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An Empirical Relationship between Fourier and Response Spectra Using Spectrum-Compatible Times Series

The Fourier amplitude spectrum (FAS) is widely used in seismology and earthquake engineering as it provides valuable information regarding frequency dependent amplitude of the ground motion. However, for structural design and assessment, the preferred representation of seismic hazard continues to be based on the elastic response spectrum. Therefore, conversions between these spectra are often required. In this article, the connection between FAS and the 5% damping pseudo-acceleration response spectrum (5% PSA) is explored using large data sets of spectrum-compatible time series generated from white noise. The strong dependence of the relation between FAS and 5% PSA with strong motion duration is evidenced and a duration dependent empirical relationship between the both spectra is developed. The equation is validated using recorded ground motions and spectrum-compatible time series generated from the modification of these ground motions. The equation allows simpler one-step conversions when compared to iterative approaches based on RVT theory or time-consuming methodologies that require the generation of spectrum-compatible time series.