## 2 Methods of Analysis
(**B**) HVSR graphed as a contour plot of amplitude as a function of frequency (x-axis) and azimuth from the geographic north (0\({}^{\circ}\)) to south (180\({}^{\circ}\)), corresponding to the rotation angle of the two horizontal components of ground motion (y-axis). The colour scale quantifies the H/V amplitudes. Below, the HVSRs obtained for the 18 different rotation angles are also separately graphed as a function of frequency. (**C**) Results by the time-frequency (TF) polarization analysis [27] obtained by using the code Wavepol written by [PERSON]. The ellipticity plot vs frequency gives an indication of the possible linear polarization, this parameter being 0 when the ground motion is linearly polarized. Moreover, the polarization strike and dip given by the analyzed time series is cumulated and plotted using polar plots, the contour scale representing the relative frequency of occurrence of each value, and the distance to the center being the signal frequency in Hz. tion (e.g., [5; 6]). The covariance matrix is calculated using overlapping moving windows (the length tailored on the basis of the predominant signal frequencies). The eigenvalues and eigenvectors are determined by solving the algebraic eigenproblem and through the code POLARSAC [47; 48; 49]. They correspond, respectively, to the axis length and to the axis orientation of the polarization ellipsoid that represent the particle motion in the data window. The polarization azimuth is the angle between the projection of the largest eigenvector on the horizontal plane and the geographic north. Further details about the covariance matrix analysis can be found in Section 1, and in [17] Appendix A. In Figure 1A, an example is given, reporting: (i) filtered signals of the three components of ground motion; (ii) eight examples of polarization ellipsoids with different shape (elongation, horizontality, and flatness) and related to different seismic phases; (iii) values of polarization azimuth (i.e., the projection on the horizontal plane of the eigenvector associated to the maximum eigenvalue) versus time. The employed color scale related to the reliability scale is based on the hierarchical criterion as introduced in [34]. We show two rose diagrams in order to show the influence of the application of this hierarchical criterion on the final representation of ground motion azimuth results (1). Another widely exploited technique is represented by the time--frequency (TF) polarization analysis, proposed by [50] and used by [28]. This technique can provide quite robust results, overcoming the bias that could be introduced by the denominator spectrum in the SSR and HVSR calculation. In Figure 1C, we show some examples obtained through the code Wavepol written by [PERSON]. An ellipticity plot vs frequency gives an indication about possible linear polarization, this parameter being close to 0 for linearly polarized ground motion. Moreover, the polarization strike and dip obtained all over the time series analyzed are represented using polar plots, where the distance to the center represents the signal frequency in Hz, and the contour scale is related to the relative frequency of occurrence of each value. In the same frequency band where HVSR shows amplification, the ellipticity reaches its minimum values (under 0.2), indicating linearly-polarized ground motion (Figure 1C). Moreover, the strike polar plot shows polarization between N40\({}^{\circ}\) and N50\({}^{\circ}\), consistent with the HVSRs. Finally, the dip polar plot confirms that the ground motion polarization is concentrated on the horizontal plane, with predominant values between 90\({}^{\circ}\) and 100\({}^{\circ}\). The performance in the use of these three techniques to constrain directional amplification was recently tested on Ischia Island by [51], through over 70 ambient noise measurements. They confirmed coherent outcomes.