## 2 Materials and Methods
### Bell Tower Experimental Dynamic Characterization
Generally, a torsional mode may be present on irregular structures since the center of mass and center of stiffness do not coincide. The estimation of \(\Delta\) can be retrieved by ambient seismic noise measurements performed on at least two points in the same structure level [36] by calculating the displacement spectra. For the best possible estimation of the structure propensity to be affected by torsional effects, it is essential to measure a position close to the barycenter axis of the building to detect the amount of translation and one at one end of the building, where the torsional component is also supposed to be recorded. The simultaneity of the recordings is not essen  
Figure 5: **(a)** Location of the passive seismic single-station synchronous surveys performed at the base and at the top floor of Messina Bell Tower; (b) torsional mode identification: north–south and east–west displacement spectra related to the recordings carried out at the tower top floor; (c) rocking mode verification: top, original signals in time related to the \(Z\) components of the records performed at the tower base; bottom, amplitude relative motion of the signals filtered in the time domain, highlighting the 180\({}^{\circ}\) phase shift between the two opposite ends of the structure base. tial but makes it more immediate to establish whether the measured points move in-phase (same direction) or in phase opposition (opposite direction). Following these indications, two synchronous measurements were carried out at the highest floor of the bell tower; for each horizontal component, the displacement spectra were calculated. By comparing the spectra for homologous components of the recording acquired at the barycenter with that of the measurement acquired at one end, it is possible to identify a torsional mode when a spectral peak is observed in the lateral measurement and at the same frequency, the peak disappears in the barycenter measurement (Figure 5b). In this work, those proposed by Eurocode 8 [37] for which the ratio \(\Delta\) must not exceed 20% and 40% of \(\delta_{\mathrm{avg}}\) were considered as thresholds. Torsional effects showing values of \(\Delta\leq 1.2\) are considered weak, values of \(1.2<\Delta\leq 1.4\) are associated with a moderate torsional effect, and values of \(\Delta>1.4\) (strong torsional effects) are considered significant. The rocking motion generally refers to a rotational response of a structure around a horizontal axis at or near its base, caused by alternating uplift and contact loss. In idealized models, this phenomenon is often associated with rigid bodies rocking on perfectly stiff supports. However, in real structures, the manifestation of rocking is typically more complex. It may involve partial uplift, local detachment, foundation compliance, or even slight soil deformation, all of which affect the geometry and stiffness of the rotation axis. Consequently, the axis of rotation is not strictly horizontal or fixed, and the rocking motion may appear coupled with other dynamic behaviors such as horizontal bending or torsion. Despite these complexities, rocking can still be identified by specific kinematic signatures, such as out-of-phase vertical displacements at opposite corners of the base and strong phase relationships across components. When rocking motion occurs, the base of the building oscillates around a horizontal rocking axis. The vertical displacements of two distant points, positioned on opposite sides of the rocking axis, are in phase but exhibit opposite amplitudes, resulting in a 180\({}^{\circ}\) phase shift [38]. To assess this behavior, two synchronous ambient vibration measurements were carried out using three-component velocimeters, positioned at opposite corners of the tower's base (Figure 5a). No artificial excitation was applied; the structure was excited only by environmental sources. The instruments were synchronized via radio link.