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Ground motions could be modelled as amplitude and frequency modulated process. The frequency modulation through a time transformation results in the modelled motions in the new timescale being a stationary process except for the amplitude modulation. The assessment of power spectral density (PSD) and the lagged coherence in the transformed timescale is presented in this study. It is shown theoretically and numerically that the PSD functions obtained through time transformation in the original timescale should not be used as an amplitude modulation function, and that the lagged coherence in the new or auxiliary timescale differs from that in the original timescale.

journal of earthquake engineering

On the Estimation of Power Spectral Density and Lagged Coherence of Time Transformed Nonstationary Seismic Ground Motions and Their Use to Simulate Synthetic Records