## 2 Region, Data, Method
### Seismic Noise Parameters
#### 2.4.1 Minimum Normalized Entropy of Squared Orthogonal Wavelet Coefficients En  
When processing signals using orthogonal wavelets, the choice of a basis is determined using the criterion for the minimum entropy of the distribution of wavelet coefficients [42]. Let \(c_{i}^{(k)}\) are the wavelet coefficients of the analyzed signal \(x(t)\), \(t=1\),..., \(L\) are a discrete indexes numbering successive values of the time series.  
The superscript \(k\) is the number of the level of detail of the orthogonal wavelet decomposition; the subscript \(j\) numbers the sequence of time interval centers in the vicinity of which the signal convolution, with finite elements as its basis, is calculated.  
We used 17 orthogonal Daubechies wavelets: 10 ordinary bases with minimal support and a number of vanishing moments from 1 to 10, and 7 Daubechies symlets [42] with a number of vanishing moments from 4 to 10.  
For each basis, the normalized entropy of the distribution of the squared coefficients was calculated and a basis was found that ensures the minimum entropy:  
\[En=-\sum_{k=1}^{m}\sum_{j=1}^{M_{k}}p_{j}^{(k)}.\ln\left(p_{j}^{(k)}\right)/ ln(N_{r})\to min\,,\ \text{when}\ p_{j}^{(k)}=\left|c_{i}^{(k)}\right|^{2}/\sum_{i,i}\left|c_{i}^{( i)}\right|^{2}.\]  
Here \(m\) is the number of levels of detail taken into consideration; \(M_{k}\) is the number of wavelet coefficients at the level of detail with number \(k\).  
The number of levels \(m\) depends on the length \(L\) of the analyzed samples.  
For example, if \(L=2^{n}\), then \(m=n\), \(M_{k}=2^{(n-k)}\). If the length \(L\) is not equal to a power of two, then the signal \(x(t)\) is padded with zeros to the minimum length \(N\), which is greater than or equal to \(L\): \(N=2^{n}\geq L\).  
In this case, among the number \(2^{(n-k)}\) of all wavelet coefficients at level \(k\), only \(L\cdot 2^{-k}\) coefficients correspond to the decomposition of the real signal, while the remaining coefficients are equal to zero due to the addition of zeros to the signal \(x(t)\).  
Thus, \(M_{k}=L\cdot 2^{-k}\), and only \"real\" coefficients are used to calculate the entropy. The number \(N_{r}\) is equal to the number of \"real\" coefficients, that is, \(N_{r}=\sum_{k=1}^{m}M_{k}\). By construction, \(0\leq En\leq 1\).  
When estimating the wavelet spectral exponent \(\beta\), the orthogonal wavelet decomposition of the signal fragments in the current daily time window [5] is used, which was previously used in [43] to analyze the noise component of signals from a network of 1203 GPS stations in Japan before the Tohoku mega earthquake on March 11, 2011, and in [36; 39] when processing noise data from the Kamchatka Peninsula.  
For each station, the time series of the four seismic noise parameters were obtained with a time step of 1 day for the time period 2011-2021. When calculating the statistical parameters of the noise, the low-frequency polygenic components in the daily continuous records of the seismic signal with a frequency of 1 min were preliminarily filtered by the 8 th order polynomial at each station. Such filtering and the subsequent transition to the first differences of the averaged 1-min data provided the suppression and compensation of tidal, atmospheric, other natural effects, and anthropogenic activity in the original continuous records.