We define the average velocity of coseismic sense slip during an SSE as the total slip divided by the event duration, vSSE = s/T. We consider SSE duration to define the total interval of time over which an event occurs, which may include along strike migration, rather than the period of detection at a single geodetic station. SSE velocities computed from observations of the durations (Figure 1a) and slip magnitudes of previously recognized SSEs [Schwartz and Rokosky, 2007] show a decrease in vSSE with magnitude from 2,000–3,000 mm/yr at MW = 6 to 70–400 mm/yr at MW ≈ 7.2 (Figure 1b). We derive a slip velocity law consistent with these observations by considering empirical scaling relationships for SSE duration, stress drop, and OE rupture area. Ide et al.  found a linear relationship between SSE moment, M0, and event duration, T, M0 ≈ T × 10τ (τ = 12–13), that holds over nine orders of magnitude in moment (Figure 1a). Substituting this definition of T and slip, s, as a function of seismic moment, s = M0/μA, into the definition of average velocity gives vSSE = 10τ/μA, where μ is the crustal shear modulus. Empirical studies of OE dimensions have shown that rupture area, A (km2), scales with moment magnitude as log10A = a + bMW [Wells and Coppersmith, 1994]. We extrapolate this relationship to the sparsely observed MW > 8 regime neglecting any possible break in scaling at large OE magnitude. Estimated scaling values for OEs of all slip styles are a = −3.49 ± 0.16, b = 0.91 ± 0.03, while for the thrust style slip that characterizes subduction zones, a = −3.99 ± 0.36, b = 0.98 ± 0.06 [Wells and Coppersmith, 1994]. Estimates of creep event stress drops have revealed that, for a given seismic moment, the area over which a creep event occurs is 10–100 times larger than that of an OE [Brodsky and Mori, 2007]. This order of magnitude increase in rupture area can be incorporated into an SSE magnitude-area scaling law by modifying the Wells and Coppersmith  OE scaling law coefficient a such that a′ = a + 1 (km2) or a′ = a + 7 (m2). With this definition of SSE rupture area, the average SSE slip velocity, vSSE (in m/s), as a function of magnitude is
By combining the estimated scaling values from Ide et al.  and Wells and Coppersmith , and assuming a characteristic shear modulus of 30 GPa we find log10vSSE = (−1.49 ± 0.66) − (0.91 ± 0.03)MW averaged over all styles of slip (Figure 1b). Focusing on rupture area scaling for thrust earthquakes [Wells and Coppersmith, 1994] characteristic of subduction zones, we find log10vSSE = (−0.99 ± 0.86) − (0.98 ± 0.06)MW (with the concise approximation vSSE = mm/yr). The SSE slip velocity law agrees remarkably well with all of the observed events excluding those that represent afterslip following an OE (Figure 1b). The nature of this distinction may result from the generation of large-scale coseismic stresses or an ambiguity in the determination of the dominant post-seismic deformation process. To avoid the possibility of incorrectly combining the effects of two separate phenomena, we focus our analysis on the SSEs that emerge in the absence of triggering by macroscale seismicity.
Figure 1. Slow slip event duration and slip velocity as a function of magnitude. SSEs are from the Schwartz and Rokosky  compilation where duration, displacement, and scalar moment are reported. White squares are SSEs that occurred in the absence of macroscopic seismic triggering while dark gray squares are SSEs classified as post-seismic. Black lines represent reported uncertainties. (a) Observed SSE duration, T, and Ide et al.  scaling law (gray shading) shows the increase in event duration with magnitude. (b) Mean slip velocity and derived scaling laws. The regions shaded in white and outlined in gray show the convex hulls encompassing each of the two classes of SSEs. Note that there is negligible overlap between these two slip velocity regimes. Pink and orange shading indicate the minimum and maximum bounds on the slip velocity derived from the thrust and inclusive ordinary earthquake rupture area scaling laws, respectively [Wells and Coppersmith, 1994]. An approximate analytic expression, vSSE = (mm/yr), is shown as a red line. The region outlined in blue highlights SSEs with MW > 7.5 and vSSE < 120 mm/yr (less than the convergence rate at most subduction zones), which would not be expressed as reversals in geodetic position time series but rather as apparent partial elastic coupling.
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