**3. Application to the detection of preseismic slip for megathrust earthquakes**

As pre- and post-seismic changes, intense LFT activity began to occur almost directly below the 2004 Parkfield earthquake about three weeks before the earthquake and has continued only apart from the hypocenter over for four years (Nadeau & Guilhem, 2009; Shelly, 2009), which means that the distance from the hypocenter of triggering earthquake may also affect the sensitivity of LFT to pre- and post-seismic slip (Shelly, 2009).

In this section, we try to apply preseismic change of slow earthquake migration to the detection of megathrust earthquakes on the basis of characteristics of slow earthquake migration as described in the section 2.

#### **3.1 A test model of slow earthquake migration for long travel distance**

Fig. 8 shows a 3-D model of a subduction plate boundary derived from Fig. 2. Its frictional parameter is the same as Fig. 3 in order to investigate slow earthquake migration for long distance across the center of large asperity along strike direction as observed south-western Japan (Obara, 2010).

These differences from MA are explained as follows. SA has shorter recurrence intervals and smaller moment release because of smaller asperity size with shorter characteristic distance than those of MA. The smaller moment release makes propagation speed slower (0.03 km/day for SA is smaller than 0.2 km/day for LA), which causes that recurrence interval of SA is relatively much shorter than the passage time of aseismic slip across more than twice the SA diameters (10 km). In addition, locking of SA soon after the occurrence of slow earthquakes, due to their short characteristic distance, tends to prevent aseismic slip propagation. Therefore, slow earthquakes occur again soon after the passage of aseismic slip from asperity No. 29 as shown in Figs. 7n-o. This is why propagation process of SA as shown in Figs. 7n-o appears to be bilateral, rather than the unilateral propagation seen in

Fig. 5 clearly shows that only slow slip events occur at depth of 30 km where frictional property is slightly stable and uniform along strike, while various slow earthquakes including very low-frequency events (orange color in Fig. 5) are generated by chain reaction between small asperities. This result suggests that chain reaction model as shown in Fig. 1

Fig. 7 shows that MA has recurrence interval longer than that of SA, which is also seen for migration distance. These results may suggest that we can estimate asperity size on the basis

For example, migration of low-frequency tremor observed in Kii and Tokai area tends to be unilateral with longer travel distance and loger recurrence interval of slip events, while the tremor in Shikoku tends to be shorter recurrence interval and shorter travel distance (e.g., Obara, 2010). These results suggest that size of asperities generating slow earthquakes in Kii and Tokai is larger than that in Shikoku. Therefore, investigating slow earthquake migration process is important to estimate the characteristics of small

**3. Application to the detection of preseismic slip for megathrust earthquakes**  As pre- and post-seismic changes, intense LFT activity began to occur almost directly below the 2004 Parkfield earthquake about three weeks before the earthquake and has continued only apart from the hypocenter over for four years (Nadeau & Guilhem, 2009; Shelly, 2009), which means that the distance from the hypocenter of triggering earthquake may also affect

In this section, we try to apply preseismic change of slow earthquake migration to the detection of megathrust earthquakes on the basis of characteristics of slow earthquake

Fig. 8 shows a 3-D model of a subduction plate boundary derived from Fig. 2. Its frictional parameter is the same as Fig. 3 in order to investigate slow earthquake migration for long distance across the center of large asperity along strike direction as observed south-western

**2.4 Discussions of chain reaction effect on slow earthquake migration** 

can explain various types of slow earthquakes occur in the same region.

of migration distance and recurrence interval of slow earthquakes.

the sensitivity of LFT to pre- and post-seismic slip (Shelly, 2009).

**3.1 A test model of slow earthquake migration for long travel distance** 

migration as described in the section 2.

Japan (Obara, 2010).

Figs. 7a-7e.

asperities.

Fig. 8. A 3-Dimensional model of a subduction plate boundary with frictional parameter *a-b* (Eq. 3), where the color scale is the same as Fig. 2.

#### **3.2 Long-term change in the migration speed of slow earthquake swarms**

Figs. 9a and 9b show the spatiotemporal evolution of the slip velocity normalized by *V*pl at 115 km down-dip from the trench (along green line in Figs. 9d and 9e) in the interseismic and preseismic stages, respectively. Close-up of the slip velocity pattern in the rectangle in Fig. 9b is shown in Fig. 9c. Figs. 9d and 9e show the snapshots of the normalized slip velocity 20 years after and 0.86 years before a megathrust earthquake, respectively.

Based on Figs. 9a-9c, we calculate the migration speeds of slow earthquake swarms by tracking transients with slip rate ranging from 2 to 10 *V*pl (indicated by yellow color). Periods of larger slip rate (from 10 to 100 *V*pl indicated by orange colors) are difficult to find in Fig. 9b because of their short duration, except for times later than -0.2 years in Fig. 9b.

The dominant migration speed is calculated to be approximately 0.3 to 1 km/day during the interseismic stage (Fig. 9a), while 1 to 3 km/day in the preseismic stage (Fig 9b). Therefore, the simulation results suggest that monitoring of the migration speeds of slow earthquake swarms as well as recurrence intervals are useful to forecast great earthquakes.

Approximately one month before the megathrust earthquake, Fig. 9b shows that the dominant slip velocity for |Strike| < 40 km becomes higher than 10 *V*pl (orange) and is sustained over a long duration time (more than one month). This implies that the moment release rates of slow earthquake swarms near the locked region of LA just before a megathrust earthquake tend to be significantly higher than that in the interseismic stage.

Fig. 9. (a)(b) Spatiotemporal evolution of slip velocities at the "Dip" of 115 km along strike (green line in Figs. 9d and 9e) in the interseismic and preseismic stages, respectively, after Ariyoshi et al. (2011b). Color scale is the same as Fig. 4. The broken lines in (a) denote the migration speed in km/day. (c) Close up of the slip velocity evolution in the spatiotemporal region enclosed by the green rectangle in (b), keeping the aspect ratio of space to time. (d)(e) Snapshots of the slip velocity field (d) 20 years after and (e) 0.86 year before the occurrence time of the megathrust earthquake. The ellipse enclosed by the purple curve in (e) represents a large aseismic slip event activating slow earthquakes as shown by the ellipse in (b).

Fig. 9d suggests that the slip velocity is approximately less than 0.5 *V*pl (aqua) in the region surrounding the SA (boxed area) and less than 0.1 *V*pl (blue) dominantly along the center of

Fig. 9. (a)(b) Spatiotemporal evolution of slip velocities at the "Dip" of 115 km along strike (green line in Figs. 9d and 9e) in the interseismic and preseismic stages, respectively, after Ariyoshi et al. (2011b). Color scale is the same as Fig. 4. The broken lines in (a) denote the migration speed in km/day. (c) Close up of the slip velocity evolution in the spatiotemporal region enclosed by the green rectangle in (b), keeping the aspect ratio of space to time. (d)(e) Snapshots of the slip velocity field (d) 20 years after and (e) 0.86 year before the occurrence time of the megathrust earthquake. The ellipse enclosed by the purple curve in (e) represents a

large aseismic slip event activating slow earthquakes as shown by the ellipse in (b).

Fig. 9d suggests that the slip velocity is approximately less than 0.5 *V*pl (aqua) in the region surrounding the SA (boxed area) and less than 0.1 *V*pl (blue) dominantly along the center of the SA belt (green line), except for the region where a slow earthquake migration occurs (yellow and orange). Fig. 9e suggests that the area of higher slip velocity (orange) covering SAs in the preseismic stage tends to be larger than in the interseismic stage as shown in Fig. 9d, and there is no region in which the slip velocity is less than 0.1 *V*pl. Slip velocity in LA becomes higher due to the preseismic slip, especially about one year before the megathrust earthquake. These results mean that preseismic slip of LA promotes higher moment release rates of slow earthquake due to its higher slip velocity.
