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Decay of aftershock density with distance does not indicate triggering by dynamic stress


Resolving whether static1,2,3 or dynamic4,5,6,7,8 stress triggers most aftershocks and subsequent mainshocks is essential to understand earthquake interaction and to forecast seismic hazard9. Felzer and Brodsky10 examined the distance distribution of earthquakes occurring in the first five minutes after 2 ≤ M < 3 and 3 ≤ M < 4 mainshocks and found that their magnitude M ≥ 2 aftershocks showed a uniform power-law decay with slope −1.35 out to 50 km from the mainshocks. From this they argued that the distance decay could be explained only by dynamic triggering. Here we propose an alternative explanation for the decay, and subject their hypothesis to a series of tests, none of which it passes. At distances more than 300 m from the 2 ≤ M < 3 mainshocks, the seismicity decay 5 min before the mainshocks is indistinguishable from the decay five minutes afterwards, indicating that the mainshocks have no effect at distances outside their static triggering range. Omori temporal decay, the fundamental signature of aftershocks, is absent at distances exceeding 10 km from the mainshocks. Finally, the distance decay is found among aftershocks that occur before the arrival of the seismic wave front from the mainshock, which violates causality. We argue that Felzer and Brodsky10 implicitly assume that the first of two independent aftershocks along a fault rupture triggers the second, and that the first of two shocks in a creep- or intrusion-driven swarm triggers the second, when this need not be the case.

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Figure 1: Alternative explanations for the distance decay of seismicity density.
Figure 2: Distance decay in Japan during 5-min and 1-s periods.
Figure 3: Comparison of earthquakes 5 min before and after mainshocks.
Figure 4: Omori decay for near-field and remote seismicity.
Figure 5: Map of nominal ‘mainshock–aftershock’ pairs.


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We thank K. Felzer, E. Brodsky, D. Jackson, S. Steacy, J. Hardebeck, R. Harris, and I. Main for comprehensive reviews; and Z. Peng, J. Vidale and Y. Okada for comments.

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Correspondence to Keith Richards-Dinger.

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Richards-Dinger, K., Stein, R. & Toda, S. Decay of aftershock density with distance does not indicate triggering by dynamic stress. Nature 467, 583–586 (2010).

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