Toward a Unified View of Tremor and Slow Slip

Evidence from Japan suggests that deep non-volcanic tremor consists of myriad Low Frequency Earthquakes (LFEs) on the subduction interface, with focal mechanisms consistent with plate convergence [Shelly et al., Nature 2007; Ide et al., GRL 2007]. Thus I adopt the view that tremor and the accompanying slow slip represent two manifestations of slip on the same interface, and that they should be explainable using the same constitutive framework. Here I explore various incarnations of rate-and-state (r-s) friction. Episodic slow slip may result from (1) a transition from velocity-weakening to velocity-strengthening behavior at less than slow-slip speeds [Kato, EPSL 2003; Shibazaki and Iio, GRL 2003]; (2) "standard" r-s friction, meaning with velocity-independent material parameters, on a fault whose length is properly "tuned" and that possesses high pore pressure (low effective stress) [Liu and Rice, JGR 2005; 2007], or (3) fault-zone dilatancy coupled with pore pressure reduction and diffusion [Segall and Rubin, EOS, 2007]. Using the most appropriate laboratory constitutive law it seems that (2) requires too much "tuning" [Rubin, JGR, in press], but many aspects of slow slip events, including their low stress drop (~10 kPa in Cascadia and Japan), are most easily explained by effective stresses as low as 1 MPa. This is consistent with expectations from seismology and petrology, and with the sensitivity of tremor to tides and surface waves. LFE's are most simply interpreted as resulting from material heterogeneity that makes their source region more seismogenic than the surroundings, for which embarrassingly many options exist. The largest LFE's in Japan appear to have magnitudes about 1.5 but durations roughly 10 times longer than "typical" M1.5 earthquakes. A fundamental question is "what makes them slow?". Two answers are (1) elastodynamics and (2) something else. For circular ruptures moment is proportional to stress drop and the radius cubed, so for circular earthquakes rate-limited by elastodynamics a factor of 10 increase in duration can be explained by a factor of 1000 decrease in stress drop. This seems unreasonable, but a factor of 100 decrease (so a factor of 5 increase in duration) is not, if the LFE stress drop is the same 10 kPa as the slow slip stress drop. This is within striking distance of the observations, and if this explains tremor, the question becomes "where are the M2, 3, and 4 elastodynamic events that would be expected of a typical Gutenberg-Richter distribution?". One possibility is that there is a characteristic length scale for slip in the tremor source region [Watanabe et al., GRL 2007], which would be of order 300 m for a 10-kPa M1.5 event. A potential length scale is the "compaction length" that arises during porous flow in a viscously-deforming matrix. A second possibility is that LFE moment is only weakly sensitive to the size of the underlying heterogeneity. Colliding creep waves increase the slip speed locally by multiple orders of magnitude, and for some constitutive laws might give rise to this insensitivity. Such a tremor source is appealing because creep waves arise in all sorts of simulations that include material heterogeneity. It could also give rise to spatially-elongate LFE sources, which might help explain some aspects of their spectra as well as allow larger stress drops for the same duration. If LFE's are rate-limited by "something else", then the question becomes "What process can reasonably increase the speed of >105 sources to the point that they radiate detectable energy, without letting them slide or propagate fast enough to be limited by elastodynamics?". At the moment, "slow but elastodynamic" seems like the most promising line of investigation.