Received wisdom relates that static stress change associated with an earthquake mainshock is the prime mover of its aftershocks. But a fresh look at the data points the finger at wave-surfing dynamic stress.
When a door is jammed, there are various things you can do to dislodge it — that is, to overcome the frictional resistance between it and its frame. You can nonchalantly push a bit harder (apply a static stress). Less elegantly, you can take a run at it and barge it open (apply a dynamic stress). And, if completely exasperated, you can rattle the handle back and forth (apply a cyclic stress). If you are already pushing very hard, it might take only a small extra heave or tap to free the door, leaving you making your entrance face down on the floor (feeling a large stress change from a small additional stress). Occasionally, tapping from the other side (applying a negative stress) can also help. Lastly, if you lean on the door long enough, it can give way spontaneously (through environmentally assisted weakening processes).
Such is the complexity of the physics of friction, even for a single pair of surfaces in contact. In this issue, Felzer and Brodsky (page 735)1 try to pin down the relative contribution of some of these effects in a more complex context: the triggering of earthquake aftershocks. They examine the rate of decay with distance from the epicentre of the frequency of aftershocks following small and medium-sized earthquakes in the southern Californian catalogue. Their conclusion is that dynamic stresses radiated by seismic waves from the original shock dominate the aftershock-triggering mechanism over a wide range of distances between 0.2 and 50 kilometres from the fault rupture.
This comes as something of a surprise. From basic ‘dislocation theory’ for an earthquake source, one would expect the static stress changes induced by movement of rock in the original event to dominate aftershock generation near the fault. The effect of static stress should, compared with that of dynamic stress, decay quickly with distance: dynamic stress is transported over large distances by seismic waves.
If the orientations of both the original and a potential fault are known, dislocation theory can be used to calculate the changes induced by an earlier event in the static stress along, and at right angles to, the potential fault. By adding these up in a given proportion to define a resultant ‘Coulomb’ stress change, it is possible to assess whether these changes have brought a fault closer to failure2. This method has been used in several case studies to predict the location both of aftershocks (defined as being smaller than a mainshock) and more general triggered events (which can be the same size as, or very occasionally larger than, a triggering event).
Such studies often assume that triggered events are more likely when a fault is optimally oriented for failure from the start3. In real-life examples, the extra shove needed for triggering that emerges from these models often seems implausibly small: the largest aftershock of the Sumatra–Andaman earthquake of Boxing Day 2004, for instance, occurred where Coulomb stress was predicted to have increased by 104 Pa — just a tenth of atmospheric pressure4. Accordingly, ‘rate and state friction’5, a phenomenon observed in the laboratory in which friction between rocks depends on slide velocity, has been invoked as a temporary stress-amplification effect3. An alternative hypothesis has it that the locations of triggered events are already primed to be in a near-critical state, making them susceptible to small stress perturbations2. A combination of both effects is also a possibility.
But although the static triggering hypothesis works for earthquake pairs in many individual case studies, the method only marginally improves predictions of the location of large triggered events. A global study, based on a representative sample of earthquakes with known fault-plane orientations in the Centroid Moment Tensor (CMT) catalogue, found that only 61% of the triggered events occurred in areas of increased Coulomb stress6. Similarly, an analysis of all the CMT catalogue events showed no strong directional dependence of triggering frequency relative to the orientation of the potential mainshock fault planes7.
One suggestion is that static triggering works better when the effects of several — temporally distinct — large earthquakes are superimposed and short-range triggering effects (within one fault length) dominate. An example is a sequence of earthquakes that has worked along the North Anatolian fault in the past few hundred years, and which has focused attention on the next potential ‘domino’ in the line — in the Sea of Marmara near Istanbul8.
Felzer and Brodsky take a different tack1. First, they look at aftershocks of small and medium-sized events, where the sampling statistics are good. Second, they ignore the direction of the aftershocks, and concentrate on how the frequency of triggered events declines with increasing distance. They also restrict the maximum range considered to avoid contamination from background random seismicity, and, importantly, they use a new, extremely accurate catalogue of events9 with epicentres pinpointed to within some tens of metres.
The authors conclude that the frequency of aftershocks decays with distance as a single inverse power law with an exponent of around −1.35. This decay is too gradual to be attributed to static stresses, which would in any case be implausibly tiny (less than 10 Pa) in the case of distant aftershocks of small events. But the exponent is consistent with the rate of attenuation of the maximum amplitude of seismic waves with distance when geometric spreading and wave absorption and scattering effects are taken into account. This implies that dynamic, rather than static, stress is the culprit.
Further work is required to pin down the exact mechanisms at work, however — notably the relative contributions to aftershock triggering of surface waves and shear waves (which travel through Earth's interior) emanating from a mainshock. Surface waves are in general more dispersed than shear waves, and, to return to the analogy of the door, apply more of an extended rattle than a sharp tap. They also decay in amplitude more slowly with distance, and their direction does not depend so strongly on the orientation of the original fault. Systematic variations in the frequency content and duration of the wave field could explain some of the scatter observed in the data obtained by Felzer and Brodsky1. The nature of aftershocks at distances greater than 50 kilometres, where the data are dominated by background noise and are thus not considered by the authors, also needs attention. This will become possible only in the future, as more data on such distant aftershocks are required.
Dynamic stress transfer alone cannot explain the observed delay time for large events, or the observation of a power-law decay of the number of aftershocks with time — exactly the form predicted by the static processes of rate and state friction10 and environmentally assisted crack growth11. Nevertheless, Felzer and Brodsky's work goes some way to satisfying us that earthquake aftershocks from small and moderate-sized original shocks, at least, are most likely to be triggered by a mechanism that is carried along on the crest of a wave.