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Empirical ground-motion prediction equations (GMPEs) require adjustment to make them appropriate for site-specific scenarios. However, the process of making such adjustments remains a challenge. This article presents a holistic framework for the development of a response spectral GMPE that is easily adjustable to different seismological conditions and does not suffer from the practical problems associated with adjustments in the response spectral domain. The approach for developing a response spectral GMPE is unique, because it combines the predictions of empirical models for the two model components that characterize the spectral and temporal behavior of the ground motion. Essentially, as described in its initial form by Bora et al. (2014), the approach consists of an empirical model for the Fourier amplitude spectrum (FAS) and a model for the ground-motion duration. These two components are combined within the random vibration theory framework to obtain predictions of response spectral ordinates. In addition, FAS corresponding to individual acceleration records are extrapolated beyond the useable frequencies using the stochastic FAS model, obtained by inversion as described in Edwards and Fah (2013a). To that end, a (oscillator) frequency-dependent duration model, consistent with the empirical FAS model, is also derived. This makes it possible to generate a response spectral model that is easily adjustable to different sets of seismological parameters, such as the stress parameter Delta sigma, quality factor Q, and kappa kappa(0). The dataset used in Bora et al. (2014), a subset of the RESORCE-2012 database, is considered for the present analysis. Based upon the range of the predictor variables in the selected dataset, the present response spectral GMPE should be considered applicable over the magnitude range of 4 <= M-w <= 7.6 at distances <= 200 km.
Adjustment of empirically derived ground motion prediction equations (GMPEs), from a data- rich region/site where they have been derived to a data-poor region/site, is one of the major challenges associated with the current practice of seismic hazard analysis. Due to the fre- quent use in engineering design practices the GMPEs are often derived for response spectral ordinates (e.g., spectral acceleration) of a single degree of freedom (SDOF) oscillator. The functional forms of such GMPEs are based upon the concepts borrowed from the Fourier spectral representation of ground motion. This assumption regarding the validity of Fourier spectral concepts in the response spectral domain can lead to consequences which cannot be explained physically.
In this thesis, firstly results from an investigation that explores the relationship between Fourier and response spectra, and implications of this relationship on the adjustment issues of GMPEs, are presented. The relationship between the Fourier and response spectra is explored by using random vibration theory (RVT), a framework that has been extensively used in earthquake engineering, for instance within the stochastic simulation framework and in the site response analysis. For a 5% damped SDOF oscillator the RVT perspective of response spectra reveals that no one-to-one correspondence exists between Fourier and response spectral ordinates except in a limited range (i.e., below the peak of the response spectra) of oscillator frequencies. The high oscillator frequency response spectral ordinates are dominated by the contributions from the Fourier spectral ordinates that correspond to the frequencies well below a selected oscillator frequency. The peak ground acceleration (PGA) is found to be related with the integral over the entire Fourier spectrum of ground motion which is in contrast to the popularly held perception that PGA is a high-frequency phenomenon of ground motion.
This thesis presents a new perspective for developing a response spectral GMPE that takes the relationship between Fourier and response spectra into account. Essentially, this frame- work involves a two-step method for deriving a response spectral GMPE: in the first step two empirical models for the FAS and for a predetermined estimate of duration of ground motion are derived, in the next step, predictions from the two models are combined within the same RVT framework to obtain the response spectral ordinates. In addition to that, a stochastic model based scheme for extrapolating the individual acceleration spectra beyond the useable frequency limits is also presented. To that end, recorded acceleration traces were inverted to obtain the stochastic model parameters that allow making consistent extrapola- tion in individual (acceleration) Fourier spectra. Moreover an empirical model, for a dura- tion measure that is consistent within the RVT framework, is derived. As a next step, an oscillator-frequency-dependent empirical duration model is derived that allows obtaining the most reliable estimates of response spectral ordinates. The framework of deriving the response spectral GMPE presented herein becomes a self-adjusting model with the inclusion of stress parameter (∆σ) and kappa (κ0) as the predictor variables in the two empirical models. The entire analysis of developing the response spectral GMPE is performed on recently compiled RESORCE-2012 database that contains recordings made from Europe, the Mediterranean and the Middle East. The presented GMPE for response spectral ordinates should be considered valid in the magnitude range of 4 ≤ MW ≤ 7.6 at distances ≤ 200 km.