Error Analysis of Spatially Varying Seismic Ground Motion Simulation by Spectral Representation Method

Abstract

This paper investigates statistical errors in the simulation of spatially varying seismic ground motions modeled by evolutionary Gaussian vector processes and simulated by the spectral representation method (SRM). Formulas are derived for both bias and random errors of the simulated evolutionary power spectral density (EPSD), time-varying correlation function, and standard deviation with respect to the target (idealized) ones. The closed-form error formulas for the EPSD are further simplified under specified conditions. It is shown that the simulated nonstationary characteristics are all unbiased, the closed-form random error formulas for the EPSD can reduce to those for stationary simulations, and the predicted random errors match those given by the ensemble average. By using the random error formulas, the factors influencing the random errors are investigated. The results show that the SRM implementation scheme involving both random amplitudes and phase angles would cause larger random errors, and increasing the number of samples and frequency intervals would reduce these errors. Closed-form error formulas are finally used to estimate errors in the simulation of spatially varying seismic ground motions for the Tsing Ma suspension bridge.