GNGTS 2016 - Atti del 35° Convegno Nazionale

GNGTS 2016 S essione 2.1 283 In this equation, a , b , c , d , e i , f j , h 2 are the parameters that have to be derived through a non-linear regression: it was carried out on a dataset consisting of 264 recordings, relative to 69 events of magnitude between 4.0 to 6.8, acquired by 119 stations located at distances up to 208 km from the event source. Since the complete functional form (1) may not be applicable if information on source or site properties are missing and considering that the available regression dataset might be unable to provide good constraints for the calculation of some of the equation parameters, simpler functional forms were also tested excluding some of the terms present in Eq. (1). To compare the effectiveness of different equations, tests were carried out by evaluating prediction errors on a validation dataset, distinct from the regression dataset, consisting of 112 recordings relative to 108 events of magnitude between 4.0 and 6.8, acquired by 41 stations located at distances up to about 203 km. The best predictive performances turned out to be provided, for PHA, by the equation (2) and, for PHV, by the equation (3) where the binary variables s 1 and s 2 , accounting for site effects, are both set to 0 for rock site (class B) and, alternatively, s 1 to 1 and s 2 to 0 or vice versa, for stiffer (class C) and softer (class D) soil types, respectively. The main inferences derived from the test results are that, at least within the magnitude- distance range covered by the database employed (i.e. magnitude between 4.0 and 6.8 and distance up to about 200 km): 1) the inclusion of dummy variables accounting for focal mechanism and the adoption of a magnitude-dependent rate of attenuation with distance do not improve PHA and PHV predictions; 2) better performances are obtained with functional forms predicting a significant deviation from the attenuation rate expected for a purely geometric spreading, taking into account anelastic attenuation; 3) the inclusion of site effect terms under the form of binary dummy variables, while improves PHV predictions, appears ineffective for PHA estimates. A possible explanation for the last observation is that, at a site, peak accelerations do not shows a systematic amplification for any shaking, the amplification factor being strongly influenced by wave spectral energy content, which depends on event magnitude and wave travel path. At this regard, residuals of Eq. (2) were calculated on the validation dataset and averaged on different ranges of source magnitude and recording distance to examine their possible dependence on such elements. In particular, Fig.1 shows, to the left, residual progressive averages calculated for distances and magnitudes between minimum and increasing upper bounds, and, complementarily, to the right, progressive averages for ranges between increasing lower bounds and maximum. This figure shows that, at lower magnitudes and shorter distances, residuals observed at sites on rock (class B) are higher than on soil, whereas the contrary occurs at larger magnitudes (approximately starting from 5.0) and longer distances (approximately starting from 20 km). Since recordings from shorter distances of lower magnitude events typically have spectral energy peaks at higher frequencies, the larger residuals observed under such conditions can be due to a stronger response of rocks at such frequencies, in comparison to softer grounds. This observation suggests that site effect cannot be effectively modelled in equations predicting PHA over a range of magnitude 4.0÷7.0 by a simple dummy variable, and a more complex modelling including frequency dependence could be needed (e.g. Sandikkaya et al. , 2013). Comparatively, this problem is not encountered for peak velocity predictions. Fig. 2 shows the results of the analysis of residuals obtained applying the equation that best predicts