  A solution method is developed for a model of ice shelf vibrations in
response to ocean waves, in which the ice shelf thickness and seabed beneath
the ice shelf vary over distance, and the ice shelf/sub--ice--shelf cavity are
connected to the open ocean. The method combines a decomposition of the ice
shelf motion into free modes of vibration, a finite element method for the
cavity water motion, and a non-local operator to connect to the open ocean. An
investigation is conducted into the effects of ice shelf thickening, seabed
shoaling and the grounding-line conditions on ice shelf vibrations, induced by
regular incident waves in the swell regime. Further, results are given for ice
shelf vibrations in response to irregular incident waves, and
ocean-to-ice-shelf transfer functions are derived. The findings add to evidence
that ice shelves experience appreciable vibrations in response to swell, and
that ice shelf thickening and seabed shoaling can have a considerable influence
on predictions of how ice shelves respond to ocean waves.
