# Spatial Correlations of Global Seismic Noise Properties
## 6 Seismic-Noise Response to the Irregularity of the Earth's Rotation
A short third segment was identified based on the results of data processing for 2021-2022 due to an unusually large spike in the response of noise properties to the LOD. The maximum value of the response in Figure 11b was reached at the time corresponding to the date 9 May 2022. The \"naive\" forecast, in which 534 days are added to this date, gives the most probable date for the future strong event as being 24 October 2023. A more realistic prediction would be to blur this date with some uncertainty interval. However, it is not yet possible to give such an interval due to the short history of using the seismic-noise response to the LOD as a predictor. Similar to how it was done to identify the places of concentration of the maxima of spatial correlations of seismic noise in Figure 8, we can search for places where the maximum response of seismic-noise properties to the uneven rotation of the Earth is most likely. The results of such a search are shown in Figure 12. Comparison of Figure 12a,b shows that the maximum response to the LOD is concentrated in the subarctic regions. In addition to the issue of the synchronization of seismic-noise properties, which are reflected in the graphs in Figures 5-7, we also studied the synchronization of seismic-noise responses to the irregularity of the Earth's rotation. Previously, this issue has been considered for the synchronization of seismic-noise responses to LODs in Japan and California [16]. For each reference point, we estimated the correlation of the response at this point with the responses at all other points. It should be taken into account that the correlated responses themselves were calculated in sliding time windows of 365 days with a shift of 3 days. These were \"short\" time windows. In this case, we needed to take a certain number of consecutive \"short\" windows and form a \"long window\" from them, such that it contained a sufficiently large number of estimates of the noise responses to the LOD in the \"short\" time windows. Next, 250 adjacent \"short\" windows were selected to form a \"long\" window. Correlation coefficients between the responses to the LOD at various  
Figure 11: (**a**) Logarithm of the released seismic energy (in joules) in a sequence of time intervals 365-days long, taken with an offset of 3 days; (**b**) average values of maximum coherences between LOD and daily DJ-index values at 50 reference points; (**c**) the correlation function between the logarithm of the released seismic energy and the average value of the maximum coherence between the LOD and the seismic-noise DJ-index at 50 reference points. reference points were calculated in a sliding \"long\" window with a shift of 1, that is, in a time window with a length of \(365+3\)-\((250-1)=1112\) days, which is approximately 3 years. A shift of 1 count meant a real shift of 3 days. The goal of such calculations for each reference point was the average correlations of responses over all other reference points. As a result of such averaging, 50 dependences of the same type as shown in Figure 5 were obtained. In order to obtain an integrated measure of the correlation of global noise responses to the LOD, the average dependences for all reference points needed to be averaged secondarily. As a result, we obtained the graph shown in Figure 13.  
Figure 12: (a,b) Probability densities of the seismic-noise index \(\gamma\) response maxima to LOD before and after 2011; (c) histogram of numbers of reference points, in which the maximum values of the index \(\gamma\) response to LOD were realized in a sliding time window of 5 years. Figure 13: The average value of the correlation coefficients between the seismic-noise index \(\gamma\) responses per LOD for each of the 50 control points with responses at other points. Figure 13 shows the change in time of the measure of synchronization of the response of seismic noise to the irregularity of the Earth's rotation. This graph also shows the growth of correlations, similar to the growth of the initial correlations in Figure 6.