Natural Hazards

, Volume 69, Issue 3, pp 1335–1350 | Cite as

A study of earthquake inter-occurrence times distribution models in Taiwan

  • Chi-Hsuan Chen
  • Jui-Pin Wang
  • Yih-Min Wu
  • Chung-Han Chan
  • Chien-Hsin Chang
Original Paper

Abstract

Statistical studies on earthquake recurrence time probabilities have frequently been applied to seismic hazard analyses. In Taiwan, an instrumental catalog provides a good opportunity to examine statistical attributes of earthquakes around the study region, with the objective to evaluate the seismic risk and earthquake potential for hazard mitigation. With the completeness of recordings, seismic rates for small-to-moderate magnitudes can be obtained. An elimination of aftershocks was performed using a double-link cluster analysis method. The time intervals between a series of events (the inter-occurrence periods) are stationary with an identical temporal distribution. Based on the goodness-of-fit testing between a few models and observation, we suggested the use of the Gamma distribution in modeling this variable, earthquake inter-occurrence periods, for the study region. Accordingly, unified relationship was constructed, and statistical limitations of sparse sampling for devastating earthquakes (such as M ≥ 6.0 or 7.0) could be resolved. The empirical result evaluated by introducing the conditional probability indicates that the recurrence probability of a M ≥ 7.0 earthquake is 78.8 % within 10 years in Taiwan region.

Keywords

Statistical seismology Inter-occurrence periods Gamma distribution Recurrence probability 

Notes

Acknowledgments

We thank Paul Wessel and Walter Smith for developing and supporting the GMT mapping tools. This work was supported by Central Geological Survey, Central Weather Bureau, and the National Science Council, Taiwan. We thank Prof. Thomas Glade and two anonymous reviewers for their constructive comments.

References

  1. Bak P, Tang C (1989) Earthquakes as a self-organized critical phenomenon. J Geophys Res 94(B11):15635–15637CrossRefGoogle Scholar
  2. Bak P, Christensen K, Danon L, Scanlon T (2002) Unified scaling law for earthquakes. Phys Rev Lett 88(178501):1–4Google Scholar
  3. Chakravarti IM, Laha RG, Roy J (1967) Handbook of methods of applied statistics, vol 1. Wiley, Volume I, pp 392–394Google Scholar
  4. Cheng SN, Wang TB, Lin TW, Jiang CH (2010) Establishment of Taiwan earthquake catalog, vol 54. Seismology Technical Report of Central Weather Bureau, pp 575–605Google Scholar
  5. Corral Á (2004) Long-term clustering, scaling, and universality in the temporal occurrence of earthquakes. Phys Rev Lett 92:108501CrossRefGoogle Scholar
  6. Corral Á (2006) Dependence of earthquake recurrence times and independence of magnitudes on seismicity history. Tectonophys 424:177–193CrossRefGoogle Scholar
  7. Davis SD, Frohlich C (1991) Single-link cluster analysis of earthquake aftershocks: decay laws and regional variations. J Geophys Res 96:6336–6350Google Scholar
  8. Dieterich JH (1994) A constitutive law for rate of earthquake production and its application to earthquake clustering. J Geophys Res 99(B2):2601–2618CrossRefGoogle Scholar
  9. Field EH (2007) Overview of the working group for the development of regional earthquake likelihood models (RELM). Seismol Res Lett 78(1):7–16CrossRefGoogle Scholar
  10. Gutenberg B, Richter CF (1944) Frequency of earthquakes in California. Bull Seismol Soc Am 34:185–188Google Scholar
  11. Hagiwara Y (1974) Probability of earthquake occurrence as obtained from Weibull distribution analysis of crustal strain. Tectonophys 23:313–318CrossRefGoogle Scholar
  12. Hasumi T, Akimoto T, Aizawa Y (2009a) The Weibull-log Weibull transition of the interoccurrence time statistics in the two-dimensional Burridge-Knopoff Earthquake model. Phys A 388:483–490CrossRefGoogle Scholar
  13. Hasumi T, Akimoto T, Aizawa Y (2009b) The Weibull-log Weibull distribution for interoccurrence times of earthquakes. Phys A 388:491–498CrossRefGoogle Scholar
  14. Hasumi T, Chen CC, Akimoto T, Aizawa Y (2010) The Weibull-log Weibull transition of interoccurrence time for synthetic and natural earthquakes. Tectonophys 485:9–16CrossRefGoogle Scholar
  15. Hsu MT (1961) Seismicity in Taiwan (Formosa). Bull Earthq Res Int Tokyo Univ 29:831–847Google Scholar
  16. Jackson DD, Kagan YY (1999) Testable earthquake forecasts for 1999. Seismol Res Lett 70(4):393–403CrossRefGoogle Scholar
  17. Jacob KH (1984) Estimates of long-term probabilities for future great earthquakes in the Aleutians. Geophys Res Lett 11:295–298CrossRefGoogle Scholar
  18. Jordan TH (2006) Earthquake predictability, brick by brick. Seismol Res Lett 77(1):3–6CrossRefGoogle Scholar
  19. Kagan YY, Knopoff L (1981) Stochastic synthesis of earthquake catalogs. J Geophys Res 86:2853–2862CrossRefGoogle Scholar
  20. Kagan YY, Knopoff L (1987) Statistical short-term earthquake prediction. Science 236(4808):1563–1567CrossRefGoogle Scholar
  21. Knopoff L, Kagan Y, Knopoff R (1982) b-values for fore- and aftershocks in real and simulated earthquake sequences. Bull Seismol Soc Am 72:1663–1676Google Scholar
  22. Lin CH (1996) Crustal structures estimated from arrival differences of the first P-waves in Taiwan. J Geol Soc China 39:1–12Google Scholar
  23. Ogata Y (1988) Statistical models for earthquake occurrence and residual analysis for point processes. J Am Stat As 83:9–27CrossRefGoogle Scholar
  24. Pacheco JF, Scholz CH, Sykes LR (1992) Changes in frequency-size relationship from small to large earthquakes. Nature 355:71–73CrossRefGoogle Scholar
  25. Purcaru G (1975) A new magnitude-frequency relation for earthquakes and a classification of relation types. Geophys J R Astron Soc 42:61–79CrossRefGoogle Scholar
  26. Rhoades DA, Gerstenberger MC (2009) Mixture models for improved short-term earthquake forecasting. Bull Seismol Soc Am 99(2):636–646CrossRefGoogle Scholar
  27. Rikitake T (1974) Probability of an earthquake occurrence as estimated from crustal strain. Tectonophys 23:299–312CrossRefGoogle Scholar
  28. Saichev A, Sornette D (2006) Universal distribution of inter-earthquake times explained. Phys Rev Lett 97:078501CrossRefGoogle Scholar
  29. Savage JC (1992) The uncertainty in earthquake conditional probabilities. Geophys Res Lett 19:709–712CrossRefGoogle Scholar
  30. Schwartz DP, Coppersmith KJ (1984) Fault behavior and characteristic earthquakes-examples from the Wasatch and San Andreas fault zones. J Geophys Res 89:5681–5698CrossRefGoogle Scholar
  31. Shimazaki K, Nakata T (1980) Time-predictable recurrence model for large earthquakes. Geophys Res Lett 7:279–282CrossRefGoogle Scholar
  32. Snedecor GW, Cochran WG (1989) Statistical methods, 8th edn. Iowa State University Press, IowaGoogle Scholar
  33. Stephens MA (1974) EDF statistics for goodness of fit and some comparisons. J Am Stat As 69:730–737CrossRefGoogle Scholar
  34. Talbi A, Yamazaki F (2009) Sensitivity analysis of the parameters of earthquake recurrence time power law scaling. J Seismol 13(1):53–72CrossRefGoogle Scholar
  35. Ustaszewski K, Wu YM, Suppe J, Huang HH, Chang CH, Carena S (2012) Crust-mantle boundaries in the Taiwan–Luzon arc-continent collision system determined from local earthquake tomography and 1D models: Implications for the mode of subduction polarity reversal. Tectonophysics. doi:10.1016/j.tecto.2011.12.029 (in press)
  36. Utsu T (1972) Large earthquakes near Hokkaido and the expectancy of the occurrence of a large earthquake of Nemuro. Rep Coord Comm Earthq Predict 7:7–13Google Scholar
  37. Utsu T (1974) A three-parameter formula for magnitude distribution of earthquake. J Phys Earth 22:71–85CrossRefGoogle Scholar
  38. Utsu T, Ogata Y, Matsuura S (1995) The centenary of the Omori formula for a decay law of aftershock activity. J Phys Earth 43:1–33CrossRefGoogle Scholar
  39. Wang JH (1989) The Taiwan telemetered seismographic network. Phys Earth Planet Inter 58:9–18CrossRefGoogle Scholar
  40. Wang CY, Shin TC (1998) Illustrating 100 years of Taiwan Seismicity. Terr Atmos Ocean Sci 9:589–614Google Scholar
  41. Wang JP, Chan CH, Wu YM (2011) The distribution of annual maximum earthquake magnitude around Taiwan and its application in the estimation of catastrophic earthquake recurrence probability. Nat Hazard. doi:10.1007/s11069-011-9776-x Google Scholar
  42. Wiemer S (2001) A software package to analyse seismicity: ZMAP. Seismol Res Lett 72:373–382CrossRefGoogle Scholar
  43. Wiemer S, Wyss M (2000) Minimum magnitude of completeness in earthquake catalogs: examples from Alaska, the Western United States, and Japan. Bull Seismol Soc Am 90(4):859–869CrossRefGoogle Scholar
  44. Wu YM, Chen CC (2007) Seismic reversal pattern for the 1999 Chi–Chi, Taiwan, Mw7.6 earthquake. Tectonophys 429:125–132CrossRefGoogle Scholar
  45. Wu YM, Chiao LY (2006) Seismic quiescence before the 1999 Chi–Chi, Taiwan Mw7.6 earthquake. Bull Seismol Soc Am 96:321–327CrossRefGoogle Scholar
  46. Wu YM, Chen CC, Zhao L, Chang CH (2008a) Seismicity characteristics before the 2003 Chengkung, Taiwan, earthquake. Tectonophys 457:177–182CrossRefGoogle Scholar
  47. Wu YM, Chang CH, Zhao L, Teng TL, Nakamura M (2008b) A comprehensive relocation of earthquakes in Taiwan from 1991 to 2005. Bull Seismol Soc Am 98:1471–1481CrossRefGoogle Scholar
  48. Yeh YH, Tsai YB (1981) Crustal structures of central Taiwan from inversion of P-wave arrival times. Bull Inst Earth Sci 1:83–102Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Chi-Hsuan Chen
    • 1
    • 2
  • Jui-Pin Wang
    • 3
  • Yih-Min Wu
    • 1
  • Chung-Han Chan
    • 1
  • Chien-Hsin Chang
    • 4
  1. 1.Department of GeosciencesNational Taiwan UniversityTaipeiTaiwan
  2. 2.Central Geological SurveyMinistry of Economic AffairsNew Taipei CityTaiwan
  3. 3.Department of Civil and Environmental EngineeringThe Hong Kong University of Science and TechnologyKowloonHong Kong
  4. 4.Central Weather BureauTaipeiTaiwan

Personalised recommendations