ALBERT

Description: A method for deriving kappa ( ) scaling factors that can be applied to ground-motion prediction equations (GMPEs) to account for site-specific estimates is described. This method relies on inverse random vibration theory as implemented in the computer program Strata ( Kottke and Rathje, 2008a , b ) to derive a Fourier amplitude spectrum (FAS) that is consistent with the response spectrum from the GMPE. The GMPE host values are estimated by fitting the high-frequency FAS with the Anderson and Hough (1984) scaling function. The derived FAS are then scaled from their host value to a target . Random vibration theory ( Cartwright and Longuet-Higgins, 1956 ) is then used to convert the scaled FAS to response spectra, and scaling factors are computed by the ratio of the scaled response spectra to the GMPE response spectra. In contrast to the commonly used hybrid empirical method ( Campbell, 2003 ), the proposed approach does not require a full seismological model for the stochastic parameters (stress drop, whole-path attenuation, etc.) of the host and target regions and does not assume that response spectral shape of GMPE is consistent with that of the representative point-source stochastic model for the host region, which can lead to inappropriate response spectral scaling factors. Finally, the effects of the well-known trade-off between and stress drop scaling are reduced. The method, when applied within the frequency limitations discussed in this paper, can be used to incorporate scaling into GMPEs.

Description: The reference rock site condition has two important applications for ground-motion prediction in the stable continental region of central and eastern North America (CENA). (1) It represents the site condition for which ground motions are computed using semiempirical ground-motion prediction equations. In addition, (2) it represents the site condition to which site amplification factors, which are used to modify ground-motion intensity measures for softer site condition, are referenced (i.e., site amplification is unity for reference rock). We define reference rock by its shear ( S )- and compression ( P )-wave velocities, as well as a site attenuation parameter ( 0 ), which is used in stochastic ground-motion simulation methods. Prior definitions of reference rock conditions in CENA were based mostly on indirect large-scale crustal velocity inversions and judgment. We compile and interpret a unique database of direct velocity measurements to develop criteria for assessing the presence of reference rock site condition based on measured seismic velocities and their gradient with respect to depth. We apply the criteria to available profiles and perform rigorous statistical analysis from which we recommend S - and P -wave velocities of 3000 and 5500 m/s, respectively, for the reference rock condition. We recommend that, for practical applications, use ranges of reference S - and P -wave velocities of 2700–3300 m/s and 5000–6100 m/s, respectively. The ranges are based on a ±5% change in amplification using quarter-wavelength theory. We do not find evidence for regional dependence of the reference velocities, which are derived principally from three general geographic regions: (1) Atlantic coast, (2) continental interior, and (3) Appalachian Mountains. Our data do not provide reference velocities for the Gulf Coast region. The recommended velocity-compatible reference rock site kappa is 0.006 s.

Description: The random-vibration theory (RVT) approach to equivalent-linear site-response analysis is often used to simulate site amplification, particularly when large numbers of simulations are required for incorporation into probabilistic seismic-hazard analysis. The fact that RVT site-response analysis does not require the specification of input-time series makes it an attractive alternative to other site-response methods. However, some studies have indicated that the site amplification predicted by RVT site-response analysis systematically differs from that predicted by time-series approaches. This study confirms that RVT site-response analysis predicts site amplification at the natural site frequencies as much as 20%–50% larger than time-series analysis, with the largest overprediction occurring for sites with smaller natural frequencies and sites underlain by hard rock. The overprediction is caused by an increase in duration generated by the site response, which is not taken into account in the RVT calculation. Correcting for this change in duration brings the RVT results within 20% of the time-series results. A similar duration effect is observed for the RVT shear-strain calculation used to estimate the equivalent-linear strain-compatible soil properties. An alternative to applying a duration correction to improve the agreement between RVT and time-series analysis is the modeling of shear-wave velocity variability. It is shown that introducing shear-wave velocity variability through Monte Carlo simulation brings the RVT results consistently within ±20% of the time-series results.

Description: Time-averaged shear-wave velocity in the upper 30 m of a site ( V S 30 ) is the most common parameter used to characterize seismic site response in ground-motion models. However, in central and eastern North America (CENA), only 6% of the seismic recording stations that contributed data to the Next Generation Attenuation-East (NGA-East) project have measurement-based V S 30 values. We describe a shear-wave velocity ( V S ) measurement database for CENA that was compiled to support the development of proxy-based methods for V S 30 estimation. Using this database, we develop a hybrid geology-slope approach for V S 30 estimation that utilizes newly considered large-scale geologic maps, the extent of Wisconsin glaciation, sedimentary basin structure, and 30 arcsec topographic gradient. Nonglaciated sites have relatively modest natural log dispersion of V S 30 ( ln V =0.36) relative to glaciated regions ( ln V =0.66), indicating better proxy-based predictability of V S 30 for the former. Based on these findings, we provide estimates of natural log mean and standard deviation of V S 30 for NGA-East recording stations in a station database, available in the electronic supplement to this article. Electronic Supplement: Updated Next Generation Attenuation-East (NGA-East) station database and central and eastern North America (CENA) V S measurement database.

Description: The reference rock site condition has two important applications for ground-motion prediction in the stable continental region of central and eastern North America (CENA). (1) It represents the site condition for which ground motions are computed using semiempirical ground-motion prediction equations. In addition, (2) it represents the site condition to which site amplification factors, which are used to modify ground-motion intensity measures for softer site condition, are referenced (i.e., site amplification is unity for reference rock). We define reference rock by its shear (S)- and compression (P)-wave velocities, as well as a site attenuation parameter (kappa (sub 0) ), which is used in stochastic ground-motion simulation methods. Prior definitions of reference rock conditions in CENA were based mostly on indirect large-scale crustal velocity inversions and judgment. We compile and interpret a unique database of direct velocity measurements to develop criteria for assessing the presence of reference rock site condition based on measured seismic velocities and their gradient with respect to depth. We apply the criteria to available profiles and perform rigorous statistical analysis from which we recommend S- and P-wave velocities of 3000 and 5500 m/s, respectively, for the reference rock condition. We recommend that, for practical applications, use ranges of reference S- and P-wave velocities of 2700-3300 m/s and 5000-6100 m/s, respectively. The ranges are based on a + or -5% change in amplification using quarter-wavelength theory. We do not find evidence for regional dependence of the reference velocities, which are derived principally from three general geographic regions: (1) Atlantic coast, (2) continental interior, and (3) Appalachian Mountains. Our data do not provide reference velocities for the Gulf Coast region. The recommended velocity-compatible reference rock site kappa is 0.006 s.

Description: The random-vibration theory (RVT) approach to equivalent-linear site-response analysis is often used to simulate site amplification, particularly when large numbers of simulations are required for incorporation into probabilistic seismic-hazard analysis. The fact that RVT site-response analysis does not require the specification of input-time series makes it an attractive alternative to other site-response methods. However, some studies have indicated that the site amplification predicted by RVT site-response analysis systematically differs from that predicted by time-series approaches. This study confirms that RVT site-response analysis predicts site amplification at the natural site frequencies as much as 20%-50% larger than time-series analysis, with the largest overprediction occurring for sites with smaller natural frequencies and sites underlain by hard rock. The overprediction is caused by an increase in duration generated by the site response, which is not taken into account in the RVT calculation. Correcting for this change in duration brings the RVT results within 20% of the time-series results. A similar duration effect is observed for the RVT shear-strain calculation used to estimate the equivalent-linear strain-compatible soil properties. An alternative to applying a duration correction to improve the agreement between RVT and time-series analysis is the modeling of shear-wave velocity variability. It is shown that introducing shear-wave velocity variability through Monte Carlo simulation brings the RVT results consistently within + or -20% of the time-series results.

Description: A method for deriving kappa (kappa ) scaling factors that can be applied to ground-motion prediction equations (GMPEs) to account for site-specific kappa estimates is described. This method relies on inverse random vibration theory as implemented in the computer program Strata (Kottke and Rathje, 2008a,b) to derive a Fourier amplitude spectrum (FAS) that is consistent with the response spectrum from the GMPE. The GMPE host kappa values are estimated by fitting the high-frequency FAS with the Anderson and Hough (1984) kappa scaling function. The derived FAS are then scaled from their host kappa value to a target kappa . Random vibration theory (Cartwright and Longuet-Higgins, 1956) is then used to convert the kappa scaled FAS to response spectra, and kappa scaling factors are computed by the ratio of the kappa scaled response spectra to the GMPE response spectra. In contrast to the commonly used hybrid empirical method (Campbell, 2003), the proposed approach does not require a full seismological model for the stochastic parameters (stress drop, whole-path attenuation, etc.) of the host and target regions and does not assume that response spectral shape of GMPE is consistent with that of the representative point-source stochastic model for the host region, which can lead to inappropriate response spectral scaling factors. Finally, the effects of the well-known trade-off between kappa and stress drop scaling are reduced. The method, when applied within the frequency limitations discussed in this paper, can be used to incorporate kappa scaling into GMPEs.