GNGTS 2021 - Atti del 39° Convegno Nazionale

GNGTS 2021 S essione 2.2 336 the observations available for two magnitude levels ( M w =4.0 and M w =6.3), for V S30 =450 ± 100 m/s and for different SoF. It is noted that, at both short and long periods, the observations (dots) are mostly included in the range of the empirical predictions (continuous line: median, dashed line: ±σ V ). However, at T=0.1s, the empirical model tends to underestimate the data at very short di- stances (less than R JB <10 km), especially for larger magnitude events. Such a bias is related to the low proportion of near-fault records in the ITA18, which makes the prediction poorly constrained in the range of short distances. To improve the predictios in epicentral region, we decided to introduce in the GMM a correc- tion factor capable of describing more accurately the amplification of VH spectral ratios which typically occurs in near-source conditions for large magnitude events, as described in the fol- lowing section. Correction factor for near-source effects In order to determine the proper functional form for the modeling of the correction factor, the residuals of ITA18 with respect to NESS1.0 data have been computed as follows: In Figure 2, the predictions of vertical SA(0.1s), left, and SA(1.0s), right, from the ITA18 model (i.e. V GMMs from this study and Lanzano et al., 2019, respectevely) are compared with the observations availabl magnitude levels ( M w =4.0 and M w =6.3), for V S 30 =450 ± 100 m/s and for different SoF. It is noted that short and long periods, the observations (dots) are mostly included in the range of the empirical pr (continuous line: median, dashed line:  V ). However, at T=0.1s, the empirical model tends to underesti data at very short distances (less than R JB <10 km), especially for larger magnitude events. Such a bias is r the low proportion of near-fault records in the ITA18, which makes the prediction poorly constrained in the short distances. To improve the predictios in epicentral region, we decided to introduce in the GMM a correction factor c describing more accurately the amplification of VH spectral ratios which typically occurs in near-source c for large magnitude events, as described in the following section. CORRECTION FACTOR FOR NEAR-SOURCE EFFECTS In order to determine the proper functional form for the modeling of the correction factor, the residuals with respect NESS1.0 data have been computed as follows: δ C =log10(VH OBS,NESS )-log10(VH ITA18 ) (5) where VH OBS,NESS represents the observed VH from NESS1.0 dataset and VH ITA18 represents the predicted ratios from the ITA18 model as in Eq. (1). As the residuals analysis shows a variation with respect to the different explanatory variables, the functional form for the correction term is defined as follows: where VH OBS,NESS represents the observed VH from NESS1.0 dataset and VH ITA18 represents the predicted ra the ITA18 model as in Eq. (1). As the residuals analysis shows a variation with respect to the different explanatory variables, the functi for the correction term is defined as follows: δ R ¿ a R + F MR ( M W , SoF ) + F DR ( R ) + F SR ( V S 30 ) where δ R is the residual as in Eq. (5), a R is the offset, F M R ( M W , SoF ) is the source function, F D R ( distance function, and F S ( V S 30 ) is the site term. F MR ( M W , SOF ) = b R M W + f jR SoF j F DR ( R ) = c R log 10 R F S ( V S 30 ) = k R log 10 ( V 0 800 ) The coefficients, b R , f jR , c R , and k R , and variables R , Mw and V 0 are defined as in the VH ITA1 However, the pseudo depth used herein is h R =1 km, obtained from some trial regressions. An improved VH model, referred to as VH ITA18-NESS hereafter, is then proposed as follows: log 10 VH ITA 18 − NESS = log 10 ( VH ITA 18 ) + ¿ max ⁡ ( δ ¿¿ R , 0 ) ¿ ¿ (10) RESULTS Figure 3 shows the comparison of VH spectra from ITA18 and ITA18-NESS models with other GMMs, BO2011, GA2011 and BC2016, for M w 6.5 scenarios (TF) at both short (left: R JB =5 km) and large (right km) distances and for different soil conditions ( V S 30 =800 m/s , V S 30 =400 m/s and V S 30 =200 m/s). To est unknown variables, the procedure of [Kaklamanos et al. 2011] is applied: assuming a dip angle  =4 hanging-wall site, for M w 6.5, R JB =5 (50) km corresponds to R rup of about 10 (52) km. For BC2016, other are considered as the default values suggested by the model itself. (6) where δ R is the residual as in Eq. (5), a R is the offset, F MR ( M W , SoF ) is the source function, F DR ( R ) is the distance function, and F S ( V S30 ) is the site term. here VH OBS,NESS represents the observed VH from NESS1.0 dataset and VH ITA18 represents the predicted ra the ITA18 model as in Eq. (1). As the residuals analysis shows a variation with respect to the different explanatory variables, the functio for the correction term is defined as follows: δ R ¿ a R + F MR ( M W , SoF ) + F DR ( R ) + F SR ( V S 30 ) where δ R is the residual as in Eq. (5), a R is the offset, F M R ( M W , SoF ) is the source function, F D R ( distance function, and F S ( V S 30 ) is the site term. F MR ( M W , SOF ) = b R M W + f jR SoF j F DR ( R ) = c R log 10 R F S ( V S 30 ) = k R log 10 ( V 0 800 ) The coefficients, b R , f jR , c R , and k R , and variables R , Mw and V 0 are defined as in the VH ITA1 However, the pseudo depth used herein is h R =1 km, obtained from some trial regressions. An improved VH model, referred to as VH ITA18-NESS hereafter, is then proposed as follows: log 10 VH ITA 18 − NESS = log 10 ( VH ITA 18 ) + ¿ max ⁡ ( δ ¿¿ R , 0 ) ¿ ¿ (10) RESULTS Figure 3 shows the comparison of VH spectra from ITA18 and ITA18-NESS models with other GMMs, BO2011, GA2011 and BC2016, for M w 6.5 scenarios (TF) at both short (left: R JB =5 km) and large (right: km) distances and for different soil conditions ( V S 30 =800 m/s , V S 30 =400 m/s and V S 30 =200 m/s). To esti unknown variables, the procedure of [Kaklamanos et al. 2011] is applied: assuming a dip angle  =4 hanging-wall site, for M w 6.5, R JB =5 (50) km corresponds to R rup of about 10 (52) km. For BC2016, other are considered as the default values suggested by the model itself. At large distance ( R JB =50 km) and for rock/stiff site conditions (Figure 3-b, d), the models show co results, while some differences become appreciable for soft soil site (Figure 3-f), for which BC2016 an R (7) , ITA18 va ( ) + S V is h u S V W + j g 1 However, the pseudo depth used herein is h = m so ) ¿ ¿ (10) wi S 30 dure of [Kaklamanos et al. are considered as the default values suggested by the model itself. (8) whe e VH OBS,NESS represents the observed VH f om NESS1.0 ataset and VH ITA18 represents the pr d cted ra the ITA18 model as in Eq. (1). As the residuals analysis shows a variation with respect to the different explanatory variables, the functio for the correction term is defined as follows: δ R ¿ a R + F MR ( M W , SoF ) + F DR ( R ) + F SR ( V S 30 ) where δ R is the residual as in Eq. (5), a R is the offset, F M R ( M W , SoF ) is the source function, F D R ( distance function, and F S ( V S 30 ) is the site term. F MR ( M W , SOF ) = b R M W + f jR SoF j F DR ( R ) = c R log 10 R F S ( V S 30 ) = k R log 10 ( V 0 800 ) The coefficients, b R , f jR , c R , and k R , and variables R , Mw and V 0 are defined as in the VH ITA1 However, the pseudo depth used herein is h R =1 km, obtained from some trial regressions. An improved VH model, referred to as VH ITA18-NESS hereafter, is then proposed as follows: log 10 VH ITA 18 − NESS = log 10 ( VH ITA 18 ) + ¿ max ⁡ ( δ ¿¿ R , 0 ) ¿ ¿ (10) RESULTS Figure 3 shows the comparison of VH spectra from ITA18 and ITA18-NESS models with other GMMs, BO2011, GA2011 and BC2016, for M w 6.5 scenarios (TF) at both short (left: R JB =5 km) and large (right: km) distances and for different soil conditions ( V S 30 =800 m/s , V S 30 =400 m/s and V S 30 =200 m/s). To esti unknown variables, the procedure of [Kaklamanos et al. 2011] is applied: assuming a dip angle  =4 hanging-wall site, for M w 6.5, R JB =5 (50) km corresponds to R rup of about 10 (52) km. For BC2016, other are considered as the default values suggested by the model itself. At large distanc ( R JB =50 km) and for rock/stiff site conditions (Figure 3-b, d), the models show co results, whil some differences b come appreciabl for soft soil site (Figure 3-f), for which BC2016 an NESS show a limited amplification with respect to other models. At short distance ( R JB =5 km) and soft (9) The coefficients, b R , f jR , c R , and k R , and variables R , Mw and V 0 are defined as in the VH ITA18 model. However, the pseudo depth used herein is h R =1 km, obtained from some trial regres- si ns. An improved VH model, referred to as VH ITA18-NESS hereafter, is then proposed as follows: where VH OBS,NESS represents the observed VH from NESS1.0 dataset and VH ITA18 represents the predicted ra the ITA18 model as in Eq. (1). As the esiduals analysis shows a variation with respect to the different explana ory variables, the functio for th correction term is efined as follows: δ R ¿ a R + F MR ( M W , SoF ) + F DR ( R ) + F SR ( V S 30 ) where δ R is the residual as in Eq. (5), a R is the offset, F M R ( M W , SoF ) is the source function, F D R ( distance function, and F S ( V S 30 ) is the site term. F MR ( M W , SOF ) = b R M W + f jR SoF j F DR ( R ) = c R log 10 R S ( V S 30 ) = k R log 10 ( V 0 800 ) The coefficients, b R , f jR , c R , and k R , and variables R , Mw and V 0 are defined as in the VH ITA1 However, the pseudo depth used herein is h R =1 km, obtained from some trial regressions. An improved VH m del, referred to as VH ITA18-NESS h reafter, is then proposed as follows: log 10 VH ITA 18 − NESS = log 10 ( VH ITA 18 ) + ¿ max ⁡ ( δ ¿¿ R , 0 ) ¿ ¿ (10) RESULTS Figure 3 shows the comparison of VH spectra from ITA18 and ITA18-NESS models with other GMMs, BO2011, GA2011 and BC2016, for M w 6.5 scenarios (TF) at both short (left: R JB =5 km) and large (right: km) distances and for diffe ent s il conditions ( V S 30 =800 m/s , V S 30 =400 m/s and V S 30 =200 m/s). To esti unknown variables, the procedure of [Kaklamanos et al. 2011] i appli d assuming a dip ngle  =4 hanging-wall site, for M w 6.5, R JB =5 (50) km corresponds to R rup of about 10 (52) km. For BC2016, other are considered as the default values suggested by the model itself. At large distance ( R JB =50 km) and for rock/stiff site conditions (Figure 3-b, d), the models show co results, while some differences become appreciable for soft soil site (Figure 3-f), for which BC2016 an NESS show a limited amplification with respect to other models. At short distance ( R JB =5 km) and soft spread of the GMM predictions is significant due to the different modeling assumptions for linear (our mo BO2011) and non-linear (GA2011 and BC2016) models. In general, at short distances, ITA18-NESS predic (10) Results Figure 3 shows the comparison of VH spectra from ITA18 and ITA18-NESS models with other GMMs, namely, BO2011, GA2011 and BC2016, for M w 6.5 scenarios (TF) at both short (left: R JB =5 km) and large (right: R JB =50 km) distances and for different soil conditions ( V S 30 =800 m/s, V S 30 =400 m/s and V S 30 =200 m/s). To estimate the u kn wn variables, t e procedure of [Kaklamanos et al. 2011] is applied: assuming a dip angle δ=40° and a hanging-wall site, for M w 6.5, R JB =5 (50) km corresponds to R rup of about 10 (52) km. For BC2016, other variables are considered as the default valu s suggested by the model itself. At large distance ( R JB =50 km) and for rock/stiff site conditions (Figure 3-b, d), the models show comparable results, while some differences become appreciable for soft soil site (Figure 3-f), for which BC2016 and ITA18-NESS show a limited amplification with respect to other mo- dels. At short di tance ( R JB =5 km) and soft sites, spread of the GMM predictions is significant due to the different modeling assumptions for linear (our models and BO2011) and non-linear