Recent ground motion simulations based on the spectral element method have mainly focused on source-internal problems. Reports on seismic responses due to plane wave incidence are rare, even though these are frequently encountered in site effect analysis and soil-structure interaction simulations. In this study, a seismic motion simulation method for 2D complex sites under plane SH wave incidence is proposed based on high-precision spectral element method (SEM) and multi-transmitting formula (MTF). The accuracy and stability of this method are validated through numerous numerical examples. Comparisons with analytical solutions and extended results demonstrate the high simulation accuracies for the ground motions in 2D complex site models when SH plane waves are vertically incident from the bottom. Compared with MTF in the traditional finite-element method (FEM), MTF integrated into SEM demonstrates better performance for both high- and low-frequency stabilities. First, until to the third-order MTF, this method shows a fairly good ability to eliminate high-frequency instability. This instability only occurs when the artificial wavespeed, c_a, adopted in the MTF is larger than about five times the physical velocity, c_s. For the most common case of c_a = c_s, long-term stable results can be achieved without any special treatments. In addition, under the condition of no interventions, the low-frequency drift instability for MTF in SEM is considerably lessened compared with that of MTF in FEM, and the drift instability can also be eliminated by a smaller perturbation parameter than in the latter. The method presented in this study combines the advantages of SEM and MTF, and exhibits better stability performance, indicating good application prospects for wave motion simulations of plane wave incidence problems.

最近基于谱元法的地面运动模拟主要集中在源内部问题上。尽管在场地效应分析和土壤-结构相互作用模拟中经常遇到由于平面波入射而引起的地震反应的报道，但很少见。提出了一种基于高精度谱元法（SEM）和多传输公式（MTF）的平面SH波入射下二维复杂场地地震运动模拟方法。通过大量的数值例子验证了该方法的准确性和稳定性。与解析解决方案的比较和扩展的结果表明，当SH平面波从底部垂直入射时，二维复杂场地模型中的地面运动具有很高的模拟精度。与传统的有限元方法（FEM）中的MTF相比，集成到SEM中的MTF在高频和低频稳定性方面均表现出更好的性能。首先，直到三阶MTF为止，此方法显示出消除高频不稳定性的相当不错的能力。这种不稳定性仅在人工波速，MTF中采用的c _a大于物理速度c _s的五倍。对于最常见的c _a = c _s情况，无需任何特殊处理即可获得长期稳定的结果。此外，在没有干预的情况下，与FEM中的MTF相比，SEM中MTF的低频漂移不稳定性大大降低，并且还可以通过使用比后者更小的扰动参数来消除漂移不稳定性。本研究提出的方法结合了SEM和MTF的优点，具有较好的稳定性能，为平面波入射问题的波运动模拟提供了良好的应用前景。