# Spatial Correlations of Global Seismic Noise Properties
## 5 Estimation of Spatial Long-Range Correlations of Seismic-Noise Properties  
The simplification of the statistical structure of seismic noise manifests itself in a decrease in the average value of the index \(\gamma\) (Figure 3), and it is also reflected in an increase in entropy (1) and a decrease in the width of the multi-fractal singularity spectrum support width (\"loss of multifractality\"). These changes in noise properties are indicators of the transition of a seismically active region (including the whole world) to a critical state [3,17]. Another indication of an increase in seismic hazard is an increase in the average correlation as well as the radius of strong correlations between noise properties in different parts of the system. In order to find out how the spatial scale of correlations changes with time, for each reference point we calculated the correlation coefficient between the index \(\gamma\) values at this point and at all other reference points. We performed these calculations in a sliding time window 365 days long with a shift of 3 days. Next, for each reference point, we calculated the average value of the correlation coefficient with the values of \(\gamma\) at all other reference points. Since the result of calculating such an average value depends on the time window, we obtained graphs of changes in average correlations for all reference points. Figure 5 shows examples of graphs of changes in correlations for nine reference points. From the graphs in Figure 5, a general trend towards an increase in the average correlations for each reference point is noticeable. As a result of averaging all the graphs of the type shown in Figure 5 for all 50 reference points, we obtained a general graph of average correlations, as shown in Figure 6.  
It can be noticed from the graph in Figure 6 that the time interval 2004-2016, in which the index \(\gamma\) decreases (Figure 3), corresponds to an increase in average correlations between the properties of noise at various reference points and that there is a transition from small correlations before 2004 to fairly large correlations after 2016. Figure 4: (**a,b**) The probability densities of the distribution of the minimum values of the seismic-noise index \(\gamma\) in a network of 50 control points before and after 2011; (**c**) histogram of numbers of control points, in which the minimum values of the index \(\gamma\) were realized in a moving time window 365 days long. Figure 5: Graphs of the average correlation coefficients of the index \(\gamma\) for 9 reference points with values at other reference points in a moving time window of 365 days with a mutual shift of 3 days. Figure 6: The average correlation coefficient between the values of the DJ-index \(\gamma\) at each control point with the values at other points. Red lines show linear trends for 3 intervals of time marks of the right ends of windows with a length of 365 days: 1998–2004, 2004–2016 and 2016–2023. On the last time fragment, the linear trend coincides with the average value. In order to assess the scale of strong correlations between seismic-noise properties, for each reference point we defined another point that had a maximum correlation with this point, provided that this maximum exceeded the threshold of 0.8, and we calculated the distance between these points. Figure 7 shows the graphs of the changes in the average and maximum values of the distances between points for which the correlation maxima exceeded 0.8. It can be seen from the graph in Figure 7b that after 2011 there was a sharp increase in the maximum distance at which strong maximum correlations occur. Thus, the growth of average correlations, which is visible in Figure 6, was supplemented by an explosive growth of the maximum scale of strong correlations. It is of interest to identify those reference points in the vicinity of which strong correlations most often occur.