# Spatial Correlations of Global Seismic Noise Properties
## 6 Seismic-Noise Response to the Irregularity of the Earth's Rotation  
The connection between the irregular rotation of the Earth and seismicity was investigated in [23]. The influence of strong earthquakes on the Earth's rotation was studied in [24, 25]. Figure 9 shows a graph of the time series of the length of the day for the time interval 1997-2022. Further, the LOD time series is used as a kind of \"probing signal\" for the properties of the seismic process [15, 16, 17, 3, 18]. To study the relationship between the properties of the seismic process and the irregularity of the Earth's rotation, the squared coherences maxima between the LOD and the properties of seismic noise at each reference point were estimated. The coherences were estimated in moving time windows of 365 days with a shift of 3 days  
Figure 8: (**a,b**) The probability densities of the correlation maxima for index \(\gamma\) values at each reference point with index values at other reference points before and after 2011; (**c**) a histogram of the numbers of reference points, in which the correlation maxima for values of \(\gamma\) at each reference point with the values at other points in a moving time window of 5 years were realized. Figure 9: Time series plot of the length of a day for the time interval 1997–2022. Day-length data (LOD) are available from the website at: [[https://hpiers.obspm.fr/iers/eop/eopC04/eopC04.1962-now](https://hpiers.obspm.fr/iers/eop/eopC04/eopC04.1962-now)]([https://hpiers.obspm.fr/iers/eop/eopC04/eopC04.1962-now](https://hpiers.obspm.fr/iers/eop/eopC04/eopC04.1962-now)) (accessed on 1 January 2023). using a vector (two-dimensional) fifth-order autoregressive model [15; 16; 17; 18]. In what follows, these maximum coherences will be referred to as the seismic-noise responses to the LOD. Figure 8 shows examples of the LOD response graphs at nine reference points. We define the integrated response of global seismic noise to the LOD as the average of the responses of the type shown in Figure 10 from all 50 reference points. Let us compare the behavior of the average response to the LOD with the amount of released seismic energy. To do this, we calculate the logarithm of the released energy as a result of all earthquakes in a moving time window 365 days long with a shift of 3 days. In Figure 11a,b, there are graphs of the logarithm of the released energy and the average response to the LOD. It is visually noticeable that bursts of the average maximum coherence in Figure 11b precede the energy spikes in Figure 11a. In order to quantitatively describe this delay, we calculated the correlation function between the curves in Figure 11a,b. The graph of this correlation function for time shifts of \(\pm\)1200 days is shown in Figure 11c. The estimate of the correlation function in Figure 11c between the logarithm of the released seismic energy in Figure 11a and the average response of seismic noise to the LOD had a significant asymmetry and was shifted to the region of negative time shifts, which corresponded to the coherence maxima being ahead of the maxima of seismic energy emissions. The correlation maximum corresponded to a negative time shift of 534 days. This estimate of cross-correlations produced a foundation to propose that the burst shown in Figure 11b by the magenta line may precede a major earthquake with an average delay of 1.5 years. The curve in Figure 11b can be split into three sections. The first two intervals with time marks of the right ends of windows before and after 2012 differ significantly from each other by their mean values presented by red lines. Figure 10: Plots of maximum squared coherence between index \(\gamma\) and LOD in a moving time window of 365 days with mutual shift of 3 days for 9 reference points. The third time interval in Figure 11b is presented by the magenta line and refers to the processing of the most recent data which correspond to right-hand end windows after 2021, i.e., referring to the time span of 2020-2022.