I observe highly significant tidal triggering of earthquakes prior to the 2011 Mw 9.1 Tohoku-Oki earthquake. Strong statistical correlations between tidally-induced stresses and earthquake occurrence times are identified in the northern part of the Tohoku-Oki source region, where the mainshock rupture initiated, in the several to ten years before the Tohoku-Oki earthquake. The tidal phase distribution of earthquakes in this period exhibits a peak where the shear stress is at its maximum to promote failure. On the other hand, no significant tidal correlation is found after the Tohoku-Oki mainshock. These observations suggest that tidal triggering occurs over a decade-long period preceding the Tohoku-Oki earthquake, and the initial rupture site of this event is already critically stressed in this precursory stage.
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 Temporal changes of tidal triggering have now also been observed in several subduction zones. Of special interest is precursory behavior of triggering signals prior to the occurrence of large earthquakes. In the focal region of the devastating 2004 Sumatra megathrust earthquake (Mw 9.0), tidal triggering was detected only in several to ten years preceding this giant earthquake and vanished afterwards [Tanaka, 2010]. Similar precursory changes were found for the other huge events in Sumatra in 2005 (Mw 8.6) and 2007 (Mw 8.5). An earlier study in Tonga [Tanaka et al., 2002a] also documented tidal triggering prior to the 1982 South Tonga earthquake (Mw 7.5). These observations suggest that tidal stress perturbations can trigger earthquakes when the regions reach a critical state for failure in large/great earthquakes.
 In the present study, I focus on the 11 March 2011 Tohoku-Oki earthquake, which ruptured a long segment of the subduction plate interface between the Pacific and North America plates offshore Japan. The Global Centroid Moment Tensor (CMT) solution for this event had a magnitude Mw of 9.1 [Nettles et al., 2011], which was the largest in Japan's recorded history. I examine spatio-temporal changes in correlations between tides and earthquakes in the Tohoku-Oki region, to report a detection of possible tidal triggering signals prior to this massive earthquake.
 In the analysis, I use shallow earthquakes (depths less than 70 km) in the Global CMT catalog from 1976 to 2011. The data include the Quick CMT solutions from September to December 2011. Using this long catalog, we can assess the changes in tidal influence over the past few decades. I only analyze earthquakes of magnitude (Mw) 5.0 or greater. The distribution of these events is shown in Figure 1. The threshold magnitude is determined by examining the magnitude-frequency plot observed in this region. I select a 500 km × 200 km rectangular area enclosing the rupture of the 2011 Tohoku-Oki earthquake. The area is also shown in Figure 1, as well as the centroid location of the Tohoku-Oki mainshock [Nettles et al., 2011]. When measuring the spatial distribution of correlations, I consider a somewhat larger area encompassing this 500 km × 200 km rectangular region (see section 4). Thus, in total, 541 earthquakes are used in this study.
 The calculated tidal stresses are resolved onto the fault plane of each earthquake. The amplitude of the stresses is 0.5–0.7 kPa for shear stresses and 6–15 kPa for normal stresses. The problem is the ambiguity in determining the fault plane from among the two nodal planes of an earthquake focal mechanism. The shear stresses on the orthogonal nodal planes are the same, but the normal stresses are not. In the present study, I thus only focus on the shear stresses acting in the slip direction. The effects of fault-normal and Coulomb failure stresses will be discussed in a later section (section 5).
 Each event is assigned a tidal phase angle with respect to the tidal stress time series at the time of occurrence. The phases of 0° and ±180° are defined to be at the times of tidal stress maxima and minima, respectively. The distribution of phase angles is then examined for a possible tidal correlation by using the Schuster's test [e.g., Emter, 1997], which gives the probability p that the phase distribution is random. The null hypothesis of random earthquake occurrence within a tidal cycle can be rejected at a significance level of 1 − p. The smaller the value of p, the higher the confidence level of the correlation between tides and earthquakes.
Figure 2 shows the temporal change of Schuster's test p-value for all events within the rectangular study area indicated in Figure 1. A time window of 3000 days is selected to ensure a sufficient number of earthquakes (>10) for statistical analysis [Schuster, 1897], and is shifted by 500 days. During the investigation period, the p-value remained above 10%. While the p-value somewhat decreased before the Tohoku-Oki earthquake (p = 12%), it failed to attain statistical significance at the 95% or even the 90% level. Using all events in the area, we cannot find any significant signals of tidal triggering.
 However, the analysis of spatial p-value distribution in the pre-shock period reveals the existence of significant tidal correlations in this period. The distribution is shown in Figure 3. I focus on the 3000 days just prior to the 2011 Tohoku-Oki earthquake, and use a spatial moving window of 200 km × 200 km that is moved by 50 km both in the along-strike and along-dip directions beyond the boundary of the rectangular study area defined in Figure 1. The grid interval is several times larger than the location errors of the earthquakes (less than 10 km). For the window which includes 20 or more earthquakes, the p-value is indicated in the 50 km × 50 km square at the center of the window by gray scale shading. Small p-values (dark shades) are found in the northern part of the area. The smallest p-value of 0.34% (above the 99% confidence level) is observed in the window denoted by A. The entire size of this window is also shown by a light gray square (hereafter this 200 km × 200 km volume is referred to as region A). We find that the epicenter (initial rupture point) of the Tohoku-Oki earthquake was located in region A. We also note that the largest foreshock (Mw 7.4), which occurred two days before the Tohoku-Oki mainshock, was within this low-p region. This evidence suggests that significant correlations did exist in and near the initial rupture site before the 2011 Tohoku-Oki earthquake.
Figure 4a shows the temporal evolution of p-value in region A. Beginning in the 2000s, the p-value began to drop gradually with time, which lasted up to the occurrence of the Tohoku-Oki mainshock. Until then, the p-value had been stable (larger than 30%) for about 25 years, indicating absence of significant correlation over this time period. After the Tohoku-Oki earthquake, the p-value returned again to the level of insignificant correlation (p = 34%). This region's prominent correlation was identified only in about a decade before the Tohoku-Oki earthquake. Figure 4b shows the phase distribution of earthquakes in the 3000 days prior to the Tohoku-Oki earthquake. The correlation before the Tohoku-Oki mainshock can be seen as a tendency for earthquakes to occur when shear stresses enhancing slip are highest. The distribution shows a strongly unimodal peak near 0° tidal phase.
5. Discussion and Conclusions
 In the present study, I investigate correlations between tidal phase and the earthquake origin times, to observe triggering signals before the 2011 Tohoku-Oki earthquake. The earthquake-tide correlation is found in the northern part of the Tohoku-Oki rupture area, which includes the mainshock and foreshock epicenters. This correlation, in excess of the 99% confidence level, exists for several to ten years preceding the Tohoku-Oki earthquake, but not in the other time of the investigation period. The spatial and temporal behavior of these tidal signals suggests that the detected correlation could be a precursor to the Tohoku-Oki mainshock.
 The phase distribution in the pre-mainshock time period exhibits a strong influence of tidal shear stress increments (Figure 4b). The earthquakes preferentially occurred at times of encouraging shear stresses. Assuming binomial distribution, the observed increase in the rates of earthquakes during the half tidal cycle of encouraging stresses (within a phase between −90° and 90°) would be expected by chance with a probability of only 2.0%. This simple binomial test [e.g., Cochran et al., 2004] also confirms highly significant tidal influence (98% significance level) before the 2011 Tohoku-Oki earthquake.
 Throughout the analysis, I only consider shear stresses because of difficulties in determining the fault plane from the two nodal planes. Here I focus on reverse-faulting earthquakes and try to evaluate the effects of normal stresses. For these events, the selection of the fault plane can be better made. The data used for this analysis are the events that occurred in region A in the 3000 days prior to the Tohoku-Oki earthquake. Out of the 47 events, I identify 40 reverse-faulting earthquakes (with the rake angle ranging between 60° and 120°, following Tanaka et al. [2002b]). The west-dipping nodal planes for these earthquakes are roughly consistent with the geometry of the subducting plate interface. I assume them as the fault planes and examine tidal correlations. The data restricted to reverse-faulting again show a strong correlation with tidal shear stresses (Figure S1a in the auxiliary material). The value of p is 0.03%, which is smaller (higher confidence) than that observed for the data including all earthquakes. The earthquakes also correlate well with normal stresses (p = 0.12%), but a clear increase in the rate of events is observed during times of compressional stresses inhibiting fault slip (Figure S1b). I also examine Coulomb failure stresses giving different values of friction coefficient (μ) between 0 and 1 (Figure S2). All exceed the 99% confidence level (p < 1%), but the correlations are extremely high for μ < 0.1. The best correlation is observed for μ = 0 (shear stress only), which implies that shear stresses could effectively control triggering of earthquakes.
 Prior to the 2011 Tohoku-Oki earthquake, the region surrounding the Tohoku-Oki epicenter had shown a pronounced decrease in b-value for about ten years [Nanjo et al., 2011]. An extremely low-b zone primarily extends seaward from the mainshock epicenter, about 100∼150 km long along the trench axis. This location nearly coincides with the area of precursory low p-values (the area of dark shades in Figure 3). Seismic quiescence, which began about 20 years before the Tohoku-Oki mainshock, was also found in the adjacent, deeper area of the low-b and low-p anomaly [Katsumata, 2011]. The crustal movements observed by the GPS stations near this quiescence suggest that the quiescence was induced by a precursory slow slip. Such a slip would influence the neighboring crustal deformation and accelerate stress accumulation on shallower locked portions. The coincidence of low p with low b also lends support to the hypothesis that the region had been highly stressed for a decade-long period.
 A similar space-time pattern of tidal triggering signals has been reported over a wide range of mainshock magnitudes, but the duration of the precursor varies considerably. A significant decrease in p-value was observed in eight to ten years before the Sumatra [Tanaka, 2010] and Tohoku-Oki giant earthquakes (Mw 8.5–9.1), in four to six years before large subduction zone earthquakes (Mw 7.5–7.9) [Tanaka et al., 2002a, 2004], and in only one to two years before moderate-sized earthquakes (M 4.5–4.9) in Tokai, central Japan [Tanaka et al., 2006]. The duration is longer for a larger mainshock, suggesting that the precursor time scales with the mainshock magnitude. A complete set of observations including additional intermediate-scale cases (M 5.0–7.0) would provide a quantitative relationship between the duration of tidal triggering precursor and the mainshock size, which could help predict the possible magnitude of an impending earthquake.
 I am grateful to J. E. Vidale, R. Harris, and an anonymous reviewer for their helpful comments to the paper.
 The Editor thanks Danielle Sumy and John Vidale for their assistance in evaluating this paper.