# Precursory Tidal Triggering of the 2011 Mw 9.0 Tohoku Aftershocks
## 4 Discussion  
The Schuster test, which was utilized to statistically analyze the times of occurrences of earthquakes, revealed a significant correlation between the aftershocks of the 2011 Mw 9.0 Tohoku earthquake, Japan, and Earth tides. Furthermore, the Schuster spectrum showed that the most obvious periods in the datasets are 0.5 days and 1 day. This is consistent with the period of diurnal and semidiurnal tides, indicating that the seismic activity that followed the Mw 9.0 mainshock might have been triggered by Earth tides. The period of the Earth tide depends on the relative location of the Moon, the Sun, and the Earth. Thus, it is affected by (1) the period of rotation of the Earth about its axis, which is approximately 24 h; (2) the period of revolution of the Moon around the Earth, and the variation of the declination and the distance between the center of the Moon and the Earth, which is approximately one month; and (3) the period of the revolution of the Earth around the Sun, which is one year.  
The results of this paper show that short-period tides can trigger seismicity in Japan, consistent with the conclusions of related studies [25]. When the tidal force acts on the focal area, the stress state of the focal area and the stage of earthquake nucleation are the key factors determining the tidal triggering effect [38; 39; 40]. If the stress state of the focal area is in a stage of critical instability [11; 39; 41], the oscillatory loading of the tidal force will promote seismicity. In other words, when the stress in the focal area is in a critical state, the tidal stress might increase the crustal stress slightly, possibly triggering an earthquake. Earth tides vary in space and time; thus, they only trigger earthquakes under favorable conditions. Aftershock activity following a mainshock is the most vulnerable condition for earthquakes triggered by short-period tides. This may be due to the occurrence and stress accumulation of the mainshock. The stress in the earthquake area accumulates, which is conducive to earthquake triggering by the tidal force.  
The results of this paper do not reveal a correlation between the aftershocks of the Mw 9.0 Tohoku earthquake and long-period Earth tides. This is due to the attenuation speed and the duration of the aftershock sequence. On the other hand, semidiurnal and diurnal tides show more obvious oscillatory characteristics. The influence of long-period tides on regional seismicity and its related conditions needs to be studied in detail on a long-duration earthquake sequence.  
For the physical mechanism of tidal triggering, more detailed aftershock data are needed, including the focal mechanism of the aftershocks. The same tidal stress tensor might have either positive or negative effects on the shear fracture. Moreover, the type of seismic fault has an important influence on tidal triggering. Therefore, analyses that neglect the focal mechanism and fault type cannot contribute substantially to the understanding of the physical mechanism of earthquake tide triggering.  
We also found that the tidal correlation depends on the earthquake magnitude and the focal depth. Small events (\(M<5.0\)) and deep events (depth \(>30\) km) are more easily triggered by tides. It is difficult to clearly explain the effect of the focal depth. We have briefly discussed that changes in stress or strain at large depths are not significantly reduced compared to those on Earth's surface in this region. The mechanism of the magnitude dependence on tidal triggering has been discussed by [PERSON] et al. [14], which is a good candidate to interpret the phenomenon of the Mw 9.0 Tohoku earthquake aftershocks.