Guided wave propagation across sharp lateral heterogeneities: the complete wavefield at a cylindrical inclusion

Abstract

We present an exact treatment of wave propagation across a cylindrical inclusion embedded in a layered waveguide, which may serve as a test case allowing an estimation of the accuracy and validity range of approximation methods applied to surface wave propagation. Since, in contrast to a plane vertical interface, a cylindrical inclusion is of finite spatial extent, the test case presented here is especially well suited to assess the quality of approaches based on scattering theory. The wavefield is represented by Love and Rayleigh type modes. A 3‐D orthonormality relation is derived, expressed as an integral over the cylinder surface which allows a direct and unique computation of basis solutions. After solving a linear system of equations these basis solutions are superimposed to form the complete wavefield both within and outside the cylinder. It is shown that exact continuity of displacements and tractions at the interface can not be achieved with propagating modes only. Non‐propagating modes, which have complex wavenumbers and hence decay in the propagation direction, have to be included in the modal series. In contrast to propagating modes, complex modes have vanishing energy flux. Numerical results are presented for a layered halfspace, where only propagating modes were used, and for a layered waveguide for various sizes of the cylindrical inclusion. Astonishingly, vertical and horizontal displacements behave very differently. For instance, the scattered vertical displacement generated by an incoming Rayleigh fundamental mode is clearly dominated by the mode itself, while the scattered horizontal displacement is severely influenced by the excited higher Rayleigh modes. This might explain the difficulties met when interpreting horizontal components of surface wave data within a single‐mode concept. Copyright © 1992, Wiley Blackwell. All rights reserved