Figure 2 shows space–time plots of detected LFEs from April 2004 to August 2015. Each major streak, occurring on a distance scale of up to 100 km, indicates an intensive burst of LFEs migrating along the fault-strike direction, corresponding to a major ETS episode with equivalent Mw ~ 6.0 (Hirose and Obara 2010; Sekine et al. 2010; Hirose and Kimura 2020). In the western part of Shikoku Island, we identify long-lasting bursts of LFEs during 2010 and 2014 (horizontal bars in Fig. 2); these correspond to geodetic detections of long-term slow slip events in the Bungo Channel using GNSS data (Yoshioka et al. 2015; Ozawa 2017). It is notable that series of LFE swarms occurred along strike intermittently during the long-term SSEs. These results are similar to bursts of LFEs detected during the 2006 SSE in the Mexican subduction zone (Frank et al. 2018). These observations suggest that a large-scale, long-term SSE contains a multitude of smaller, temporally clustered events (Jolivet and Frank 2020).
The equivalent moment magnitude of the 2010 SSE (Mw 6.9) in the Bungo Channel is larger than that of the 2014 event (Mw 6.5; Yoshioka et al. 2015; Ozawa 2017). The number of LFEs detected during the 2010 long-term SSE was also greater than the number detected during the 2014 event, indicating that the energy released by each SSE controls the extent of LFE activity. We also recognize a slight increase in the number of LFEs in 2006, which roughly corresponds to a minor long-term SSE (Mw ~ 6.3) reported by Takagi et al. (2019). This slight increase implies the occurrence of a smaller SSE than those in 2010 and 2014.
The 2011 Mw 9.0 Tohoku-Oki earthquake occurred during the analysis window. However, we observed no significant behavioral differences between LFEs before and after the megathrust rupture, except for an enhancement of rupture connectivity between several segments from Bungo Channel to the eastern Shikoku (red shaded bars in Fig. 2). The occurrence rate remained similar, regardless of stress perturbations induced by the megathrust rupture. This observation is consistent with Kono et al. (2020), who demonstrated that there were no temporal variations in the estimated rate of seismic moment release by tectonic tremor along the Nankai subduction zone as a result of the Tohoku-Oki earthquake. But, note that the spatio-temporal evolution of LFEs has changed from ~ 2012, in Shikoku island where major ETS episodes more frequently migrated long-distance through multiple segments than before the Tohoku-Oki earthquake. This behavioral difference has indicated an enhancement of rupture connectivity (Takagi et al. 2016), and resulted in an increase in the number of short-term SSEs with larger slip extent and seismic moment after 2012 (Hirose and Kimura 2020).
As a distinct example of an ETS episode (Fig. 3), major LFE activity was initiated beneath western Shikoku on 25 May 2012, then migrated eastward along strike, spreading over a distance of up to 100 km during the following 8 days. Five days later, a second burst of activity began further east, across an LFE gap. The secondary activity appears roughly in agreement with the extrapolated propagation of the front of the initial sequence. These migration fronts of LFEs showed clear parabolic curves (broken red lines in Fig. 3a); that is, the front location is proportional to the square root of time elapsed from the initial event (\( \sim \sqrt {Dt} \)). The diffusion coefficient \( D \) of the two sequences is ~ 104 m2/s, within the range of values reported by previous studies using tectonic tremor signals (Ide 2010; Ando et al. 2012).
Before the main front of the migrating LFEs was reached, minor LFE activity started at a position of − 210 km projected along strike, indicated by the gray dotted-line rectangle in Fig. 3a. The occurrence rate of minor LFEs rapidly increased, to ~ 8 × the base rate (8R in Fig. 3b), when the migrating front of the major LFEs merged with that of the minor ones. This observation suggests that a minor SSE combined with the major SSE propagating in the fault-strike direction. The merging of two SSEs probably caused local acceleration of fault slip, resulting in intensive LFE activity after the passage of the slip front. A temporal acceleration in slip induced by the merging of two SSEs has been reported along the Cascadia subduction zone based on geodetic measurements (Bletery and Nocquet 2020), but on a much larger scale.
As another example, Fig. 4a shows bilateral diffusion-like along-strike migration of the LFE front, with \( D \) = 104 m2/s, that initiated on 14 October 2009 in the eastern Kii Peninsula, Japan. Activation of LFEs started at a distance of ~ 55 km along strike with a delay of approximately 5 days relative to passage of the main SSE front, which was moving toward the southwest. Delayed LFEs occurred to fill the LFE gap. As observed in Cascadia (Wech and Bartlow 2014), weak tremor-less slip might occur within this gap when the main front undergoes early migration toward the southwest, resulting in the connection of two spatially disjoint LFE areas. The LFEs terminate at a reduced slip rate when the migrating slip front reaches a non-critically stressed patch (Wech and Bartlow 2014), but the slight increase in loading rate can trigger additional slip at a distance.
During the slow long-distance migrations of LFEs, the migration patterns are categorized as diffusion-like and linear-like styles. The diffusive migrations can be identified during the other periods as listed up in Additional file 3: Table S1, in addition to the two periods in Figs. 3 and 4. The diffusive migrations are often observed in the western Shikoku and the eastern Kii Peninsula. This may be due to a higher spatial resolution of LFEs at the two areas, where the radiated energies of tremors show the largest values among the entire tremor belt (Annoura et al. 2016), resulting in a high signal-to-noise ratio.
As shown in Figs. 3c and 4b, LFE activity occurred intermittently during or after the passage of the main front of migrating LFEs, indicated by striped patterns of intense activity that occurred as the front passed. Along the stripes, LFEs migrated in the along-dip and along-strike directions. Intermittent LFEs were reported by Shelly et al. (2007b) for a few ETS episodes in western Shikoku. The present study discovers that intermittent LFEs are pervasive along the Nankai subduction zone and have occurred over at least the 11-year study window (Fig. 1). ETS also contains a series of smaller, temporally clustered slow slip transients, as seen during the long-term SSE at Bungo Channel (Fig. 2). These observations, on different temporal and spatial scales, imply that intermittent slow slip may be a scale-invariant property of slow earthquakes.
The intermittent stripes of activity show distinct spatial and temporal patterns in LFE swarm evolution over distances up to 15 km (Fig. 5). The migration speeds are quite fast, and reach ~ 60 km/h; similarly, the rapid LFE migrations of Shelly et al. (2007b) occurred at rates of 25–150 km/h in western Shikoku. Some of fast migrations in the western Shikoku obey a diffusion-like evolution (broken red lines in Fig. 5), while others can be explained by linear propagations. It is hard to convincingly demonstrate the diffusion-like migration at small scale, because the spatial scale is approaching the spatial resolution of LFE location and the number of events during each fast sequence becomes small. However, we believe that fast short-distance migration also follows a diffusional behavior as like the slow long-distance migration of ETS episodes (Figs. 3 and 4).
In the case of the diffusive migration, \( D \) is estimated to be ~ 105 m2/s, an order of magnitude greater than for slow long-distance migration of ETS episodes (Figs. 3 and 4). Rapid migration can have a short duration (~ 10 min) and small length scale (~ 15 km), in contrast to slow long-distance migration of ETS episodes (Figs. 3a and 4a). Along the Cascadia subduction zone, similar rapid migration of tremor streaks was reported by Ghosh et al. (2010). Most of the streaks propagated at velocities of 30–110 km/h, with a peak of ~ 70 km/h, over distances of < 40 km. Although Cascadia tremor migration speeds have the same velocity range as those in Nankai, the length scale in Cascadia is much greater than in Shikoku, which roughly corresponds to the width of the deep tremor band (Ide 2012).
In summary, slow long-distance migration of LFEs during an ETS episode contains a series of slip events comprising pulses of more rapid slip with short-distance migrations (Shelly et al. 2007b). The migration speed of LFEs increases with decreasing length scale, which is similar to observations of tectonic tremor migration (Houston et al. 2011; Obara et al. 2012). The present study suggests that high-speed migration of LFEs may follow a diffusion pattern, even at shorter length scales (Fig. 5). Two fast short-distance migrations in Fig. 5f, g occurred during the slow long-distance migration of ETS episodes shown in Fig. 3. These features imply that a diffusional process controls slow slip at multiple temporal and length scales. As Kano et al. (2018a) proposed, slow slip can be explained by a stress diffusion model with lubrication by fluid, consisting of along-strike heterogeneities in the effective strengths of brittle patches embedded in a ductile shear zone along the plate boundary fault.
We consider that the present LFE catalog (Additional file 2) will be useful for understanding the long-term behavior of minor and major slow slip events along the Nankai subduction zone. The present study uses only LFEs with relatively high SNR as template events to reduce the total computation time. The selected LFEs are representative of the overall behavior of slow slip transients, but increasing the number of template events in future work will allow us to examine the spatio-temporal evolution of LFE activity at finer scales.