The effect of submergence on the scattering by the interface between two semi-infinite sheets

This paper considers the reflection and transmission of a flexural-gravity wave within ice sheets floating on water as it propagates through a series of abrupt changes in ice sheet characteristics. The canonical problem involves one such junction at which two semi-infinite ice sheets of different properties are either frozen together or separated by a crack. Unlike most mathematical approaches to problems involving ice sheets, we allow the ice sheets to adopt a variable submergence according to their thickness. The problem is solved using integral equations formulated through the matching of eigenfunction expansions.