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 In recent years slow slip events (SSE) have been observed to occur at regular intervals on the deep portions of subduction zone interfaces. These are accompanied by seismic tremor that occurs over their duration. It has been observed that tremor activity shows transient modulations in response to earth tides and the passage of seismic waves from distant earthquakes. Here we show, for the first time, geodetic evidence for the triggering of an interplate SSE itself by teleseismic surface waves. This SSE, in southwest Japan, which had an equivalent magnitude Mw 5.3 and duration of 1.5 days, was triggered by the surface waves of a Mw 7.6 earthquake in Tonga. This evidence was captured by a newly deployed sensitive strainmeter network. The triggered SSE occurred on a place on the plate interface where the recurrence time for such events had almost expired, whereas other regions, at up to 90% of the recurrence time, were not triggered. This provides information for the conditions for triggering and generation of SSEs and, perhaps, for regular earthquakes.
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 Episodic slow slip events (SSEs) and tremor found in southwest (SW) Japan are characterized by their regular recurrence with an interval of several months [Obara et al., 2004; Obara, 2010], less than half of those in Cascadia [Rogers and Dragert, 2003]. Transient activation of tremor by the passage of seismic waves has also been observed without SSEs, mainly in western Shikoku [Miyazawa et al., 2008], 300 km west of the current target, the Kii peninsula region (Figure 1). Such triggered tremor events have become well documented, particularly showing the clear correlation with the oscillations of the passing surface waves [Rubinstein et al., 2007; Miyazawa and Brodsky, 2008]. However, although some tremor has been seismically observed to continue longer after the triggering [Peng et al., 2009; Shelly et al., 2011], direct geodetic evidence, which is essential to constrain slip and stress drop of SSEs, has not reported to show the occurrence of SSEs on plate interfaces [Smith and Gomberg, 2009]. One observation mentioned possible teleseismic triggering of tremor/SSE on a subduction zone but it was not definitive due to the existence of preceded tremor activities and absence of geodetic evidence to allow for the examination of the onset timing [Rubinstein et al., 2009]. The relevant geodetic reports on SSEs are limited only on tidal modulation of an ongoing SSE [Hawthorne and Rubin, 2010], the statistical increase of their occurrence during typhoons [Liu et al., 2009] and dynamically triggered slip lasting for ten minutes below a volcano [Johnston et al., 2004].
 To understand the physics of earthquake generation, earthquake triggering is a useful phenomenon allowing to estimate triggering stress. The causative stress perturbations by seismic waves range from 0.1 kPa to 10 kPa [Miyazawa et al., 2008; Peng et al., 2008; Gomberg, 2010] and by tides of a few kPa [Nakata et al., 2008; Thomas et al., 2009]. These values are close to stress drop of SSEs [Miyazaki et al., 2006]. Regular earthquakes are also triggered dynamically [Gomberg et al., 2001] and statically [King et al., 1994] by earthquakes. However, there is always a difficulty to clarify the pre-stress level caused by tectonics, necessary to understand the triggering mechanism. By overcoming this problem, we must identify what controls the earthquake triggering, particularly regarding a huge unknown, the triggered event sizes.
 We used the data from a borehole strainmeter network recently deployed by the Geological Survey of Japan enabling us to detect relatively small SSEs in Kii. The strainmeters are suitable for this study because they are generally more sensitive to SSEs than tiltmeters deployed nationwide [Itaba et al., 2010]. We also use short period and broadband seismometers to determine tremor hypocenters and triggering stress, respectively. We detail analysis methods and treatments of data in the auxiliary material.
Figure 1 shows the tremor activities in SW Japan excited after the arrival of teleseismic waves from the Tonga Mw 7.6 March 2009 earthquake. The tremor was induced in Kii, western Shikoku and Tokai around 4:00, March 20 2009 (Japan Standard Time). The episode of triggered tremor ceased after less than an hour in western Shikoku and Tokai, but lasted more than 1.5 days in Kii. This indicates that the phenomenon in Kii was fundamentally different, as we shall see in what follows.
 The strainmeter records in Kii (Figure 2b) showed obvious anomalies initiated at the time of the wave arrival and lasting until around 20:00 next day (see Figure 3 for station locations). These attained a change of up to 1 × 10−8 strain. The tremor activity (Figure 2c) also started simultaneously with the arrival of the teleseismic waves. By closely observing the onset of the strain anomaly for the components experienced large changes (Figure 2d), we can see the obvious abrupt changes in the trends of the temporal strain evolution around the surface wave arrivals; the amount of the observed strain rate in this initial moment were maintained almost equally for the whole event period (Figure 2b). The strain records of the other stations nearby are shown in Figure S1. We can also roughly identify the temporal inflexion point even on the strain records alone, particularly in the records filtered at the lower frequency, within about 2000 seconds after the wave arrival. The seismogram at a nearby station (HGM) also clearly recorded the tremor activation correlated with the wave arrivals (Figure 2f). Such anomalies were not recognizable on the tilt records (Figure S1). The networked sensitive and high sampling strain records exclusively captured these geodetic anomalies without any special processing. This set of the strain records is the first direct evidence of a interplate SSE triggered by teleseismic waves.
 We performed an inversion analysis given a fault on the plate interface [Itaba et al., 2010] (detailed in the auxiliary material) to estimate the location, size and slip of the triggered SSE, from the strain changes observed by four stations (Figure 3). We can see the obtained optimum fault model with Mw 5.3 overlaps the tremor locations and explains the observed strain changes well.
 We now examine the generation conditions of this event in the following three aspects. First, we estimated the stress change on the plate interface due to the teleseismic wave from the Tonga event based on an observed seismogram using the method of Miyazawa and Brodsky . We used the seismogram at the nearest F-net broadband station, KIS (Figure 3) and found that the Raleigh wave, a candidate to cause the triggering [Miyazawa and Brodsky, 2008], induced the maximum displacement of 4.3 × 10−4 m with the predominant period of 25 s. On the plate interface at depth of 30 km, the maximum Coulomb stress was of about 0.6 kPa given the frictional coefficient of 0.6 (the maximum normal and shear stresses were about 0.9 kPa and 0.4 kPa, respectively). These levels are about one order smaller than that attained in SW Japan by the 2004 Mw9.2 Sumatra earthquake and similar to that by the 2007 Mw8.1 Solomon earthquake. Both these cases triggered transient tremor [Miyazawa et al., 2008].
 Second, we found in the space-time patterns of tremor/SSEs in this region (Figure 4) that the triggered SSE is in the central segment in between the eastern and western segments. The repeating tremor/SSEs primarily break one segment with occasional multiples. The regular recurrences intervals are estimated to be about 120 ± 20 days for the central segment, and 170 ± 10 days for the eastern segment [Obara, 2010]. Here we find that, on the central segment, the last event prior to the triggered event occurred 138 days earlier. In fact, this is the same as the regular interval. Therefore, we can presume that the critical stress level for a spontaneous rupture, determined as a function of fault strength [Madariaga and Olsen, 2000], had been almost reached by the tectonic loading over this segment. Since the regular recurrence pattern suggests that the tectonically accumulated stress is almost dropped to a certain baseline due to SSEs every time, we can estimate the contribution of the tectonic stress from the stress drop. We obtained the stress drop of the triggered SSE to be about 11 kPa, which is comparable to that of a non-triggered event, e.g., about 7 kPa for one on November 2008.
 On the other hand, for the eastern segment, large tremor/SSE breaking the whole segment was not triggered associated with the teleseismic wave although a few scattered short events were seen. There, the elapsed time from the previous event was also about 130 days, but which there is about 75% of the mean recurrence period, strongly suggesting that sufficient tectonic stress had not yet accumulated on this segment to make it susceptible to triggering. In Tokai and western Shikoku the elapsed times were about 20% and 90% of the regular recurrence periods, respectively. The latter elapsed time defines the estimate upper limit thus far to be below the triggering threshold.
 Finally, we inspect effects of a nearby SSE in time and space, the nearest of which was on February 2009 breaking the western segment (Figure 4). We obtain a rough estimate of the static Coulomb stress change up to 1 kPa rapidly decreasing with distance from the segment boundary. Obviously, it has a small influence on the bulk of the central segment (Figure S3).
 The above results show, at least for this case, that the clock advance [Gomberg et al., 1998; Gomberg, 2010] of the triggered SSE was very small, and, with insufficient stress accumulation due to tectonic loading, a small transient stress perturbation would not generate an SSE. Thus, we will conclude that the extent and magnitude of the static stress increment, which is usually controlled by the tectonic loading, primarily determines whether a triggered event grows afterward, say, to the size of an SSE. From this respect, we presume the triggering of SSEs differs in the mechanism from that of transient tremor in its sensitivity to transient stresses.
 We check the relevance of the earth and ocean tidal stresses by using the algorithm of Tsuruoka et al. . In Figure 2d, we find that the day of the triggering was nearly at neap tide and larger Coulomb stress was experienced during the last half a month; Figure 2g shows that the tidal stress at the moment of the triggering was 0.4 kPa, about two-thirds of the teleseismic contribution. Given also the tectonic stress accumulation must be negligible in the last few days before the SSE, we can conclude that the tidal stress was not the primary factor of the current triggering although it could contribute. In addition, while our data is insufficient for quantifications yet, possibly the seismic waves might reduce somewhat a triggering threshold due to their much higher stressing rate than that of the tide as suggested for triggering of regular small earthquake [Gomberg and Davis, 1996].
 All these observational results are basically understandable with the stick-slip mechanism common in physical earthquake models for both slow and regular earthquakes [Carlson et al., 1994; Madariaga and Olsen, 2000; Shibazaki and Shimamoto, 2007; Ando et al., 2010; Nakata et al., 2011], suggesting large earthquakes cannot occur without sufficient stress accumulation over a large area and a slight stress perturbation can trigger an event only near the critical stress state. But this theoretical expectation is usually very hard to be quantitatively evaluated and verified by observations because of the fundamental difficulty of estimating the stress and strength at depth, often limiting our scope to the contributions due to well-documented phenomena such as preceding earthquakes [King et al., 1994; Gomberg, 2010].
 We found the first evidence for the triggering of an inter-plate SSE by teleseismic surface waves. This evidence was captured by a strainmeter network. The underlying regularity of the recurrence and the frequent occurrence of the SSEs gave us unique opportunity for understanding earthquake physics, and further applications are promising. Our results provide the constraints on the stationary-regional and transient-local states of ambient stress and strength at depth, which help to understand the generation mechanism of large events including slow earthquake and regular brittle failure earthquakes.
 We thank N. Takeda for providing catalogues of the locations of tremor and helpful suggestions. H. Tsuruoka kindly provided his computational algorithm for tides. We use Hi-net and F-net data provided by National Research Institute for Earth Science and Disaster Prevention, and data from University of Tokyo and Nagoya University. Beneficial comments by C. Scholz and critical reviewing by M. Johnston improved the paper. This work was partially supported by MEXT KAKENHI (21107007).
 The Editor thanks an anonymous reviewer for their assistance in evaluating this paper.