8 - Computation of surface waves by reciprocity considerations

Summary

Introduction

It is shown in this chapter that the reciprocity theorem can be used to calculate in a convenient manner, that is, without the use of integral transform techniques, the surface-wave motion generated by a time-harmonic line load or a time-harmonic point load applied in an arbitrary direction in the interior of a half-space. The virtual wave motion that is used in the reciprocity relation is also a surface wave. Hence the calculation does not include the body waves generated by the loads. For a point load applied normally to the surface of a half-space, it is shown in Section 8.6 that the surface-wave motion is the same as obtained in the conventional manner by the integral transform approach.

It is well known that the dynamic response to a time-harmonic point load normal to the surface of the half-space was solved by Lamb (1904), who also gave explicit expressions for the generated surface-wave motion. The surfacewave motion can be obtained as the contribution from the pole in inverse integral transform representations of the displacement components. The analogous transient time-domain problem for a point load normal to the surface of the half-space was solved by Pekeris (1955). The displacements generated by a transient tangential point load applied to the half-space surface were worked out by Chao (1960).