Geophysical Research Letters

Complex characteristics of slow slip events in subduction zones reproduced in multi-cycle simulations



[1] Since the discovery of slow slip events along subduction zone interfaces worldwide, dense geodetic and seismic networks have illuminated detailed characteristics of these events and associated tremor. High-resolution observations of tremor, where the spatial-temporal evolution is presumed to reflect that of the underlying slow slip events, show highly complex patterns in which the origins remain poorly understood. We present a new, computationally efficient modeling technique that reproduces many features of observed slow slip events, including slow initiation, coalescence of separate events, and rapid back-propagation of renewed slip over previously slipped regions. Rapid back propagation speeds are explained as a consequence of rate- and state-dependent frictional healing, consistent with analytical solutions developed in support of the simulations.

1. Introduction

[2] Recent geodetic observations in subduction zones have revealed the widespread occurrence of intermittent strain release in the form of slow slip events (SSEs) along the subduction interface [e.g., Schwartz and Rokosky, 2007]. In Cascadia, which is the basis of the simulations presented here, SSEs typically have durations of 1–4 weeks, with 2–4 cm of slip, and occur every 9–21 months [Dragert et al., 2001]. In the well-instrumented Nankai and Cascadia subduction zones, slow slip is always accompanied by low-level tectonic tremor, which indicates that tremor observations can be used as a proxy for slip [Miller et al., 2002; Obara et al., 2004; Aguiar et al., 2009]. High-resolution tremor observations indicate highly complex space-time patterns, which include slow, incoherent initiation and termination of events, and simultaneous slip in multiple locations [Boyarko and Brudzinski, 2010; Obara, 2010]. Forward propagation speeds range from 5–18 km/day [Dragert et al., 2001; Miller et al., 2002; Obara et al., 2004; Aguiar et al., 2009; Boyarko and Brudzinski, 2010; Obara, 2010], while back propagation speeds across previously slipped areas range from 100–300 km/day [Houston et al., 2011], and along-dip propagation speeds range from to 24–4000 km/day [Shelly et al., 2007; Ghosh et al., 2010, 2012], respectively. Although various processes have been proposed that may influence these complex patterns, neither a physical mechanism nor a quantitative model has been agreed upon [Ando et al., 2010; Houston et al., 2011; Ghosh et al., 2010, 2012; Ide, 2010; Rubin, 2011]. This study presents high-resolution simulations that reproduce many of the observed space-time characteristics of SSEs.

2. Model

[3] The simulations use an idealized subduction zone configuration, where the mega-thrust is divided into three sections based on sliding characteristics: a seismogenic zone, a transition zone (where SSEs occur), and a creeping zone (Figure 1). The rate- and state-dependent formulation is employed to represent constitutive properties of the mega-thrust interface. This formulation is based on laboratory observations and has found widespread use in modeling different modes of slip including earthquakes, slow slip, and continuous creep [Dieterich, 1979, 1981; Ruina, 1983]:

display math

where τ and σ are the shear and normal stress, respectively; μ0, a, and b are experimentally determined constants; inline image is sliding speed; inline image is a normalizing constant; θ is a state variable that evolves with time, slip, and normal stress history; and Dcis the characteristic sliding distance over which state evolves. The seismogenic zone is modeled as rate-weakening:b > a, where steady-state fault strength decreases with increasing slip speed and enables unstable earthquake slip. Because this study focuses on the time between great mega-thrust earthquakes, the seismogenic zone does not slip in these particular simulations. In contrast, the creeping zone is modeled as rate-strengthening:b < a (b = 0.008; a = 0.010), where the fault slides stably at rates determined by the current stress levels. The transition zone is modeled as rate-weakening with a gradient inb (b = 0.011 − 0.013; a = 0.010) such that it is nearly rate-neutral (b = a) at its lower edge. Both the transition and creeping zones are assigned low effective normal stress, 4 MPa, consistent with thermal modeling [Peacock et al., 2002], seismological inferences [Kodaira et al., 2004], and comparable to effective normal stress values used by Liu and Rice [2005, 2007].

Figure 1.

Fault model used in this study. The seismogenic zone, the section of the mega-thrust that generates great earthquakes, is located between depths of 5 and 25 km. The transition zone is located at depths of 25 km and 40 km. The creeping zone is located at depths > 40 km. Slip on the fault is pure-thrust with a convergence rate of 37 mm/yr. The fault is 552 km × 286 km and dips 12°. Fault elements are 2 km × 2 km in the seismogenic and transition zones (red and green, respectively) and 4 km × 4 km in the continuous creep zone (blue). Total number of fault elements is 26,634.

[4] We employ the simulation code, Rate-State-Quake-Simulator, RSQSim, to model the various sliding behaviors and to investigate how slip propagates during SSEs. The code fully incorporates 3D stress interactions, which includes the effects of normal stress fluctuations on sliding friction, and incorporates rate- and state-dependent frictional properties. RSQSim has been used to model strike-slip faults with complex geometries [Dieterich and Richards-Dinger, 2010] and SSEs along a Cascadia-like mega-thrust [Colella et al., 2011]. For computational efficiency the simulations of earthquakes and SSEs utilize analytic solutions for spontaneous nucleation of events [Dieterich, 1992; Fang et al., 2010], and event-driven computational steps as opposed to time stepping at closely spaced intervals. The event steps in the computation consist of changes in sliding speed for creeping elements, and transitions between stationary and slow slip conditions for elements that participate in SSEs. SSEs are modeled as slow earthquakes, wherein the slip speed during a SSE is specified as an input parameter based on observations (10−6 m/s) [Ikari et al., 2009], rather than an outcome of the calculations. The imposed slip speed acts as a proxy for whatever process limits the slip speed in nature, as the mechanism that is actually responsible remains unclear. Otherwise simulations are fully deterministic in nucleation, propagation speed, extent of slip, and final distribution of slip. For more details about RSQSim, see the auxiliary material. As implemented, our model may bear some resemblance to those that employ a variant of rate-state friction that gives rate-weakening at slow slip speeds and rate-strengthening at high slip speeds [Shibazaki and Iio, 2003; Shibazaki et al., 2012]. Whereas those methods in effect impose something of a “soft” speed limit to slow slip, here a strict limit is set, with the advantage that the efficiency of the algorithm allows us to run simulations of more than 100,000 events.

3. Results

[5] Results reported here are from simulations with ∼200,000 SSEs that occur over ∼200 years with equivalent moment magnitudes that range from ∼Mw4.0 to ∼Mw7.0. Characteristics of simulated SSEs, which include inter-event times, average slips, and durations, are consistent with characteristics of observed SSEs in Cascadia and Nankai (Figure S1).

[6] Simulated SSEs exhibit complex patterns similar to observed tremor patterns [Shelly et al., 2007; Kao et al., 2009; Boyarko and Brudzinski, 2010; Ghosh et al., 2010, 2012; Ide, 2010; Houston et al., 2011; Wech and Creager, 2011] (Figure 2). 1) Incoherent slip typically occurs for several days before developing into a coherent rupture front, similar to tremor studies [Houston et al., 2011] (Figure 2). 2) Different regions often slip simultaneously, which results in overlapping rupture times (Figures 2a, 2c, 2e, and 2g), referred to as “jumping” in some tremor studies [Boyarko and Brudzinski, 2010; Obara, 2010]. 3) Slip propagates along strike in a variety of ways, which includes unilateral (Figure 2a) and bilateral propagation (Figure 2c) and bilateral convergence, where slip initiates in discontinuous locations and then coalesces [Boyarko and Brudzinski, 2010] (Figures 2e and 2g). 4) Incoherent slip occurs for several days at the end of an event, similar to tremor studies [Houston et al., 2011]. 5) Rupture propagation speeds often vary along strike for an individual SSE [Boyarko and Brudzinski, 2010; Ghosh et al., 2012]. 6) Back-propagating pulses across previously slipped regions propagate faster than the main front (Figures 2a, 2c, 2e, and 2g, black rectangles), similar to rapid tremor reversals [Houston et al., 2011]. 7). Rapid along-dip slip appears in SSE simulations (Figures 2b, 2d, 2f, and 2h), similar to reported along-dip, or convergence-parallel, tremor streaks [Shelly et al., 2007; Ghosh et al., 2010, 2012]. In addition, the simulations show that the speed of the back-propagating pulses slow down as they propagate away from the initial rupture front (Figures 2a, 2c, 2e, and 2g), a behavior that has yet to be observed (see section 4).

Figure 2.

Space-time evolution of slip during simulated SSEs. Colors correspond to the number of patches along-strike or along-dip (left and right panels, respectively) that slip at a given time. Note the high background rate of scattered very small slip events. (a) Example of unilateral propagation. (b) Along-dip evolution of slip from SSE in Figure 2a. (c) Example of bilateral propagation. (d) Along-dip evolution of slip from SSE in Figure 2c. (e) Example of bilateral convergence. (f) Along-dip evolution of slip from SSE in Figure 2e. (g) Example of an SSE where slip occurs at non-contiguous locations, where the region of slip eventually overlap. (h) Along-dip evolution of slip from SSE in Figure 2g. Black rectangles highlight back propagation pulses.

[7] Propagation speeds for larger simulated SSEs, Mw ≥ 6.3 are shown in Figure 3. Forward propagation speeds range from 9–22 km/day (Figure 3a). Along-strike back propagation speeds range from 30–140 km/day (Figure 3b). Along-dip propagation speeds range from 20–270 km/day (Figure 3c).

Figure 3.

Distribution of propagation speeds for simulated SSEs. (a) Forward propagation speeds, where speeds represent the average of 2-day average speeds for all events with >6 days of coherent propagation. (b) Back propagation. (c) Slip-parallel propagation.

4. Discussion

[8] The patterns of observed and simulated SSEs are significantly different and more complex than those of earthquake slip events. Some complexities observed in simulated SSEs (1–4 above) may be attributed to near rate-neutral (b-a ∼ 0) values particularly near the base of the transition zone. Additionally the high rate of occurrence of simulated SSEs combined with very long event durations result in the frequent occurrence of simultaneous slip at scattered locations. In turn, initially independently slipping regions may interact and coalesce (e.g. bilateral convergence). The high background rates of SSEs are a consequence of low stress drops (0.01–0.1 MPa for simulated SSEs compared to typical stress drops in earthquakes of 1–10 MPa). The very long event durations are a consequence of very slow slip speeds (1 μm/s for simulated SSEs compared to slip speeds of ∼1 m/s for earthquakes) and low propagation speeds.

[9] The forward propagation speeds in the simulations are consistent with analytical solutions (see auxiliary material). The solutions show the propagation speed is proportional to the imposed slip speed, but is otherwise relatively insensitive, at least within the range of parameters adopted here, to parameters such as grid spacing that do not appear in standard continuum models of rate-and-state friction. The variation in forward propagation speeds in the simulations is also consistent with several recent studies of tremor in Cascadia [Boyarko and Brudzinski, 2010; Ghosh et al., 2012]. Such variations have been suggested to be related to stress or material heterogeneity on the subduction zone interface and will be explored in the future.

[10] The same solutions indicate that back propagation speeds should be ∼4× faster than the main front, which is in agreement with speeds from the simulations. Observations of rapid tremor reversals indicate back propagation speeds of ∼10–30× faster than forward propagation speeds [Houston et al., 2011]; one possible explanation for this difference from the simulations is that the slip speed in the simulations is held at a fixed value, while slip speed in the actual back-propagating pulses may be 2–8× higher than at the main front.

[11] In the simulations, the more rapid speed of back propagation is a consequence of time-dependent frictional healing after termination of slip behind the main rupture front, a characteristic feature of rate-state friction (Figure 4). For renewed slip to occur, the stress at the rupture front must rise to surmount the strength of the interface, which is dependent on the time a patch has had to heal since last slipping. For the main rupture front, which propagates across an area of the interface that has not slipped since the last SSE, this time will be on the order of a year, compared to minutes to hours for reactivated slip in backward or along-dip propagating fronts. Because the stressing rate at the rupture front is primarily controlled by slip speed, which is fixed, a lower stress barrier for reactivated slip means it can propagate at much faster speeds. However, because an element heals as the logarithm of elapsed time, it seems difficult to account for the full range of observed propagation speeds by this mechanism alone. A specific prediction of this mechanism, which can be tested against future observations, is that back propagation speeds are fastest immediately behind the main rupture front and decrease as the back-propagating front encounters parts of the fault that have had more time to heal since slipping during passage of the main front, which is seen in the simulations (Figures 2a, 2c, 2e, and 2g).

Figure 4.

Stress as a function of time for an element involved in the backward propagation pulse shown in inset. Inset is the event shown in Figure 2a.

[12] The source of the rapid along-dip, or convergence-parallel, streaks is less obvious. They might result when slip behind the main front stops in a spatially coherent way. Under these circumstances, renewed slip of nearby, along-dip elements may be ready to slip nearly simultaneously as a result of a relatively low frictional strength from very little time for frictional-healing and a relatively high stressing rate from the main front. For a discussion of model parameters that appear to affect the along-dip propagation speeds seeauxiliary material. Ando et al. [2010] and Ghosh et al. [2010]suggest rapid, along-dip tremor streaks may arise when the main front propagating along strike intersects, at an oblique angle, a string of tremor sources aligned along-dip, such as striations caused by subducted seamounts [Ide, 2010]. This possibility will be explored in future studies.

[13] In summary, this is the first modeling technique that has reproduced high-resolution characteristics of observed SSEs, which include slow, incoherent initiation, complex slip patterns and speeds during events, and more rapid back and along-dip propagation, over 100 s of cycles. To achieve back and along-dip propagation speeds as rapid as those observed, non-uniform slip speeds, heterogeneity, or more complicated friction laws [Rubin, 2011] might be required. Reports of extremely high slip-parallel propagation speeds could also represent apparent speeds that result when the main front obliquely encounters dip-parallel streaks with enhanced capability to generate tremor. Such conditions will be modeled in the future. Additionally, RSQSim will be employed to explore the effects SSEs have on the up-dip, seismogenic zone of the mega-thrust, which is responsible for world's largest earthquakes.


[14] We thank Associate Editor, Andrew Newman, Heidi Houston, and an anonymous reviewer for their comments and suggestions that improved the manuscript. Research supported by the U.S. Geological Survey (USGS), Department of the Interior, under USGS award G11AP20015. This material is also based upon work supported by the National Science Foundation under grant 1135455. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the U.S. Government.

[15] The Editor thanks Heidi Houston and an anonymous reviewer for their assistance in evaluating this paper.