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Earthquakes

Relationships in a slow slip

The size and duration of disparate, slow, low-amplitude earthquake processes seem to obey a single scaling law. The relationship is very different from that which governs their more violent and impulsive cousins.

Subduction zones — those regions of Earth's crust where one tectonic plate dives beneath another — are usually associated with frequent and violent earthquake activity. But not always. Occasionally, the downgoing tectonic plate lurches slowly, smoothly and almost silently under the overriding plate, accompanied by weak bursts of tremors1,2. These subtle episodes of tremors and slow slip, low in amplitude (and therefore only recently discovered), but lasting up to months, are sometimes associated with as much deformation as a magnitude-7 regular earthquake.

In this issue, Ide et al. (page 76)3 present the first compilation of these slow processes' fundamental seismic parameters, and obtain relationships between them that are very different from those of regular earthquakes. These investigations are of more than academic interest: the slow-slip processes might signal times of enhanced probability for potentially hazardous regular earthquakes4, and the zone where they are active might delineate the lower boundary of the locked zone storing stress for the next megathrust earthquake5.

The fundamental descriptive parameters of regular earthquakes, such as size and duration, follow relationships over many orders of magnitude called scaling laws6. The primary measure of earthquake size, its seismic moment, is calculated by multiplying the rock rigidity, the slipping area and the amount of lateral slip, known as the fault offset. Slipping area and fault offset vary greatly, so the seismic moment itself varies over more than ten orders of magnitude. Another crucial parameter, the velocity of a rupture's propagation, is quasi-constant: it is controlled dynamically by the seismic waves generated by the already broken and slipping portion of the fault, which travel at a constant velocity set by the rock's material properties. Over a wide range of sizes, therefore, the fault length involved in an earthquake is proportional to the earthquake's duration. Furthermore, a rough proportionality between fault offset and fault length leads to a well-known scaling law: earthquake duration is proportional to the cube-root of seismic moment6,7.

For slow-slip events, on the other hand, the control by dynamic waves is absent. The relations between seismic moment, length, rupture velocity, duration and offset are probably therefore also different. The subdued signals, and the events' gradual beginnings and endings, make determining these quantities a tricky undertaking.

Ide and colleagues' insight3 was to recognize that many different slow-slip phenomena might be aspects of the same process, and so follow a single scaling law. This was not immediately obvious, because these processes occur on such highly varying scales of space and time, and so had been detected and analysed with different instrumentation and techniques. Most slow-slip events occur in subduction zones, but some instances have been reported8 on the San Andreas Fault, a very different strike–slip fault where two plates slide past each other laterally. Improved geodetic and strain monitoring since the 1990s have detected single silent earthquakes with magnitude up to 7.5, slow aseismic afterslip following large earthquakes, and episodic slow-slip events. Improved analysis applied to more-complete archives of seismic data has also revealed long-duration, low-amplitude tremor similar to that seen below active volcanoes, and many earthquakes of anomalously low frequency.

All these slow events are distinguished from regular earthquakes of the same size, by definition, by their longer durations. But strikingly, Ide et al. show that, for the whole menagerie, duration is roughly proportional to seismic moment — rather than to its cube-root, as for regular earthquakes. The implication, that tremor amplitude does not grow much with increasing seismic moment or event duration, is consistent with the amplitude-limited appearance of some tremor episodes.

The authors explore the implications of their new scaling law, assuming two possible relations for how fault offset grows with fault length, L. First, they assume that the two are proportional, as for regular earthquakes. In this case, duration is proportional to L3, the drop in stress during an event is constant and about 100 times lower than for regular earthquakes, and rupture velocity must change as L−2. The authors' alternative assumption is that fault offset is quasi-constant, limited by the accumulated strain due to plate motion since the previous major slow-slip event. This leads to a duration proportional to L2, a larger drop in stress for smaller events, and a rupture velocity that changes as just L−1.

The data collected so far are insufficient to distinguish between the two models. The authors favour the second, pointing out that duration proportional to L2 has the form of a diffusive process, and that fluids have been detected in the Nankai subduction zone in Japan. The fluid diffusivity that would be inferred from some of their results, however, is more than 1,000 times larger than known values in shallow tectonic crust.

A key to further progress will be more accurate location of slow events. Recent results in Japan by some members of the same research team show that the low-frequency earthquakes lie on a dipping plane at, or very near, the subduction interface9. But non-volcanic tremor has also been observed to the west, far above the subducting slab10, and tremor episodes in the Cascadia subduction zone off the US Pacific coast, although more difficult to locate accurately, seem to span a large range of depths11. The debate on the nature of the tremor process is currently tipping towards a shear–slip origin, rather than fluid movement12. A better idea of the space-time development of the slow phenomena would also help to adjudicate.

The approach taken by Ide et al.3 is a natural first step, but subject to possible pitfalls. Their lumping together of seemingly disparate events might conflate a single event with a series of events. Comparing small to large slow-slip phenomena involves comparing individual migrating low-frequency events to parameters derived from their overall migration pattern13, somewhat analogous to comparing a mainshock to subevents within the mainshock. It's not entirely clear that a valid scaling law can be gleaned from comparing apples and oranges — or rather, papayas and papaya seeds. Also questionable is the authors' assumption in their analysis that slow events have a circular geometry. Considering the tectonic setting of slow slip along the lower edge of the locked portion between the overriding and downgoing plates in a subduction zone, an assumption of constant or limited width, at least for the larger events, might be more appropriate.

As a provocative first synthesis, the results of Ide et al. raise further questions. How long is a particular location in a large slow-slip episode active? Do events repeat in detail? Are there events intermediate between slow and regular earthquakes? That so many questions naturally arise and are already being attacked with such alacrity is a sign of the intense interest in the nature of such phenomena in the geophysical and wider community.

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Houston, H., Vidale, J. Relationships in a slow slip. Nature 447, 49–50 (2007). https://doi.org/10.1038/447049a

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