## 4 Correlation between the Structural Monitoring and the Seismic Activity
In order to verify the hypotheses presented by the authors in the correlation between AE and seismic data, the historical time series of the seismic data were reported for two time windows containing the periods of the AE monitoring, performed on the tower structure and then in the timber structure positioned in the bell cell. The data related to the seismic time series were assessed and obtained from the Italian National Institute of Geology and Volcanology (INGV) that reported all the seismic events recorded by the National Seismic Network ([[http://terremoti.ingv.it/instruments](http://terremoti.ingv.it/instruments)]([http://terremoti.ingv.it/instruments](http://terremoti.ingv.it/instruments))). Figure 12: The average \(b\)-values before the “anticipator” event (12 April 2018) is equal to 0.95. After this, an evident reduction in the average value equal to 15% is observed (average \(b\)-value = 0.82). The main event occurred about 50 days after (5 June 2018). After the \(m_{L}\): 3.1, no event with greater magnitude were registered for three months. The following reduction of the local magnitudes based on the distance between the monitored site and the epicenter according to the following report is assumed:  
\[m_{L}^{*}=\left(1-\frac{d}{100}\right)m_{L} \tag{8}\]  
where \(m_{L}\)* is the reduced local magnitude; \(m_{\rm{L}}\) is the actual local magnitude and \(d\) is the distance, measured in km, between the epicenter and the Bell Tower of the Turin Cathedral. In Figure 13 the two seismic time series were represented together with the variations of the average \(b\)-values. Figure 13: _Cont._  
These variations trends resulted particularly evident for both the two considered periods (10 May 2018-30 June 2018 and 1 August 2019-25 September 2019). For each period, two couples of events were recognized, each of them formed by one anticipant and one main event (the anticipant and the main events are distinguished by stars on the \(x\)-axis of the graph). The average values of the \(b\)-value before the anticipating events are 1.34 and 2.01 for the two periods, respectively (see Figure 13a,b). The reduced local magnitudes for the two anticipants are \(m_{L}\)\({}^{*}\) = 1.5 (1 June 2018, Inverso Pinasca, 44\({}^{\circ}\)57\({}^{\prime}\) N 7\({}^{\circ}\)13\({}^{\prime}\) E, near Turin); and \(m_{L}\)\({}^{*}\) = 1.0 (24 August 2019, Torre Pellice, 44\({}^{\circ}\)49\({}^{\prime}\) N 7\({}^{\circ}\)14\({}^{\prime}\) E). After these two events two phases, the first of about seven days and the second of about eight days with average \(b\)-values of 0.58 and 1.85 were observed for the two time windows. After these intervals, the expected seismic main events \(m_{L}\)\({}^{*}\) = 2.3 and \(m_{L}\)\({}^{*}\) = 1.9 took place (Figure 13a,b). These two events were both anticipated by the previously mentioned series where the average \(b\)-values encountered reductions of 56% and 8%. After the occurrence of the two events recognized as main events, the \(b\)-values trends returned to grow significantly--the average \(b\)-values were 1.22 for the first time window  
Figure 13: The seismic time series are represented together with the variations of the AE average \(b\)-values detected on the structures of the tower: (**a**,**b**) \(b\)-value time series considering the seismic activity along 40-day time windows. In both the two cases the average \(b\)-values demonstrated an evident reduction in correspondence of foreshocks periods between the anticipating and the main event. (**c**,**d**) At the same time, the \(b\)-value time series have been computed for AE data and correlated to the seismic activity for a period of 25 days contained in the previous larger time intervals. and even 2.82 for the second (Figure 13a,b). The evidence here reported is useful to understand that the discrimination criterion reported by [PERSON] and [PERSON] (2019) [21] can be applied to seismic series with reduced magnitude values (\(0.5<m_{L}<3\)) and also in the case of rescaled values that follow the reduction rule reported in Equation (8).