Extension of Coupled-Modes Method to Waveguides with Elastic Bottom

In this paper, the coupled-modes method of acoustic propagation is extended to waveguides with smoothly varying fluid-elastic interfaces. To formulate the problem without recourse to the SH wave component from the ground up, we employ the {uz,uv}-formulation developed in seismology. The result is remarkably different from that for fluid-fluid interfaces; the boundary conditions imposed at fluid-elastic interfaces give rise to terms including unknown boundary values so that the differential system obtained is not closed. To make the system closed, additional compatibility and constraining conditions have to be imposed.