# Eigenstate Transition of Multi-Channel Time Series Data around Earthquakes
## 3 Results  
In this section, we show the results of the time dependence of the eigenstate. We show an example of the time dependence of the channel contribution \(|w_{i}^{(p)}|\) as a contour plot in Figure 4 and the occupancy rate \(\eta\) and first eigenvalue in Figure 5.  
Here, we denoted the time from Y to Z of the Xth day in 2016 as \"2016/X/Y-Z.\" In Figure 4, the horizontal axis is the time whose origin is 2016/072/00 and the vertical axis is composed of the channel number \(i\). (Unfortunately, the data from 22:30 in the 72 nd day to 10:30 the 91 st day are not available due to a malfunction of the observatory.) As seen, the random contribution is confirmed for the time far from the Mie earthquake.  
At the beginning, we show the time dependence of the channel contribution \(|w_{i}^{(p)}|\) around the Mie earthquake as contour plot in Figure 6.  
While the state 20 days before the earthquake shown in Figure 4 has a random contribution, the state of some hours before the earthquake is shown in Figure 6A,B, and it has a strong contribution from channels 1 to 3. Then, the state of several tens of minutes before the earthquake is shown in Figure 6C and it has a strong contribution from channels 2 and 3. Thus, it seems that the contribution from channels 1, 2, and 3 increase before the earthquake. After the earthquake, the eigenstate is mainly consists of channel 3, which is considered due to a change of a crustal state. The first eigenvalue, i.e., the first eigenvalue, has a sharp peak at the time the earthquake occurred in Figure 7C. As shown in Figure 7C, the occupancy rate remains high several tens of minutes before the earthquake.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Mie** & **Kumamoto** & **Fukushima** \\ \hline \hline \multicolumn{1}{c}{Occurred} & 92 th 02:39 & 106 th 16:25 & 326 th 20:59 \\ \hline \multirow{6}{*}{Objective time} & 91 st 16:00–20:00 & 106 th 08:00–12:00 & 326 th 12:00–16:00 \\  & 91 st 20:00–24:00 & 106 th  
Figure 5: Occupancy rate and eigenvalue for 2016/72/00-04.  
Figure 6: Transition of the eigenstate around the Mie earthquake for **(A)** 2016/091/16-19, **(B)** 2016/091/20-24, **(C)** 2016/092/00-04, **(D)** 2016/92/04-08, **(E)** 2016/92/08-12, **(F)** 2016/92/12-16. The down arrow shows the time the earthquake occurred.  
Next, we show the case of the Kumamoto earthquake. Except around earthquake, the contribution from channel 1 and 2 is always high, as shown in Figure 8. However, the time in which the occupancy rate keeps almost 100% is longer before the earthquake (Figure 9A,B) than after the earthquake (Figure 9E,F).  
Finally, we show the results of the Fukushima earthquakes in Figures 10 and 11. At the beginning of the analyzed time, channel 3 has already mainly contributed to the eigenstate while channel 1 and 2 slightly contribute. After that, the states keeps until the end of analyzed time. On the other hand, as seen in Figure 11, eigenvalue shows a similar behavior with EWSs. Namely the first eigenvalue increases from 8 h before the earthquake, and is calm down after the earthquake.  
Figure 7: Occupancy rate and the first eigenvalue around the Mie earthquake for (**A**) 2016/091/16-19, (**B**) 2016/091/20-24, (**C**) 2016/092/00-04, (**D**) 2016/92/04-08, (**E**) 2016/92/08-12, (**F**) 2016/92/12-16. The down arrow shows the time the earthquake occurred.  
Figure 8: Transition of the eigenstate around the Kumamoto earthquake for (**A**) 2016/106/8-12, (**B**) 2016/106/12-16, (**C**) 2016/106/16-20, (**D**) 2016/106/20-24, (**E**) 2016/107/0-4, (**F**) 2016/107/4-8.  
Figure 9: _Cont._  
Figure 10: Transition of the eigenstate around the Fukushima earthquake for (**A**) 2016/326/12-16, (**B**) 2016/326/16-20, (**C**) 2016/326/20-24, (**D**) 2016/327/00-04, (**E**) 2016/327/04-08, (**F**) 2016/327/08-12.  
Figure 9: Occupancy rate and the first eigenvalue around the Kumamoto earthquake for (**A**) 2016/106/8-12, (**B**) 2016/106/12-16, (**C**) 2016/106/16-20, (**D**) 2016/106/20-24, (**E**) 2016/107/0-4.