- Open Access
Interval modulation of recurrent slow slip events by two types of earthquake loading
© Mitsui; licensee Springer. 2015
- Received: 2 January 2015
- Accepted: 15 April 2015
- Published: 25 April 2015
Geodetic studies have discovered recurrent spontaneous slow slip events (SSEs) at major faults. The SSE recurrence intervals should reflect stress states at the faults, including load effects of large earthquakes in neighboring areas. Here, we focus on temporal changes of the SSE recurrence intervals. We perform numerical model experiments with the rate- and state-dependent friction in a three-dimensional elastic medium to simulate the SSE recurrence interval changes by the earthquake loading effects. One result is gradual shortening of the SSE recurrence intervals owing to a nucleation process of a nearby large earthquake, as revealed by several previous studies. This effect reflects magnitude of the elastic interaction between the SSE and earthquake areas. As an example, when the distance between the SSE and earthquake areas is almost zero, a short-term rapid decrease of the SSE recurrence intervals precedes the earthquake occurrence (approximately by a decade). The other result is that external stress perturbation, as large as 0.1 MPa, can reduce the SSE recurrence intervals to a similar extent. Furthermore, the interval modulation by the stress perturbation continues for a prolonged period until the occurrence of the adjacent earthquake. Both effects may be observable, as is advancing at the Boso zone, Japan, but their separation is difficult under the present circumstances.
- Slow slip events
- Recurrence interval
- Elastic interaction
- Numerical modeling
- Rate and state friction
Development of geodetic measurements revealed the existence of spontaneous slow slip events (hereafter called SSE) at major faults (Linde et al. 1996; Hirose et al. 1999). In particular, on some subduction plate interfaces, large SSEs over Mw 6 have occurred repeatedly (e.g., Dragert et al. 2001; Ozawa et al. 2003; Dragert et al. 2004; Heki and Kataoka 2008). Their mean recurrence intervals are on the order of several months to several years.
Focusing on this issue, we select three subduction zones for comparison: the Boso zone, the northern Cascadia zone, and the Yaeyama zone, Japan. Although there are other subduction zones with SSEs (e.g., some zones in southwest Japan, the Alaska zone, the Guerrero zone, the Costa Rica zone, et al.), the selected three zones have experienced many (not less than eight) and large (over Mw 6) SSEs. Figure 1 exhibits their locations in the Pacific-rim scale. We also show the approximate regional locations of the SSE areas and the source areas of nearby large earthquakes at the same scale by Figure 1, referring to many previous studies. The Boso SSEs occurred at the plate interface around 140.4°E, −35.1°N (e.g., Hirose et al. 2012). The source fault of the 1923 Kanto earthquake (Mw-8 class) estimated geodetically (Ando 1971) is located on the west side of the SSE area. At the northern Cascadia zone, the SSEs occurred in an approximate range of 124.0°W to 123.7°W, and −48.1°N to 48.4°N (e.g., Rogers and Dragert 2003; Szeliga et al. 2008). The source area of the megathrust earthquakes, possibly as large as Mw 9, was estimated in the shallower part along the whole Cascadia subduction zone (e.g., Atwater 1987; Leonard et al. 2010). Beneath the Yaeyama Islands, Japan, the SSE area is located around 123.8°E, −24.5°N (Heki and Kataoka 2008). The Yaeyama Islands had been attacked by huge tsunamis in the past thousands of years. Nakamura (2009a) proposed that the 1771 Yaeyama tsunami was caused by a large thrust (possibly interplate) earthquake of which source area was near the Ryukyu Trench.
As Figure 1 shows, the distance between the SSE and the earthquake areas at the Boso zone is shorter than those at the northern Cascadia and the Yaeyama zone. This point is assured although the estimated sources of the SSEs and the earthquakes have much uncertainty. The SSE and the earthquake areas at the Boso zone are adjacent and might overlap partly, while their distances at the other zones are on the order of 100 km. On the other hand, the notable shortening of the SSE recurrence interval only occurred at the Boso zone (we will discuss the details in a later discussion section). This correspondence is worthy of note.
Here, we perform numerical experiments with a frictional system targeting the effects of large earthquakes on SSE recurrence intervals. We do not assume a bit complex distribution of the SSE areas as the previous studies (Ariyoshi et al. 2009; Matsuzawa et al. 2010) but set simpler models to investigate the effect of the distance between SSE and earthquake areas via the earthquake nucleation process. We further investigate the external stress perturbation effect as the 2011 Tohoku-oki earthquake for the Boso zone.
where t is the time and u is the slip amount. The stiffness kernel K in the three-dimensional elastic full space is described by some preceding studies (e.g., Kato 2003).
We simultaneously solved the above equations in the Fourier domain (e.g., Kato 2003). Thus, artificial periodic boundary conditions are introduced on the four sides of the model fault. To reduce their effects, we set steady-slip zones around the four sides. The procedure for numerical integration is following our previous work (Mitsui and Hirahara 2011).
The frictional parameters in the SSE area are A = 0.03 MPa, B = 0.045 MPa, and L = 0.8 cm; those in the earthquake area are A = 3 MPa, B = 4.5 MPa, and L = 20 cm; and those in the intermediate zone are A = 0.9 MPa, B = 0.3 MPa, and L = 20 cm. The parameter values more or less followed some previous numerical studies (e.g., Kato 2004). Note that only the L values for mimicking actual large slip events are several orders of magnitude different from those estimated in laboratory experiments (see the discussion in Guatteri et al. (2001)). The S-wave velocity c s and the rigidity G are assumed to be 3.5 km/s and 34.3 GPa, respectively. The plate loading rate v 0 is 10 cm/year. The numerical grid size is about 710 m. This value is sufficiently smaller than a critical grid size (e.g., Rice 1993) ~ GL/(B − A), which is approximately 4600 m for the earthquake area and 18,000 m for the SSE area. We confirmed that the SSE recurrence interval is about 13 months if we do not set the earthquake area. Here, we define the event recurrence interval as a period between a time when the rising slip velocity reaches the plate loading rate v 0 and the last time for the same condition. Likewise, the recurrence interval of the earthquake without the SSE area is approximately 310 years.
To investigate the external stress perturbation effect, we test a step-like (static) shear stress change during the interseismic period (e.g., Perfettini et al. 2003; Cho et al. 2009) in additional experiments. The details are described in a later discussion section.
Of course, the decreasing rates depend on frictional parameters as well as the distance between the SSE and the earthquake areas. By way of experiment, we change the frictional parameters A and B in the intermediate zone. When we set A = 0.12 MPa, B = 0.045 MPa as a weaker intermediate zone, the long-term decreasing rates gain and reach 0.01 to 0.1 (month/year). In contrast, when we set A = 9 MPa, B = 3 MPa as a stronger intermediate zone, the long-term decrease rates are almost 0. Weaker intermediate zone, which can be attributed to high pore fluid pressure on a fault, favors larger decreasing rate of the SSE recurrence intervals. Moreover, the size of the SSE and earthquake areas also affects the decreasing rates of the SSE intervals. We checked some cases when the earthquake area is far larger than the SSE area and found that the decreasing rates of the SSE intervals tend to be greater for a larger earthquake area. All the effects of the distance between the SSE and earthquake areas, the weakness of the intermediate zone, and the size of the SSE and earthquake areas reflect the magnitude of the elastic interaction.
Actual interval of SSE recurrence
Our numerical results indicated that the distance between the SSE and the earthquake areas is truly one of the important parameters for the temporal change of the SSE recurrence interval. This fact qualitatively agrees with the observation as was mentioned in the introduction section.
The occurrence times of the SSEs at the three subduction zones
N. Cascadia a
September 1997, June 1998
February 1999, September 1999
March 2000, October 2000
March 2001, October 2001
March 2002, September 2002
April 2003, October 2003
April 2004, November 2004
May 2005, August 2005
January 2006, July 2006
January 2007, February 2007
October 2007, May 2008
November 2008, July 2009
December 2009, July 2010
February 2011, October 2011
In order to extract the trends, we fit the data by the least squares method using the linear function (black broken line). The slope of the regression line of the Boso zone is −2.90(±0.80) (month/year), where the error range represents the standard error of estimate. The slopes of the n. Cascadia zone and the Yaeyama zone are −0.12(±0.10) (month/year) and −0.04(±0.08) (month/year), respectively. We find that the SSE recurrence intervals tend to be shorter in all the zones, although the data on the SSE recurrence intervals may not be sufficient yet to discuss this point. The degree of the data variation implies that the long-term decreases of the SSE recurrence intervals, which are far milder than the short-term decreases, are not observable in natural phenomena.
External stress perturbation effects on SSE activity
The observed large decreasing rate of the SSE recurrence intervals at the Boso zone might truly result from the nucleation process of the neighboring earthquake, however, the effect of the 2011 Tohoku earthquake should not be ignored. The Mw 9.0 Tohoku earthquake and its afterslip caused a non-negligible Coulomb stress change (e.g., King et al. 1994) at most 0.1 MPa (Hirose et al. 2012), although the epicenter of the Tohoku earthquake (142.9∘E, −38.1∘N) was about 400 km far from the Boso SSE zone.
In order to check the degree of such an external stress perturbation effect, we perform another experiment. We add a step-like (static) shear stress change on the whole fault, alternative to the Coulomb stress change, as large as 0.1 MPa during the interseismic period for model 3.
We found that the shortening of the SSE recurrence intervals by the external stress perturbation can be as rapid as the short-term decrease by the earthquake nucleation (Figures 7 and 8). We also found that the external stress perturbation easily hide the long-term decreasing rate. The stress perturbation effect may appear in the rapid decrease of the SSE recurrence intervals at the Yaeyama zone around 2005 to 2007 (see Figure 6). It might be related to afterslip of the M7-class 2002 Hualien earthquake (Nakamura 2009b) which occurred on the east coast of Taiwan and on the west side of the SSE zone, or magma injection in the back-arc Okinawa Trough (Tu and Heki 2014).
In the case of the Boso SSE, the recurrence intervals was actually decreasing (Figure 6), which might correspond to the nucleation of the adjoining large earthquake, but that after the 2011 Tohoku earthquake should be strongly affected by the external stress perturbation. This fact suggests that the current frictional state at the Boso SSE zone is complicated. In terms of the development of earthquake seismology, it is necessary to monitor the crustal deformation continuously until the future occurrence of the adjoining large earthquake.
We investigated interval modulation of SSEs by two types of earthquake loading: effects of nucleation and external stress perturbation. We confirmed that SSE recurrence intervals tend to be shorter owing to a nucleation process of a nearby large earthquake, based on the numerical modeling with the frictional system. The decreasing rate of the SSE intervals depends on magnitude of the elastic interaction. One important point is the distance between the SSE and earthquake areas. When the distance between the SSE and earthquake areas is nearly zero with the same size of the SSE and earthquake areas, the short-term further decrease in the SSE recurrence intervals occurs just before the earthquake occurrence. Only the short-term decrease can be as significant as the fluctuation of the SSE recurrence intervals by external stress perturbation. The effect of the external stress perturbation on the SSE recurrence intervals continues until the occurrence of the adjacent earthquake.
YM thanks Kosuke Heki for discussing and providing the data. Incisive comments by two anonymous reviewers improved the manuscript. We use Generic Mapping Tools (Wessel and Smith 1995) to draw the maps.
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