Elastic waves trapped above a cylindrical cavity

The existence of trapped elastic waves above a circular cylindrical cavity in a half space is demonstrated. These modes propagate parallel to the cylinder and their amplitude decays exponentially as the observer moves away from it. Dispersion relations connecting the frequency with the wavenumber along the cylinder are obtained using an analytical technique based on multipole expansions, and solved numerically. Critical frequencies at which modes cut on and off are determined and a range of contour plots illustrating the displacement fields are presented.