Modeling short and long term slow slip events in the seismic cycles of large subduction earthquakes

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2010jb007566, 2010 Modeling short and long term slow slip events in the seismic cycles of large subduction earthquakes Takanori Matsuzawa, 1 Hitoshi Hirose, 1 Bunichiro Shibazaki, 2 and Kazushige Obara 1,3 Received 19 March 2010; revised 12 August 2010; accepted 20 August 2010; published 1 December [1] Slow slip events (SSEs) occur in the deeper extents of areas where large interplate earthquakes are expected in subduction zones, such as the Nankai region of Japan and the Cascadia region of North America. In the Nankai region, SSEs are divided into long and short term SSEs, depending on their duration and recurrence interval. We modeled and examined the occurrence of long and short term SSEs and changes in their behavior during the seismic cycles of large interplate earthquakes. In these numerical simulations we adopted a rate and state dependent friction law with cutoff velocities and assumed that the distribution of pore fluid controls the recurrence interval of both long and short term SSEs. The recurrence intervals of reproduced short term SSEs decrease during a long term SSE, as observed in western Shikoku, in the Nankai region. The recurrence intervals of both types of SSEs become shorter in the later stages of interseismic periods. Large interplate earthquakes nucleate between the region where SSEs occur and the locked region of the large earthquakes, as suggested from observations of the 1944 Tonankai earthquake. Our numerical results suggest that the stress buildup process in a seismic cycle affects the recurrence behavior of SSEs. Citation: Matsuzawa, T., H. Hirose, B. Shibazaki, and K. Obara (2010), Modeling short and long term slow slip events in the seismic cycles of large subduction earthquakes, J. Geophys. Res., 115,, doi: /2010jb Introduction [2] Recent studies using dense geodetic and seismic networks have revealed various slow earthquakes in subduction zones including slow slip events (SSEs), nonvolcanic tremors and very low frequency earthquakes [e.g., Obara, 2002; Ito et al., 2007; Schwartz and Rokosky, 2007]. SSEs are located deep in the expected source region of large interplate earthquakes in the Nankai region of Japan [e.g., Obara et al., 2004] and in the Cascadia region of North America [e.g., Dragert et al., 2001; McGuire and Segall, 2003; Rogers and Dragert, 2003]. In Mexico SSEs occur in the deeper part of the strongly coupled seismogenic zone in the Guerrero seismic gap [Lowry et al., 2001; Larson et al., 2004; Yoshioka et al., 2004; Brudzinski et al., 2007]. In the Nankai region, written historical documents show that large interplate earthquakes occur repeatedly at an interval of 100 to 200 years [e.g., Ishibashi, 2004]. In Cascadia Clague [1997] reported, based on geological studies, that the average interval between large interplate earthquakes is about 500 years. In Mexico SSEs occur in the seismic gap. As these SSEs occur close to the locked region of large earthquakes, they 1 National Research Institute for Earth Science and Disaster Prevention, Tsukuba, Japan. 2 International Institute of Seismology and Earthquake Engineering, Building Research Institute, Tsukuba, Japan. 3 Now at Earthquake Research Institute, University of Tokyo, Tokyo, Japan. Copyright 2010 by the American Geophysical Union /10/2010JB may cause stress accumulation around the locked region of large interplate earthquakes [e.g., Dragert et al., 2004] and, thus, be closely related to the process of stress buildup in seismic cycles for large interplate earthquakes. It is also possible that the stress buildup around the locked region in turn affects the behavior and occurrence of SSEs. Because detailed observations of SSEs [e.g., Hirose and Obara, 2005, 2010; Sekine et al., 2010] and studies of seismic velocities [e.g., Kodaira et al., 2004; Matsubara et al., 2009] are available in this region, we should develop a numerical model that includes SSE activity and the generation of large interplate earthquakes to understand the stress buildup process in seismic cycles and the nucleation of large interplate earthquakes in the Nankai region. [3] SSEs in the Nankai region are classified as short or long term depending on their duration and recurrence intervals [e.g., Hirose and Obara, 2005]. Short term SSEs have typical durations of several days and intervals of several months and are found along with belt like tremor distributions [Sekine et al., 2010]. Tremors and very low frequency earthquakes become active when short term SSEs occur [e.g., Ito et al., 2007; Matsuzawa et al., 2009]. In contrast, longterm SSEs have typical durations of several months or more, and recurrence intervals of several years, and are found only in the Tokai and Bungo channel regions in Nankai [Hirose et al., 1999; Ozawa et al., 2001, 2002, 2007; Miyazaki et al., 2003, 2006; Hirose and Obara, 2005]. In the Bungo channel the deeper part of the slip region of long term SSEs seems to overlap the slip region of short term SSEs as shown in Figure 1a [Hirose and Obara, 2005; Sekine et al., 2010]. 1of14

2 Figure 1. (a) Black and gray rectangles show the fault planes of short term slow slip events (SSEs) [Sekine et al., 2010] and a long term SSE [Hirose and Obara, 2005], respectively. Thick lines show the tops of estimated fault planes. (b) Black lines show occurrence times of the short term SSEs shown in Figure 1a. The gray rectangle shows the typical slip duration of a long term SSE [e.g., Ozawa et al., 2007]. The recurrence intervals of short term SSEs have been observed to shorten during long term SSEs both in the Bungo channel (Figure 1b) [e.g., Hirose and Obara, 2005] and in the Tokai region [e.g., Obara, 2010]. [4] The existence of water in the vicinity of SSE source regions is suggested by several studies. Shelly et al. [2006] and Matsubara et al. [2008] revealed that the ratio of P to S wave velocities (V P /V S ) is high at the source region of tremor activity in the Shikoku region. Audetetal.[2009] suggested that fluid water exists around the source region of tremors and SSEs in Cascadia, based on receiver function analysis. Song et al. [2009] reported that an ultraslow velocity layer exists around the region of SSEs in Guerrero. These studies imply that pore fluid exists and is confined to the vicinity of the plate interface where SSEs occur. Such confined water indicates that the pore pressure is high in the SSE region. In addition, Kodaira et al. [2004] and Matsubara et al. [2009] showed that the V P /V S ratio remains higher in shallower areas in the source region of long term SSEs than in the surrounding region. This suggests that long term SSE source regions are also characterized by water related properties and implies that the pore pressure may also be high in the long term SSE regions. [5] In previous numerical studies, Kato [2003] reproduced SSEs in a two dimensional (2 D) model, using a rate and state dependent friction law. His simulation, however, did not reproduce the recurring short term SSEs observed in the Nankai region. Liu and Rice [2005] used a three dimensional (3 D) model to numerically simulate slow transient events that propagate in the lateral direction. Their model also failed to reproduce the repeating occurrence of SSEs. Liu and Rice [2007, 2009] reproduced recurring SSEs by assuming high pore pressure in the SSE region in a 2 D model and examined parameters to control the behavior of transient events. Lateral propagation of SSEs was not reproduced in these studies, as their calculations were in two dimensions only. Ariyoshi et al. [2009] simulated slow earthquakes caused by small asperities and suggested that chain reactions of small patches of asperities can explain SSEs. Their model, however, did not reproduce the observed slip propagation velocity. The slip propagation velocity of Ariyoshi et al. [2009] ranges from 0.03 to 3 km/day, which is highly dispersed and slower than the observed migration of tremors and SSEs, which ranges between 5 and 15 km/day [Obara, 2002; Rogers and Dragert, 2003; Hirose and Obara, 2010]. [6] In fault models using common rate and statedependent friction laws, the style of slip is determined by the ratio of the width W of the generation zone to the critical cell size h * [Liu and Rice, 2007; Rubin, 2008]. As SSEs can be reproduced in a very limited range of W/h * in the slip law, Rubin [2008] suggested that another mechanism to stabilize the slip should be included in numerical models and proposed two other models to reproduce SSEs: a transition of friction from velocity strengthening to velocity weakening [Shimamoto, 1986] and the dilatancy effect [Segall and Rubin, 2007]. Shibazaki and Shimamoto [2007] reproduced short term SSEs in 2 D and 3 D models using a rate and state dependent friction law with a low cutoff velocity for the evolution effect, which models a transition of friction from velocity strengthening to velocity weakening behavior with increasing slip velocity. Recently, Shibazaki et al. [2010] reproduced SSE segmentation, incorporating the distribution of tremors in western Shikoku and the configuration of plate boundaries. Rubin [2008], however, suggested that experimental support is insufficient for the friction law adopted by Shibazaki and Shimamoto [2007]. Although many numerical SSE models have been proposed [Liu and Rice, 2007, 2009; Shibazaki and Shimamoto, 2007; Ariyoshi et al., 2009; Shibazaki et al., 2010], there have been no studies investigating the relationship between 2of14

3 Figure 2. (a) Model space of a thrust fault in a two dimensional (2 D) elastic medium. The width of the fault is km. (b) Model space in a 3 D elastic medium. The length and width of the fault are 140 and km, respectively. The dip angle is 15. x and z axes are the strike and vertical downward directions, respectively. A periodic boundary condition is set at the horizontal boundary. long and short term SSEs and the relationship between SSEs and the nucleation of large earthquakes in 3 D models. [7] In this paper we numerically simulate both long term and short term SSEs in seismic cycles of large interplate earthquakes and discuss the behavior of SSEs obtained, adopting a rate and state dependent friction law with cutoff velocities. First, we simulate short term and long term SSEs separately in 2 D models and examine the basic behaviors of our model. Then we simulate long term and short term SSEs in a single 3 D model and examine the behaviors of SSEs under more realistic conditions that allow interaction and slip propagation between the short term and the longterm SSE regions. We also discuss the relationship between SSEs and the stress buildup process that leads to the nucleation of large earthquakes, as stress accumulated by the slip of SSEs is expected to relate to large earthquakes and their nucleation. 2. Numerical Model and Parameters [8] SSEs occur in the friction transition zone between stick slip sliding and stable plastic deformation, where deformation properties shift from brittle to ductile regimes. Shimamoto [1986] experimentally simulated the transition of friction using halite at room temperature and showed that velocity strengthening behavior occurred at low slip velocities. This changed to velocity weakening behavior at intermediate velocities and then back to velocity strengthening behavior at high velocities. A similar frictional property is also found in chrysotile serpentine [Moore et al., 1997]. As discussed previously the transition of friction from velocityweakening to velocity strengthening behavior as the velocity increases is a possible model for simulating SSEs. Shibazaki and Shimamoto [2007] successfully reproduced repeating short term SSEs assuming a rate and state dependent friction law with a small cutoff velocity for the evolution effect. Beeler [2009] also proposed constitutive laws that explain the N shaped curve of frictional coefficients observed by Shimamoto [1986] and reproduced SSEs in a single mass slider model. Though this frictional behavior is not well founded for application in SSE regions as discussed by Rubin [2008], the friction law with cutoff velocities is more easily introduced to numerical simulations than incorporating other physical processes and is expected to approximate other stabilizing mechanisms with velocitydependent friction that have a transition from velocityweakening to velocity strengthening behavior. In this study we model a frictional property transition adopting a rateand state dependent friction law with cutoff velocities as in Shibazaki and Shimamoto [2007]. [9] Okubo [1989] proposed a rate and state dependent friction law with cutoff velocities, in which the frictional stress t can be written as ¼ e 0 a ln v 1 v þ 1 þ b ln v 2 þ 1 d c ; ð1þ where s e is the effective pressure given by the difference between normal stress and pore pressure. a, b, and m 0 are frictional constitutive parameters in a rate and statedependent friction law. n and are slip velocity and a state variable, respectively. v 1 and v 2 are cutoff velocities for the direct and evolution effects, respectively. d c is a critical displacement scaling factor for evolution effects. As we adopt the aging law [Ruina, 1983] in our simulation, the temporal evolution of state variable is given by d v ¼ 1 : dt d c As at steady state is d c /v, the steady state frictional stress can be written as h ss ¼ e 0 a ln v 1 v þ 1 þ b ln v i 2 v þ 1 : ð3þ Taking the derivative of equation (3) with respect to ln v, the rate dependence of steady state frictional stress can be written as d ss d ln v ¼ a b e : ð4þ 1 þ v=v 1 1 þ v=v 2 The critical velocity, at which friction changes from velocity strengthening to velocity weakening behavior, can be written as ð2þ v cr ¼ ðb aþv 2 a bv ð 2 =v 1 Þ : ð5þ We assume that a, b 0, v > 0, and v 1 v 2 in our model. Equations (4) and (5) therefore show that friction is always velocity weakening when a b (v 2 /v 1 ) < 0 and always velocity strengthening when a b > 0. When a b (v 2 /v 1 )> 0 and a b < 0, friction is velocity weakening at v < v cr and velocity strengthening at v cr < v. The actual range of v cr was 3of14

4 Figure 3. Distributions of constitutive law parameters. (a) Solid, dashed, dotted, and thick gray lines show the depth distributions of a, b, v 2,andv cr, respectively. We note that v cr is positive at depths of between 24 and 32.5 km. (b) Solid and dashed lines show the depth distribution of effective normal stress (s eff ) in the 2 D long and short term SSE models, respectively. Dotted line shows d c /s eff. (c) Distribution of effective normal stress in the 3 D model. (d) Filled circles show the location where slip velocities are plotted in Figure 5. Distance along the dip direction measured from the trench axis is also indicated on the vertical axis. found to be approximately 10 5 to 10 7 m/s in experiments using halite [Shimamoto, 1986, 1989] and chrysotile serpentine [Moore et al., 1997]. [10] In our numerical models we set a subducting plate interface as a flat plane dipped at 15 in a 2 D or3 D semiinfinite elastic medium (Figure 2). We assumed that the slip and plate loading directions are perpendicular to the strike of the fault and that the loading velocity is constant and homogeneous on the plate interface. In the 3 D case we posed periodic boundary conditions at the horizontal edge of the fault. The plate interface is divided into 2000 cells in the 2 D models and a array of rectangular cells in the 3 D model. The temporal evolution of the slip velocity on the cells is calculated incorporating the frictional stress on each cell and the elastic interactions between cells. The time derivative of shear stress t i on the ith cell is given by d i dt ¼ X j G dv i k i;j V pl v j 2 dt : ð6þ G, b, and V pl are rigidity, S wave velocity, and loading velocity at the plate interface, respectively; k i,j is an elastostatic kernel that gives the stress change at the center of the ith cell caused by uniform slip over the jth cell and is calculated from the elastic response in a semi infinite medium [Iwasaki and Sato, 1979]. The second term on the right hand side of equation (6) is a radiation damping term to approximate seismic radiation [Rice, 1993]. In our simulation G and b are assumed to be 30 GPa and 3.5 km/s, respectively. V pl is assumed to be 6 cm/yr, based on the plate convergence velocity in the Shikoku region [Heki and Miyazaki, 2001]. Equations (1), (2), and (6) are solved using the Runge Kutta method with adaptive step size control [Press et al., 1996]. [11] For all simulations we assumed that a, b, and v 2 are functions of depth as shown in Figure 3a. The cutoff velocity v 1 is spatially homogeneous and equals 1 m/s. Although v 1 mitigates velocity strengthening when v > v 1, such a change is not supported by the experimental results of brittle ductile transitions [e.g., Shimamoto, 1986]. Therefore, to avoid another complication from the cutoff velocity v 1,we 4of14

5 assume that v 1 is much faster than the slip velocity of nucleation and the SSEs discussed in our model. Therefore, v cr has a positive value at depths between 24 and 32.5 km and is about 10 7 m/s (Figure 3a) at depths of about 30 km, where SSEs occur. This value is similar to experimental results (10 5 to 10 7 m/s) and the estimated peak velocity ( 10 7 m/s) of actual short term SSEs [Hirose and Obara, 2010], though the value of v cr should be confirmed by the further rock experiments under hot conditions of SSE regions. Random fluctuations with a magnitude of 10% are also assigned to parameter b. We assumed that effective normal stress is very low (Figures 3b and 3c) in the SSE region (Figure 3d). In addition, as discussed in section 1, seismic explorations around the long and short term SSE regions suggest that the distribution of hydraulic parameters may characterize the occurrence and the recurrence intervals of SSEs. Thus, in our 2 D simulation, two models with different distributions of effective normal stress are assumed to reproduce short and long term SSEs (Figure 3b). In the short term SSE model, pore pressure increases from a depth of 24 km and is close to the lithostatic pressure below 28 km. In the long term SSE model, pore pressure starts to increase from a shallower depth but is kept slightly lower at depths of km than in the short term SSE model. This slightly lower pore pressure (i.e., high effective normal stress) in the long term SSE region reflects the observation that stress drops of long term SSEs are higher than those of short term SSEs. For example, the stress drop of short and long term SSEs in the Bungo channel region are estimated by Hirose and Obara [2005] to be and 66 kpa, respectively, assuming rectangular faults. Therefore, we assume slightly higher effective normal stress to cause higher stress drops in the long term SSE model than in the short term SSE model, while the frictional parameters a and b vary as functions of depth and are common in our models. [12] In the 3 D model we assumed a patch of long term SSEs surrounded by a short term SSE region (Figure 3c). The long term SSE region is shown in gray around x =0at depths of about 28 km. The vertical distribution of effective normal stress coincides with the long term SSE model in the 2 D case (Figure 3b) in the range from x = 10 to 10 km and matches the short term SSE model in the 2 D case at x < 15 km and x > 15 km. Small values of d c should be assumed in the SSE region, while large values of d c are expected in the locked region, where large earthquakes occur [e.g., Ide and Takeo, 1997]. In our simulation we simply assumed that s e /d c is kept constant at depths below 1.5 km (Figure 3b) in both the 2 D and the 3 D cases. A consequence of the s e /d c assumption is that d c is large in the locked region. In addition, Liu and Rice [2007] showed that the parameter W/h * controls the periodic behavior of SSEs, defining W as the length from the bottom of the locked region to the depth of neutral friction (i.e., a b=0) and h * as h * ¼ 2G0 d c ; ð7þ ðb aþ e where G is defined as G for antiplane strain and G/(1 n) for plane strain (n is Poisson s ratio). As a and b are functions of depth, holding s e /d c constant in a 3 D model means that W/h * is kept constant in the lateral direction. [13] To simulate earthquakes numerically, cell sizes should be smaller than a critical nucleation size. Rice [1993] indicates that equation (7) gives the critical nucleation size h *. When fault healing is unimportant, Rubin and Ampuero [2005] show that the half length of the nucleation patch size is L 1:3774G0 d c b e : ð8þ In our model the minimum values of h * and L v are 2.28 and 1.95 km, respectively. In our 2 D models the length of each cell is km. In our 3 D model the cell size is 0.7 km for the strike direction and km for the along dip direction. Thus, the cell sizes in both the 2 D and the 3 D simulations are smaller than the nucleation lengths. We note that h * and L v are derived for a rate and state dependent friction law without cutoff velocities. However, larger characteristic nucleation sizes are expected in our simulations than in those without cutoff velocities, as slip tends to be less accelerated in our model. In the case of v > v cr, velocity strengthening behavior dominates in our model. When v v 2 and v < v cr, recalling the assumption that v 2 v 1, the weakening rate of t ss in our model (equation (4)) is lower than in the cases without cutoff velocities (i.e., dt ss /d(ln v)=a b). When v <<v 2, the characteristic scales of h * and L v are well approximated by the values given by equation (7) or (8), as the effect of cutoff velocities is not dominant. Therefore, h * and L v constitute a sufficient condition for numerical stability, as the velocityweakening rate in our model is always lower than the rate without cutoff velocities. 3. Numerical Results of 2 D Models [14] Figure 4a shows the results of a 2 D long term SSE model. At a depth of 15 km, fast slip events, which exceed 0.1 m/s, repeat at intervals of 116 years. In the period between these events, the slip velocity stays below m/s and is much slower than the subduction velocity ( m/s). This is interpreted as being the slip region for large interplate earthquakes, which is locked in the interseismic period. The simulated recurrence interval matches the occurrence of large earthquakes, which repeat at intervals of years in the Nankai subduction zone. In contrast, SSEs with velocities of about 10 6 m/s are found at depths of about 30 km and recur at several year intervals (Figure 4a). This recurrence interval is also similar to the actual long term SSEs observed in the Bungo channel region [Hirose et al., 1999; Hirose and Obara, 2005]. The interval between SSEs shortens through the interseismic period and is reset when a large earthquake occurs, as discussed later. [15] Figure 4b shows the results of a 2 D short term SSE model. Large interplate earthquakes repeat at intervals of 113 years in this case as well as in the long term SSE model. SSEs recur at a depth of about 30 km at intervals of several months (Figure 4c). Their recurrence intervals are similar to the intervals of short term SSEs observed in the Nankai subduction zone [Hirose and Obara, 2005; Sekine et al., 2010]. [16] Our 2 D models reproduced long and short term SSE behavior, assuming a different distribution of hydraulic 5of14

6 Figure 4. Slip velocity in 2 D SSE models. Dashed gray and solid black lines show the velocity at depths of 15 and 28 km, respectively. Horizontal axis shows the time measured from the occurrence of the second interplate earthquake in numerical simulations. Black arrows in each plot show the occurrence of large interplate earthquakes. (a) Slip velocity in the 2 D long term SSE model. (b) Slip velocity in the 2 D short term SSE model. (c) Expanded view of the large interplate earthquake labeled e1 in Figure 4b. parameters at the deeper extent of the locked region, as suggested in previous results of seismic explorations [Kodaira et al., 2004; Matsubara et al., 2009] and SSE stress drops [Hirose and Obara, 2005]. Shortening of SSE recurrence intervals is observed during interseismic periods in both the long and the short term SSE models (Figures 4a and 4c). 4. Numerical Results of 3 D Models 4.1. Slow Slip Events (SSEs) in Seismic Cycles [17] The results of our 3 D model are shown in Figure 5. Large interplate earthquakes are also reproduced in this model, and repeat at an interval of 112 years (Figure 5a). Figure 5b is a scaled up version of Figure 5a during an interseismic period. In our 3 D simulation both short and long term SSEs are reproduced within a single model. At a depth of about 30 km, short and long term SSEs repeat at intervals of several months and several years, respectively. The peak SSE velocity in the 3 D model fluctuates more than in 2 D models, especially for short term SSEs. This is interpreted to be an effect of the 3 D medium, which allows SSEs to propagate and interact in the horizontal direction (see also Figure 7c). The displacement of each short term SSE is about 0.5 cm, similar to observed values of 1 cm [Sekine et al., 2010]. Figure 5c is a scale up of Figure 5a near the time of a large earthquake. The recurrence intervals of long and short term SSEs shorten before a large earthquake compared to those after a large earthquake, similar to the 2 D model results Characteristic Parameters in SSEs [18] Figures 6a 6e are snapshots of slip velocity when a short term SSE occurs. The short term SSE starts at 55 km on the horizontal scale at a depth of about 30 km (Figure 6a) and then propagates bilaterally. Propagation of slip from the left boundary (Figure 6c) is due to periodic boundary conditions in the horizontal direction. The short term SSE finally terminates at the margin of the long term SSE region (Figures 6d and 6e). Figures 7e 7g show the horizontal cross section of slip velocity at a depth of 30 km when short term SSEs occur. The slip propagation velocity of these events ranges from 2 to 16 km/day, which is similar to the observed propagation velocity of tremors and short term SSEs (5 to 15 km/day). In the figures the propagation velocity is estimated for each day when the slip velocity of SSEs exceeds m/s. At the other times, from 55 to 75 years on the time scale, 94% of the daily propagation velocities are distributed between 2 and 20 km/day, which agrees with the observed propagation velocities. [19] Shibazaki and Shimamoto [2007] and Rubin [2008] showed that the relationship between the propagation velocity v r and the peak slip velocity v peak is well explained by the equation [Ida, 1973; Ohnaka and Yamashita, 1989] v peak ¼ D b G v r; where g is an order of unity and Dt b is the breakdown strength drop, defined as the difference between the peak stress and the residual frictional stress. As the peak velocity ð9þ 6of14

7 Figure 5. (a) Slip velocity in a 3 D SSE model. Black arrows show the occurrence of large interplate earthquakes. Horizontal axis is the time measured from the occurrence of the second interplate earthquake in the numerical simulation. Dashed gray lines show the slip velocity at point A in Figure 3d. Red and black solid lines show the slip velocities at points B and C in Figure 3d, respectively. Point B is located at the center of the long term SSE region. Point C is located in the short term SSE region. Horizontal axis shows the time measured from the occurrence of the second interplate earthquake in the numerical simulation. (b) Expanded view of Figure 5a in the interseismic period indicated by the orange bar at the top in Figure 5a. (c) Expanded view of Figure 5a around the interplate earthquake. The period is indicated by the green bar in Figure 5a. in our model is stabilized by cutoff velocities, fluctuations in v r smaller than the range given by Ariyoshi et al. [2009] may reflect that the peak velocity is controlled by some stabilizing mechanisms as discussed previously. [20] Figures 6f 6j show snapshots of the occurrence of a long term SSE. Comparing Figures 6a and 6f, it can be seen that the slip velocity increases around the long term SSE region before a long term SSE occurs. This reflects the accumulation of stress from stable slip around the patch and from short term SSEs that recur around the long term SSE region. The long term SSE then begins from that location (Figures 6f and 6g) and propagates bilaterally to the shortterm SSE region (Figure 6h). The distribution of slip velocity at a depth of 30 km is shown in Figure 7c. Elevated slip velocity caused by stress accumulation can be seen clearly in the long term SSE region ( 15 km < x <15 km) before long term SSEs occur. In Figure 7c the regular recurrence of short term SSEs fluctuates when the next long term SSE approaches, as this elevated slip velocity seems to affect adjacent short term SSE regions. [21] Duration and slip velocity are also characteristic parameters of short and long term SSEs. The short term SSEs in western Shikoku have characteristic durations of several days and a peak slip velocity of 10 7 m/s [Hirose and Obara, 2010]. These are similar to our model results (Figures 5 and 7e 7g), which range between 10 8 and 10 6 m/s. Long term SSEs last about 1 year and have peak velocities of m/s in the Bungo channel and < m/s in the Tokai region [Miyazaki et al., 2003, 2006]. As shown in Figure 5b the modeled slip velocity exceeds the subduction velocity ( m/s) for several months to a year, which is similar to the observed values. The peak velocity of about 10 7 m/s, however, which appears at the end of long term SSEs, is up to 10 times faster than that observed. It is still possible that such a high velocity, because it occurs only for a short time, averages out and cannot be detected in analyses using GPS data. It would then be classified by tiltmeter observations as one of the active shortterm SSEs that occur during a long term SSE [Hirose and Obara, 2005]. 7of14

8 Figure 6. Slip velocity distribution at each time step in the 3 D model. Vertical and horizontal axes show the depth and along strike distance, respectively. Time in years is indicated above each panel. (a e) Short term SSE labeled S3 in Figure 7c. (f j) Long term SSE labeled L1 in Figure 7c. (k o) Nucleation of the large interplate earthquake labeled E1 in Figure 7a. Color scale for all plots is shown at the right of each line of snapshots Stress Accumulation and Nucleation of Large Earthquakes [22] Figure 7a shows the temporal evolution of slip velocity at x = 50 km on the horizontal axis during seismic cycles. Just after a large interplate earthquake, the region at depths between 7 and 28 km is locked. However, the locked region gradually narrows during the interseismic period. The bottom of the locked region migrates upward owing to stress accumulated by the slip of SSEs and stable sliding in deeper areas (Figures 7a and 8). Such migration can be seen in the displacement as well (Figure 9). The top of the locked region migrates via stable sliding in its shallower reaches, as a stable sliding region is also assumed there (Figure 3a). This migration is slower than that in the deeper reaches. A dark region with many thin blue vertical lines appears at depths between 28 and 32 km in Figure 7a, showing that SSEs occur repeatedly and slip is only episodic in that depth range. In contrast, the slip is not episodic but proceeds in a stable fashion, with only small fluctuations above and below this region as shown in Figures 7a and 9. [23] At a depth of about 24 km, the slip velocity starts to accelerate just before a large earthquake occurs (Figures 6k 6o). This acceleration finally grows into a large earthquake (Figure 6o), suggesting that the nucleation of the large earthquake occurred in this region. Figures 7b and 7d are the vertical and horizontal cross sections of slip velocity around a large interplate earthquake. Short term SSEs become very active before the large earthquake and the activity moderates after it occurs, especially around the area where the nucleation occurred (x = 50 km). Another interesting feature is that the nucleation of large earthquakes starts between the SSE region and the locked region where large earthquakes occur, not in the SSE region itself, as is evident in Figures 6k 6o and 7b. [24] As shown in Figure 6o, the slip velocity below the SSE region exceeds 10 4 m/s when a large earthquake occurs. Figure 9 also shows that this region slips coseismically. Analyses of tsunamis and geodetic data, however, suggest that the coseismic slip in the SSE region was small in the 1946 Nankai earthquake [Baba et al., 2004; Ito and Hashimoto, 2004]. This may be caused by the assumption of a small s e and d c in the deep region. In Figure 9a, a slip deficit during the interseismic period is found even below the SSE region because the strain accumulation in the locked region also affects the slip of the surrounding region. While this slip deficit in such deep regions is released coseismically in our model, the coseismic slip seems to be further decelerated by another physical process such as fully plastic deformation [Shimamoto, 1986] or the dilatancy effect [Segall and Rubin, 2007]. Perhaps the slip deficit that is not released coseismically is relaxed by afterslip. The difference in coseismic slip is, however, not significant in our discussion about SSEs and nucleation, although a model with these effects may be appropriate in future studies to simulate entire seismic cycles. 8of14

9 Figure 7. Spatial and temporal distribution of slip velocity in seismic cycles from the 3 D model. Black and green arrows show the occurrence of large earthquakes and transient events, respectively. (a) Vertical cross section at x = 50 km and temporal evolution in several seismic cycles. (b) Enlargement of temporal axis around the large earthquake labeled E1 in Figure 7a. (c) Horizontal cross section at a depth of 30 km during the interseismic period indicated by the orange bar in Figure 7a. Blue bars mark the occurrence of long term SSEs. Small red arrows mark the short term SSEs shown in Figures 7e and 7f. (d) Horizontal cross section at a depth of 30 km near the large interplate earthquake labeled E1 in Figure 7a. (e g) Left plots show horizontal cross sections at a depth of 30 km around short term SSEs labeled S3, S2, and S1, respectively, in Figure 7c. Yellow lines show slip propagation velocities of 2, 5, and 10 km/day. Right plots show the propagation velocity of each short term SSE when the slip velocity exceeds m/s. Crosses show SSE propagation in the positive direction, while open circles show propagation in the negative direction of the x axis. 9of14

10 Figure 8. Stress changes at x = 50 km in the 3 D model. Changes are measured from the stress 1 year after a large earthquake. (a) Temporal evolution of slip velocity. Black arrows show the occurrence of large earthquakes. (b) Dashed orange, solid black, dashed blue, and solid red lines show the stress change distributions at t = 25, 50, 75, and 100 years, respectively Recurrence Intervals of SSEs [25] Figure 10 shows the temporal change in the recurrence intervals of SSEs in our 2 D and 3 D models. In the 2 D cases the recurrence intervals of SSEs tend to decrease during interseismic periods and are reset to their initial intervals after a large interplate earthquake in both the longand the short term SSE models (Figures 10a and 10b). Recurrence intervals in the 3 D case also tend to decrease in the interseismic period for long and short term SSEs (Figures 10c and 10d) as in the 2 D models. In the case of long term SSEs in the 3 D model, intervals fluctuate widely just after a large earthquake (Figure 10c), as slip is slightly irregular at this stage (Figure 5a). Recurrence intervals fluctuate more in the 3 D model than in the 2 D cases, especially for short term SSEs. This is caused by the 3 D medium, which allows SSEs to migrate and interact in the horizontal direction. The recurrence intervals of short term SSEs are also affected and shortened by long term SSEs as shown in Figures 5b and 7c. This interaction is similar to observations in the Bungo channel (Figure 1b). [26] The recurrence intervals of long term SSEs fluctuate widely in the later stages of an interseismic period (starting years after the previous large earthquake) in the 3 D model. Such fluctuations are also found in the 2 D shortand long term SSE models (Figures 10a and 10b). As shown in Figures 7a and 9b, a transient event occurs at a depth of between 24 and 28 km, which corresponds to the boundary region between the locked region and the SSE region. This transient event is not a seismic event but a slow one because its slip velocity is about 10 6 m/s. Similar transient events are also simulated in previous studies [e.g., Liu and Rice, 2007]. After this transient event the slip velocity decelerates in this region (Figures 7a and 9b). This deceleration may cause a temporary lengthening of recurrence intervals after the transient event (Figures 10c 10e). In the 2D short and long term SSE models the decrease and increase in recurrence intervals before earthquakes also correspond to the occurrence of the transient events. This result suggests that the slip velocity between the locked region and the SSE region affects variations in the recurrence intervals. [27] The recurrence interval of SSEs decreases again just before large earthquakes (Figure 10), especially below the nucleation zone (x = 50 km in Figure 7d). This suggests that nucleation causes frequent occurrence of short term SSEs. As shown in Figure 7a the slip velocity increases in the slip region of the transient event, then recovers to its previous level. Finally, slip accelerates greatly between the locked and the SSE regions (Figures 6m and 6n) with frequent SSEs (Figure 7d). This nucleation leads to a large earthquake (Figure 6o). 5. Discussion [28] Our numerical simulation reproduced short and long term SSEs and interplate earthquakes within a single model, assuming a distribution of effective normal stress (Figure 3c). Our result is consistent with the characteristic periods and durations of actual SSEs in the Nankai region. In our simulation it is assumed that s e / d c is constant below a depth of 1.5 km (Figure 3b). While this assumption may be too simplistic, applying it successfully reproduces various characteristics of both long and short term SSEs as shown in the previous section. [29] To examine the assumption on s e / d c we tested cases where d c below a depth of 28 km was set 1.5 and 2 times larger than in our studied model. The recurrence of shortand long term SSEs and large earthquakes was reproduced in both cases. The recurrence intervals also decreased during interseismic periods. However, the typical peak velocities dropped to about m/s when d c was 1.5 times larger than in our model and to about to m/s when d c was twice as large. This suggests that when d c increases, it becomes dominant over the velocity strengthening behavior of the friction law, causing much slower slip. In the case where d c is doubled, as v cr is about 10 7 m/s, the frictional behavior is velocity weakening even at the peak velocities of 10 of 14

11 Figure 9. (a) Slip at x = 0 km in a 3 D model. Lines are plotted for every year. Distance in years from the reference time is shown by the periodic color scale, which repeats at an interval of 50 years. Black arrows show the occurrence of large earthquakes. (b) Accumulated displacement at x = 0 km measured from t = 0 years. Black, red, blue, and green lines show displacement at depths of 20, 24, 28, and 32 km, respectively to m/s. Liu and Rice [2007, 2009] showed that smaller values of W/h * cause slower peak velocities. Our slower peak velocity may be caused by the smaller W/h * that follows from a larger d c, recalling equation (7). Though the range of model parameters that can reproduce actual SSEs should be examined in a wider parameter space in a future study, our obtained qualitative behaviors are robust for some fluctuations in s e /d c. In our model, as the peak velocities, stress drops, propagation, and duration velocities are similar to observations, the space of possible parameters related to these values may be relatively well constrained. [30] Audet et al. [2009] suggested that pore fluid in the SSE region in Cascadia is sealed by a low permeability boundary. Perhaps the difference between short and longterm SSE regions may be characterized by the permeability, which may cause the difference in effective normal stress as assumed in our model. However, it is also unclear whether the short and long term SSE regions are characterized by the same physics (e.g., high pore pressure caused by a lowpermeability boundary) or controlled by differences in other frictional properties. In addition, as shown in Figures 6a 6e and 7c, short term SSEs terminate at the margin of the longterm SSE region in our model. In contrast, there seems to be some overlap of the short term and long term SSE regions in western Shikoku (Figure 1a) and the Tokai region [e.g., Ozawa et al., 2002; Sekine et al., 2010]. However, it is still not clear whether they actually overlap, as the available geodetic data are not sufficient to constrain a conclusive, detailed slip distribution. Further observation and detailed analysis would improve the model of the distribution of frictional parameters to simulate a more realistic spatial relationship of long and short term SSEs. [31] Large earthquakes in our simulation nucleate from the region between the SSE region and the locked region. The hypocenter depths of the 1944 Tonankai and 1946 Nankai earthquakes were about 20 km and 10 km, respectively, if we assume the epicenter estimated by Kanamori [1972] and the subducting plate configuration inferred by Baba et al. [2006]. There is a gap of more than 8 km in depth between the epicenters of the large earthquakes and the SSE region. Linde and Sacks [2002] suggested that the nucleation of the 1946 Nankai earthquake occurred at a depth of about 15 km based on Kobayashi et al. [2002]. The depth of nucleation in our model, however, is km, deeper than these previous results, though the nucleation in our model also starts between the SSE region and the locked region as for the previous results. These differences imply that the bottom of the actual locked region may be shallower than in our simulation, and the frictional behavior may be more stable between the SSE region and the locked region than we expected. We examined the effect of such a stable sliding region, changing the frictional property from a b < 0 (Figure 3) to a b > 0 at a depth of about 24 km. In this case, large interplate earthquakes nucleated at depths of km. This also produced shortening of the recurrence intervals in the seismic cycle, though the change is smaller than the results shown in Figures 5 through 10. It may be possible that the assumption on the distribution of s e affects the location of nucleation of large earthquakes. We also tested the case where s e starts to decrease at a depth of 18 km, which is shallower than the depth of 24 km in the original model. In this case, the SSE region becomes wider and ranges between 22 and 32 km in depth. Even in this case, large earthquakes nucleate from the region between the locked and the SSE regions. These results support our findings regarding the nucleation and SSEs, since they also hold in a model in which nucleation occurs in a shallower region. However, further research in frictional properties and deformation mechanisms is required to model the behavior of this region, because the preceding assumptions are not based on rock experiments. [32] Figure 8a shows the stress buildup measured from the level existing 1 year after a large earthquake. The peak of stress at the bottom of the locked region migrates upward and increases during the interseismic period, while stress changes in the SSE region are kept small by episodic slip. Stress buildup in the locked region is characterized by yielding and slip in the surrounding region. Slip between the locked region and the SSE region affects the occurrence of SSEs as already discussed. This implies that the stress 11 of 14

12 Figure 10. SSE recurrence intervals measured at a depth of 28 km. Black arrows indicate the occurrence of large earthquakes in each simulation. (a) Recurrence intervals in a 2 D long term SSE model. (b) Recurrence intervals in a 2 D short term SSE model. (c) Recurrence intervals at x =0(i.e.,a long term SSE region in a 3 D model). Small gray arrows show the occurrence of transient events. (d) Recurrence interval of SSEs at x = 50 km (i.e., short term SSE region in a 3 D model). (e) Expanded view of Figure 10d around a large interplate earthquake. An SSE is identified when the ratio of the maximum peak to the next minimum peak of slip velocity exceeds the threshold of 100 for Figures 10a 10c and of 10 for Figure 10d. The lower threshold is used for Figure 10d because the peak to peak amplitude of velocities in the short term SSE region in the 3 D model (Figure 5b) is sometimes lower than in the other cases (Figures 4 and 5a). buildup process and frictional properties in this region may be inferred from the observation of SSEs. As our numerical model is not based on well founded assumptions, especially with regard to frictional properties, the validity of the numerical model should be examined carefully in further observations and experiments. However, as discussed previously, some mechanisms that stabilize slip velocity lead to the characteristic propagation velocity observed in SSEs. Although our model is based on the brittle ductile transition, this friction law is applicable to other mechanisms with velocity dependent stabilizing mechanisms. In the case of such frictional properties, similar behavior seems to be expected. Our results suggest that the transient events and nucleation of interplate earthquakes may actually be detectable and be a key to earthquake predictions, because the slip of these events expected from our results is larger than that of the SSEs that are detected by current geodetic networks. 6. Conclusions [33] In this paper, we have reproduced short and longterm SSEs and large interplate earthquakes in 2 D models as well as within a single 3 D model. In the 3 D model the recurrence intervals of short term SSEs shorten during a long term SSE as observed in the Bungo channel. The reproduced propagation velocity of short term SSEs ranges from 2 to 20 km/day, similar to observed values. The recurrence interval of long and short term SSEs shortens during interseismic periods. The interval decrease is affected by the distribution of slip velocity between the locked region and the SSE region. In addition, large earthquakes nucleate in this region, where stress accumulates owing to the slip of 12 of 14

13 SSEs and stable sliding in the deeper extent. Our simulation also suggests that SSEs and tremors may enable us to infer the stress buildup process at the bottom of the locked region. [34] Acknowledgments. We would like to thank the two anonymous reviewers and the Associate Editor for providing helpful suggestions. A discussion with T. Shimamoto was fruitful. The Generic Mapping Tools [Wessel and Smith, 1998] program was used to prepare the figures. References Ariyoshi, K., T. Hori, J. P. Ampuero, Y. Kaneda, T. Matsuzawa, R. Hino, and A. Hasegawa (2009), Influence of interaction between small asperities on various types of slow earthquakes in a 3 D simulation for a subduction plate boundary, Gondwana Res., 16, , doi: /j. gr Audet, P., M. G. Bostock, N. I. Christensen, and S. M. Peacock (2009), Seismic evidence for overpressured subducted oceanic crust and megathrust fault sealing, Nature, 457, 76 78, doi: /nature Baba, T., P. R. Cummins, T. Hori, and Y. Kaneda (2006), High precision slip distribution of the 1944 Tonankai earthquake inferred from tsunami waveforms: Possible slip on a splay fault, Tectonophysics, 426, Beeler, N. M. (2009), Constructing constitutive relationships for seismic and aseismic fault slip, Pure Appl. Geophys., 166, , doi: /s Brudzinski, M., E. Cabral Cano, F. Correa Mora, C. DeMets, and B. Márquez Azúa (2007), Slow slip transients along the Oaxaca subduction segment from 1993 to 2007, Geophys. J. Int., 171, , doi: /j x x. Clague, J. J. (1997), Evidence for large earthquakes at the Cascadia subduction zone, Rev. Geophys., 35(4), , doi: /97rg Dragert, H., K. Wang, and T. S. James (2001), A silent slip event on the deeper Cascadia subduction interface, Science, 292, Dragert, H., K. Wang, and G. Rogers (2004), Geodetic and seismic signatures of episodic tremor and slip in the northern Cascadia subduction zone, Earth Planets Space, 56, Heki, K., and S. Miyazaki (2001), Plate convergence and long term crustal deformation in central Japan, Geophys. Res. Lett., 28(12), , doi: /2000gl Hirose, H., and K. Obara (2005), Repeating short and long term slow slip events with deep tremor activity around the Bungo channel region, Earth Planets Space, 57, Hirose, H., and K. Obara (2010), Recurrence behavior of short term slow slip and correlated nonvolcanic tremor episodes in western Shikoku, southwest Japan, J. Geophys. Res., 115, B00A21, doi: / 2008JB Hirose, H., K. Hirahara, F. Kimata, N. Fujii, and S. Miyazaki (1999), A slow thrust slip event following the two 1996 Hyuganada Earthquakes beneath the Bungo Channel, southwest Japan, Geophys. Res. Lett., 26(21), , doi: /1999gl Ida, Y. (1973), The maximum acceleration of seismic ground motion, Bull. Seismol. Soc. Am., 63, Ide, S., and M. Takeo (1997), Determination of constitutive relations of fault slip based on seismic wave analysis, J. Geophys. Res., 102(B12), 27,379 27,391, doi: /97jb Ishibashi, K. (2004), Status of historical seismology in Japan. Ann. Geophys., 47, Ito, T., and M. Hashimoto (2004), Spatiotemporal distribution of interplate coupling in southwest Japan from inversion of geodetic data, J. Geophys. Res., 109, B02315, doi: /2002jb Ito, Y., K. Obara, K. Shiomi, S. Sekine, and H. Hirose (2007), Slow earthquakes coincident with episodic tremors and slow slip events, Science, 315, , doi: /science Iwasaki, T., and R. Sato (1979), Strain field in a semi infinite medium due to an inclined rectangular fault, J. Phys. Earth, 27, Kanamori, H. (1972), Tectonic implications of the 1944 Tonankai and the 1946 Nankaido earthquakes, Phys. Earth Planet. Inter., 5, Kato, N. (2003), A possible model for large preseismic slip on a deeper extension of a seismic rupture plane, Earth Planet. Sci. Lett., 216, Kobayashi, A., N. Manago, and A. Yoshida (2002), Sea level change at Uragami just before the 1946 Nankai earthquake, J. Geodetic Soc. Japan, 48, Kodaira, S., T. Iidaka, A. Kato, J. O. Park, T. Iwasaki, and Y. Kaneda (2004), High pore fluid pressure may cause silent slip in the Nankai trough, Science, 304, Larson, K. M., A. R. Lowry, V. Kostoglodov, W. Hutton, O. Sánchez, K. Hudnut, and G. Suârez (2004), Crustal deformation in Guerrero, Mexico, J. Geophys. Res., 109, B04409, doi: /2003jb Linde, A. T., and I. S. Sacks (2002), Slow earthquakes and great earthquakes along the Nankai trough, Earth Planet. Sci. Lett., 203, Liu, Y., and J. R. Rice (2005), Aseismic slip transients emerge spontaneously in three dimensional rate and state modeling of subduction earthquake sequences, J. Geophys. Res., 110, B08307, doi: /2004jb Liu, Y., and J. R. Rice (2007), Spontaneous and triggered aseismic deformation transients in a subduction fault model, J. Geophys. Res., 112, B09404, doi: /2007jb Liu, Y., and J. R. Rice (2009), Slow slip predictions based on granite and gabbro friction data compared to GPS measurements in northern Cascadia, J. Geophys. Res., 114, B09407, doi: /2008jb Lowry, A. R., K. M. Larson, V. Kostoglodov, and R. Bilham (2001), Transient fault slip in Guerrero, southern Mexico, Geophys. Res. Lett., 28(19), , doi: /2001gl Matsubara, M., K. Obara, and K. Kasahara (2008), Three dimensional P and S wave velocity structures beneath the Japan Islands obtained by high density seismic stations by seismic tomography, Tectonophysics, 454, , doi: /j.tecto Matsubara, M., K. Obara, and K. Kasahara (2009), High V P /V S zone accompanying nonvolcanic tremors and slow slip events beneath southwestern Japan, Tectonophysics, 472, 6 17, doi: /j.tecto Matsuzawa, T., K. Obara, and T. Maeda (2009), Source duration of deep very low frequency earthquakes in western Shikoku Japan, J. Geophys. Res., 114, B00A11, doi: /2008jb McGuire, J. J., and P. Segall (2003), Imaging of aseismic fault slip transients recorded by dense geodetic networks, Geophys. J. Int., 155, Miyazaki, S., J. J. McGuire, and P. Segall (2003), A transient subduction zone slip episode in southwest Japan observed by the nationwide GPS array, J. Geophys. Res., 108(B2), 2087, doi: /2001jb Miyazaki, S., P. Segall, J. J. McGuire, T. Kato, and Y. Hatanaka (2006), Spatial and temporal evolution of stress and slip rate during the 2000 Tokai slow earthquake, J. Geophys. Res., 111, B03409, doi: / 2004JB Moore,D.E.,D.A.Lockner,S.Ma,R.Summers,andJ.D.Byerlee (1997), Strengths of sepentinite gouges at elevated temperatures, J. Geophys. Res., 102(B7), 14,787 14,801, doi: /97jb Obara, K. (2002), Non volcanic deep tremor associated with subduction in southwest Japan, Science, 296, Obara, K. (2010), Phenomenology of deep slow earthquake family in southwest Japan: Spatiotemporal characteristics and segmentation, J. Geophys. Res., 115, B00A25, doi: /2008jb Obara, K., H. Hirose, F. Yamamizu, and K. Kasahara (2004), Episodic slow slip events accompanied by non volcanic tremors insouthwest Japan subduction zone, Geophys. Res. Lett., 31, L23602, doi: / 2004GL Ohnaka, M., and T. Yamashita (1989), A cohesive zone model for dynamic shear faulting based on experimentally inferred constitutive relation and strong motion source parameters, J. Geophys. Res., 94(B4), , doi: /jb094ib04p Okubo, P. G. (1989), Dynamic rupture modeling with laboratory derived constitutive relations, J. Geophys. Res., 94(B9), 12,321 12,335, doi: /jb094ib09p Ozawa, S., M. Murakami, and T. Tada (2001), Time dependent inversion study of the slow thrust event in the Nankai trough subduction zone, southwestern Japan, J. Geophys. Res., 106, , doi: / 2000JB Ozawa, S., M. Murakami, M. Kaidzu, T. Tada, T. Sagiya, Y. Hatanaka, H. Yarai, and T. Nishimura (2002), Detection and monitoring of ongoing aseismic slip in the Tokai region, central Japan, Science, 298, Ozawa, S., H. Suito, T. Imakiire, and M. Murakami (2007), Spatiotemporal evolution of aseismic interplate slip between 1996 and 1996 and between 2002 and 2004, in Bungo channel, southwest Japan, J. Geophys. Res., 112, B05409, doi: /2006JB Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vertterling (1996), Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed., 963 pp., Cambridge University Press, New York. Rice, J. R. (1993), Spatio temporal complexity of slip on a fault, J. Geophys. Res., 98(B6), , doi: /93jb Rogers, G., and H. Dragert (2003), Episodic tremor and slip on the Cascadia subduction zone: The chatter of silent slip, Science, 300, Rubin, A. M. (2008), Episodic slow slip and rate and state friction, J. Geophys. Res., 113, B11414, doi: /2008jb Rubin, A. M., and J. P. Ampuero (2005), Earthquake nucleation on (aging) rate and state faults, J. Geophys. Res., 110, B11312, doi: /2005jb of 14