GNGTS 2021 - Atti del 39° Convegno Nazionale

GNGTS 2021 S essione 2.2 334 Functional form On the basis of the preliminary data analysis (not reported here), the functional form for the VH ITA18 median model is defined as follows: first approach has the main limitation of posing a potential inconsistency between the disaggregation controlling the horizontal and vertical hazard, leading to serious obstacles in the selecti of three-co ground motion time histories for dynamic structural analyses. For these reasons, the most commonly used is to generate the vertical spectrum by making use of empirical models for VH ratios [Gülerce and Abr 2011; Bommer et al. 2011; Akkar et al. 2014; Bozorgnia and Campbell 2016; Poggi et al. 2019]. This a although simplified, avoids the issues of performing vector-valued PSHA [Bazzurro and Cornell 2002] i both horizontal and vertical components and the full treatment of their correlation. The main aim of this study is to develop an empirical GMM for VH ratios of Spectral Acceleration (S Ground Acceleration (PGA) and Peak Ground Velocity (PGV) for Italian crustal earthquakes. The regr calibrated using the same dataset adopted by Lanzano et al. (2018) to develop the horizontal GMM, thus consistency between the two models, both in terms of validity range and functional form. To account for t of near-source conditions on the VH ground motion, a near-source correction term is proposed, follo Referenced Empirical Approach [Atkinson 2008; 2010]. In this approach, for a given GMM, a correctiv computed on the basis of the residuals between the prediction and additional data, suitable to model specifi on the ground motion. In our case, the corrective term for the reference ITA18 GMM is calibrated base analysis of residuals with respect to a worldwide dataset of near-source recordings, namely, NESS1.0 [Pa 2018]. Figure 1 shows the conceptual framework at the basis of the methodology proposed to develop the It GMM accounting for near-source effects. FUNCTIONAL FORM On the basis of the preliminary data analysis (not reported here), the functional form for the VH ITA1 model is defined as follows: log 10 Y ¿ a + F M ( M W , SoF ) + F D ( M W , R ) + F S ( V S 30 ) where Y is the VH ratios for PGA, PGV and 36 ordinates of 5% damped SA in the range 0.01-10 s, a is t F M ( M W , SOF ) is the source function, F D ( M W , R ) is the distance function and F S ( V S 30 ) is the site t functional form is consistent with the one adopted for the horizontal GMM of [Lanzano et al. 2019], apa minor modification regarding the source term owing to the more limited dependence of VH on M w (h magnitude scaling is controlled by a simple linear function, whereas in [Lanzano et al. 2019] by a stepw function). Specifically, the source term consists of two terms: (1) where Y is the VH ratios for PGA, PGV and 36 ordinates of 5% damped SA in the range 0.01-10 s, a is the offset, (GMM) specifically developed for the vertical response spectral ordinates [Chiou and Youngs 2013;Boz Campbel 2016; Gülerce et al. 2017; Çağnanet al. 2017]; (2) use a GMM for the Vertical-to-Horizontal (v horizontal (VH) response spectral acceleration ratios to scale the horizontal Uniform Hazard Spectrum ( first approach has the main limitation of posing a potential inconsistency between the disaggregation controlling the horizontal and vertical hazard, leading to serious obstacles in the selection of three-c ground motion time histories for dynamic structural analyses. For these reasons, the most commonly used is to generate the vertical spectrum by making use of empirical models for VH ratios [Gülerce and Ab 2011; Bommer et al. 2011; Akkar et al. 2014; Bozorgnia and Campbell 2016; Poggi et al. 2019]. This although simplified, avoids the issues of performing vector-valued PSHA [Bazzurro and Cornell 2002] both horizontal and vertical components and the full treatment of their correlation. The main aim of this study is to develop an empirical GMM for VH ratios of Spectral Acceleration ( Ground Acceleration (PGA) and Peak Ground Velocity (PGV) for Italian crustal earthquakes. The re calibrated using the same dataset adopted by Lanzano et al. (2018) to develop the horizontal GMM, thu consistency between the two models, both in terms of validity range and functional form. To account for of near-source conditions on the VH ground motion, a near-source correction term is proposed, foll Referenced Empirical Approach [Atkinson 2008; 2010]. In this approach, for a given GMM, a correcti computed on the basis of the residuals between the prediction and additional data, suitable to model speci on the ground motion. In our case, the corrective term for the reference ITA18 GMM is calibrated bas analysis of residuals with respect to a worldwide dataset of near-source recordings, namely, NESS1.0 [P 2018]. Figure 1 shows the conceptual framework at the basis of the methodology proposed to develop the I GMM accounting for near-source effects. FUNCTIONAL FORM On the basis of the preliminary data analysis (not reported here), the functional form for the VH ITA model is defined as follows: log 10 Y ¿ a + F M ( M W , SoF ) + F D ( M W , R ) + F S ( V S 30 ) where Y is the VH rat os for PGA, PGV and 36 ordinates of 5% damped SA in the range 0.01-10 s, a is F M ( M W , SOF ) is the source function, F D ( M W , R ) is the distance function and F S ( V S 30 ) is the site functional form is consistent with the one adopted for the horizontal GMM of [Lanzano et al. 2019], ap minor modification regarding the source term owing to the more limited dependence of VH on M w ( magnitude scaling is controlled by a simple linear function, whereas in [Lanzano et al. 2019] by a step function). Specifically, the source term consists of two terms: is the source function, (GMM) specifically developed for th vertical response spectral ordi ates [Chiou a Campbel 2016; Gülerce et al. 2017; Çağnanet al. 2017]; (2) use GMM for the Ve horizontal (VH) response spectral acc leration ratios to scale the horizontal Unifor first approach has the main limi ation of p sing a pot ntial inconsistency be we controlling the horizontal an ver ical hazard, le ding to serious obstacles in th gr und motion time histories for dynamic structural analyses. For these reasons, the is to gene ate the vert cal sp ctrum by making use f empi ical models for VH r Bomm r et al. 2011; Akkar et al. 2014; Bozorgnia and Campbell 2016; Po althoug s mplified, avoids the issues of p rforming vector-valued PSHA [Bazzur both horizontal and ver ical components and the full treatment of their correlation. The main aim of this study s to develop an empirical GMM for VH ratios f S Ground Acceleration (PGA) and Peak Ground Velocity (PGV) for Italian crustal calibr ed using he same dat set adopted by Lanzano et al. (2018) to develop the consistency between the two mode s, both in terms of validity range and functional of near-source conditions on the VH ground motion, a nea -source correction t Referenced Empirical Approach [Atkinson 2008; 2010]. In this approach, f a g c mputed on the basis of e resi uals between the pre ic ion and additional data, s on the ground moti n. In our case, the co rective term for the reference ITA18 G analysis of residuals with respect o a wo ldwide dataset of near-source recordings, 2018]. Figure 1 shows the conceptual framework at the basis f th methodo gy pro GMM ac ounting for near-source effects. FUNCTIONAL FORM On the basis of the prelimina y da a analysis (not rep rted here), the functional f model is defined as follows: log 10 Y ¿ a + F M ( M W , SoF ) + F D ( M W , R ) + F S ( V S 30 ) wh re Y is the VH ratios f PGA, PGV an 36 ordinates of 5% damped SA in the F M ( M W , SOF ) is the source function, F D ( M W , R ) is the distance function and functional form is consistent with the ne adopted for the hori ontal GMM of [La minor modification r garding the source term owing to the more limited depende magnitu e scaling is controlled by a simple linear function, whereas in [Lanzano function). Sp cifi ally, he source term consists of two terms: is the distance function and ches can be used o devel p vertic l design seismic spectra i the framework of a Assessment (PSHA): (1) perform hazard integrations using Ground Motion Models d for the vertical response spectral ordinates [Chiou and Youngs 2013;Bozorgnia and 2017; Çağnanet al. 2017]; (2) use a GMM for the Vertical-to-Horizontal (vertical-to- ctral acceleration ratios to sc le the horizontal Uniform Hazard Spectrum (UHS). The limitation of posing a p tential inconsistency between the disaggregation scenarios d vertical hazard, leading to serious obstacles in the selection of three-component for dynamic structural analyses. For these rea ons, th most commonly used approach ectrum by making use of empirical models for VH ratios [Gülerce and Abrahamson kkar et al. 2014; Bozorgnia and Campbell 2016; Poggi et al. 2019]. This approach, he issues of performing vector-valued PSHA [Bazzurro and Cornell 2002] including mponents and the full treatment of their correlation. is to develop an empirical GMM for VH ratios of Spectr l Acceleration (SA), Peak and Peak Ground Velocity (PGV) for Italian crustal earthquakes. The r gres i n is aset adopted by Lanzano et al. (2018) to develop the horizontal GMM, thus ensuring models, both in terms of validity range and functional form. To account for the effect the VH ground motion, a near-source correction term is proposed, following the ach [Atkinson 2008; 2010]. In this approach, for a given GMM, a corrective term is residuals between the prediction and additional data, suitable to model specific effects r case, the corrective term for the refe ence ITA18 GMM is calib ated based on the pect to a worldwide dataset of near-source recordings, namely, NESS1.0 [Pacor et al. ceptual framework at the basis of the methodology proposed to develop the Italian VH urce effects. ary data analysis (not reported here), the functional form for the VH ITA18 median ) + F D ( M W , R ) + F S ( V S 30 ) (1) PGA, PGV and 36 ordinates of 5% damped SA in the range 0.01-10 s, a is the offset, e function, F D ( M W , R ) is the distance function and F S ( V S 30 ) is the site term. The with the one adopted for the horizontal GMM of [Lanzano et al. 2019], apart from a the source term owing to the more limited dependence of VH on M w (herein the ed by a simple linear function, whereas in [Lanzano et al. 2019] by a stepwise linear urce term consists of two terms: is the s te t rm. The functi nal form is consi tent wi h the o e adopted for the hori- zontal GMM of [Lanzano et al. 2019], apart from a minor modification regarding the source term owing to the more limited dependence of VH on M w (herein the magnitude scaling is controlled by a simple linear function, whereas in [Lanzano et al. 2019] by a stepwise linear function). Spe- cifically, the source term consists of two terms: F M ( M W , SoF ) = b M W + f j SoF j (2) where coefficient b controls the source scaling and the coefficients f j provide the correction for the Faulting (SoF) of the event. SoF j s are dummy variables, introduced to specify SS ( j =1), reverse TF ( j normal NF ( j =3) focal mechanism types. The regression is performed constraining to zero the coefficient fo faulting ( f 3 = 0 ¿ . The path term is defined as: F D ( M W , R ) = [ c 1 ( M − M ref ) + c 2 ] log 10 R where the first term is the magnitude-dependent geometrical spreading and the second is the distance att M ref is the reference magnitude assumed to be constant for all periods with a value of 6.0, while c 1 and c path coefficients. The distance is computed as R = √ R JB 2 + h 2 , in which R JB is substituted by R rup when model coefficients related to R rup , and h is the pseudo-depth, assumed to be constant for all periods with a 5 km. The values of M ref =6 and h=5 km were calibrated from a first stage non-linear regression. Finally, the site term is defined as a function of the time-averaged shear wave velocity in the top 30 meters ( F S ( V S 30 ) = k log 10 ( V 0 800 ) (2) where coefficient b controls the source scaling and the coefficients f j provide the correction for the Style of Faulting (SoF) of the event. SoF j are dummy variables, introduced to specify SS ( j =1), reverse TF ( j =2), and normal NF ( j =3) focal mechanism types. The regression is performed constraining to zero the coefficient for nor al faulting ( F M ( M W , SoF ) = b M W + f j SoF j (2) wher coefficient b cont ols the source scaling and the Faulting (SoF) of the event. SoF j s are dummy variables, normal NF ( j =3) focal mechanism types. The regression is in f 3 = 0 ¿ . The path term is defined as: F D ( M W , R ) = [ c 1 ( M − M ref ) + c 2 ] log 10 R where the first term is the magnitude-dependent geometric M ref is the reference magnitude assumed to be constant fo path coeff ients. The distance is computed as R = √ R JB 2 + model coefficients related to R rup , and h is the pseudo-dept 5 km. The values of M ref =6 and h=5 km were calibrated fr Finally, the site ter is defined as a function of the time-ave F S ( V S 30 ) = k log 10 ( V 0 800 ) in which V 0 = V S 30 when V S 30 ≤ 1500 m / s and V 0 = 15 . h term is defined as: F M ( M W , SoF ) = b M W + f j SoF j (2) where coefficient b controls the source scaling and the coefficients f j provide the correction for the Faulting (SoF) of the event. SoF j s are dummy variables, introduced to specify SS ( j =1), reverse TF ( j normal NF ( j =3) focal mechanism types. The regress on is performed constraining to zero the coefficient fo faulting ( f 3 = 0 ¿ . The pa h term is defin d as: F D ( M W , R ) [ c 1 ( M − M ref ) + c 2 ] log 10 R where the first term is the magnitude-dependent geometrical spreading and the second is the distance att M ref is the reference magnitude assumed to be constant for all periods with a val e of 6.0, while c 1 and path coefficients. The distance is computed as R = √ R JB 2 + h 2 , in which R JB is substituted by R rup when model coefficients related to R rup , and h is the pseudo-depth, assumed to be constant for all periods with a 5 km. The values of M ref =6 and h=5 km were calibrated from a first stage non-line r regression. Finally, the site term is defined as a function of the time-averag d shear wave velocity in the top 30 meters ( F S ( V S 30 ) = k log 10 ( V 0 800 ) in which V 0 = V S 30 when V S 30 ≤ 1500 m / s and V 0 = 1500 m / s otherwise. Because the record samplin hard-rock sites is poor, the upper bound of the V S 30 scaling, corresponding to 1500 m/s, above w (3) where the first term is the magnitude-dependent geometrical spreading and the second is the distance attenuation, M ref is the reference magnitude assumed to be constant for all periods with a value of 6.0, while c 1 and c 2 are the path coefficients. The distance is computed a M ( M W , SoF ) = b M W + f j SoF j (2) here coefficient b controls the source scaling nd the coefficien s f j provide the correc ion f the Style of aulting (So ) of the event. SoF j s are dummy variables, i troduced to specify SS ( j =1), reverse TF ( j =2), and ormal NF ( j =3) focal mechanism types. The regres ion is performed constraining to zero the coefficient for norm l ulting ( f 3 = 0 ¿ . The path term is defined as: D ( M W , R ) = [ c 1 ( M − M ref ) + c 2 ] log 10 R (3) here the first term is the magnitude-dependent geometrical spreading and the sec d is the distance attenuation, ref is the reference magnitude assumed to be constant for all p riods with a value of 6.0, whil c 1 a c 2 are the ath coefficients. The distance is compute as R = √ R JB 2 + h 2 , in which R JB is substituted by R rup when using the odel coefficients related to R rup , an h is the pseudo-depth, assumed to be constant for all periods with a value of km. The values of M ref =6 and h=5 km were calibrated from a first stage non-linear regression. inally, the site term is defined as a function of the time-averaged she r wave velocity in the top 30 meters ( V S 30 ): S ( V S 30 ) = k log 10 ( V 0 800 ) (4) which V 0 = V S 30 when S 30 ≤ 1500 m / s and V 0 = 1500 m / s otherwise. Because the record sampling of very ard-rock sites is poor, the upper bound of the V S 30 scaling, correspo ding to 1500 m/s, above which the , i whic R JB is substituted by R rup when using the mod l coefficients related to R rup , and h is the pseudo-depth, assume o be stan for all periods with a value of 5 km. The values of M ref =6 and h=5 km were calibrated from a first stage non-linear regression. Finally, the site term is defined as a function of the time-averaged shear wave velocity in the top 30 m ters ( V S30 ): F M ( M , SoF ) = b M + f j SoF j (2) here coefficient controls the source scaling and the coefficients f j provide the correction for the Faulting S F) of the eve t. SoF j s are dummy variables, introduced to specify SS ( j =1), reverse TF ( j n mal NF ( j =3) focal mechanism typ s. The regression is perfor ed constraining to zero the coefficient fo faulting ( f 3 . he pa h ter is defin d as: D ( W , ) [ 1 ( ref ) 2 ] l 10 R here the first ter is the agnitude-dependent geo etrical spreading and the second is the distance att ref is the reference agnitude assu ed to be constant for all periods ith a value of 6.0, hile 1 and path coefficients. The distance is computed as R = √ R JB 2 + h 2 , in which R JB is substituted by R rup when model coefficients related to R rup , and h is the pseudo-depth, assu ed to be constant for all periods ith a 5 km. The values of M ref =6 and h=5 km were calibrated from a first stage non-linear regression. Finally, the site term is defin d as a function of the ti -averaged shear ave velocity in the top 30 eters ( F S ( V S 30 ) = k log 10 ( 0 ) in hich 0 V S 30 hen S 30 / s and 0 / s other ise. ecause the record sa plin hard-rock sites is poor, the upper bound of the S 30 scaling, corresponding to 1500 /s, above w (4) in which V 0 =V S30 when V S30 ≤1500 m/s and V 0 ≤1500 m/s otherwise. Because the record sampling of Fig. - Flowchart of the methodology adopted for the empiric l estimation of VH gr und motion odel.