A frequency-dependent ground-motion spatial correlation model of within-event residuals for Fourier amplitude spectra

Ground motion time series recorded at stations separated by up to about 50 km show a frequency-dependent spatial coherency structure, and the corresponding ground motion intensity measures are found to be correlated. As omitting this correlation can result in underestimation of seismic losses in risk analysis, it is critical to quantify the spatial correlation structure for ground motion Fourier spectra estimated at different sites during a single event within a region. Toward this goal, we have developed an empirical frequency-dependent spatial correlation model for the within-event residuals of effective Fourier amplitude spectra from the Pacific Earthquake Engineering Research Center (PEER) Next Generation Attenuation (NGA) West2 database. The correlation model shows slower decrease of the spatial correlation with distance at lower frequencies compared with higher frequencies, in agreement with the underlying ground motion data, and no significant dependence on the magnitude of the earthquakes is observed. We use this empirical model to incorporate frequency-dependent spatial correlation into a hybrid deterministic-stochastic broadband ground motion generation module, which successfully generates synthetic time series for seven western US earthquakes with frequency-dependent spatial correlation that closely mimics that of the empirical model. Furthermore, the method also significantly improves the correlation for spectral accelerations, cumulative absolute velocities, and Arias intensities, compared with that derived from the original broadband module.