Estimation of wavelet coherence of seismic ground motions

The relation between the nonstationary seismic ground motions at two sites is often char-acterized using lagged coherence and phase spectrum. Their evaluation is most often carried out using ordinary Fourier analysis (i.e., without windowing) by assuming that they are time invariant. In the present study, the assessment of time-varying coherence is carried out based on the auto-and cross-wavelet power spectrum. The coherence is expressed in terms of lagged wavelet coherence and wavelet phase spectrum. For the analysis, the generalized Morse wavelets are employed, and the ground-motion records for several events from dense arrays located in Taiwan are used. It was shown that without adequate smoothing in scale and time, the obtained lagged wavelet coherence varies drastically in time and frequency (i.e., scale). A parametric analysis shows that the estimated coherence is sensitive to the degree of smoothing. The results of the lagged wavelet coherence and wavelet phase spectrum are time varying and frequency varying. This is in contrast with the time-invariant lagged coherence and phase spectrum assumed for the amplitude modulated evolutionary stochastic process. It is inferred from the results that the use of a time-varying coherence should be considered for seismic ground motions modeled as nonstationary processes.