Green's function for three‐dimensional elastic wave equation with a moving point source on the free surface with applications

Abstract

ABSTRACTHigh‐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.