## 2 Materials and Methods
### Bell Tower Experimental Dynamic Characterization
Figure 4: (**a**) Location of the passive seismic single-station synchronous surveys (Vertical C) performed inside the Messina Bell Tower; (**b**) horizontal-to-horizontal spectral ratio plot obtained for the north–south component; (**c**) shape modes related to the vibration frequencies identified for north–south component; (**d**) horizontal-to-horizontal spectral ratio plot obtained for the east–west component; (**e**) shape modes related to the vibration frequencies identified for the east–west component. In the script, the cross-correlation between two signals coming from two different devices and relating to the same direction (e.g., north-south) is calculated. Through this procedure, the similarities between the signals are assessed, normalized concerning the maximum value, given by the bell tolling, and the position of this point is determined to identify the delay. This procedure is performed between all possible signal pairs, which in our case are six. After assessing the cross-correlation between the signals, the alignment of the signals is carried out concerning the signal that starts first. At the end of this procedure, four synchronous signals with a duration of 9 min each were extracted. In this research, the dynamic characterization of the structure, specifically identifying frequencies and modes of vibration, was carried out using the Standard Spectral Ratio (SSR) technique. This involves calculating the ratio of the Fourier spectra of signals from horizontal directions, measured at vertically aligned locations, with a reference record taken at ground level [34]. The structure's natural frequencies are then determined through a straightforward identification of the spectral peaks. In particular, the Fourier spectrum of each component is computed by dividing the signal into 20 s, non-overlapping windows. A window length of 20 s represents a reasonable compromise between temporal and frequency resolution. Shorter windows enhance temporal resolution but degrade frequency resolution, particularly for low frequencies. In contrast, longer windows improve frequency resolution but may obscure rapid temporal variations in the signal. Considering these trade-offs, a 20 s window was chosen to optimize both temporal and frequency resolution, with a particular focus on the low-frequency range of interest. The engineering frequency range of primary interest typically spans from 0.5 to 10 Hz. Therefore, the lowest frequency of interest was assumed to be 0.5 Hz, corresponding to a period of 2 s (T = 1/f). To achieve improved spectral resolution, the analysis window should be at least ten times the period of the lowest frequency under investigation. Thus, a 20 s window was selected to ensure that the minimum resolvable frequency completes at least 10 full cycles within the analysis window. Each window is detrended, tapered, padded, fast Fourier transformed, and smoothed using triangular windows whose width is 1% of the central frequency. The peaks identification is performed on the distinct individual spectra normalized to a reference spectrum related to a signal acquired at the ground level. Additional single-station passive seismic acquisitions were performed to assess the possibility of the structure being subject to rocking and torsion modes (Figure 5a) and to obtain preliminary information on the damping of the structure. All structural design codes take into account the possibility of torsional effects occurring in a building as they can contribute to a significant increase in damage under high stresses. Ambient noise recordings on the highest floor of a building [35] allow the identification of its propensity to experience torsional effects. The stress increase (\(\Delta\)) due to structural irregularities or uneven distribution of masses can be evaluated using the relationship:  
\[\Delta=\frac{\delta_{\text{max}}}{\delta_{\text{avg}}} \tag{1}\]  
where \(\delta_{\text{max}}\) and \(\delta_{\text{avg}}\) are the displacements at the side and center of the building on the last floor, respectively.