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The deterministic nature of earthquake rupture

Nature volume 438, pages 212–215 (2005)Cite this article

Abstract

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 Ï„pmax, Ï„d and magnitude.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Geology and Geophysics, University of Wisconsin Madison, 1215 W. Dayton Street, Wisconsin, 53706, Madison, USA

    Erik L. Olson

  2. Department of Earth and Planetary Science, University of California Berkeley, 307 McCone Hall, California, 94720, Berkeley, USA

    Richard M. Allen

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  1. Erik L. Olson
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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). https://doi.org/10.1038/nature04214

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