Validity of the reciprocity approach for determination of surface wave motion

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Expressions for the displacements and the stresses for surface wave motion generated by a time-harmonic line load applied to the surface of an isotropic linearly elastic half-space are determined in a simple manner by the use of the reciprocity theorem. It is shown that their amplitudes show perfect agreement with the corresponding amplitudes obtained in the conventional manner by applying the Fourier transform technique. As an application of the reciprocity approach, the surface wave motion generated by uniform pressure over a cylindrical cavity located on the surface of a half-space has been determined. The analytical results have been verified by comparison with boundary element method (BEM) results. For a prescribed frequency and depth of the cavity, the analytical and BEM results are graphically displayed versus the surface length of the cavity, and show excellent agreement.

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