GNGTS 2015 - Atti del 34° Convegno Nazionale

it was found that the rms err values are mostly lower than rms sc , but this may not be true when the number nR of samples identified as Rayleigh-type is extremely low. In such cases, correlation between accuracy and precision can worsen and HVIP curves characterized by smaller scatter may not be those also affected by smaller errors. As an example, Fig. 1 shows the relation between scatter and error values for the case of the signal surf100sn1. If one considers the results of all the analyses, independently on the number nR 2Hz of samples used to calculate the HVIP peak value (i.e. for azimuth=30°- 40° and frequency = 2.00 Hz), the correlation between errors and scatters appears rather weak, with minimum scatter found for analysis results affected by relatively large errors. On the contrary, excluding the results obtained with nR 2Hz < 200, the correlation is much better and the choice of the estimate affected by the lowest scatter would result in an H/V curve close to the optimal one from the point of view of accuracy. On the other hand, excessively loose criteria of wave identification, which would generate a very large number of samples identified as Rayleigh-type, is not an effective approach. Indeed, this would cause the inclusion in the calculation of HVIP of a considerable number of estimates of H/ V strongly scattered around the average, which make the precision a poor estimator of accuracy. These results suggest that a good criterion to define the analysis parameters is to try different combinations, selecting the one providing the minimum scatter rms sc among the combinations that classify a significant number of Rayleigh-type data samples (at least 200 for the peak frequency). Using this criterion, the percentage of classified samples on the total is correlated to the signal-to-noise ratio characterizing the analyzed recording and the value of scatter rms sc provides an upper bound for the root mean square of errors rms err . Fig. 2 shows the HVIP curves corresponding to the best estimates, in terms of accuracy and precision, obtained analyzing the six synthetic signals according to the aforementioned criterion. These curves are compared with the actual values of H/V ratio of Rayleigh waves and with the curves obtained from analyses conducted with the classical Nakamura’s technique. The latter was conducted subdividing the synthetic time series into 20 s windows, smoothing the spectra of horizontal and vertical components through a triangular average on frequency intervals of ±5% of the central frequency, and averaging the spectral ratios of different time windows after having discarded those showing abnormally high or low H/V ratios throughout the frequency band analyzed. The resulting “HVNR” curves were calculated at azimuth intervals of 10°: for directionally polarized signals (surf100, surf100sn3, surf100sn1) the comparison was made with the curve obtained along the direction N35°E, which showed the largest H/V values, whereas, for the case of isotropic signals (surf100i, surf100sn3i, surf100sn1i), both euclidean and geometric averages between north and east components were calculated. For those signals whose background noise has amplitude much lower than the signal (surf100, surf100i), the HVIP provides very good estimates of the real H/V ratios of Rayleigh Fig. 1 – Comparison between scatters (root mean square of deviations of instantaneous H max /V values from mean HVIP values) and root mean square of errors (HVIP deviations from the actual H/V values) relative to instantaneous polarization analyses conducted with different parameter combination on the synthetic signal surf100sn1. Open and full circles represent data relative to analyses that classified less or more than 200 samples of Rayleigh type, respectively, at the peak frequency of 2 Hz. 78 GNGTS 2015 S essione 2.2