VARIATIONAL BOUND PRINCIPLE FOR SURFACE-WAVE SCATTERING

The use of a variational bound principle to determine surface wave solutions will be examined. It will be demonstrated that the vibrational solution for the surface wave velocity in a semi-infinite substrate is bounded from below and that the value of this bound coincides with the exact solution in the simple case of the substrate only. In the presence of an overlay, the variational solution for the surface wave velocity still maintains the boundedness property, but the solution has changed to reflect the perturbing effect of the overlay. Improved reflection coefficients and velocity shifts are calculated, including the second-order effects of evanescent waves. The variational bound approach provides a simple but powerful alternative to other conventional methods in which each Floquet component of the solution is treated separately. Bulk wave coupling requires a separate treatment as the bound principle is violated in this case.