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Testing time-predictable earthquake recurrence by direct measurement of strain accumulation and release


Probabilistic estimates of earthquake hazard use various models for the temporal distribution of earthquakes, including the ‘time-predictable’ recurrence model formulated by Shimazaki and Nakata1 (which incorporates the concept of elastic rebound described as early as 1910 by H. F. Reid2). This model states that an earthquake occurs when the fault recovers the stress relieved in the most recent earthquake. Unlike time-independent models (for example, Poisson probability), the time-predictable model is thought to encompass some of the physics behind the earthquake cycle, in that earthquake probability increases with time. The time-predictable model is therefore often preferred when adequate data are available, and it is incorporated in hazard predictions for many earthquake-prone regions, including northern California3, southern California4,5, New Zealand6 and Japan7. Here we show that the model fails in what should be an ideal locale for its application — Parkfield, California. We estimate rigorous bounds on the predicted recurrence time of the magnitude 6 1966 Parkfield earthquake through inversion of geodetic measurements and we show that, according to the time-predictable model, another earthquake should have occurred by 1987. The model's poor performance in a relatively simple tectonic setting does not bode well for its successful application to the many areas of the world characterized by complex fault interactions.

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Figure 1: Parkfield segment of the San Andreas fault.
Figure 2: Bootstrap distributions for moment, moment deficit rate, and inter-event time.
Figure 3: Constrained inversion and bootstrap procedure.
Figure 4: Approximate joint probability density function (indicated on contours) for transition depth and deep slip-rate.

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  1. Shimazaki, K. & Nakata, T. Time-predictable recurrence model for large earthquakes. Geophys. Res. Lett. 7, 279–282 (1980)

    Article  ADS  Google Scholar 

  2. Reid, H. F. The California Earthquake of April 18, 1906 Report of the state earthquake investigation commission Vol. 2 (Carnegie Institute, Washington DC, 1910)

    Google Scholar 

  3. Working Group on California Earthquake Probabilities Earthquake probabilities in the San Francisco Bay Region: 2000 to 2030 – A summary of findings US Geological Survey open-file report 99-517 (USGS, Reston, VA, 1999)

    Google Scholar 

  4. Working Group on California Earthquake Probabilities Seismic hazards in southern California: probable earthquakes, 1994 to 2024. Bull. Seismol. Soc. Am. 85, 379–439 (1995)

    Google Scholar 

  5. Cramer, C. H., Petersen, M. D., Tianqing, C., Toppozada, T. R. & Reichle, M. A time-dependent probabilistic seismic-hazard model for California. Bull. Seismol. Soc. Am. 90, 1–21 (2000)

    Article  Google Scholar 

  6. Stirling, M. W. Proc. 12th World Conference on Earthquake Engineering (New Zealand Society for Earthquake Engineering, Pergamon, Oxford, 2000)

    Google Scholar 

  7. Annaka, T. & Yashiro, H. Risk Analysis (eds Rubio, J. L.Brebbia, C. A. and Uso, J-L.) (WIT Press, Boston, 1998)

    Google Scholar 

  8. Segall, P. & Harris, R. Earthquakes deformation cycle on the San Andreas fault near Parkfield, California. J. Geophys. Res. 92, 10511–10525 (1987)

    Article  ADS  Google Scholar 

  9. Bakun, W. H. & McEvilly, T. V. Recurrence models and Parkfield, California, earthquakes. J. Geophys. Res. 89, 3051–3058 (1984)

    Article  ADS  Google Scholar 

  10. Roeloffs, E. & Langbein, J. The earthquake prediction experiment at Parkfield, California. Rev. Geophys. 32, 315–336 (1994)

    Article  ADS  Google Scholar 

  11. King, N. E., Segall, P. & Prescott, W. Geodetic measurements near Parkfield, California, 1959-1984. J. Geophys. Res. 92, 2747–2766 (1987)

    Article  ADS  Google Scholar 

  12. Murray, J. R., Segall, P., Cervelli, P., Prescott, W. & Svare, J. Inversion of GPS data for spatially variable slip-rate on the San Andreas fault near Parkfield, CA. Geophys. Res. Lett. 28, 359–362 (2001)

    Article  ADS  Google Scholar 

  13. Harris, R. A. & Segall, P. Detection of a locked zone at depth on the Parkfield, California, segment of the San Andreas fault. J. Geophys. Res. 92, 7945–7962 (1987)

    Article  ADS  Google Scholar 

  14. Snay, R. A. Enhancing the geodetic resolution of fault slip by introducing prior information. Manuscr. Geodetica 14, 391–403 (1989)

    Google Scholar 

  15. Savage, J. C. Equivalent strike-slip earthquake cycles in half-space and lithosphere-asthenosphere Earth models. J. Geophys. Res. 95, 4873–4879 (1990)

    Article  ADS  Google Scholar 

  16. Johnson, H. O., Agnew, D. C. & Hudnut, K. Extremal bounds on earthquake movement from geodetic data: Application to the Landers earthquake. Bull. Seismol. Soc. Am. 84, 660–667 (1994)

    ADS  Google Scholar 

  17. Efron, B. & Tibshirani, R. J. An Introduction to the Bootstrap: Monographs on Statistics and Applied Probability 57 (Chapman and Hall, New York, 1993)

    Book  Google Scholar 

  18. Segall, P. & Du, Y. How similar were the 1934 and 1966 Parkfield earthquakes? J. Geophys. Res. 98, 4527–4538 (1993)

    Article  ADS  Google Scholar 

  19. Tsai, Y.-B. & Aki, K. Simultaneous determination of the seismic moment and attenuation of seismic surface waves. Bull. Seismol. Soc. Am. 59, 275–287 (1969)

    Google Scholar 

  20. Smith, S. W. & Wyss, M. Displacement on the San Andreas fault subsequent to the 1966 Parkfield earthquake. Bull. Seismol. Soc. Am. 58, 1955–1973 (1968)

    Google Scholar 

  21. Rice, J. R. & Ruina, A. L. Stability of steady frictional sliding. J. Appl. Mech. Trans. ASME 50, 343–349 (1983)

    Article  ADS  Google Scholar 

  22. Dieterich, J. & Kilgore, B. Implications of fault constitutive properties for earthquake prediction. Proc. Natl Acad. Sci. USA 93, 3787–3794 (1996)

    Article  ADS  CAS  Google Scholar 

  23. Dieterich, J. A constitutive law for rate of earthquake production and its application to earthquake clustering. J. Geophys. Res. 99, 2601–2618 (1994)

    Article  ADS  Google Scholar 

  24. Simpson, R. W., Schulz, S. S., Dietz, L. D. & Burford, R. O. The response of creeping parts of the San Andreas Fault to earthquakes on nearby faults: Two examples. Pure Appl. Geophys. 126, 665–685 (1988)

    Article  ADS  Google Scholar 

  25. Toda, S. & Stein, R. Response of the San Andreas fault to the 1983 Coalinga-Nuñez earthquakes: An application of interaction-based probabilities for Parkfield. J. Geophys. Res. 107, 10.1029/2001 JB000172, 2002

  26. Gao, S., Silver, P. G. & Linde, A. T. Analysis of deformation data at Parkfield, California: Detection of a long-term strain transient. J. Geophys. Res. 105, 2955–2967 (2000)

    Article  ADS  Google Scholar 

  27. Ben-Zion, Y., Rice, J. R. & Dmowska, R. Interaction of the San Andreas fault creeping segment with adjacent great rupture zones and earthquake recurrence at Parkfield. J. Geophys. Res. 98, 2135–2144 (1993)

    Article  ADS  Google Scholar 

  28. Cole, A. T. & Ellsworth, W. L. Earthquake clustering and the long-term evolution of seismicity near Parkfield, California, 1931-1994. Seismol. Res. Lett. 66, 28 (1995)

    Article  Google Scholar 

  29. Wahba, G. Spline Models for Observational Data (Society for Industrial and Applied Mathematics, Philadelphia, 1990)

    Book  Google Scholar 

  30. Ellsworth, W., Waldhauser, F. & Cole, A. A new view of the San Andreas Fault: Implications for earthquake interaction at Parkfield. Extended abstract for the 17th Course of the International School of Geophysics “Fault Interaction by Stress Transfer: New Horizons for Understanding Earthquake Occurrence”, Ettore Majorana Foundation and Centre for Scientific Culture, Erice, Italy, 17--23 June 2000.

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We thank P. Cervelli, J. Savage, R. Tibshirani, J. Langbein, W. Prescott, J. Svarc and H. Johnson for comments and advice. Funding was provided by Stanford University Graduate Fellowships and a USGS National Earthquake Hazards Reduction Program grant.

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Correspondence to Jessica Murray.

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Murray, J., Segall, P. Testing time-predictable earthquake recurrence by direct measurement of strain accumulation and release. Nature 419, 287–291 (2002).

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