The Kanto seismic corridor surrounding Tokyo has hosted four to five M ≥ 7 earthquakes in the past 400 years. Immediately after the Tohoku earthquake, the seismicity rate in the corridor jumped 10-fold, while the rate of normal focal mechanisms dropped in half. The seismicity rate decayed for 6–12 months, after which it steadied at three times the pre-Tohoku rate. The seismicity rate jump and decay to a new rate, as well as the focal mechanism change, can be explained by the static stress imparted by the Tohoku rupture and postseismic creep to Kanto faults. We therefore fit the seismicity observations to a rate/state Coulomb model, which we use to forecast the time-dependent probability of large earthquakes in the Kanto seismic corridor. We estimate a 17% probability of a M ≥ 7.0 shock over the 5 year prospective period 11 March 2013 to 10 March 2018, two-and-a-half times the probability had the Tohoku earthquake not struck.
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 We seek to understand the source and consequences of a remarkable increase in seismicity rate beneath greater Tokyo. Our goal is to transform these observations into a time-dependent occurrence probability of large, damaging earthquakes. The Kanto seismic corridor has produced many large damaging earthquakes since the founding of Edo (now, Tokyo) in AD 1603. These include the 1649 M ~ 7.0, 1767 M ~ 7.0, 1812 M ~ 7.1, the Ansei-Edo 1855 M = 7.1–7.4 that all but destroyed Tokyo, and 1856 M ~ 6.8 earthquakes [Grunewald and Stein, 2006]. Although the depths of these events are unknown, and Usami  provides somewhat different magnitudes and locations for them, the similarity of the intensity patterns for the 1855 Ansei-Edo earthquake and a 70 km deep 2005 M = 6.0 event near Chiba suggests that the 1855 and 2005 events have similar hypocenters [Bozkurt et al., 2007]. Toda et al.  argued that these earthquakes, like the 40-80 km deep smaller shocks of the Kanto seismic corridor, are the product of the movement of a fragment of the Pacific slab wedged between the Pacific plate below and the Eurasian plate above. Ishida  identifies what we regard as the Kanto fragment as a highly deformed Philippine Sea plate slab.
2 Seismicity Observations
 Even though Tokyo lies 300 km southwest of the high slip portion of the M = 9 rupture, and 100 km southwest of its M = 7.9 aftershock (Figure 1a), the seismicity rate in the Kanto seismic corridor jumped by a factor of 10 immediately after the M = 9 Tohoku earthquake (Figures 1b–1c), as reported by Toda et al. [2011a], Ishibe et al. , and Hirose et al. . The seismicity rate gain occurred at the same depth of pre-Tohoku shocks (Figures 1b–1c). Maps of the seismicity rate change are shown in Figure S1, it is spatially quite stable.
 The time series of M ≥ 3 seismicity (Figure 2a) shows a steady background rate during 2006–2010, followed by a sudden jump and decay that resembles aftershock activity, evident at least to M ≥ 5. Sometime during June–December 2011, the seismicity stopped decaying and has since remained constant (Figure 2b). This departure from the decay was not associated with any large Kanto shock (Figure 2a). The Kanto corridor earthquakes could be regarded as off-fault aftershocks of the Tohoku-oki earthquake. A decay exponent p of 0.44 ± 0.07 would be needed to match their decay statistically with Omori process, about half a typical aftershock value. Even if the decay could be matched by Omori decay, the apparent background rate increase cannot. In contrast, the b value for Kanto seismicity before the Tohoku main shock is indistinguishable from that afterward (Figure S2).
3 Static Coulomb Stress Model
 Here we attempt to explain the observations by static stress transfer, seeking to explain the seismicity decay, the focal mechanism change, and the new background rate. The static Coulomb stress change caused by fault slip, ΔCFF = Δτ + μΔσn, where Δτ is the shear stress change on the receiver (positive in the direction of presumed fault slip), Δσn is the fault-normal stress change (positive when unclamped), and μ is the effective coefficient of friction [King et al., 1994; Harris, 1998]. We treat the 2011 source as an elastic dislocation in a halfspace with Young's modulus 8 × 105 bar and Poisson's ratio 0.25 and resolve ΔCFF on “receiver” faults identified from seismicity alignments, tomography, and tectonic interpretation in Toda et al.  or from focal mechanisms.
 We use the 11 March 2011 M = 9.0 source model of Ide et al.  inverted from broadband seismic stations. We also include the Mw = 7.9 aftershock, modeled as a simple tapered square following Toda et al. [2011b]. Because Kanto is so far from the 2011 rupture, the results are insensitive to the slip distribution; the stress transfer scales with the main shock seismic moment and is most dependent on the inferred geometry and friction on the faults beneath Kanto. Toda et al. [2011b] tested friction coefficients of 0.0, 0.4, and 0.8 on the focal mechanisms of Tohoku aftershocks during March 2011 and found the best fit to the Coulomb stress change for 0.4, which we adopt here.
 The 60–80 km deep lower surface of the Kanto fragment is calculated to have been brought ~1 bar closer to failure (Figure 3) and its upper surface (not shown) 0.3 bar closer to failure [Toda et al., 2011b]. The Off-Boso portions of the Japan trench megathrust were also brought 2 bars closer to failure (Figure 3). Both regions experienced strong seismicity rate increases, with off-Boso gain higher than that in the Kanto seismic corridor, consistent with the Coulomb modeling. The Off-Boso might be partially uncoupled, as assumed by Nishimura et al.  and Uchida and Matsuzawa .
 To test whether the calculated stresses are responsible for the changes in seismicity rate and relative focal mechanism abundances, we next calculate the stress imparted to the 96 focal mechanisms that occurred in the Kanto seismic corridor during the year after the main shock, finding that 93% were brought closer to failure by the M = 9.0 main shock and M = 7.9 aftershock. For non-zero friction, ΔCFF is dissimilar on the two nodal planes of each mechanism, so we randomly choose one plane of each pair. The significance of the 93% must be judged relative to a control population; for that, we calculate stress from the 2011 main shock to the 338 focal mechanisms in the same area before the main shock during 1997–2010, since these are unaffected by the Tohoku stress transfer. We randomly draw 96 mechanisms from this set 10,000 times and find that 78 ± 8% (±2σ) were positively stressed (Figures 4c–4d), and so the gain in promoted mechanisms is significant at more than 95% confidence. The gain arises in part because the rate of normal mechanisms dropped by half after the main shock. Although earthquakes with normal mechanisms occurred in roughly the same locations and depths before the M = 9 event and afterward, the zone of post-Tohoku quakes is more restricted spatially than beforehand (Figure 4, dotted ellipses). The change in the abundance of normal mechanism is significant at the 67% confidence level with respect to the 1997–2010 duration of the National Research Institute for Earth Science and Disaster F-net catalog (Figure S3). Thus, both the single-fault Kanto receiver of Figure 3 and the individual nodal planes of Figure 4 are consistent with stress transfer from the Tohoku-oki main shock.
4 Rate/State Coulomb Model of Seismicity Time Series
 We therefore use the seismicity rate equation of rate/state friction of Dieterich  to model the time-dependent response of seismicity to the static stress change on each nodal plane, following Toda et al. . In rate/state friction, a sudden stress increase amplifies the background rate, with the seismicity rate undergoing a step and decay resembling Omori aftershock decay, regardless of whether the shock is on or off the main shock rupture surface. We calculate the rate/state evolution of seismicity caused by the static stress imparted to the nodal planes of all 338 pre-mainshock focal mechanisms, these are used as proxies of available nucleation sites. From the histogram of the stress changes on the nodal planes (Figure 2b, inset), the mean increase of 1 bar is consistent with the simple planar model of Figure 3, but there is a range from −3 to +4 bar on the nodal planes. Most planes receive a stress increase from the 2011 main shock and so undergo a seismicity rate gain (Figure 2b, light blue curves). However, because of the diversity of strikes, dips, and rakes, some planes receive a stress decrease and shut down (horizontal light blue lines). The predicted seismicity rate evolution of each of the 676 planes is shown as a light blue curve, their daily ensemble mean is the single dark blue curve.
 In the initial model (Figure 2b, blue curve), we use the observed 2006–2010 background rate and fit the postmain shock data with the constitutive parameter times the normal stress, Aσ (0.5 bar), and fault stressing rate τ▪ (0.25 bar/yr). The first post-Tohoku year is well fit, but the curve subsequently diverges from the observations. To fit the full time series, we increase Aσ to 0.6 bar and include a stressing rate increase to 0.7 bar/yr at the time of the Tohoku earthquake (Figure 2b, green curve; individual time histories not shown). The values of Aσ needed to fit the decay, 0.5–0.6 bar, overlap the 0.4–0.5 bar found for California studies [Toda et al., 2005; Toda et al., 2012]. The stressing rates of 0.25-0.70 bar/yr are higher than that in the California studies.
5 Large Earthquake Probability Forecast
 The ratio of small to large shocks, or b value, is needed to transform the modeled rate of M ≥ 3 earthquakes into the probability of M ≥ 6.5 and M ≥ 7.0 events. The lower the b value, the higher the probability of large shocks. For Japan as a whole, b = 0.9 (Figure S4). For the three ≤ M ≤ 6 earthquakes in the Kanto seismic corridor during 2009–2012, b = 0.75, but the magnitude-frequency slope has a kink at M = 4.1, which might be caused by the maximum 60 km depth of displacement magnitudes [Harada et al., 2004] (Figure S2). Over a slightly larger area, Grunewald and Stein  found b = 1.07 by combining instrumental earthquakes for 1923–2003 (4.5 ≤ M ≤ 6.5) with historical earthquakes since 1649 (6.6 ≤ M ≤ 7.4). For b = 0.9 and the given observed 0.15 M ≥ 3/d earthquake rate before Tohoku, the M ≥ 7 interevent time would be ~73 years, in accord with the 400 year record. If the M = 4.1 kink were a real feature of the data, a b value of 0.9 would project the rate of M ≥ 3 shocks to M ≥ 7.0. We thus regard b = 0.75 as too low, b = 0.9 as likely, and b = 1.0 as possible.
 The forecast rates and probabilities are given in Table 1. For b = 0.9, the tripled earthquake rate results in a 5 year M ≥ 7 probability rising from 7% before the main shock to 17% in the next 5 years, a gain of 260%. For M ≥ 6.5, the probability rises from 18% before the main shock to 41% afterward, a similar gain. Thus, a 3.0-fold increase in the M ≥ 3 rate corresponds to a 2.6-fold increase in large earthquake probability. The gain is the same for b = 1.0, but the probabilities are lower. The forecast includes only earthquakes nucleating beneath Kanto. M ≥ 7.8 Japan trench or Sagami trough megathrust events are also capable of strong shaking in the Kanto basin.
Table 1. Probabilities of Large Earthquakes Striking Greater Tokyo (the Kanto Seismic Corridor) During the Next Five Years (11 March 2013 to 10 March 2018) and Next Year (11 March 2013 to 10 March 2014)
Pre-M9 Tohoku Main Shock
Post-M9 Tohoku Main Shock
5 Year Probability (%)
1 Year Probability (%)
5 Year Probability (%)
5 Year Probability Gain (%)
1 Year Probability (%)
1 Year Probability Gain (%)
Probability, P = 1 − exp(−N), where N is the expected number of events. N = Annual Rate × years. This estimate excludes earthquake sources on the Japan trench or Sagami tough megathrusts.
b = 0.9
b = 1.0
b = 0.9
b = 1.0
6 Discussion and Conclusions
 Because the Kanto seismicity did not decay back to the pre-Tohoku rate, we included a new stressing rate after the Tohoku main shock, whose origin is uncertain. The most likely explanation is stress due to postseismic creep or viscoelastic rebound. From onland GPS data, Ozawa et al.  identify two sources of postseismic megathrust creep, each with ≥1 m of slip (Figure 1a). On the basis of repeating earthquakes, Uchida and Matsuzawa  infer that the patch near Choshi slipped ~0.5 m in the first 9 months after the main shock. The eastern patch coincides with a ≥2 bar Coulomb stress increase caused by the 2011 main shock (Figure 3, red zone). Slip of 1 m on these offshore sources would transfer 0.1-0.2 bar to the thrust faults beneath Kanto, increasing their stressing rate, although not enough to account for the modeled change from 0.25 to 0.7 bar/yr. Viscoelastic relaxation could also increase the stressing rate.
 There is a counterargument to our claim of an increased earthquake probability: the post-Tohoku seismicity in the Kanto seismic corridor could simply accompany accelerated creep on uncoupled thrust faults beneath Kanto. Uchida and Matsuzawa  infer fault slip on the Japan trench megathrust and in the Kanto seismic corridor from repeating earthquakes, estimating a 30 mm/yr slip rate in the Kanto seismic corridor during 1993–2010 and 320 mm slip from 11 March to 31 December 2011 or about 10 times the pre-Tohoku rate. This increase resembles the M ≥ 3 time series in Figure 2b, which just means that the rate of the repeaters is proportional to the seismicity rate as a whole. The pre-Tohoku slip rate in the Kanto seismic corridor inferred by Uchida and Matsuzawa  is about the fragment motion rate deduced by Toda et al. , implying that slip beneath Kanto could be fully uncoupled. If so, the accelerated post-Tohoku slip on corridor faults could shed—not increase—the stress imparted by Tohoku, much as a high rate of small shocks is seen along the creeping sections of the San Andreas fault.
 However, two observations make this alternative unlikely: First, there is a history of large earthquakes in the corridor. Among them, the 2005 M = 6.0 shock struck at 80 km depth, where the smaller shocks also occur, and so stress demonstrably accumulates on the corridor faults; they cannot be fully uncoupled. Second, the Kanto b value did not change after the 2011 main shock, and so Kanto is not experiencing a heightened rate of small shocks alone, the increased rate extends to M = 6. Thus, in our judgment, the most defensible conclusion is that the corridor is at least partially coupled and accumulating stress, that the stress jumped in 2011 and is now being imparted at three times its foregoing rate, and so the probability of large shocks has climbed with the rate of small ones.
 We thank Justin Rubinstein and Naoki Uchida for invaluable reviews, and Eric Calais for editorial acumen. R.S.S. is grateful for a research visit to IRIDeS of Tohoku University, and S.T. is grateful for a research visit to the GEM Foundation, both in 2013. Coulomb 3.3 was used for stress calculations (www.coulombstress.org).