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Figure 15. Magnitude-independent ¢,, values obtained using residuals from the PRP database for data from three regions and the regions combined. Also shown is the homoskedastic ¢,, model. The color version of this figure is available only in the electronic edition.

Figure 15 Magnitude-independent ¢,, values obtained using residuals from the PRP database for data from three regions and the regions combined. Also shown is the homoskedastic ¢,, model. The color version of this figure is available only in the electronic edition.

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Terminology Used for Residual Components and Their Standard Deviations *std(-) denotes the standard deviation operator. Table | in which 6S2S, represents the systematic deviation of the observed ground motion at site s (i.e., the site term) from t he median event-corrected ground motion predicted by the GMPE, and 6WS,, is the site- and event-corrected residual. The standard deviations of the 6S2S, and 6WS,, terms are enoted by ¢s25 and @,,, respectively. Table 1 summarizes he components of the total residual, their respective standard eviations, and the terminology used for each standard eviation component. GMPEs represent the variability over space (i.e ., Across many different sites and sometimes many regions), yet the re- sulting models are applied to a single site. However, multiple recordings from similar events recorded at individual sites generally display lower variability than indicated by the sigma values of GMPEs (e.g., Atkinson, 2006; Rodriguez-Marek et al., 2011). The reason for these differences is t are site-to-site variations among sites characterize same site parameterization (e.g., Vs39 value), and t hat there d by the hese var- iations are included within the sigma values of GMPEs, but these variations are not present when considering a si ngle site.
Terminology Used for Residual Components and Their Standard Deviations *std(-) denotes the standard deviation operator. Table | in which 6S2S, represents the systematic deviation of the observed ground motion at site s (i.e., the site term) from t he median event-corrected ground motion predicted by the GMPE, and 6WS,, is the site- and event-corrected residual. The standard deviations of the 6S2S, and 6WS,, terms are enoted by ¢s25 and @,,, respectively. Table 1 summarizes he components of the total residual, their respective standard eviations, and the terminology used for each standard eviation component. GMPEs represent the variability over space (i.e ., Across many different sites and sometimes many regions), yet the re- sulting models are applied to a single site. However, multiple recordings from similar events recorded at individual sites generally display lower variability than indicated by the sigma values of GMPEs (e.g., Atkinson, 2006; Rodriguez-Marek et al., 2011). The reason for these differences is t are site-to-site variations among sites characterize same site parameterization (e.g., Vs39 value), and t hat there d by the hese var- iations are included within the sigma values of GMPEs, but these variations are not present when considering a si ngle site.
Figure 1. Schematic diagram of the modifications to the host ground-motion prediction equation (GMPE) to obtain site-specific hazard curves.
Figure 1. Schematic diagram of the modifications to the host ground-motion prediction equation (GMPE) to obtain site-specific hazard curves.
Figure 2. (a) Fourier amplitude spectra (FAS) derived from GMPEs and used to compute xo, (b) original and Vs—kappa adjusted FAS for Ky = 0.0011 s, and (c) V;—kappa adjustment factors applied to median response spectral accelerations predicted by the three selected GMPEs using three target values for kp. ASO8 is Abrahamson and Silva (2008), CY08 is Chiou and Youngs (2008), and AC10 is Akkar and Cagnan (2010).
Figure 2. (a) Fourier amplitude spectra (FAS) derived from GMPEs and used to compute xo, (b) original and Vs—kappa adjusted FAS for Ky = 0.0011 s, and (c) V;—kappa adjustment factors applied to median response spectral accelerations predicted by the three selected GMPEs using three target values for kp. ASO8 is Abrahamson and Silva (2008), CY08 is Chiou and Youngs (2008), and AC10 is Akkar and Cagnan (2010).
Figure 4. —Thyspunt site with geologic formations and site char- acterization locations. Numbers and letters indicate boreholes in which shear-wave velocities were measured (Bommer et al., 2014). The color version of this figure is available only in the electronic edition. Figure 3. Vs—kappa adjustments from California to South Africa (with a target xo of 0.0028 s) for four magnitudes and distances from | to 50 km; the heavy black dashed line represents the V;—kappa adjustments corresponding to M, 5.7 and Ryg 10.1 km.
Figure 4. —Thyspunt site with geologic formations and site char- acterization locations. Numbers and letters indicate boreholes in which shear-wave velocities were measured (Bommer et al., 2014). The color version of this figure is available only in the electronic edition. Figure 3. Vs—kappa adjustments from California to South Africa (with a target xo of 0.0028 s) for four magnitudes and distances from | to 50 km; the heavy black dashed line represents the V;—kappa adjustments corresponding to M, 5.7 and Ryg 10.1 km.
sure 5. Site-specific shear-wave velocity model for the Thyspunt site: (a) median shear-wave velocity profile and (b) oj, vs Profile.
sure 5. Site-specific shear-wave velocity model for the Thyspunt site: (a) median shear-wave velocity profile and (b) oj, vs Profile.
Figure 6b plots computed p values versus depth for dif- ferent values of th using bin widths of Ath = 2 m and Ad = 5 m. The influence of th is not strong, which suggests a correlation model that is independent of interlayer separa- tion. Figure 6c shows the computed p values versus depth in which p is computed using all pairs of adjacent layers using Ad = Im. There is no systematic variation of p with depth, and thus an average p value of 0.5 was used. are plotted versus depth in Figure 7. These 10 realizations show that the layer thicknesses vary from profile to profile and the thickness generally increases with depth. The simu- lated profiles are located both above and below the median Vs model, and a single profile may be above the median at some depths and below the median at others. One-hundred simulated velocity profiles were developed for the site- response analyses. Using 100 simulations, both the median velocity profile and the variation of oj,y, with depth were captured by the Monte Carlo simulations
Figure 6b plots computed p values versus depth for dif- ferent values of th using bin widths of Ath = 2 m and Ad = 5 m. The influence of th is not strong, which suggests a correlation model that is independent of interlayer separa- tion. Figure 6c shows the computed p values versus depth in which p is computed using all pairs of adjacent layers using Ad = Im. There is no systematic variation of p with depth, and thus an average p value of 0.5 was used. are plotted versus depth in Figure 7. These 10 realizations show that the layer thicknesses vary from profile to profile and the thickness generally increases with depth. The simu- lated profiles are located both above and below the median Vs model, and a single profile may be above the median at some depths and below the median at others. One-hundred simulated velocity profiles were developed for the site- response analyses. Using 100 simulations, both the median velocity profile and the variation of oj,y, with depth were captured by the Monte Carlo simulations
Figure 9. Scenario spectra used as input into the site-response analyses. (AFE, annual frequency of exceedance; HF, high fre- quency; LF, low frequency.)
Figure 9. Scenario spectra used as input into the site-response analyses. (AFE, annual frequency of exceedance; HF, high fre- quency; LF, low frequency.)
Figure 8. Modulus reduction and damping curves for rock from Schnabel (1973) and Choi (2008).
Figure 8. Modulus reduction and damping curves for rock from Schnabel (1973) and Choi (2008).
Figure 10. (a) Computed amplification factors (AFs) for 100 Monte Carlo simulations for a single-input motion spectrum, and (b) stan- dard deviation of the natural logarithm of AF (6;, 4p). The input motion for these analyses is the 10-> LF spectrum (Fig. 8).
Figure 10. (a) Computed amplification factors (AFs) for 100 Monte Carlo simulations for a single-input motion spectrum, and (b) stan- dard deviation of the natural logarithm of AF (6;, 4p). The input motion for these analyses is the 10-> LF spectrum (Fig. 8).
Figure 11. Amplification versus Sa, for T = 0.01, 0.1, 0.2, and 0.4 s.
Figure 11. Amplification versus Sa, for T = 0.01, 0.1, 0.2, and 0.4 s.
Figure 12. Period dependence of oj, ap, Oy, aNd jot for the site-response model. oj, 4p represents the variability in AF from the 1D site-response modeling, o,, represents the epistemic uncer- tainty in mean estimates of AF from 1D site-response modeling, and Ctotal 18 the square root of the sum of the squares of oj, ap and o,,.
Figure 12. Period dependence of oj, ap, Oy, aNd jot for the site-response model. oj, 4p represents the variability in AF from the 1D site-response modeling, o,, represents the epistemic uncer- tainty in mean estimates of AF from 1D site-response modeling, and Ctotal 18 the square root of the sum of the squares of oj, ap and o,,.
Figure 13. Schematic representation of the sigma model. The top two boxes (in bold) have alternative homoskedastic and heter- oskedastic models.
Figure 13. Schematic representation of the sigma model. The top two boxes (in bold) have alternative homoskedastic and heter- oskedastic models.
Figure 14. _ ¢,, values obtained by fitting the magnitude-depen- dent model to the PEGASOS Refinement Project (PRP) residuals for different magnitude bins (R < 200 km). Results are shown sepa- rately for data from three regions, as well as the regions combined. The heteroskedastic @,, model is shown for the magnitude corre- sponding to the center of the magnitude bin. The color version of this figure is available only in the electronic edition.
Figure 14. _ ¢,, values obtained by fitting the magnitude-depen- dent model to the PEGASOS Refinement Project (PRP) residuals for different magnitude bins (R < 200 km). Results are shown sepa- rately for data from three regions, as well as the regions combined. The heteroskedastic @,, model is shown for the magnitude corre- sponding to the center of the magnitude bin. The color version of this figure is available only in the electronic edition.
Figure 16. NGAz models (AS08, Abrahamson and Silva, 2008; CB08, Campbell and Bozorgnia, 2008; BA08, Boore and Atkinson, 2008; and CY08, Chiou and Youngs, 2008). CY08 was selected as the heteroskedastic t model, and CY08(M6) was selected as the homoskedastic t model.
Figure 16. NGAz models (AS08, Abrahamson and Silva, 2008; CB08, Campbell and Bozorgnia, 2008; BA08, Boore and Atkinson, 2008; and CY08, Chiou and Youngs, 2008). CY08 was selected as the heteroskedastic t model, and CY08(M6) was selected as the homoskedastic t model.
Figure 18. — Site-to-site variability at borehole depth as a func- tion of the shear-wave velocity at the borehole level from the KiK- net data for selected oscillator periods. The standard deviations are computed by postulating a linear standard deviation model and per- forming a maximum-likelihood regression.
Figure 18. — Site-to-site variability at borehole depth as a func- tion of the shear-wave velocity at the borehole level from the KiK- net data for selected oscillator periods. The standard deviations are computed by postulating a linear standard deviation model and per- forming a maximum-likelihood regression.
Figure 19. Schematic representation of the Thyspunt probabi- listic seismic-hazard analysis sigma model.
Figure 19. Schematic representation of the Thyspunt probabi- listic seismic-hazard analysis sigma model.
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