Generalized Closed-Form Solutions for Moving-Source Lamb’s Problem

The three types of Lamb’s problems we have studied previously, despite differences in the relative positions of the source and field, share a common characteristic: the source’s location in space is fixed. As one of the important applications of the Lamb’s problem, this chapter explores an extended scenario—the seismic wave field generated by a moving source; specifically, the response of the isotropic, homogeneous elastic half-space surface to a vertical load moving at a constant velocity along a specific direction on the surface, termed the moving-source Lamb’s problem (abbreviated as \(\mathcal {M}\mathcal {L}\mathcal {P}\) hereafter). This can be viewed as a natural extension of the classical \(\mathcal {L}\mathcal {P}_1\) .