TY - JOUR A1 - Bora, Sanjay Singh A1 - Scherbaum, Frank A1 - Kuehn, Nicolas A1 - Stafford, Peter T1 - On the Relationship between Fourier and Response Spectra: Implications for the Adjustment of Empirical Ground-Motion Prediction Equations (GMPEs) JF - Bulletin of the Seismological Society of America N2 - The functional form of empirical response spectral ground-motion prediction equations (GMPEs) is often derived using concepts borrowed from Fourier spectral modeling of ground motion. As these GMPEs are subsequently calibrated with empirical observations, this may not appear to pose any major problems in the prediction of ground motion for a particular earthquake scenario. However, the assumption that Fourier spectral concepts persist for response spectra can lead to undesirable consequences when it comes to the adjustment of response spectral GMPEs to represent conditions not covered in the original empirical data set. In this context, a couple of important questions arise, for example, what are the distinctions and/or similarities between Fourier and response spectra of ground motions? And, if they are different, then what is the mechanism responsible for such differences and how do adjustments that are made to Fourier amplitude spectrum (FAS) manifest in response spectra? The present article explores the relationship between the Fourier and response spectrum of ground motion by using random vibration theory (RVT). With a simple Brune (1970, 1971) source model, RVT-generated acceleration spectra for a fixed magnitude and distance scenario are used. The RVT analyses reveal that the scaling of low oscillator-frequency response spectral ordinates can be treated as being equivalent to the scaling of the corresponding Fourier spectral ordinates. However, the high oscillator-frequency response spectral ordinates are controlled by a rather wide band of Fourier spectral ordinates. In fact, the peak ground acceleration, counter to the popular perception that it is a reflection of the high-frequency characteristics of ground motion, is controlled by the entire Fourier spectrum of ground motion. Additionally, this article demonstrates how an adjustment made to FAS is similar or different to the same adjustment made to response spectral ordinates. For this purpose, two cases: adjustments to the stress parameter (Delta sigma) (source term), and adjustments to the attributes reflecting site response (V-S - kappa(0)) are considered. Y1 - 2016 U6 - https://doi.org/10.1785/0120150129 SN - 0037-1106 SN - 1943-3573 VL - 106 SP - 1235 EP - 1253 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Kuehn, Nicolas M. A1 - Scherbaum, Frank T1 - A partially non-ergodic ground-motion prediction equation for Europe and the Middle East JF - Bulletin of earthquake engineering : official publication of the European Association for Earthquake Engineering N2 - A partially non-ergodic ground-motion prediction equation is estimated for Europe and the Middle East. Therefore, a hierarchical model is presented that accounts for regional differences. For this purpose, the scaling of ground-motion intensity measures is assumed to be similar, but not identical in different regions. This is achieved by assuming a hierarchical model, where some coefficients are treated as random variables which are sampled from an underlying global distribution. The coefficients are estimated by Bayesian inference. This allows one to estimate the epistemic uncertainty in the coefficients, and consequently in model predictions, in a rigorous way. The model is estimated based on peak ground acceleration data from nine different European/Middle Eastern regions. There are large differences in the amount of earthquakes and records in the different regions. However, due to the hierarchical nature of the model, regions with only few data points borrow strength from other regions with more data. This makes it possible to estimate a separate set of coefficients for all regions. Different regionalized models are compared, for which different coefficients are assumed to be regionally dependent. Results show that regionalizing the coefficients for magnitude and distance scaling leads to better performance of the models. The models for all regions are physically sound, even if only very few earthquakes comprise one region. KW - Ground-motion prediction equation KW - Non-ergodic PSHA KW - Hierarchical model Y1 - 2016 U6 - https://doi.org/10.1007/s10518-016-9911-x SN - 1570-761X SN - 1573-1456 VL - 14 SP - 2629 EP - 2642 PB - Springer CY - Dordrecht ER -