| Summary: | Flexure and extension of ice shelves in response to incident ocean surface gravity waves have been linked to iceberg calving, rift growth, and even disintegration of ice shelves. Most modeling studies utilize a plate bending model for the ice, focusing exclusively on flexural gravity waves. Ross Ice shelf seismic data shows not only flexural gravity waves, with dominantly vertical displacements, but also extensional Lamb waves, which propagate much faster with dominantly horizontal displacements. Our objective is to model the full-wave response of ice shelves, including ocean compressibility, ice elasticity, and gravity. Our model is a 2D vertical cross-section of the ice shelf and sub-shelf ocean cavity. We quantify the frequency-dependent excitation of flexural gravity and extensional Lamb waves and provide a quantitative theory for extensional Lamb wave generation by the horizontal force imparted by pressure changes on the vertical ice shelf edge exerted by gravity waves. Our model predicts a horizontal to vertical displacement ratio that increases with decreasing frequency, with ratio equal to unity at $\sim$0.001 Hz. Furthermore, in the very long period band ($<0.003$ Hz), tilt from flexural gravity waves provides an order of magnitude larger contribution to seismometer horizontal components than horizontal displacements from extensional Lamb waves.
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