Elastic waves generated by high-speed trains

High-speed trains can generate vibrations that propagate away from the track. We present an accurate and efficient method for computing the vibrations in an elastic half-space at both small and large distances from the track. The method takes possible oscillatory behavior of the train into account. We conclude that vibrations, generated by oscillating trains, can be observed at large distances from the track, even if the train speed is lower than the Rayleigh wave speed.