## 5 Discussion  
A new method for estimating the intensity (activity measures) of the Earth's surface tremor based on measurements by a network of GPS sensors is proposed. The method is based on estimating the trajectory of points corresponding to the maxima of the average weighted probability densities of the distribution of extreme values of tremor statistics in a sliding time window. As tremor statistics, we chose the minimum values of the entropy of the distribution of squared orthogonal wavelet coefficients and the entropy of the power spectrum, as well as the maximum values of the spectral index calculated for the power spectra and the average values of the squared wavelet coefficients. A method has also been developed for estimating the variability of the spatial correlation of tremor properties based on estimates of the correlation values of statistics in an auxiliary network of reference points in a sliding time window. Methods which used values of spectral index for GPS time series investigations were elaborated in [1; 2; 3; 4; 5; 6] for identifying models of GPS noise. Similar methods were applied in [21; 22; 23] for detecting regions which are suspected for increased seismic danger although these methods are based on detrended fluctuations analysis (DFA). However, these methods do not investigate evolution of points providing maximum to probability density of extreme values of spectral index and entropy of GPS noise within moving time window what is the key tool in the current article. The developed methods were applied to the data of the GPS network in Japan in 2009-2021. Five areas of tremor activity were identified in the center and south of Japan, and a time point (2016) for a significant restructuring of the tremor activation mode was determined. Anomalies of tremor activity were obtained, presumably associated with the preparation of the Tohoku, 11 March 2011, \(M=9.1\), \(Lat=38.32^{\circ}\), \(Lon=142.37^{\circ}\) and Kumamoto, 16 April 2016, \(M=7\), \(Lat=32.77^{\circ}\), \(Lon=130.72^{\circ}\) earthquakes. The trajectory of the points of maximum average probability densities of the distribution of extreme values of tremor statistics and their belonging to the selected 5 activity areas in Figure 6 demonstrates a clear division into two large time fragments with significantly different behaviors; before and after 2016. The interval after 2016 is characterized by stable seasonal periodicity of switching the trajectory of the maxima of the average probability density between the first and fourth clusters. For the first time interval before 2016, we cannot notice such regularity. Thus, it could be called \"chaotic,\" although this name simply underlines the existence of the change point in the behavior of maxima trajectory. During the two years 2014-2016, tremor activity is concentrated in the south of Japan, in the fifth cluster (Figure 6(a)). It is possible that this 2-year concentration of the tremor activation maximum in the fifth cluster reflects the preparation of the Kumamoto earthquake. We also note that the north of Japan in 2009-2021 does not apply to abnormal areas of GPS tremor. It follows from the graphs in Figure 7 that all average tremor properties are subject to a strong annual periodicity. Note that the maxima of the average correlation \(\rho_{\tau}^{*}\), the average number \(n_{\tau}^{*}\) of pairs of reference points with strong correlations, and the average maximum distances \(d_{\tau}^{*}\) of strong correlations correspond to the time windows falling on the winter period and the beginning of spring. Up until 2016, there was a gradual decrease in the annual peaks of the mean values of these measures of tremor activity intensity. After 2016, the average correlations reached a background level of random fluctuations in the vicinity of 0.2, while the values of the measures \(n_{\tau}^{*}\) and \(d_{\tau}^{*}\) were almost equal to zero. The first half of 2010 displays the maximum value of annual bursts of tremor activity.