On the Lagged Coherence Estimation for Seismic Ground Motions
X.Z. Cui
Abstract
Abstract This article questioned and examined the adequacy of using the Fourier transform (FT) to estimate the frequency-dependent but time-independent lagged coherence of ground motions following evolutionary theory, which was widely used in the stochastic ground-motion modeling. Accurate estimation of lagged coherence is paramount for understanding the spatial variability and model development of seismic ground motions. FT was widely applied in the estimation of lagged coherence and for coherence model development, whereas its adequacy was never investigated. First, by assuming the ground motions as evolutionary processes, this study critically examines the application of the FT for estimating frequency-dependent only coherency and lagged coherence. Notably, the investigation reveals the FT’s limitations in accurately calculating lagged coherence for nonstationary ground motions, demonstrating an inconsistent bias across ground motions with different nonstationary characteristics, thus rendering it unsuitable for reliable lagged coherence estimation of ground motions. To address this critical issue, a new method based on the S transform is proposed for the estimation of time-independent lagged coherence between evolutionary processes, designed to yield a consistent and negligibly small bias for ground motions with different nonstationary characteristics. The comparison of the estimated time-independent lagged coherence from real records using FT and the proposed method is also shown and substantiates the above examination. Further, by jumping out of the concept of evolutionary theory, the study also investigates both the calculated time-independent and time-dependent lagged coherence of actual historical ground motion records, providing valuable observations and discussions that contribute to a more robust understanding of the spatial and temporal dependencies inherent in seismic excitations. This research offers a more reliable approach for characterizing the complex coherence structure of nonstationary ground motions, crucial for advanced seismic risk and resilience assessments.