Skip to main content
SpringerLink
Log in

Application of Bayesian Markov Chain Monte Carlo method with mixed gumbel distribution to estimate extreme magnitude of tsunamigenic earthquake

  • Hydro-Climatological Analysis for Floods and Droughts
  • Published:
KSCE Journal of Civil Engineering Aims and scope Submit manuscript

Abstract

Earthquake or tsunami is a disaster that could bring massive life damages and economic loss. Although various studies on forecasting the earthquake have been conducted, the Gutenberg-Richter equation is generally used in practice. In this study, a practical method using statistical frequency analysis was suggested to estimate extreme magnitude of tsunamigenic earthquake. The study employed Bayesian approach to take into account uncertainty of earthquake occurrence corresponding to specific return periods, and mixed distribution functions to incorporate the effect of intermittent occurrence of earthquake into frequency analysis. This study utilized tsunamigenic earthquake data acquired from NOAA (National Oceanic and Atmospheric Administration), for Kamchatka and Kuril Island, Japan within Kamchatka-Kuril-Japan Trench. Using the Metropolis Hasting Markov Chain Monte Carlo (MH-MCMC) sampling, the parameters were estimated for the tsunamigenic earthquake data. Considering the uncertainty of parameters, 95% credible intervals were constructed for various return periods. This study quantified the uncertainty of possibility of earthquake occurrence so that it could be utilized as basic reference for earthquake risk analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alves, I. F. and Neves, C. (2011). “Extreme value distributions.” International Encyclopedia of Statistical Science, pp. 493–496, DOI: 10.1007/springerreference_205330.

    Chapter  Google Scholar 

  • Benjamin, J. R. (1970). Probability, statistics, and decision for civil engineers, McGraw-Hill, New York.

    Google Scholar 

  • Brooks, S. P. and Gelman, A. (1998) “General methods for monitoring convergence of iterative simulations.” Journal of Computational and Graphical Statistics, Vol. 7, No. 4, pp. 434–455, DOI: 10.1080/10618600.1998.10474787.

    MathSciNet  Google Scholar 

  • Byrdina, S, Shebalin, P., Narteu, C., and Le Moüel, J. L. (2006) “Temporal properties of seismicity and largest earthquakes in SE Carpathians.” Nonlinear Processes in Geophysics, Vol. 1, No. 6, pp. 629–639, DOI: 10.5194/npg-13-629-2006.

    Article  Google Scholar 

  • Campbell, K. W. (1982). “Bayesian analysis of extreme earthquake occurrences. Part I. Probabilistic hazard model.” Bulletin of the Seismological Society of America, Vol. 72, No. 5, pp. 1689–1705.

    Google Scholar 

  • Chib, S. and Greenberg, E. (1995). “Understanding the metropolishastings algorithm.” The American Statistician, Vol. 49, No. 4, pp.327–335, DOI: 10.2307/2684568.

    Google Scholar 

  • Chung, E. S. and Kim, S. U. (2013). “Bayesian rainfall frequency analysis with extreme value using the informative prior distribution.” KSCE Journal of Civil Engineering, KSCE, Vol. 17, No. 6, pp. 1502–1514, DOI: 10.1007/s12205-013-0189-0.

    Article  MathSciNet  Google Scholar 

  • Coles, S. (2001). An introduction to statistical modeling of extreme values, Springer Series in Statistics, London, DOI: 10.1007/978-1-4471-3675-0.

    Book  MATH  Google Scholar 

  • Coles, S. and Pericchi, L. (2003). “Anticipating catastrophes through extreme value modelling.” Journal of the Royal Statistical Society: Series C (Applied Statistics), Vol. 52 No. 4, pp. 405–416, DOI: 10.1111/1467-9876.00413.

    Article  MATH  MathSciNet  Google Scholar 

  • Congdon, P. (2007). Bayesian statistical modelling, John Wiley & Son, New York

    Google Scholar 

  • Cornell, C. A. (1968). “Engineering seismic risk analysis.” Bulletin of the Seismological Society of America, Vol. 58. No. 5, pp. 1583–1606.

    Google Scholar 

  • Downes, G. L. and Stirling, M. W. (2001). “Groundwork for development of a probabilistic tsunami hazard model for New Zealand.” International Tsunami Symposium 2001 Proceedings, pp. 7–10.

    Google Scholar 

  • Galanis, O. C., Tsapanos, T. M., Papadopoulos, G. A., and Kiratzi, A. A. (2002). “Bayesian extreme values distribution for seismicity parameters assessment in South America.” Journal of the Balkan Geophysical Society, Vol. 5, No. 3, pp. 77–86.

    Google Scholar 

  • Gutenberg, B. and Richter, C. F. (1941). “Seismicity of the Earth.” Geological Society of America Special Papers, Vol. 34, pp. 1–131, DOI: 10.1130/spe34-p1.

    Article  Google Scholar 

  • Gutenberg, B. and Richter, C. F. (1944). “Frequency of earthquakes in California.” Bulletin of the Seismological Society of America, Vol. 34, pp. 185–188.

    Google Scholar 

  • Hastings, W. K. (1970). “Monte Carlo sampling methods using Markov chains and their applications.” Biometrika, Vol. 57, No. 1, pp. 97–109, DOI: 10.1093/biomet/57.1.97.

    Article  MATH  Google Scholar 

  • Holschneider, M., Zöller, G., and Hainzl, S. (2011). “Estimation of the maximum possible magnitude in the framework of a doubly truncated Gutenberg-Richter model.” Bulletin of the Seismological Society of America, Vol. 101, No. 4, pp. 1649–1659.

    Article  Google Scholar 

  • Kagan, Y. Y. (1997). “Seismic moment-frequency relation for shallow earthquakes: Regional comparison.” Journal of Geophysical Research: Solid Earth (1978–2012), Vol. 102, No. B2, pp. 2835–2852, DOI: 10.1029/96jb03386.

    Article  Google Scholar 

  • Kagan, Y. Y. and Jackson, D. D. (2000). “Probabilistic forecasting of earthquakes.” Geophysical Journal International, Vol. 143, No. 2, pp. 438–453.

    Article  Google Scholar 

  • Kagan, Y. Y. and Knopoff, L. (1984). “A stochastic model of earthquake occurrence.” Proceedings of the 8th International Conference on Earthquake Engineering, Vol. 1, pp. 295–302.

    Google Scholar 

  • Kedem, B., Chiu, L., and Karni, Z. (1990). “An analysis of the threshold method for measuring area-average rainfall.” Journal of Applied Meteorology, Vol. 29, No. 1, pp. 3–20, DOI: 10.1175/1520-0450(1990)029<0003:aaottm>2.0.co;2.

    Article  Google Scholar 

  • Kulikov, E. A., Rabinovich, A. B., and Thomson, R. E. (2005). “Estimation of tsunami risk for the coasts of Peru and northern Chile.” Natural Hazards, Vol. 35, No. 2, pp. 185–209, DOI: 10.1007/s11069-004-4809-3.

    Article  Google Scholar 

  • Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). “Equation of state calculations by fast computing machines.” The Journal of Chemical Physics, Vol. 21, No. 6, pp. 1087–1092, DOI: 10.1063/1.1699114.

    Article  Google Scholar 

  • Nordquist, J. M. (1945) “Theory of largest values applied to earthquake magnitudes. Transactions.” American Geophysical Union, Vol. 26, No. 1, pp. 29–31, DOI: 10.1029/tr026i001p00029.

    Article  Google Scholar 

  • O’Connell, D. R., Ostenaa, D. A., Levish, D. R., and Klinger, R. E. (2002). “Bayesian flood frequency analysis with paleohydrologic bound data.” Water Resources Research, Vol. 38, No. 5, pp. 16-1-16-3, DOI: 10.1029/2000wr000028.

    Google Scholar 

  • Parsons, T., Console, R., Falcone G., Murru, M., and Yamashina, K. I. (2012). “Comparison of characteristic and Gutenberg-Richter models for time-dependent M7.9 earthquake probability in the Nankai-Tokai subduction zone, Japan.” Geophysical Journal International, Vol. 190, No. 3, pp.1673–1688, DOI: 10.1111/j.1365-246x.2012.05595.x.

    Article  Google Scholar 

  • Parvez, I. A. (2007). “On the Bayesian analysis of the earthquake hazard in the North-East Indian peninsula.” Natural Hazards, Vol. 40, No. 2, pp. 397–412, DOI: 10.1007/s11069-006-9002-4.

    Article  Google Scholar 

  • Reis, J. D. S. and Stedinger, J. R. (2005). “Bayesian MCMC flood frequency analysis with historical information.” Journal of Hydrology, Vol. 313, No. 1, pp. 97–116, DOI: 10.1016/j.jhydrol.2005.02.028.

    Article  Google Scholar 

  • Shevchenko, G.V., Zolotukhin, D. E., and Tikhonov, I. N. (2013). “A method for the estimation of tsunami risk along Russia’s far east.” Journal of Tsunami Society International, Vol. 32, No. 4, pp. 212–220.

    Google Scholar 

  • Silbergleit, V. and Prezzi, C. (2012). “Statistics of major Chilean earthquakes recurrence.” Natural Hazards, Vol. 62, No. 2, pp. 445–458, DOI: 10.1007/s11069-012-0086-8.

    Article  Google Scholar 

  • Singh, C., Singh, A., and Chadha, R. K. (2009). “Fractal and b-value mapping in Eastern Himalaya and Southern Tibet.” Bulletin of the Seismological Society of America, Vol. 99, No. 6, pp. 3529–3533, DOI: 10.1785/0120090041.

    Article  Google Scholar 

  • Sornette, D., Knopoff, L., Kagan, Y. Y., and Vanneste, C. (1996). “Rankordering statistics of extreme events: Application to the distribution of large earthquakes.” Journal of Geophysical Research: Solid Earth (1978–2012), Vol. 101, No. B6, pp. 13883–13893, DOI: 10.1029/96jb00177.

    Article  Google Scholar 

  • Triep, E. G., and Sykes, L. R. (1997). “Frequency of occurrence of moderate to great earthquakes in intracontinental regions: Implications for changes in stress, earthquake prediction, and hazards assessments.” Journal of Geophysical Research: Solid Earth (1978–2012), Vol. 102, No. B5, pp. 9923–9948, DOI: 10.1029/96jb03900.

    Article  Google Scholar 

  • Tsapanos, T. M., Bayrak, Y., Cinar, H., Koravos, G. C., Bayrak, E., Kalogirou, E. E., Taspanou, A. V., and Vougiouka, G. E. (2014). “Analysis of largest earthquakes in Turkey and its vicinity by application of the Gumbel III distribution.” Acta Geophysica, Vol. 62, No. 1, pp. 59–82, DOI: 10.2478/s11600-013-0155-8.

    Article  Google Scholar 

  • Utsu, T. (1999) “Representation and analysis of the earthquake size distribution: a historical review and some new approaches.” Seismicity Patterns, their Statistical Significance and Physical Meaning, pp. 509–535, DOI: 10.1007/978-3-0348-8677-2_15.

    Chapter  Google Scholar 

  • Viglione, A., Merz, R., Salinas, J. L., and Blöschl, G. (2013). “Flood frequency hydrology: 3. A Bayesian analysis.” Water Resources Research, Vol. 49, No. 2, pp. 675–692, DOI: 10.1029/2011wr010782.

    Article  Google Scholar 

  • Yadav, R. B. S., Tsapanos, T. M., Bayrak, Y., and Koravos, G. C. (2013). “Probabilistic appraisal of earthquake hazard parameters deduced from a Bayesian approach in the northwest frontier of the Himalayas.” Pure and Applied Geophysics, Vol. 170, No. 3, pp. 283–297, DOI: 10.1007/s00024-012-0488-2.

    Article  Google Scholar 

  • Yoo, C., Jung, K. S., and Kim, T. W. (2005). “Rainfall frequency analysis using a mixed Gamma distribution: evaluation of the global warming effect on daily rainfall.” Hydrological Processes, Vol. 19, No. 19, pp. 3851–3861, DOI: 10.1002/hyp.6178.

    Article  Google Scholar 

  • Yoo, C., Kim, K., Kim, H. S., and Park, M. J. (2007). “Estimation of areal reduction factors using a mixed gamma distribution.” Journal of Hydrology, Vol. 335, Nos. 3–4, pp. 271–284, DOI: 10.1016/j.jhydrol.2006.11.026.

    Article  Google Scholar 

  • Zimbidis, A. A., Frangos, N. E. and Pantelous, A. A. (2007). “Modeling earthquake risk via extreme value theory and pricing the respective catastrophe bonds.” ASTIN Bulletin, Vol. 37, No. 1, pp. 163–184, DOI: 10.2143/ast.37.1.2020804.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Civil and Environmental Engineering, Hanyang University, Seoul, 133-791, Korea

    Ji Yae Shin & Si Chen

  2. Dept. of Civil and Environmental Engineering, Hanyang University, Ansan, 426-791, Korea

    Tae-Woong Kim

Authors
  1. Ji Yae Shin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Si Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tae-Woong Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tae-Woong Kim.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shin, J.Y., Chen, S. & Kim, TW. Application of Bayesian Markov Chain Monte Carlo method with mixed gumbel distribution to estimate extreme magnitude of tsunamigenic earthquake. KSCE J Civ Eng 19, 366–375 (2015). https://doi.org/10.1007/s12205-015-0430-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12205-015-0430-0

Keywords

Search

Navigation