The seismic response time-domain analysis of the complex sites (complex sites-city buildings coupling) under far-field earthquakes requires the free-field seismic wave motion input at the computational truncation boundary. In order to avoid memory waste for storing time histories of boundary nodes and low parallel computing efficiency caused by frequent I/O’s

it is necessary to construct the time-domain simulation method of free-field wave matching the time-domain analysis of seismic response. For the seismic response time-domain analysis method based on the Legendre spectral element

the corresponding free-field wave time-domain simulation method for SH wave in layered media under obliquely incident plane wave is developed. First

the SH wave simulation in layered media under obliquely incident plane wave is clarified. Then the Legendre spectral element method and explicit integration schemes is adopted to establish the space-time decoupling discrete scheme for such a problem. The accuracy and stability of the proposed scheme is verified through analytical examples. Moreover

the proposed scheme is applied to compare the crust amplification effects during the seismic waves propagation from the seismic source to the bedrock site. The results show that the amplification effects in the two regions are systematically different in the low frequency range

and tend to be the same in the high frequency range. The results explain qualitatively the problem that the predicted response spectrum value over long-period and relatively long-period through the next generation seismic attenuation relationship are inconsistent with Wenchuan earthquake records. Finally

taking the analysis of mountain topography effect as the example

the proposed scheme is applied together with the Legendre spectral element method and the transmitting boundary condition to near-field external source wave simulation.