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. The inclusion of variable submergence of the ice sheet has been shown to have a considerable effect upon simulations for predicting ice thicknesses in realistic ice fields with random configurations of multiple ice heterogenieties.