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The deterministic nature of earthquake rupture


Understanding the earthquake rupture process is central to our understanding of fault systems and earthquake hazards. Multiple hypotheses concerning the nature of fault rupture have been proposed but no unifying theory has emerged1,2,3,4,5,6,7,8,9,10,11,12. The conceptual hypothesis most commonly cited is the cascade model for fault rupture1,3,10,13. In the cascade model, slip initiates on a small fault patch and continues to rupture further across a fault plane as long as the conditions are favourable. Two fundamental implications of this domino-like theory are that small earthquakes begin in the same manner as large earthquakes and that the rupture process is not deterministic—that is, the size of the earthquake cannot be determined until the cessation of rupture. Here we show that the frequency content of radiated seismic energy within the first few seconds of rupture scales with the final magnitude of the event. We infer that the magnitude of an earthquake can therefore be estimated before the rupture is complete. This finding implies that the rupture process is to some degree deterministic and has implications for the physics of the rupture process.

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Figure 1: Example waveform and τ p max calculation for a M 4.6 earthquake in southern California recorded at station GSC, 74 km from the epicentre.
Figure 2: Example waveform and τ p max calculation for the M w 8.3 Tokachi-oki earthquake, recorded at station HKD112, 71 km from the epicentre.
Figure 3: The relation between τpmax, τd and magnitude.


  1. Brune, J. N. Implications of earthquake triggering and rupture propagation for earthquake prediction based on premonitory phenomena. J. Geophys. Res. 84, 2195–2198 (1979)

    Article  ADS  Google Scholar 

  2. Fukao, Y. & Furumoto, M. Hierarchy in earthquake size distribution. Phys. Earth Planet. Inter. 37, 149–168 (1985)

    Article  ADS  Google Scholar 

  3. Ellsworth, W. L. & Beroza, G. C. Seismic evidence for an earthquake nucleation phase. Science 268, 851–855 (1995)

    Article  ADS  CAS  Google Scholar 

  4. Beroza, G. C. & Ellsworth, W. L. Properties of the seismic nucleation phase. Tectonophysics 261, 209–227 (1996)

    Article  ADS  Google Scholar 

  5. Dodge, D. A., Beroza, G. C. & Ellsworth, W. L. Detailed observations of California foreshock sequences: Implications for the earthquake initiation process. J. Geophys. Res. 101, 22371–22392 (1996)

    Article  ADS  Google Scholar 

  6. Mori, J. Rupture directivity and slip distribution of the M 4.3 foreshock to the 1992 Joshua Tree earthquake, Southern California. Bull. Seismol. Soc. Am. 86, 805–810 (1996)

    Google Scholar 

  7. Mori, J. & Kanamori, H. Initial rupture of earthquakes in the 1995 Ridgecrest, California sequence. Geophys. Res. Lett. 23, 2437–2440 (1996)

    Article  ADS  Google Scholar 

  8. Singh, S. K. et al. Implications of a composite source model and seismic-wave attenuation for the observed simplicity of small earthquakes and reported duration of earthquake initiation phase. Bull. Seismol. Soc. Am. 88, 1171–1181 (1998)

    Google Scholar 

  9. Steacy, S. J. & McCloskey, J. What controls an earthquake's size? Results from a heterogeneous cellular automaton. Geophys. J. Int. 133, F11–F14 (1998)

    Article  ADS  Google Scholar 

  10. Kilb, D. & Gomberg, J. The initial subevent of the 1994 Northridge, California, earthquake: Is earthquake size predictable? J. Seismol. 3, 409–420 (1999)

    Article  ADS  Google Scholar 

  11. Sato, T. & Kanamori, H. Beginning of earthquakes modeled with the Griffith's fracture criterion. Bull. Seismol. Soc. Am. 89, 80–93 (1999)

    Google Scholar 

  12. Ohnaka, M. A physical scaling relation between the size of an earthquake and its nucleation zone size. Pure Appl. Geophys. 157, 2259–2282 (2000)

    Article  ADS  Google Scholar 

  13. Ellsworth, W. L. & Beroza, G. C. Observation of the seismic nucleation phase in the Ridgecrest, California, earthquake sequence. Geophys. Res. Lett. 25, 401–404 (1998)

    Article  ADS  Google Scholar 

  14. Kanamori, H. The energy release in great earthquakes. J. Geophys. Res. 82, 2981–2987 (1977)

    Article  ADS  Google Scholar 

  15. Nakamura, Y. in Proc. 9th World Conf. Earthquake Eng. VII, 673–678 (1988).

  16. Allen, R. M. & Kanamori, H. The potential for earthquake early warning in southern California. Science 300, 786–789 (2003)

    Article  ADS  CAS  Google Scholar 

  17. Kanamori, H. The diversity of the physics of earthquakes. Proc. Jpn. Acad. B 80, 297–316 (2004)

    Article  Google Scholar 

  18. Nakamura, Y. in Proc. 13th World Conf. Earthquake Eng. Paper No. 908 (2004).

  19. Lockman, A. & Allen, R. M. Single station earthquake characterization for early warning. Bull. Seismol. Soc. Am. (in the press)

  20. Abercrombie, R. & Mori, J. Local observations of the onset of a large earthquake: 28 June 1992 Landers, California. Bull. Seismol. Soc. Am. 84, 725–734 (1994)

    Google Scholar 

  21. Eberhart-Phillips, D. et al. The 2002 Denali Fault Earthquake, Alaska: A large magnitude, slip-partitioned event. Science 300, 1113–1118 (2003)

    Article  ADS  CAS  Google Scholar 

  22. Nielsen, S. B. & Olsen, K. B. Constraints on stress and friction from dynamic rupture models of the 1994 Northridge, California, earthquake. Pure Appl. Geophys. 157, 2029–2046 (2000)

    Article  ADS  Google Scholar 

  23. Oglesby, D. D. & Day, S. M. Stochastic fault stress: Implications for fault dynamics and ground motion. Bull. Seismol. Soc. Am. 92, 3006–3021 (2002)

    Article  Google Scholar 

  24. Das, S. & Scholz, C. H. Why large earthquakes do not nucleate at shallow depths. Nature 305, 621–623 (1983)

    Article  ADS  Google Scholar 

  25. Mai, P. M., Spudich, P. & Boatwright, J. Hypocenter locations in finite-source rupture models. Bull. Seismol. Soc. Am. 95, 965–980 (2005)

    Article  Google Scholar 

  26. Kanamori, H., Maechling, P. & Hauksson, E. Continuous monitoring of ground-motion parameters. Bull. Seismol. Soc. Am. 89, 311–316 (1999)

    Google Scholar 

  27. Somerville, P., Irikura, K., Graves, R. P., Sawada, S. & Wald, D. Characterizing crustal earthquake slip models for the prediction of strong motion. Seismol. Res. Lett. 70, 59–80 (1999)

    Article  Google Scholar 

  28. Wells, D. L. & Coppersmith, K. J. New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bull. Seismol. Soc. Am. 84, 974–1002 (1994)

    Google Scholar 

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We thank H. Kanamori and S. Nielsen for discussions, and Y.-M. Wu and R. Hansen for making waveform data available for the study. The manuscript was improved by comments from R. Abercrombie and C. Scholz. Funding for this work was provided by the US Geological Survey NEHRP programme, the University of Wisconsin, Madison, and the University of California, Berkeley.

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Correspondence to Richard M. Allen.

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Supplementary Table 1

Earthquakes included in this study. (PDF 175 kb)

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Olson, E., Allen, R. The deterministic nature of earthquake rupture. Nature 438, 212–215 (2005).

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