GNGTS 2021 - Atti del 39° Convegno Nazionale

GNGTS 2021 S essione 1.1 20 Where a is the offset and F M describes the scaling with moment magnitude Mw. [2] The proposed FAS-GMM is calibrated for 69 ordinates of the Fourier spectrum in the frequency range from 0.5 to 25 Hz. The dataset is the same used in the work of Sgobba et al. (2021) and consists of more than 30’000 waveforms of 456 earthquakes in the magnitude range between 3.4 and 6.5, and more than 460 stations within 120 km from the epicenter. The high density of events and stations in such a relatively small region allows sampling a significant number of source-to-site ray-paths ( Fig. 1a ), thus making this dataset suitable to derive a fully non-ergodic GMM. MODELLING THE DIRECTIVITY EFFECTS ON NON-ERGODIC GMM The model is calibrated via a mixed-effect regression (Bates, 2015), providing the estimation of different repeatable effects on seismic motion (i.e. source, site and path) and reducing the random variability of the model. We adopt the same functional form of Sgobba et al (2021), to model the FAS amplitudes at each frequency: �� = + � ( ) + � ( , ) + � + 2 ���,� + 2 ������ + 2 � + � [1] Where is the offset and � describes the scaling with moment magnitude Mw. � ( ) = � ( � − � ) for � ≤ � � ( ) = � ( � − � ) otherwise [2] where � and � are coefficients obtained for the calibration and � is the hinge magnitude fixed at 5.0. Term � ( , ) is the scaling with distance R, divided into a contribution due to the geometric attenuation (coefficients � and � ) and anelastic parameter � . � ( , ) = � � � � − ��� � + � � �� �� ��� �� � � ��� + � (� ��� + ℎ � − ��� ) [3] where �� is the Joyner-Boore distance (the metric adopted for this model), ��� is the reference magnitude, ��� is the reference distance fixed at 1 km and ℎ is the pseudo depth at 6 km. where b 1 and b 2 are coefficients obtained for the calibratio and M h is the hinge magnitude fixed at 5.0. Term F R ( M,R ) is the scaling with distance R, divided into a contribution due to the geometric attenuation (coefficients c 1 and c 2 ) and anelastic parameter c 3 . [3] he dataset is the same used in the work of Sgobba et al. (2021) and consists of more than 30’000 waveforms of 456 earthquakes in the magnitude range between 3.4 and 6.5, and more than 460 stations within 120 km from the epicenter. The high density of events and stations in such a relatively small region allows sampling a significant number of source-to-site ray-paths ( Fig. 1a ), thus making this dataset suitable to derive a fully non-ergodic GMM. MODELLING THE DIRECTIVITY EFFECTS ON NON-ERGODIC GMM The model is calibrated via a mixed-effect regression (Bates, 2015), providing the estimation of different repeatable effects on seismic motion (i.e. source, site and path) and reducing the random variability of the model. We adopt the same functional for of Sgobba et al (2021), to model the FAS amplitudes at each frequency: �� = + � ( ) + � ( , ) + � + 2 ���,� + 2 ������ + 2 � + � [1] Where is the offset and � describes the scaling with moment magnitude Mw. � ( ) = � ( � − � ) for � ≤ � � ( ) = � ( � − � ) otherwise [2] where � and � are coefficients obtained for the calibration and � is the hinge magnitude fixed at 5.0. Term � ( , ) is the scaling with distance R, divided into a contribution due to the geometric attenuation (coefficients � and � ) and anelastic parameter � . � ( , ) = � � � � − ��� � + � � �� �� ��� �� � � ��� + � (� ��� + ℎ � − ��� ) [3] where �� is the Joyner-Boore distance (the metric adopted for this model), ��� is the reference magnitude, ��� is the reference distance fixed at 1 km and ℎ is the pseudo depth at 6 km. where R JB is the Joyner-B ore distance (the metric adopted for this model), M ref is the reference magnitude, M ref is the reference distance fixed at 1 km and h is the pseudo depth at 6 km. Regarding the random coefficients, in equation [1],  B e represents the between-event errors, which correspond to the av rage bias of recordings of one particular earthquake wit resp ct to the median prediction of the GMM.  S 2 S ref,s are the site-specific terms, that define the systematic bias of ground motions recorded at each station with reference to the median prediction of reference sites (see Lanzano et al ., 2020 for rock sites with flat response) and that represents a proxy of site amplification. The source terms  L 2 L source define the systematic bias of the source regions, associated with the FAS-GMM fixed-effects prediction, while  P 2 P p denotes the path-terms (which could be related to effective anisotropy in crustal velocity, density or in the attenuation. The areas for the source term  L 2 L source are identified by a clustering approach, where polygonal source areas are detected on the basis of space-time criteria, as shown in Fig. 1b . Fig. 1 - a) Map of the coverage by ray-paths (lines) connecting events (circles) and stations (triangles); b) S urce detection based on clusters. For this study, the most populat d clusters h ve been iden fied. They are: Cluster #1 (main event: L’Aquila 06/04/2009 - 01:32UTC), #4 (main event: Amatrice 24/08/2016 - 01:36UTC) and #5 (main event: Muccia 10/04/2018 - 03:11UTC). Red stars represent the mainshocks, while yellow stars are the other events.