Broadband Ground‐Motion Simulation with Interfrequency Correlations

Ground-motion simulations can be viable alternatives to empirical relations for seismic hazard analysis when data are sparse. Interfrequency correlation is revealed in recorded seismic data, which has implications for seismic risk (Bayless and Abrahamson. 2018a). However, in many cases, simulated ground-motion time series, in particular those originating from stochastic methods, lack interfrequency correlation. Here, we develop a postprocessing method to rectify simulation techniques that otherwise produce synthetic time histories deficient in an interfrequency correlation structure. An empirical correlation matrix is used in our approach to generate correlated random variables that are multiplied in the frequency domain with the Fourier amplitudes of the synthetic ground-motion time series. The method is tested using the San Diego State University broadband ground-motion generation module, which is a broadband ground-motion generator that combines deterministic low-frequency and stochastic high-frequency signals, validated for the median of the spectral acceleration. Using our method, the results for seven western U.S. earthquakes with magnitude between 5.0 and 7.2 show that empirical interfrequency correlations are well simulated for a large number of realizations without biasing the fit of the median of the spectral accelerations to data. The best fit of the interfrequency correlation to data is obtained assuming that the horizontal components are correlated with a correlation coefficient of about 0.7.