Earthquakes often induce aftershocks on other faults, but the mechanisms remain elusive. An innovative analysis tells us more about the effects of dynamic stresses caused by the passage of seismic waves.
How does an earthquake on one fault affect the likelihood of failure on nearby faults? In tackling this question, Kilb et al.1 (page 570 of this issue) distinguish between two different triggering effects and document the possible influence of one of them — seismic waves.
For anyone who has ever sat down with a child to play Don't Spill The Beans — a game in which players take turns adding beans to a shallow pot that pivots like a see-saw — it will be no surprise that earthquake triggering depends on some details of the initial earthquake rupture. In Don't Spill The Beans, dropping a bean in the pot is more likely to cause a spill than carefully adding one over the pot's pivot, even though the static load is the same in both cases. Likewise, if fault slip occurs slowly and without dynamic shaking (add that bean cautiously) the question is whether the static stress transferred to the surroundings is enough to cause failure on neighbouring faults. But earthquakes also produce seismic waves which cause intense shaking in the immediate region of the fault concerned. These dynamic stresses might also trigger aftershocks —rather like bumping the pot.
A key problem in earthquake triggering is that of understanding the effects of static stress transfer compared with those of dynamic stresses and shaking-induced fault weakening. Until now, distinguishing between these effects has been possible only when the secondary earthquake is triggered far from the original2. In this situation, changes in static stress are negligible; only dynamic stresses are significant. But 'directivity', which can amplify shaking in the direction of earthquake rupture, provides a way to distinguish between dynamic and static stresses close to an earthquake. Kilb and co-workers1 apply this approach to the magnitude 7.3 Landers earthquake of 1992. They find that aftershocks are more likely in areas of high dynamic shaking — as long as the change in static stress does not have the opposite effect and inhibit fault failure.
Research on earthquake triggering and fault interaction has been driven in part by the need to understand changes in seismic hazard on human timescales. The situation is particularly clear in the San Francisco Bay area ( Fig. 1, overleaf): a large earthquake on either the San Andreas or the Hayward fault could increase or decrease seismic risk across the entire area. But how do we codify fault interaction, and what causes one earthquake to trigger another?
One factor is surely the transfer of static (ambient) stresses3,4. Earthquakes release the stresses supported by faults and, because earthquakes are shear failures — slip parallel to the fault dominates over any net perpendicular (normal) motion — they primarily alter the shear stresses parallel to the fault. But on some faults both the normal and shear stresses are affected. Fault strength is a friction problem, so understanding earthquake triggering by stress transfer involves evaluating whether the change in so-called Coulomb failure stress (shear stress plus normal stress multiplied by the coefficient of friction) is enough to cause fault failure or inhibit it. Close to a rupture, where the potential for damaging aftershocks is greatest, the change in static stress may be of the same order as the amplitude of dynamic shaking (see Fig. 1 of the paper on page 570). So in this circumstance, aftershocks could be the result of changes in static stresses, dynamic stresses or both.
Kilb and co-workers1 show how the question can be addressed in the immediate vicinity of large earthquakes. They also introduce a new wrinkle by explicitly acknowledging that the frictional properties of faults are likely to be altered by dynamic shaking. Their thinking is sound — we have all seen stubborn jar lids come off after a good whack against the kitchen counter — but the principle has been difficult to test with previous methods and data.
In theory, the effects of dynamic stresses carried by seismic waves can be evaluated using the Coulomb failure stress and the approach developed for static stresses. But two difficulties arise.
First, the most sensitive way to evaluate fault interactions is to measure changes in the rate of seismicity. Ideally, one would evaluate variations in seismicity rate as a function of time, in the form of Fig. 1 of Kilb and co-workers, and compare them directly with the dynamic (time varying) and static Coulomb failure stress. But in most cases it is not possible to measure seismicity rates with sufficient temporal resolution. Second, we do not expect instantaneous failure of another fault, even when the stresses exceed a nominal threshold. Modern friction laws5 show that brittle frictional strength depends on strain-rate and slip history in a way that produces delayed failure in many cases. The effects are small, but critical to the initiation of earthquake-like instabilities6.
Kilb et al. have taken advantage of strong rupture directivity in the Landers earthquake to distinguish between dynamic and static stresses. Directivity effects become significant when the speed of rupture propagation approaches that of radiated seismic waves. Dynamic stress amplitudes are increased in the propagation direction, but static stresses are unaffected. The Landers mainshock propagated from southeast to northwest, producing much greater shaking to the northwest. Kilb et al. show that this region of high dynamic stressing extended at least 100 km from the end of the mainshock, producing large differences in the spatial pattern of static and dynamic stresses, and identifiable aftershocks to the northwest.
In the same way that increases in Coulomb stress promote fault failure, stress decreases should inhibit failure, and one factor that Kilb and co-workers do not address is such 'stress shadowing'3. Proponents of static-stress-transfer hypotheses for fault interaction point out that neither dynamic stress transfer nor fault-weakening by dynamic shaking can explain stress shadows. This could seem a criticism of Kilb et al.'s approach. But to my mind it is unlikely that dynamic stressing would produce stress shadows in any case: dynamic shaking is likely to strengthen faults only under unusual conditions. One way to prove the role of dynamic weakening would be to document a shaking-induced increase in seismicity within a static stress shadow, but this would be difficult given present data limitations.
Distinguishing between the influence of static and dynamic stresses in earthquake triggering is intriguing, and may help in building a more general understanding of fault interaction. In the future, initiatives such as EarthScope7 should allow detailed study of surface deformation and earthquake-induced strain changes in the Earth's crust. Those data, and more work of the sort reported by Kilb et al., will shed further light on earthquake triggering and the associated changes in seismic hazard.
Kilb, D., Gomberg, J. & Bodin, P. Nature 408, 570– 574 (2000).
Hill, D. P. et al. Science 260, 1617– 1623 (1993).
Stein, R. S. Nature 402, 605–609 ( 1999).
Harris, R. A. J. Geophys. Res. 103, 24347–24358 (1998).
Marone, C. Annu. Rev. Earth Planet. Sci. 26, 643– 696 (1998).
Scholz, C. H. Nature 391, 37–42 ( 1998).
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