Results and discussion

Inversion of the model parameters, for L=40 km, give p=1.132, c=0.002 days, L0=0.099 km for m0=2.0, γ=2.339 and K0=0.006. We fix α to 2.0, otherwise the inverted α value is low (<1.0). It is known that seismicity dominated by swarms cause the estimated α value to be unrealistically low (Hainzl et Ogata, 2005; Lombardi et al., 2006). Moreover, with a low α

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value, the model becomes more flexible and able to adjust to sudden variations in the times series, preventing it to detect ”abnormal” seismic activity in the data. We show, in Figure 6.5, the cumulative number of earthquakes and the time series of the background seismicity rate-density μ_xyt calculated for the 40 × 40 km² cell of Figure6.3.

μxyt (Eqs/day/km2) Cumulative number of earthquakes

SSE

Figure6.5 – Cumulative number of earthquakes (in red) and time series of the background seismicity rate μxyt(in blue) for the Boso area. The three transients occurring outside the 5 known SSEs are labeled A1,A2,A3.

SSEs are clearly marked by large values of μ_xyt, although the most important increase is found in 2011.2, right after the 2011 Mw9.0 Tohoku-Oki earthquake. This earthquake activated seismicity in a large region, including the eastern part of our study area (Hirose et al., 2011;

Ishibe et al., 2011; Toda et al., 2011; Toda et Stein, 2013). The high increase of background seismicity is produced because the Tohoku-Oki earthquake is located outside the studied area.

It is therefore absent from our catalog ; the triggering term ν thus cannot explain this increase in earthquake activity. Nevertheless, Kato et al. (2014) detected a possible SSE one day af-ter the Tohoku-Oki earthquake, lasting for 3-4 days. We experience difficulties in separating the increase of background seismicity due to this possible transient from the background seis-micity directly caused by the Tohoku-Oki earthquake. Moreover, after this earthquake, the completeness magnitude is higher for few days, due to difficulties in interpreting and separating earthquakes in the seismic records (Kagan,2004).

Also, we detect three other important peaks in background rate that require further atten-tion. The 1991 occurrence (A₁) is characterized by an important seismic activity (18 events

≥ m_c = 2.0 over 10 days) and could be a signature of another SSE, see Figure 6.6. Ozawa (2003) noted variations in tiltmeter data during this period, at station KTU. A northwestward direction for the tilt vector was recorded, which is consistent with a SSE occurrence (NIED, 2003). However this cannot be confirmed in the absence of GPS measurements. The 1994 and 2000 (A₂ and A₃) transients are composed of only a few earthquakes with magnitude greater 124

6.3 Relationship between changes in seismicity and seismic moment for Slow Slip Events in Boso Peninsula, Japan than m_c=2.0 (5 and 9 events, respectively), see Figures 6.7-6.8.

^R( ^R( ^R( ^R(

90/07 90/08 90/09 90/10 90/11 90/12 91/01 91/02 91/03 91/04 91/05 91/06

7LPH\UPQ

90/07 90/08 90/09 90/10 90/11 90/12 91/01 91/02 91/03 91/04 91/05 91/06

Figure 6.6 – Seismicity map between 1990 and 1991 for a larger area compared to Figure 6.3. We show in the top right graph the seismicity in Boso (box 1) and in the bottom graph the seismicity offshore the Izu-Island (box 2). Red dashed line marks the occurrence of transient A1.

These swarms took place during volcanic unrest in Izu-Island. In 2000, a magmatic intrusion preceded the eruption of Miyakejima Volcano (Nakada et al.,2005).Nishimuraet al.(2001) no-ted anomalous GPS displacements in the Boso Peninsula associano-ted with this volcanic activity.

These displacements, almost reaching 1 cm, could hide a possible SSE occurring at the time of the intrusion. The 1994 case is less obvious : moderate activity (5 earthquakes) occurred in the Boso peninsula, coincident with another moderate burst of activity underneath Izu-Island.

The anomalous sequences detected during SSE episodes are listed in Table 6.2, for the dashed box shown in Figure 6.3. All these anomalies have a probability to be abnormal greater than 95%.

We note that the numbers of earthquakes occurring during these swarms are only weakly correlated with the moments of the SSEs (Figure 6.9A), while the increases ^μxyt

μxy in background rate are, see Figure 6.9B.

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93/07 93/08 93/09 93/10 93/11 93/12 94/01 94/02 94/03 94/04 94/05 94/06

7LPH\UPQ 7LPH\UPQ

93/07 93/08 93/09 93/10 93/11 93/12 94/01 94/02 94/03 94/04 94/05 94/06

Figure 6.7 –Same as in Figure 6.6, for the period between 1994.5 and 1995.5 and for transientA2.

00/01 00/02 00/03 00/04 00/05 00/06 00/07 00/08 00/09 00/10 00/11 00/12 ^R( ^R( ^R( ^R(

00/03 00/04 00/05 00/06 00/07 00/08 00/09 00/10 00/11 00/12

Figure 6.8 –Same as in Figure 6.6, for the period between 2000.5 and 2001.5 and for transientA3.

The increase in background seismicity is well correlated (96 %) with the moment relaxed 126

6.3 Relationship between changes in seismicity and seismic moment for Slow Slip Events in Boso Peninsula, Japan

Date Numbers of ratio Probability

(year) m≥2 earthquakes µxyt/µxy to be anomalous

1996.4 10 × 18.3 >99.99 %

2002.8 29 × 29.1 99.94 %

2007.6 63 × 49.9 99.94 %

2011.8 22 × 50.3 >99.99 %

2014 21 × 18.6 97.3 %

Table 6.2 – Earthquake swarms detected by our model for L=40 km and τ=10 days, at the time of known SSEs. We note that all swarms are detected with very high significance levels.

during the SSEs, in agreement with the linear relationship found at large scale for subduction zones byIde(2013). We estimate the best linear trendMSSE =a×10 days×^µ_µ^xyt_xy with a=2.431

± 0.078 ×10¹⁶ N.m.day⁻¹ . This coefficient a can be thought of as being the long-term seismic moment rate ˙MLT per day, giving a yearly rate equal to 8.88.10¹⁸ N.m.yr⁻¹. Using the seismic moment relationship of Aki (1966),

M=G×S×D (6.5)

with a rigidity modulusG of 30 GPa, and a surfaceS of 40× 40 km², we infer a long-term (over nearly 25 years) displacement rate of 0.185 ±0.006 m/yr .

We tested the sensibility of our results withα, by rerunning our analysis for α =1.0 and α

=1.5. We found a long-term displacement of 0.178 and 0.185 ± 0.006 m/yr for these two cases, but with a lower correlation between the increases in background seismicity and the seismic moments of the SSEs (94.2 % and 94.9 %, for α=1.5 and α=1.0 respectively), see Figure 6.9B.

Our long-term displacement rate is estimated for a 25 year-long period that cover several phases of co- and inter-SSE periods. Nishimura et al. (2007) suggested a total coupling in this region during inter-SSE phases, along with a convergence rate of 23 mm/yr.

In the case where shear is totally relaxed in Boso during SSEs, i.e., there is full coupling during inter-SSE phases and full uncoupling during SSEs, the slip rate over the 1990-2014 period should equal the long-term convergence rate estimated to 23 mm/yr by Nishimuraet al.

(2007). Our estimate is 8 times higher, implying that the gains ^µ_µ^xyt_xy during SSEs would be underestimated by a factor of 8 if our argument was valid. A possible explanation for this discrepancy is that µevolves in time more slowly than does the slip rate, as expected with rate-and-state friction. Using Dieterich(1994)’s treatment, it can be shown that a sudden change in stressing rate ˙τ from ˙τ₀ to ˙τ₀^′ =x×τ˙₀ (gain x) at time t = 0 causes the rate of earthquakes to increase from µ to ^µx

1+(x−1)e^−t/t′a where t^′_a = ^t_x^a = ^t_x^a_τ˙^σ

0 is a characteristic time, see Figure6.10.

For a gain in rateµto be 8 times less than the gain in stressing rate ˙τ, after a typical time of 10 days, it is required that t^′_a = ^t_x^a ≃ _ln(x/7)¹⁰ days (assuming x ≫1). This equation relates two quantities that are largely unknown : (i) ta, the characteristic relaxation time, was estimated by

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