In the present study, we proposed a complete framework for developing a response spectral ground-motion prediction equation (GMPE), which is derived as a combination of two empirical models for Fourier amplitude spectrum (FAS) and duration (Drvto) of ground-motion. Predictions from the two models are combined within the random vibration theory (RVT) framework to obtain the response spectral ordinates. As described in the main article, Drvto is a unique measure for ground-motion duration that is estimated (from an acceleration trace) as an optimizing parameter such that the RVT-based response spectrum matches with the observed response spectrum. In order to perform a consistency check of the presented method, comparisons with the other classically developed GMPE in terms of predicted response spectra are performed. The dataset used in this study is a subset of the larger RESORCE database (Akkar, Sandıkkaya, Şenyurt, et al., 2014) compiled across Europe, the Mediterranean, and the Middle East. For performing comparisons, the GMPEs derived on the same database (Akkar, Sandıkkaya, and Bommer, 2014; Bindi et al., 2014; Bora et al., 2014) are selected. The metadata information of the dataset used in the present study is given in Table S1. In addition to that, the GMPE of Boore et al. (2014), developed in the context of the Next Generation of Attenuation models (NGA-West 2), is also included for comparison. Comparisons among the five GMPEs are shown for the same scenarios of magnitude (Mw), Joyner–Boore distance (RJB), and time-averaged shear-wave velocity in the upper 30 m of the soil column (VS30) that were used in Douglas et al. (2014).
Figures S1 and S2 depict the comparison of scaling with respect to RJB; Figure S3 depicts the comparison of scaling with respect to Mw; Figure S4 depicts the comparison of scaling with respect to VS30. Figure S5 depicts the variation of the ratio of response spectral ordinates for VS30 values of 270 and 490 m/s compared to VS30 760 m/s at RJB of 10 and 100. Figures S6 and S7 depict the comparison of median predicted response spectra among the five GMPEs. Figure S8 depicts the scaling of predicted response spectra with two additional predictor variables, stress parameter (Δσ) and path-independent high-frequency attenuation parameter (κ0) used in the empirical models derived in this study. Additionally, Tables S2, S6, and S10 contain predicted mean FAS from the present approach for earthquake magnitudes Mw 5, 6, and 7, respectively, at distances RJB = 10, 30, 50, 70, 100, 150, and 200 km, corresponding to the site with VS30 = 760 m/s and corresponding κ0 = 0.024 s. Similarly, for the same scenarios, Tables S3, S7, and S11 contain predicted mean duration (Drvto); Tables S4, S8, and S12 contain predictions for peak factor (PF); and Tables S5, S9, and S13 contain predicted response spectra that are obtained as a combination of mean FAS and Drvto predictions using RVT. All of the predictions in these tables are obtained for the median Δσ value of 8.4 MPa.
Figure S1. Comparison of distance scaling for strike-slip earthquakes corresponding to VS30 = 760 m/s for (a) PGA and (b) SA at oscillator frequency fosc = 1 Hz. Predictions from our model are obtained for Δσ = 8.4 MPa and a κ0 value of 0.024 (s) corresponding to VS30 = 760 m/s, obtained using equation (7) in the main article.
Figure S2. Comparison of distance scaling for strike-slip earthquakes corresponding to VS30 = 270 m/s for (a) PGA and (b) SA at fosc = 1 Hz. Predictions from our model are obtained for Δσ = 8.4 MPa and a κ0 value of 0.031 (s) corresponding to VS30 = 270 m/s, obtained using equation (7) in the manuscript.
Figure S3. Comparison of magnitude scaling of median-predicted PGA (top left) and response spectral ordinates for strike-slip earthquakes at fosc = 5 Hz (top right) and 1 Hz (bottom left) and 0.33 Hz (bottom right), corresponding to VS30 = 760 m/s. Predictions from our model are obtained for Δσ = 8.4 MPa and a κ0 value of 0.024 (s) corresponding to VS30 = 760 m/s, obtained using equation (7) in the manuscript. The ordering of the panels is kept in increasing order of response period in order to maintain consistency with Douglas et al. (2014).
Figure S4. Comparison of Vs30 scaling of the median ground motion for a strike-slip earthquake with Mw 7 for PGA (top left) and response spectral ordinates at fosc = 5 Hz (top right) and 1 Hz (bottom left) and 0.33 Hz (bottom right) at (a) RJB = 100 km and (b) RJB = 10 km. Predictions from our model are obtained for Δσ = 8.4 MPa and for κ0 values from equation (7), corresponding to the VS30 values shown in the comparison.
Figure S5. Comparison of ratios between SA for VS30 = 270 m/s (left) and SA for VS30 = 490 m/s (right) to SA for VS30 = 760 m/s for strike-slip earthquake Mw 7 at RJB = 100 km (top) and RJB = 10 km (bottom). Predictions from our model are obtained for Δσ = 8.4 MPa and for κ0 = 0.031, 0.027, and 0.024 (s), corresponding to VS30 = 270, 490, and 760 m/s, respectively, from equation (7) in the manuscript.
Figure S6. Comparison of median-predicted response spectra for strike-slip earthquakes corresponding to VS30 = 760 m/s at RJB = 10 km. Predictions from our model are obtained for Δσ = 8.4 MPa and a κ0 value of 0.024 (s), corresponding to VS30 = 760 m/s obtained using equation (7) in the manuscript.
Figure S7. Comparison of median-predicted response spectra for a strike-slip earthquake with Mw 7 corresponding to VS30 = 270 m/s (left) and VS30 = 760 m/s (right) at RJB = 10 km. Predictions from our model are obtained for Δσ = 8.4 MPa and for κ0 = 0.031 and 0.024 (s), corresponding to VS30 = 270 and 760 m/s, respectively, from equation (7) in the manuscript.
Figure S8. Scaling of response spectra with respect to the stress parameter (left) for Mw 5, 6, and 7, corresponding to VS30 = 760 m/s and κ0 = 0.024 (s). The right panel depicts the scaling of response spectra for Mw 6 with respect to κ0 and for Δσ = 1.5 and 15 MPa.
Download/View: Table S1. [comma-separated value file; ~197 KB]. Metadata for the dataset used in the present study. EQ lat, earthquake latitude (latitude of the epicenter in degrees); long, longitude; RC, reinforced concrete. VS30 types of measurement are as follows: CH, DH, ESAC, ESAC-FK, MASW. The last four columns (respectively) are low-cut and up-cut frequencies for comparison 1 (LowcutfreqComp1, UpcutfreqComp1) and low-cut and up-cut frequencies for comparison 2 (LowcutfreqComp2, UpcutfreqComp2).
Tables S2–S5 are for an Mw 5 earthquake at Joyner–Boore distances RJB = 10, 30, 50, 70, 100, 150, and 200 km, corresponding to the site with a time-averaged shear-wave velocity in the upper 30 m of the soil column (Vs30) of 760 m/s. (Oscillator frequencies, fosc, are listed in column 1 of each table.)
Download/View: Table S2. [comma-separated value file; ~5 KB]. Predicted mean Fourier amplitude spectra (FAS; in m/s).
Download/View: Table S3. [comma-separated value file; ~3 KB]. Predicted mean duration (Drvto; in s).
Download/View: Table S4. [comma-separated value file; ~3 KB]. Predicted peak factor (PF).
Download/View: Table S5. [comma-separated value file; ~3 KB]. Predicted response spectra (in m/s2).
Tables S6–S9 are for an Mw 6 earthquake at Joyner–Boore distances RJB = 10, 30, 50, 70, 100, 150, and 200 km, corresponding to the site with a time-averaged shear-wave velocity in the upper 30 m of the soil column (Vs30) of 760 m/s. (Oscillator frequencies, fosc, are listed in column 1 of each table.)
Download/View: Table S6. [comma-separated value file; ~6 KB]. Predicted mean Fourier amplitude spectra (in m/s).
Download/View: Table S7. [comma-separated value file; ~3 KB]. Predicted mean duration (Drvto; in s).
Download/View: Table S8. [comma-separated value file; ~3 KB]. Predicted peak factor (PF).
Download/View: Table S9. [comma-separated value file; ~3 KB]. Predicted response spectra (in m/s2).
Tables S10–S13 are for an Mw 7 earthquake at Joyner–Boore distances RJB = 10, 30, 50, 70, 100, 150, and 200 km, corresponding to the site with a time-averaged shear-wave velocity in the upper 30 m of the soil column (Vs30) of 760 m/s. (Oscillator frequencies, fosc, are listed in column 1 of each table.)
Download/View: Table S10. [comma-separated value file; ~6 KB]. Predicted mean Fourier amplitude spectra (in m/s).
Download/View: Table S11. [comma-separated value file; ~3 KB]. Predicted mean duration (Drvto; in s).
Download/View: Table S12. [comma-separated value file; ~3 KB]. Predicted peak factor (PF).
Download/View: Table S13. [comma-separated value file; ~3 KB]. Predicted response spectra (in m/s2).
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