Deformation of a layered, elastic, half-space by uniformly moving line loads

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Abstract
When a layered half-space is subjected to loads which move uniformly along its surface, the deformation of the half-space depends on the manner in which the load couples into the surface-wave modes. The uniform speed of the load selects those parts of the modal spectra that have phase velocities equal to the load speed. The restriction that the phase velocity be real leads to novel dispersion relations for the leaky modes, but the trapped mode dispersion relations are the usual ones. In this paper general expressions are derived for the solution for uniformly moving line loads on an elastic half-space containing an arbitrary number of layers. In addition to the modal contributions, the solution contains contributions from source singularities and a line integral that reduce to the static solution as the load speed tends to zero. The details are worked out for the special case of a single low-speed layer lying on a high-speed half-space. For the modes, real and imaginary parts of frequency and velocity amplitudes at various depths are presented as functions of frequency. Total velocity waveforms are shown for selected load speeds and depths.