Efficient simulation of spatially correlated non-stationary ground motions by wavelet-packet algorithm and spectral representation method

Although the classical spectral representation method (SRM) has been widely used in the generation of spatially varying ground motions, there are still challenges in efficient simulation of the non-stationary stochastic vector process in practice. The first problem is the inherent limitation and inflexibility of the deterministic time/frequency modulation function. Another difficulty is the estimation of evolutionary power spectral density (EPSD) with quite a few samples. To tackle these problems, the wavelet packet transform (WPT) algorithm is utilized to build a time-varying spectrum of seed recording which describes the energy distribution in the time-frequency domain. The time-varying spectrum is proven to preserve the time and frequency marginal property as theoretical EPSD will do for the stationary process. For the simulation of spatially varying ground motions, the auto-EPSD for all locations is directly estimated using the time-varying spectrum of seed recording rather than matching predefined EPSD models. Then the constructed spectral matrix is incorporated in SRM to simulate spatially varying non-stationary ground motions using efficient Cholesky decomposition techniques. In addition to a good match with the target coherency model, two numerical examples indicate that the generated time histories retain the physical properties of the prescribed seed recording, including waveform, temporal/spectral non-stationarity, normalized energy buildup, and significant duration.