Surface waves generated by a line load on a half-space with depth-dependent properties

• Anti-plane surface waves in an inhomogeneous half-space are modeled.
• High-frequency approximations are employed to calculate the surface wave velocity.
• The reciprocity theorem is applied to solve Lamb’s problem in the half-space.
• The model is validated by a numerical model based on representative layering.

The reciprocity theorem of elastodynamics is used in this paper to determine the surface waves that are radiated from a time-harmonic line load applied at the surface of a solid body, whose elastic moduli and mass density depend on the distance from the surface. In a high-frequency approximation, the surface wave velocity and expressions for the displacement and stresses of free surface waves are employed in the reciprocity theorem. The general expressions for the surface wave radiated by the oscillating line load, together with a virtual free surface wave, when employed in the reciprocity theorem, yield relatively simple expressions for the amplitude factor of the radiated surface wave. Results show the amplitude factor as a function of the wavenumber.