GNGTS 2013 - Atti del 32° Convegno Nazionale

(2) where the summation in the square brackets is extended over all the 2 (case i) or 3 (case ii) u k components of the ground motion from which the analytic vector is derived. The ellipse major and minor semi-axes can then obtained from (3) (4) and their vectorial product , named “planarity vector”, is normal to the plane containing the instantaneous ellipse (Schimmel and Gallart, 2003). This ellipse can degenerate in a rectilinear ground motion if . Thus one can use a parameter defined “rectilinearity” (Schim- mel and Gallart, 2004), given by (5) to define the closeness of ground motion to linear polarisation. On the basis of these theoretical principles, an approach was developed to calculate the instantaneous values of the H/V ratios of a noise recording and for the identification, within the recording, of Rayleigh wave packets. According to this approach, Eq. (1) is applied to the vertical component to obtain the instantaneous amplitude A Z ( t ) of the vertical ground oscillation. Then Eqs. (2) and (3) are applied to the two horizontal components to obtain, from the calculation of the vector , the instantaneous direction and the modulus A H ( t ) of the maximum horizontal ground oscillation. The ratio A H ( t )/ A Z ( t ) provides an instantaneous estimate of the ratio between horizontal and vertical ground motion amplitude and the direction of gives the direction of maximum horizontal ground motion. The identification of possible Rayleigh wave packets is then obtained on the basis of the recognition of a minimum number n of consecutive ground motion samples for which the planarity vector is close, within an optionally defined approximation, to an horizontal direction and, simultaneously, the and vectors are close to horizontal/vertical directions (or viceversa). The identification of possible SH-type polarisation can be derived as well from the closeness of to horizontality and from the exceedance of rectilinearity (5) over an optionally defined threshold. This kind of analysis can be carried out on the complete recording, but also on signals filtered to analyse the variation of polarisation properties with frequency. It should be underlined, however, that the same data samples could result compatible with both the identification criteria of Rayleigh and SH-type waves under resonance conditions, for which Rayleigh wave vertical component vanishes (Bard, 1999). One can then obtain some statistics on instantaneous H/V amplitude and orientation as function of frequency and azimuth for the entire signal and, separately, for the portions identified as Rayleigh or SH-type wave packets. Furthermore, the average and the standard deviation of the H/V ratios can be estimated as function of frequency- azimuth intervals. 228 GNGTS 2013 S essione 2.2