_applied_  
_sciences_  
_Article_  
Identification of Areas of Anomalous Tremor of the Earth's  
Surface on the Japanese Islands According to GPS Data  
**[PERSON]**  
Institute of Physics of the Earth, Russian Academy of Sciences, 122342 Moscow, Russia; [EMAIL_ADDRESS]  
**Abstract: Statistical properties of Earth surface tremors measured by means of GPS were investigated. This article considers measurements of the Earth's surface displacements in three orthogonal directions relayed by a network of GPS sensors with about 1200 points distributed across Japan in 2009-2021. Next, the following characteristics of the tremors were considered: the entropy of the distribution of squared orthogonal wavelet coefficients, the entropy of the distribution of power spectrum values, and the spectral index. The anomalous regions of maxima of probability densities of the distribution of extreme values of the tremor statistics were determined: entropy minima and spectral index maxima. The average density maps of the distribution of extreme value tremor statistics were found to be highly correlated with one another. This made it possible to consider a weighted average density map and identify five anomalous regions in the center and south of Japan. A trajectory of visiting anomalous regions by a sequence of points realizing local maxima of the average probability density was obtained, for which seasonal periodicity was set. Estimates of changes in the average and maximum values of the correlation coefficients of tremor properties in an auxiliary network of 16 reference points in a semi-annual time window were obtained. **  
**Keywords: GPS tremor; entropy; spectral index; probability density; correlations**  
**1. Introduction**  
Analysis of the spectral structure and models of the noise component of a GPS time series is traditionally of interest to researchers. In [1], spectral indexes were analyzed by fitting power laws to spectra and estimating their parameters using the maximum likelihood method. The effect of the flicker noise intensity of a GPS time series on velocity determination errors, depending on the measurement latitude, was studied in [2, 3]. In [4, 5, 6], the maximum likelihood method was applied to estimate the amplitudes of GPS time series noise component models for various regions of the world. The problem of estimating the error in determining the velocity based on the spectral index was considered in [7]. The use of parametric models of a GPS time series to consider the effect of gaps in data for tectonically active regions is described in [8]. In [9, 10] the high-frequency noise structure of a GPS time series for a number of areas in New Zealand and the United States was analyzed. The influence of the seasonal component of the hydrological load on the Earth's surface on the determination of the velocities of tectonic plates was studied in [11, 12]. The extraction of common spatial characteristics and seasonal components of a GPS time series using the principal component method, empirical orthogonal functions, and singular spectrum analysis was considered in [13, 14]. In [15], the high-frequency noise of a GPS time series was analyzed together with the records of the seismic network of accelerometers. The relationship between the appearance of non-stationary effects in the GPS time series and the processes of slow motions at the boundaries between crustal blocks was analyzed in [16]. Estimates of the non-stationary effects of GPS time series and station positioning stability using discrete wavelet transforms were considered in [17, 18]. In [19, 20], the coherence of the tremors of the Earth's surface measured by GPS was studied. An assessment of the fractal characteristics of a high-frequency GPS time series to identify potentially dangerous seismically active regions in Japan and California was used in [21; 22; 23].