GNGTS 2014 - Atti del 33° Convegno Nazionale

GNGTS 2014 S essione 2.1 maximum spectral amplitude ground motion, no geometric means are used in the computation of the horizontal ground motion. Previous definitions are only a limited subset of a much larger set of horizontal component measures. We have focused on the most common definitions used worldwide for PSHA in the last 20 years, evidencing their advantages and disadvantages. An exhaustive review of horizontal component definitions, including models for converting between them, is provided by Beyer and Bommer (2006). The authors show that the largest differences are those from the ENV xy definition to GM xy . Differences between GM xy , GMRotD50, GMRotI50, and RotD50 are minimal (negligible at low periods and, generally, less than 5-8%). On average, GMPEs that uses the ENV xy definition predict PGA values that are 10% greater than those based on GM xy . At larger spectral periods (e.g., T > 0.8s), ENV xy is about a factor of 1.2 larger than GM xy (Beyer and Bommer, 2006). As an illustration of this, the effect of the definition of the horizontal component of motion is shown in Fig. 1 for the Bindi et al. (2011) GMPE (hereinafter ITA10), which, in its original definition, predicts the geometric mean of the ground motion relative to the x and y components. To this end, the conversion relationships proposed by Beyer and Bommer (2006) are applied. Basically, the method consists of adjusting the median ground motion by a multiplicative factor (note that the adjustment only depends on period). The following conversions are performed: GM xy -to-ENV xy , GM xy -to-GMRotI50, and GM xy -to- RotD50. Concerning this latter conversion, RotD50 is calculated from GMRotI50 since direct conversion relationships GM xy -to-RotD50 are not available: RotD50 = GMRotI50 T < 0.1s RotD50 = GMRotI50 * (0.025 T +1) 0.1s ≤ T < 1s RotD50 = GMRotI50 * 1.025 1s ≤ T < 3s Previous equations were determined using data published in the article by Boore (2010). Concurrently, to the conversion of the median ground motion, one should adjust the value of the aleatory variability of the ground motion (sigma). In other words, the aleatory variability associated to conversion equations should be carried across into the aleatory variability of the GMPE adopted (Bommer et al. , 2005). As known, sigma is an integral part of any PSHA analysis. Therefore, the effect on the hazard of the conversion of the median ground motion shown in Fig. 1 may be “boosted” (or lowered) by the adjustment of sigma which, as known, has a large effect on the hazard (e.g., Strasser et al. , 2008, 2009). As clear from Fig. 2, sigma acts as a gain potentiometer with a log-taper (typical in audio applications); turning it up leads to increased hazard values following an exponential trend. This effect is more evident at larger mean return periods. In order to finally evaluate the impact of the horizontal component definition on the hazard, we simply calculated the ground motion hazard at a reference site (Barisciano, near L’Aquila in central Italy) by adopting the original ITA10 model and the adjusted ones. Again, sigma was adjusted following the procedure proposed by Beyer and Bommer (2006). The reference hazard model employed in the calculation considers the set of input models and parameters adopted by Barani et al. (2009) for the disaggregation of the Italian ground motion hazard maps (Gruppo di Lavoro MPS, 2004). The comparison among the resulting hazard curves is shown in Fig. 3. The ratio between the results obtained by applying the original model and the component-adjusted ones is also depicted. As clear from the figure, while GM xy , GMRotI50, and RotD50 produce analogous results, ENV xy leads to higher hazard values. Specifically, the effect on the hazard ranges from 1.12 to 1.15 in the case of PGA and from 1.23 to 1.25 in the case of S a (1.0s) (note that it tends to increase slightly with increasing the return period). As expected, these values are higher than the factors adopted for adjusting the median GM xy ground motion to ENV xy , indicating that incorporating the sigma adjustment into calculations has boosted the hazard. Analogous results (not shown here) were obtained for another site (Malcesine in northern Italy) characterized by lower seismic activity.