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

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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.


  1. 1

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

  2. 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)

  3. 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)

  4. 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)

  5. 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)

  6. 6

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

  7. 7

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

  8. 8

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

  9. 9

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

  10. 10

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

  11. 11

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

  12. 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)

  13. 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)

  14. 14

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

  15. 15

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

  16. 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)

  17. 17

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

  18. 18

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

  19. 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)

  20. 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)

  21. 21

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

  22. 22

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

  23. 23

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

  24. 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)

  25. 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. 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)

  27. 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)

  28. 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)

  29. 29

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

  30. 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) doi:10.1038/nature00984

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