Estimating Various Response Spectra from a Fourier Amplitude Spectrum

ABSTRACT Response spectra, including spectral displacement (SD), spectral velocity (SV), and spectral acceleration (SA) are important ground-motion intensity measures. To estimate ground motions in regions lacking earthquake data, a modeling approach based on random vibration theory (RVT) that combines a model of the Fourier amplitude spectrum (FAS) and a ground-motion duration model is an attractive tool. However, this RVT-based approach is currently limited to estimating SD or pseudospectral acceleration. This study aimed to develop a new approach capable of estimating various response spectra from the FAS, including not only SD but also SV and SA, based on the RVT framework. First, equations for estimating SV and SA from the FAS were derived by replacing the oscillator transfer function for SD in the traditional RVT framework with those for SV and SA, respectively. Moreover, two simple modification factors for the duration of the root mean square oscillator response were introduced to ensure that the SV and SA from the RVT approach matched those from the time-series analysis. The proposed approach maintains the use of the RVT framework for estimating SD without introducing any additional concepts; however, it can readily provide three types of response spectra simultaneously.