ABSTRACT High‐speed train seismology has come into being recently. This new kind of seismology uses a high‐speed train as a repeatable moving seismic source. Therefore, Green's function for a moving source is needed to make theoretical studies of the high‐speed train seismology. Green's function for three‐dimensional elastic wave equation with a moving point source on the free surface is derived. It involves a line integral of the Green's function for a fixed point source with different positions and corresponding time delays. We give a rigorous mathematical proof of this Green's function. According to the principle of linear superposition, we have also obtained the Green's function for a group of moving sources which can be regarded as a model of a traveling high‐speed train. Based on a temporal convolution, an analytical formula for other moving sources is also given. In terms of a moving Gaussian source, we deal with the issue of numerical calculations of the analytical formula. Applications to modelling of a traveling high‐speed train are presented. We have considered both the land case and the bridge case for a traveling high‐speed train. The theoretical seismograms show different waveform features for these two cases.

中文翻译：

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自由表面动点源三维弹性波动方程的格林函数及其应用

摘要 高速列车地震学应运而生。这种新型地震学使用高速列车作为可重复的移动地震源。因此，需要对动源的格林函数进行高速列车地震学的理论研究。导出了自由表面上具有移动点源的三维弹性波动方程的格林函数。它涉及具有不同位置和相应时间延迟的固定点源的格林函数的线积分。我们给出了这个格林函数的严格数学证明。根据线性叠加原理，我们还得到了一组运动源的格林函数，可以看作是高速列车行驶的模型。基于时间卷积，还给出了其他移动源的解析公式。就移动高斯源而言，我们处理解析公式的数值计算问题。介绍了在行驶中的高速列车建模中的应用。我们已经考虑了高速列车行驶的陆地情况和桥梁情况。理论地震图显示了这两种情况的不同波形特征。