## 2 Region, Data, Method
### Spectral Measure of Coherent Behavior of Seismic Noise Parameters
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No**} & **Date dd.mm.yyyy** & **Time** & **Coordinates, deg.** & & \\  & **Name** & **hh:mm:ss** & \(\mathbf{N}^{\circ}\) & \(\mathbf{H}\), \(\mathbf{km}\) & \(\boldsymbol{M_{\mathrm{w}}}\) & \(\boldsymbol{M_{\mathrm{0}}}\) \\  & & **Name** & **hh:mm:ss** & \(\mathbf{E}^{\circ}\) & & \\ \hline \multirow{2}{*}{1} & 24 May 2013 & \multirow{2}{*}{05:44:48} & 54.89 & 598 & 8.3 & 38.4 \\  & Sea of Okhotsk & & 153.22 & & \\ \hline \multirow{2}{*}{2} & 30 January 2016 & \multirow{2}{*}{03:25:12} & 53.98 & 577 & 7.2 & 0.8 \\  & Zhupanovskoe & & 158.55 & & & \\ \hline \multirow{3}{*}{3} & 17 July 2017 & \multirow{3}{*}{23:34:13} & 54.44 & \multirow{3}{*}{10} & \multirow{3}{*}{7.7} & 5.2 \\  & Near Islands & Aleutian & & 168.86 & & \\ \hline \multirow{3}{*}{4} & 20 December 2018 & \multirow{3}{*}{17:01:55} & 55.10 & \multirow{3}{*}{17} & 7.3 & 1.0 \\  & Uglovoye Podnyatiye & & 164.70 & & & \\ \hline \multirow{3}{*}{5} & 25 March 2020 & \multirow{3}{*}{02:49:21} & 48.96 & \multirow{3}{*}{58} & 7.5 & 2.0 \\  & North Kuril & & 158.70 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Earthquakes with \(M_{w}=7.2\)–8.3 ([[http://earthquake.usgs.gov/earthquakes](http://earthquake.usgs.gov/earthquakes)]([http://earthquake.usgs.gov/earthquakes](http://earthquake.usgs.gov/earthquakes)) (accessed on 31 December 2021)). Examples of the \(\
u(\tau,\omega)\) distribution in the time-frequency domain during 2011-2021 calculated in a sliding time window 365 days long with a step of 3 days are shown in Figures 5 and 6. The identification of synchronization effects in the diagrams was carried out taking into account the range of values \(\
u(\tau,\omega)\) in case of random manifestation. For this, a 4-dimensional time series was generated consisting of four independent realizations of Gaussian white noise, each with a length of 365 \(\times\) 10\({}^{4}\) samples. For this multidimensional  
Figure 5: Time-frequency diagrams of the spectral measure of coherence of 4-dimensional time series of seismic noise parameters \(\
u(\tau,\omega)\) in comparison with earthquakes (Table 3) according to data from (**a**) the entire network of stations, (**b**) non-volcanic, and (**c**) continental stations, as well as for the (**d**) northern, (**e**) central, and (**f**) southern groups of stations, 2011–2021. Synchronization effects of seismic noise parameters are distinguished by the values \(\
u(\tau,\omega)\geq 0.3\). Figure 6: Time-frequency diagrams of the spectral measure of coherence of 4-dimensional time series of seismic noise parameters \(\
u(\tau,\omega)\) in comparison with occurred earthquakes (Table 3) constructed from (**a**) the group of volcanic stations and (**b**) the group of coastal stations, 2011–2021. series, a time-frequency diagram of the evolution of the spectral measure of coherence was constructed in successive non-overlapping time windows 365 samples long, which provides 10,000 independent estimates of \(\
u(\tau,\omega)\). The resulting time-frequency diagram was a chaotic pattern, for which the average value of random bursts of the coherence measure is 0.008, the median is 0.006, and the maximum value is 0.15. The length of the time window corresponded to the same length of 365 samples as in construction of the diagrams in Figures 5 and 6. The double maximum value of the random fluctuations of the measure of spectral coherence in the 4-dimensional time series \(\
u(\tau,\omega)\) = 0.30 was used as the upper limit of the random occurrence of the values \(\
u(\tau,\omega)\). To visually highlight the effects of synchronization on the diagrams, the regions of spectral coherence manifestation with the values \(\
u(\tau,\omega)\geq 0.30\) are colored (Figures 5 and 6). Based on these diagrams, the time intervals and frequency bands of the anomalous coherent behavior of the discussed noise statistics' time series were identified and then correlated to the timeline of the earthquakes in Table 3.