## 3 Description of the Time Series Statistics Used
The parameter \(\beta\) in Formula (4) is the wavelet-based spectral exponent, the value of which can be found by the least squares method: \(\sum_{k=1}^{k_{\max}}\varepsilon_{k}^{2}\rightarrow\min_{\beta,\varepsilon}\). We then address the Donoho-Johnstone index (DJ-index). The threshold \(T_{DJ}\) is defined by the following formula [25; 26]:  
\[T_{DJ}=\sigma\sqrt{2\cdot\ln N} \tag{5}\]  
The threshold (5) separates rather large (informative), in their absolute values, wavelet coefficients from other coefficients which are considered to be noisy. Thus, we can consider the dimensionless signal characteristics \(\gamma\), \(0\leq\gamma\leq 1\), as the ratio of the number of the largest wavelet coefficients, for which the inequality \(|c_{k}|>\ T_{DJ}\) is fulfilled, to the number \(N\) of all wavelet coefficients. The value \(\sigma\) in the Formula (5) is the noise standard deviation estimate under the assumption that the noise is most concentrated in the first-detail level of orthogonal wavelet decomposition. The estimate of standard deviation \(\sigma\) should be robust with respect to outliers in the values of the coefficients at the first level. To provide this, a median estimate of the standard deviation for a normal random variable is used:  
\[\sigma=med\Bigl{\{}\left|c_{k}^{(1)}\right|\,\ k=1,\ldots,N/2\Bigr{\}}/0.6745. \tag{6}\]  
For each station in each time window, four surface tremor statistics are computed for the three ground displacement components where \(c_{k}^{(1)}\) are wavelet coefficients at the first level of detail. The estimate of the standard deviation \(\sigma\) from Formula (6) determines the value (5) as a threshold for extracting noise wavelet coefficients. The quantity (5) is known in wavelet analysis as the Donoho-Johnstone threshold, and the expression for this quantity is based on the formula for the asymptotic probability of the maximum deviations of Gaussian white noise [25; 26]. The DJ index \(\gamma\) values can be interpreted as a measure of the non-stationarity of seismic noise. For stationary Gaussian white noise, the index \(\gamma\) is zero. In [27; 28], the DJ index was used as one of the main statistics for investigating properties of global seismic noise. In summary, we will briefly describe in the list the characteristics of the values of the tremor statistics for stationary white Gaussian noise, which is considered as a standard of a completely random oscillation:1. The \"usual\" spectral exponent \(\alpha\) is the coefficient of regression between the logarithm of the power spectrum values and the logarithm of the period (\"spectral slope\"). For white noise, it is equal to zero (white noise has a \"flat spectrum\"). 2. Wavelet-based spectral exponent \(\beta\)--the regression coefficient between the logarithm of the mean values of the squared wavelet coefficients for each level of detail and the logarithm of the period of the central frequency corresponding to the level of detail of the wavelet decomposition (\"spectral slope\"). For white noise, it is zero. 3. Donoho-Johnstone threshold (DJ index) \(\gamma\)--the ratio of the number of \"large\" in absolute magnitude orthogonal wavelet coefficients to the total number of coefficients. For white noise, it is zero. 4. Minimum entropy \(En\) of the distribution of squared orthogonal wavelet coefficients in the enumeration of wavelet basis functions in the class of Daubechies wavelets with the number of vanishing moments from 1 to 10. For white noise, the entropy is maximum. Since we use four statistics for three components of the ground displacement vector, we obtain 12 statistics for each type of tremor. Let us put them in one matrix:  
\[\left[ \begin{array}{ccc}\alpha_{E,\max}&\alpha_{N,\max}&\alpha_{U,\max}\\ \beta_{E,\max}&\beta_{N,\max}&\beta_{U,\max}\\ \gamma_{E,\max}&\gamma_{N,\max}&\gamma_{U,\max}\\ Ein_{E,\min}&En_{N,\min}&En_{U,\min}\end{array} \right)\left(