2D Lamb’s Problem (II): Internal Source

In Chap. 2 , we conducted a detailed study of the displacement field generated in a half-space (including the surface) by a force source acting on the surface in the 2D case. Through numerical examples, we examined the characteristics of the displacement, particularly the generation of Rayleigh waves and P-S waves. However, because the source acts on the surface and there is no interface within the medium, the propagation paths of the elastic waves are relatively simple, and the displacement field is correspondingly straightforward. If the source acts within the medium (referred to as an internal source), and the observation point is also within the medium (or on the surface), it is expected that, in addition to the waves propagating directly to the observation point, some will reflect off the surface, complicating the wave field due to the presence of the surface. As a transition to the more complex 3D case, it is necessary to thoroughly investigate the behavior of the wave field under the general source-field geometric structure.