Trains generate Rayleigh waves

Below is an illustration of Rayleigh waves, typically generated by moving sources on free ground, such as vibratory compactors, overground trains, and heavy trucks. An interesting fact, the vertical displacement component of Rayleigh waves actually increase just below ground, meaning that, there is in theory a slightly increased level of vertical vibration just below the surface. Exact plane-strain solution: a stress-free surface, P and S potentials decaying with depth, and the phase speed fixed by the Rayleigh equation.

Displacements are exaggerated for visibility (linear theory). Dashed ellipses trace one column of particles: retrograde at the surface, prograde below the depth where u_x changes sign. Time is normalised to the wave period.