# Precursory Tidal Triggering of the 2011 Mw 9.0 Tohoku Aftershocks
## 1 Introduction  
The 2011 Mw 9.0 Tohoku earthquake occurred along the northeast Japan subduction zone, which is a region in which five main plates interact (Figure 1) (e.g., [1, 2]). The Pacific Plate subtracts under the Eurasian Plate and the Okhotsk Plate at a speed of 8-10 m per century along the Kuril French and the Japan Trench (e.g., [3, 4]), located off the east coast of Honshu, Japan. As the cold Pacific plate underthrusts beneath Japan, the spatial variation in friction along the plate boundaries results in strain in the rocks around the locked area of megathrust faults, which leads to energy accumulation around the stuck regions (e.g., [5]). On the other hand, the East-West convergence of northeastern Japan (Okhotsk plate) and the Amur plate form an incipient subduction zone on the eastern margin of the Japan Sea (e.g., [6, 7, 8]). The structure of this area is further complicated by the collision between the Kurilic arc and the Japanese arc in the Hidaka collision zone [3], which has produced frequent moderate to large earthquakes with complicated mechanisms, such as tectonic loading and thermal and lithological features on the edge of the plate [9]. The trench subduction zone of Japan has become the region with the highest frequency and intensity of seismic activity around the Pacific Ocean. In the trench subduction zone of Japan, there is quite a long record of large earthquakes. Except for the M-8.5 Jogan earthquake (year 869), no earthquakes with M \(\geq\) 8.5 were recorded prior to the Mw 9.0 Tohoku event [10]. These-complicated tectonic settings have featured Tohoku as a popular area for studying the mechanics and mechanisms of the occurrences of earthquakes. Previous studies have suggested that aftershocks can be triggered by static stress changes and dynamic forcing following a large earthquake (e.g., [11; 12]). Earthquake triggering disturbs the existing stress state, which can be a condition of the critical state. Earthquake triggering by Earth tides is also a possibility, since tides are always present and induce an oscillatory deformation of the solid Earth. An especially high correlation with tides has been shown for aftershocks, earthquake swarms, and earthquakes occurring in subduction zones and volcanic areas [13; 14; 15; 16], all of which consist of a large number of small shocks. The Mw 9.0 Tohoku megathrust earthquake occurred along the subduction boundary, where the tidal triggering of seismic activities has been observed by numerous previous studies (e.g., [14; 17; 18; 19]). Hence, this very large earthquake highlights the critical need for and provides the chance for a better understanding of the tidal triggering mechanism. Although the magnitude of the tidal stress is much smaller than that of a typical stress drop during an earthquake, the loading rate of the tidal stress is greater than that of the tectonic stress accumulation. Tidal stress can cyclically load and unload the crust, with various periods, and affect the time of occurrence of an earthquake to some extent [20]. Not only the amplitude but also the periodic oscillation of the tidal stress may play a role in the tidal triggering of earthquakes [17; 18; 21; 22]. Many studies have attempted to explore the correlation between Earth tides and earthquake occurrences [15; 23; 24; 25; 26; 27; 28; 29; 30], and some studies have revealed positive tidal correlations [13; 16; 20; 27; 31; 32]. A popular method is to calculate the tidal phase angle of each earthquake and obtain its distribution. Following previous studies, each event is assigned a phase angle on a linear scale from \(-180^{\circ}\) to \(180^{\circ}\) corresponding to the occurrence time, where \(0^{\circ}\) and \(\pm 180^{\circ}\) represent the maximum  
Figure 1: Seismotectonics of the study region. Aftershocks from the United States Geological Survey (USGS) catalog from 11 March 2011 to 10 April 2011 are shown by colored dots with radii proportional to the magnitude. The Mw 9.0 focal mechanism is based on Harvard Centroid Moment Tensor (CMT) results.