A new use of the elastodynamic reciprocity theorem

For an isotropic linearly elastic half-space whose elastic moduli and mass density depend on the distance from the free surface, the surface wave motion radiating from a time-harmonic point load applied normal to the surface of the half-space is considered in this paper. The surface wave velocity, which depends on the wave number, together with expressions for the displacements and stresses of free surface waves, are obtained in a high-frequency approximation. Application of the reciprocity theorem using general expressions for the surface wave radiated by the oscillating point load, together with a virtual free surface wave, yields relatively simple expressions for the amplitude factor of the radiated surface wave. For a few examples, results show the velocity of surface waves and the amplitude factor of the surface waves as a function of the wave number.