Time-varying characteristics of coherence for tri-directional seismic ground motions

The nonstationary and spatially varying characteristics of seismic ground motions affect the structural responses. The lagged coherence needs to be considered in modelling and simulating the spatially varying multi-component ground motions. The present study aims to characterize the space-time-frequency dependent (STF-dependent) lagged coherence using actual tri-directional ground motion records from dense arrays. Based on such characterization, a novel 3 x 3 STF-dependent lagged coherence matrix is developed, where only models for six elements need to be modelled by symmetry. For the assessment and model development, the records from five seismic events that were recorded by dense arrays are used, and a normalized intensity parameter is introduced. The STF-dependent lagged coherence is calculated by using the time-frequency decomposition results obtained by applying the S-transform. The results indicated that the statistics of the lagged coherence between the record components in the horizontal orthogonal direction is relatively insensitive to the rotation of the record components, and the lagged coherence between the vertical and horizontal record components could be neglected. The developed matrix includes the parametric model of the lagged coherence for two recorded components in the same direction in the horizontal plane, or in the vertical plane, and for record components in the two horizontal orthogonal directions. The use of the developed matrix for simulating a vector of nonstationary multi-direction ground motions is presented by considering spatially placed sites.