Simulation of Spatially Varying Non-Gaussian and Nonstationary Seismic Ground Motions by the Spectral Representation Method

Abstract

Simulation of sample realizations of stochastic processes is the bedrock of the Monte Carlo method, and the accurate modeling of stochastic processes is crucial to determine realistic structural responses. For seismic ground motion, its nonstationary property and spatially variability are well known. Furthermore, its non-Gaussian feature has been observed in some works. It is then necessary to simulate spatially varying ground motions accounting for its nonstationary and non-Gaussian characteristics. For this purpose, a computational procedure is developed for the simulation of non-Gaussian nonstationary spatially varying ground motions based on the spectral representation method (SRM). Translation process theory for the nonstationary non-Gaussian vector process is first proposed. By applying the proposed translation process theory, an iterative scheme is developed to estimate the underlying Gaussian evolutionary power spectral density (EPSD) matrix. The resulting underlying Gaussian EPSD matrix is used to simulate the underlying Gaussian ground motion by the SRM, which is finally mapped to the desired non-Gaussian nonstationary spatially varying ground motions. The capabilities of the proposed procedure are demonstrated by a numerical example. The statistical properties of the simulated non-Gaussian ground motions are compared with those of the simulated Gaussian ground motions.