Closed-form solutions of surface wave motions generated by a time-harmonic load applied in the interior of a half-space are determined in a simple manner by the use of reciprocity in elastodynamics. The method requires expressions for the displacement...
Closed-form solutions of surface wave motions generated by a time-harmonic load applied in the interior of a half-space are determined in a simple manner by the use of reciprocity in elastodynamics. The method requires expressions for the displacements and the stresses of free surface waves, preferably in analytical form, but numerically obtained forms can also be used. A virtual wave that satisfies appropriate conditions on the boundaries and is a solution of the elastodynamic equations is used as state in the reciprocity theorem. By choosing a suitable virtual wave, state , which is the actual solution can be solved directly from the reciprocity relations. The solutions of surface wave motions are also obtained by the use of integral transform techniques. It is then shown that the amplitudes of the scattered waves obtained by the reciprocity approach and the integral transform approach are mathematically identical.
Based on the obtained solutions of surface wave motions, a mathematical model for scattering of surface waves by a cavity at the surface of a half-space is investigated. The purpose of this study is therefore to introduce a novel theoretical approach for detection and characterization of cavities. The amplitudes of the scattered field are verified by the numerical results from the boundary element method (BEM). The analytical and BEM result are graphically displayed and show excellent agreement when the depth and the width of the cavity are small compared to the wavelength. Both results are then compared with the experiment data.
As an improvement, a model for multiple scattering of surface waves by cavities on the surface of a half-space is studied. For multiple scattering by cavities, the self-consistent method is employed to derive an implicit set of equations which approximates the scattered field. Numerical calculations based on the boundary element method are found in order to compare with the analytical results. Comparisons between the analytical and BEM results provide good agreement.