## 5 Discussion  
To assess the role of the water level as the forcing (or one of the forcings) of the time dynamics of a seismic process, it is necessary to reveal the reservoir-triggered feature in the seismicity by identifying the link between some characteristics of seismicity and water-level fluctuations. Since the water level of a reservoir generally undergoes annual cycles due to the filling and un-filling phases of the dam, a yearly oscillatory behavior in seismicity that is triggered by the reservoir might also be visible. Methods like the power spectrum of the monthly earthquake counts, the singular spectrum analysis of the monthly number of events, the Allan factor of the seismic point process, or the Schuster's spectrum of the earthquake sequence ([32] and reference therein) have been used to identify annual or quasi-annual periodicities in the time distribution of earthquakes, matching those revealed in the temporal variation in the water level, and thus allowing assessment of the existence of a dynamical link between the seismic and hydrologic processes. The seismic area analyzed in the present study is located in the vicinity of the Song Tranh 2 hydropower plant in Vietnam. The seismic rate of the area increased after the  
Figure 4: SE of \(\Delta\tau\) for the de-clustered seismic catalogue (blue) and water level (red). Two different lengths of moving windows have been selected for calculating SE: N = 50 (solid) and N = 100 (dashed). initial impoundment of the reservoir, and the seismic activity is still continuing, suggesting that the loading/unloading operations of the dam could be one of the sources of the occurring earthquakes. To assess the link between the fluctuations of the water level of the reservoir and the seismic activity of the area, we analyzed the interevent times between consecutive earthquakes that represent the transitions from one earthquake to the next in the time domain. To date, Shannon entropy has never been employed to analyze reservoir-triggered seismicity. In this paper, time-varying SE was suitable to reveal dynamical patterns in the investigated seismic series that could be correlated with the water level variability. In fact, the time-varying SE showed a quasi-periodic behavior, mimicking the oscillatory behavior of the water level. Moreover, the peaks of each cycle of the SE are mostly reached within the cycles of the water level. The behavior of the time-varying SE suggests that the reservoir-triggered seismic process at Song Tranh 2 reservoir is characterized by alternating phases of higher disorder and lower disorder. This alternating behavior is visible in the whole seismicity as well as the de-clustered seismicity. However, the SE of the seismic series for the whole seismicity apparently behaves in a much noisier manner than that of the de-clustered seismicity; such larger irregularity in the whole seismic catalogue can be due to the presence of seismic swarms or aftershock sequences, whose time dynamics are characterized by timescales lower than those of the background seismicity, thus causing the time variation in the SE to appear more irregular. Focusing on the time varying SE of the interevent times of de-clustered seismicity (Figure 4), the increasing phases of the SE nearly correspond to the loading or filling phases of the dam. The increase in the level of the water (corresponding to the increase in the volume of the water in the reservoir) might change the stress state of the area, causing the seismic system to be in a situation of greater disorder and instability that would lead to the increase in the rate of earthquake occurrence. Figure 5 shows, indeed, the synoptic variation in the water level and the number of events per 10 days in the Song Tranh 2 area; we see that most of the cycles of water level are followed by peaks of seismic activity culminating in relatively large earthquakes (indicated by the black dots).