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The S-transform and discrete orthonormal S-transform (DOST) produce time–frequency representations, which is in contrast to the wavelet transformations. Similar in the Fourier transform, the use of the S-transform and DOST provides frequency-dependent resolution with absolutely referenced phase information. Although the decomposed signal using DOST is expressed as a sum of orthonormal basis function, this is not the case if the S-transform is used. In the present study, a procedure to simulate nonstationary ground motions based on DOST is proposed based on a seed record or given a target amplitude of DOST coefficients. It is shown that the model has zero mean, and its variance equals the assigned target. Using five real records, each from a larger earthquake, the application of the DOST and S-transform to the records is carried out. Although the time–frequency resolution obtained from DOST is coarse as compared to that obtained using the S-transform, its use identifies clearly time–frequency characteristics. Samples of ground motions are simulated using the proposed method based on the amplitude of the DOST coefficients of a seed record or on the average amplitude of the DOST coefficients of a set of actual records. The comparison of the time–frequency resolution, Fourier spectrum, time-varying power distribution, and response spectrum of the simulated and seed records indicates that the proposed simulation model is a useful and practical tool to simulate nonstationary ground motions.

There are several well‐known empirical lagged spatial coherence models for seismic ground motions proposed in the literature. The models are often developed based on the ordinary Fourier transform. None of the parametric models depend on time and frequency. The present study is focused on the development of the time‐frequency dependent (TF‐dependent) lagged coherence model for the seismic ground motions. The estimation of the TF‐dependent lagged coherence is carried out using the records obtained from dense arrays in Taiwan by applying the S‐transform—a TF‐dependent windowed Fourier transform. The spectral analysis results show that the TF‐dependent lagged coherence decreases with increasing separation or increasing frequency. Most importantly, it is shown that the TF‐dependent lagged coherence varies with the time‐varying intensity within the duration of the records; a higher normalized intensity corresponds to a higher lagged coherence. This feature is included in the developed empirical parametric TF‐dependent lagged coherence model, which is a function of the frequency, the separation between recording sites, and the normalized intensity. A numerical example illustrating its application to simulate nonstationary ground motions at multiple points is presented by using the time‐frequency spectral representation method that was developed based on the S‐transform and discrete orthonormal S‐transform.

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