magnitude dependence in earthquake recurrence models, Bull. Seism. Soc. America 78, 1522–1537.Google Scholar
  4. Hagiwara, Y., 1983, A probabilistic process of earthquake occurrences in Tokyo and its adjacent areas, Eart. Pred. Res. 2, 97.104.Google Scholar
  5. Kagan, Y.Y., 1997, Statistical aspects of Parkfield earthquake sequences and Parkfiel prediction experiment, Tectonophysics 270, 270–219.Google Scholar
  6. Kotz, S. and Johnson, N.L., 1988, Encyclopedia of Statistical Wiley, New York, Vol. 9.Google Scholar
  7. Matsuda, T., Ota, Y., Ando, M. and Yonekura, N., 1978, Faulty mechanism and recurrence time of major earthquakes in southern Kanto district, Japan, as deduced from coastal terrace data, Geol. Soc, Am. Bull. 89, 1610–1618.Google Scholar
  8. Matuzawa, T., 1964, Study of Earthquakes, UNO SHOTEN, Tokyo, Japan.Google Scholar
  9. Mogi, K., 1985, Earthquake Prediction, Academic Press, Japan Inc.Google Scholar
  10. Meyer, P.L., 1972, Introductory Probability and Statistical Applications, Addison Wesley Publishing Company.Google Scholar
  11. Rhoades, D.A. and Evison, F.E., 1989, Time-variable factors in earthquake hazard, Technophysics 167, 201–210.Google Scholar
  12. Rikitake, T., 1990, Threat of an earthquake right under the capital in Japan, Earthqs. & Volc. 22, 209–210.Google Scholar
  13. Rikitake, T., 1991, Assessment of earthquake hazard in the Tokyo area, Tecnophysics 199, 121–131.Google Scholar
  14. Sieh, K., Stuiver, M. and Brillinger, D., 1989, A more prices chronology of earthquakes produced by the San Andres Fault in southern California, J. Geophys. Res. 94, 603–623.Google Scholar
  15. Sornette, D. and Knopoff, L., 1997, The paradox of the expected time until the next earthquake, Bull. Seism. Soc. Am 87(4), 789–798.Google Scholar
  16. Usami, T. and Hisamoto, S., 1970, Probability of a future earthquake with high intensity in the Tokyo area, Bull. Eartq. Res. Inst. Tokyo Univ. 48, 331.Google Scholar
  17. Usami, T., 1976, History of disastrous earthquakes in Edo (Tokyo), Bull. Earthq. Res. Inst., Tokyo Univ. 51, 231–250.Google Scholar
  18. Utsu, T., 1984, Estimation of parameters for recurrence models of earthquakes, Bull. Earthq. Res. Inst., Univ Tokyo 59, 53–56.Google Scholar
  19. Utsu, T., 1988, A catalog of large earthquakes (M≥6) and damaging earthquakes in Japan for the years 1985–1925, In: Lee, W.H.K., Meyers, H. and Shimizaki, K. (eds.), Historical Seismograms and Earthquakes of the World, Acamic Press San Diego, pp. 150–161.Google Scholar
  20. Watanabe, S., 1936, Contingency, Persistence and Periodicity of Earthquake Occurrence, Riken – Iho.Google Scholar
  21. Wesnousky, S.G., Scholz, C.H., Shimizaki, K. and Matsuda, T., 1984, Integration of geological and seismological data for the analysis of seismic hazard: A case study of Japan, Bull. Seism. Soc. Am. 74(2), 687–708.Google Scholar
  22. Winkler, R.I. and Hays, W.L., 1975, Statistic: Probability, Inference, and Decision, Holt, Rinehart and Winsten.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Sergio G. Ferraes
    • 1
  1. 1.Institute of Geophysics, (UNAM)Ciudad UniversitariaMexico CityMexico

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