GNGTS 2013 - Atti del 32° Convegno Nazionale

two separate modes can become even harder. The discontinuity of the picked maxima in correspondence of the osculation point can totally disappears: with a poorer f-k resolution the osculation point is often not recognizable. The apparent dispersion curve seems continuous in velocity, and the spectral amplitude distribution is continuous as well. The amplitude of the recorded vertical particle velocity results from the smooth transition between the contribution of the fundamental mode and the first higher mode. Polarization and osculation. As discussed by Tuan et al. (2011) and Malischewsky et al. (2008), the osculation phenomenon occurs only for certain impedance contrast cases, and has consequences also for seismic response analysis (Konno and Omachi, 1988; Castellaro and Mulargia, 2009; Mucciarelli et al. , 2009; Boaga et al. , 2011). High impedance contrasts have, in fact, also a strong impact onto seismic amplification, and are a primary target for the site characterization (Nogoshi et al. , 1970; Nakamura, 1989; Fah et al. , 2011; Bonnefoy-Claudet et al. , 2008; Hobiger et al. , 2009). It is well known that the Rayleigh wave particle motion is elliptical; the ratio between the vertical and the horizontal components, the vertical ellipticity , depends on the velocity profile. In a homogeneous half space, the ellipticity is constant for all frequencies, and a function of the Poisson’s ratio. In vertically heterogeneous media, the ellipticity is a function of frequency, and its character is strongly dependent on the velocity contrasts. The polarization of surface waves is related to the velocity structure, and the signature of the velocity structure on the polarization becomes larger with larger velocity contrast. Therefore several characterization techniques have been devised to take advantage of motion polarization. It can be shown that the magnitude of the ellipticity peak is directly related to the velocity contrast. But we want to show here that also the relationship between polarization and osculation is direct. In absence of sharp velocity contrasts, modes are well separated and the ellipticity curve is fairly flat. In presence of a strong velocity contrast, the distance between the modes is reduced and the ellipticity peak becomes more pronounced. It is evident that the cases with large velocity contrast are the most dangerous for the possible mode mis‑identification. And in these cases, the ellipticity exhibits behaviour progressively more extreme as the velocity contrast increases. It can be observed as at certain frequency f V the horizontal particle motion vanishes, and the Rayleigh wave is purely vertically polarized, and one frequency f H the vertical particle motion vanishes, and the polarization becomes horizontal. These singularities are also points where the direction of the elliptical particle motion changes: from counter‑clockwise to clockwise and to counter‑clockwise again. The peak of the vertical ellipticity takes place very close to the osculation frequency. It is important to enhance how the ellipticity discussed here refers to the fundamental mode only. The polarization of the first higher mode has an opposite behaviour, becoming vertical for frequencies smaller than the osculation frequency. Large contrasts in the subsurface produce both the mode osculation and a high peak of vertical ellipticity. Therefore, existence of such peak indicates the presence of a large velocity contrast, and the risk of osculation. The frequencies at which these two phenomena occur are related, even in multilayer models. The osculation happens because of a drop of amplitude of the vertical component, and below the osculation the vertical component reaches a zero. A Monte Carlo simulation of 2000 cases with 3 layers over a bedrock, with a large velocity contrast, is performed and analysed, and the results show the direct relationship between these frequencies (Boaga et al. , 2013). The osculation happens at a frequency between to the frequency f H of the horizontal polarization and the frequency f V of vertical polarization, the peak of vertical ellipticity curve of the fundamental mode. As a consequence we aim at demonstrating that the mode osculation 24 GNGTS 2013 S essione 3.1