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, RVTgenerated
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 highfrequency
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 (Δσ) (source term), and
adjustments to the attributes reflecting site response (VS!κ0) are considered.