GNGTS 2024 - Atti del 42° Convegno Nazionale

Session 2.1 GNGTS 2024 systematic contributions of event, source, site and path effects thanks to a mixed effect calibration technique ( Stafford, 2014 ). As already noted by Sgobba et al. (2023) , the exceptional amount of information that has been produced in Central Italy, makes this area particularly suitable for a calibration of this kind of model. The model calibrated in this study is a modified version of the one developed by Sgobba et al. (2021a) for the Central Italy and presents the following functional form: [1] 10 = + ( ) + , ( ) + δ + δ 2 + δ 2 + δ 2 + δ 0 where is the intensity measure, i.e. PGA or a spectral parameter (69 values logarithmically equispaced from 0.04 to 2 sec), , , are the fixed effects depending on ( ) , ( ) magnitude and distance metric , while , , represents the zero-mean δ δ 2 , δ 2 gaussian-distributed random effects. Details on the fixed and random terms were provided in the paper of Sgobba et al. (2021); this study is based on the analysis of the azimuthal distribution of the leftover residual , which δ 0 reflects the aleatory variability, net to the computation of the systematic effects. The azimuthal variation is fitted starting from the general expression of the directivity factor by δ 0 Boatwright (2007) : [2] = 2 [1−( ) ⁡(θ−θ 0 )] 2 + (1− ) 2 [1+( ) ⁡(θ−θ 0 )] 2 where is the Mach number from here on called , is the azimuth of the rupture direction α θ 0 and parameter which spans from 0 to 1 indicates the relative portion of the rupture length along the rupture direction . θ 0 Taking into account that there is a trade-off between the fit parameters as , , and , we have α θ to assume fixed some of these values in order to vary others. After several tests, for this work we decided to fix to 0.85 and to 0.50 and then evaluating the directivity power by the parameter α . The constrained parameters are consistent with those reported in the literature ( Ren et al., 2017 ; Convertito et al., 2017 ) and also ensure that we have a good fit in the majority of the events. For the identification of directivity effects, we adopted the same criteria of Colavitti et al. (2022) , which is based on these following points: 1. The coefficient of determination computed between the observed distribution of the 2 aleatory residual and the fit considering the model is greater than 0.50 for at δ 0 least 7 out of 69 periods investigated;