## 3 Results
### Experimental Testing of Torsional and Rocking Mode  
Two additional synchronous samplings were performed at the highest bell tower floor to assess the propensity of the structure to undergo possible torsional effects (Figure 5a). The displacement spectra of horizontal components for lateral and central measurements were compared using OriginPro 9.0.0 (64-bit) software. Analyzing the graph in which the displacement values for the N-S and E-W components of the two measurements are plotted, it is evident that, at a frequency of 3.5 Hz, the two spectra do not follow the same trend (Figure 5b). In particular, at this frequency, a spectral peak is observed in the lateral measurement that disappears in the barycenter measurement. This suggests that the mode at a frequency of 3.5 Hz is a torsional mode. The simplified equation of [PERSON] et al. [36] was used to test the propensity of a building to undergo torsional effects. The \(\Delta\) computed for the NS and EW components (Table 2) is equal to 14.05 and 10.53, respectively, highlighting the propensity of the investigated structure to undergo strong torsional effects according to the classification proposed by [PERSON] et al. [36]. Given the highly deformable nature of the subsoil on which the Messina Bell Tower rests, to verify whether the tower was subject to rocking mode, two synchronous measurements were carried out at the base of the tower, located at two opposite ends of the base (Figure 5a). Having ascertained from the SSR spectra the presence of a spectral peak at a frequency of approximately 1.4 Hz, corresponding to the fundamental mode of the structure and visible on all three components (Figure 3b,c), the signals related to the vertical (Z) components of the synchronous measurements were filtered, using a bandwidth filter around the analyzed frequency. The filtering process unveiled that the temporal trends in the vertical components exhibit a phase difference of approximately 180\({}^{\circ}\) with equivalent amplitudes at the two opposite sides of the building base (Figure 5c). This phase difference indicated that the two points were moving in opposite directions, at the same instant, a characteristic signature of rocking motion, where the structure rocks around its base rather than sliding. This observed mode concurs with the expected dynamic behavior of structures coupled to deformable subsoil, where the base experiences opposite rotations at distinct locations. The experimental results substantiate the presence of a rocking motion analogous to the behavior observed in solid-to-solid interfaces: the tower's base undergoes a balanced rotational oscillation around a central pivot, causing complementary vertical movements (one side rising while the opposite side lowers). Thus, the observed 180\({}^{\circ}\) phase shift combined with amplitude symmetry robustly supports the hypothesis that the spectral peak at approximately 1.4 Hz corresponds to the rocking mode. While structural systems prone to pure rocking are typically very sensitive to even minor changes in the excitation characteristics, the present study was conducted under weak ambient seismic noise that can be approximated as stationary over the analysis period. Under these low-amplitude conditions, the system's response can be effectively linearized, enabling us to identify a predominant dynamic behavior. The spectral peak corresponding to the rocking mode was derived from an average of multiple 20 s time window analyses, conducted over a total span of 20 min. This averaging process significantly reduces the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Frequency** & **Central Displacement** & **Lateral Displacement** & **Component** & \(\Delta\) \\
**(Hz)** & **(\(\delta_{\text{avg}}\)) mm** & **(\(\delta_{\text{max}}\)) mm** & **Component** & \(\Delta\) \\ \hline
3.531 & 0.0000066276 & 0.0000931505 & N-S & 14.05 \\ \hline
3.5 & 0.0000092254 & 0.0000971741 & E-W & 10.53 \\ \hline \hline \end{tabular}
\end{table}