Skip to main content

Advertisement

Time-dependent earthquake hazard evaluation in seismogenic systems using mixed Markov Chains: An application to the Japan area

Article metrics

  • 304 Accesses

  • 10 Citations

Abstract

A previous work introduced a new method for seismic hazard evaluation in a system (a geographic area with distinct, but related seismogenic regions) based on modeling the transition probabilities of states (patterns of presence or absence of seismicity, with magnitude greater or equal to a threshold magnitude Mr, in the regions of the system, during a time interval Δt) as a Markov chain. Application of this direct method to the Japan area gave very good results. Given that the most important limitation of the direct method is the relative scarcity of large magnitude events, we decided to explore the possibility that seismicity with magnitude MM r m contains information about the future occurrence of earthquakes with MM r m > M r m . This mixed Markov chain method estimates the probabilities of occurrence of a system state for MM r M on the basis of the observed state for MM r m in the previous Δt. Application of the mixed method to the area of Japan gives better hazard estimations than the direct method; in particular for large earthquakes. As part of this study, the problem of performance evaluation of hazard estimation methods is addressed, leading to the use of grading functions.

References

  1. Agnew, D. D. and L. M. Jones, Prediction probabilities from foreshocks, J. Geophys. Res., 96, 11959–11971, 1991.

  2. Aki, K., A probabilistic synthesis of precursory phenomena, in Earthquake Prediction, an International Review, edited by D. W. Simpson and P. G. Richards, 680 pp., M. Ewing series, v. 4, Am. Geophys. Union, Washington, D.C., 1981.

  3. Brillinger, D., Seismic risk assessment: some statistical aspects, Earthq. Predict. Res., 1 183–195, 1982.

  4. Epstein, B. and C. Lomnitz, A model for the occurrence of large earthquakes, Nature, 211, 954–956, 1966.

  5. Fedotov, S., Regularities of the distribution of strong earthquakes in Kamchatka, the Kurile Islands, and northeast Japan, Trudy Isnt. Fiz. Zemli. Acad. Nauk. SSSR., 36, 66–94, 1965.

  6. Goldman, S., Information Theory, 385 pp., Dover Publs. Inc., USA, 1953.

  7. Gumbel, E. J., Statistics of Extremes, 375 pp., Columbia University Press, New York, N.Y., 1958.

  8. Gutenberg, B. and C. Richter, Frequency of earthquakes in California, Bull. Seism. Soc. Am., 34, 185–188, 1944.

  9. Hagiwara, Y., A stochastic model of earthquake occurrence and the accompanying horizontal land deformations, Tectonophysics, 26, 91–101, 1975.

  10. Hagiwara, Y., H. Tajima, S. Izutnya, and H. Hanada, Gravity changes associated with earthquake swarm activities in the eastern part of Izu peninsula, Bull. Earthq. Res. Inst. Tokyo Univ., 52, 141–150, 1997.

  11. Herrera, C., Determinación de peligro sísmico mediante cadenas de Markov, MSc Thesis, CICESE, 86 p., 2001.

  12. International Seismological Center, On-line Bulletin, http://www.isc.ac.uk/Bull/Bull.

  13. Kagan, Y. and D. Jackson, Seismic gap hypothesis: Ten years after, J. Geophys. Res., 96, 21419–21431, 1991.

  14. Keilis-Borok, V. I. and V. G. Kossobokov, Premonitory activation of earthquake flow: algorithm M8, Phys. Earth. Planet. Int., 61, 73–83, 1990.

  15. Knopoff, L., A stochastic model for the occurrence of main sequence earthquakes, J. Geophys. Res., 75, 5745–5756, 1971.

  16. Lomnitz, C. and F. Nava, The predictive power of seismic gaps, Bull. Seism. Soc. Am., 73, 1815–1824, 1983.

  17. McCann, W., S. Nishenko, L. Sykes, and J. Krause, Seismic gaps and plate tectonics: seismic potential for major boundaries, Pure Appl. Geophys., 117, 1082–1147, 1979.

  18. Mogi, K., Migration of Seismic Activity, Bull. Earthq. Res. Inst., 46, 53–74, 1968.

  19. Nava, F. A. and V. Espíndola, Seismic hazard assessment through semi-stochastic simulation, Bull. Seism. Soc. Am., 83, 450–468, 1993.

  20. Nava, F. A., C. Herrera, J. Frez, and E. Glowacka, Seismic hazard evaluation using Markov chains; Application to the Japan area, Pure Appl. Geophys., 162, 1347–1366, 2005.

  21. Patwardhan, A. S., R. B. Kulkarni, and D. Tocher, A semi Markov model for characterizing recurrence of great earthquakes, Bull. Seism. Soc. Am., 70, 323–347, 1980.

  22. Reid, H. F., The mechanism of the earthquake, The California earthquake of April 18, 1906, Report of the Research Senatorial Commission, Carnegie Institution, Washington D.C., 2, 16–18, 1910.

  23. Richter, C., Elementary Seismology, 521 pp., W. H. Freeman, San Francisco, 1958.

  24. Shimazaki, K. and T. Nakata, Time predictable recurrence model for large earthquakes, Geophys. Res. Lett., 7, 279–282, 1980.

  25. Tsapanos, T. and A. A. Papadopoulou, A discrete Markov Model for earthquake occurrences in Southern Alaska and Aleutian Islands, J. Balkan Geophys. Soc., 2(3), 75–83, 1999.

  26. Vere-Jones, D., A Markov model for aftershock occurrence, Pure Appl. Geophys., 64, 31–42, 1966.

  27. Yong, S. and Z. Wai, The correlation between random variation and Earth solid tide Change in Rock-Groundwater system-the Mechanical Foundation for Using Change to predict Earthquake, J. Earthq. Predict. Res., 4, 3–15, 1995.

Download references

Author information

Correspondence to C. Herrera.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Herrera, C., Nava, F.A. & Lomnitz, C. Time-dependent earthquake hazard evaluation in seismogenic systems using mixed Markov Chains: An application to the Japan area. Earth Planet Sp 58, 973–979 (2006) doi:10.1186/BF03352602

Download citation

Key words

  • Earthquake Hazard
  • Markov Chains
  • seismic catalog