1. Department of Geology and Geophysics, University of Wisconsin Madison, 1215 W. Dayton Street, Madison, Wisconsin 53706, USA
2. Department of Earth and Planetary Science, University of California Berkeley, 307 McCone Hall, Berkeley, California 94720, USA

Correspondence to: Richard M. Allen² Correspondence and requests for materials should be addressed to R.M.A. (Email: rallen@berkeley.edu).

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 emerged^{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. The conceptual hypothesis most commonly cited is the cascade model for fault rupture^{1, 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.

1. Department of Geology and Geophysics, University of Wisconsin Madison, 1215 W. Dayton Street, Madison, Wisconsin 53706, USA
2. Department of Earth and Planetary Science, University of California Berkeley, 307 McCone Hall, Berkeley, California 94720, USA

Correspondence to: Richard M. Allen² Correspondence and requests for materials should be addressed to R.M.A. (Email: rallen@berkeley.edu).

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