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The structure of ice shelves is important for modelling the dynamics of ice flux from the continents to the oceans. While other, more traditional techniques provide many constraints, passive imaging with seismic noise is a complementary tool for studying and monitoring ice shelves. As a proof of concept, here we study noise cross-correlations and autocorrelations on the Amery Ice Shelf, East Antarctica. We find that the noise field on the ice shelf is dominated by energy trapped in a low-velocity waveguide caused by the water layer below the ice. Within this interpretation, we explain spectral ratios of the noise cross-correlations as P-wave resonances in the water layer, and obtain an independent estimate of the water-column thickness, consistent with other measurements. For stations with noise dominated by elastic waves, noise autocorrelations also provide similar results. High-frequency noise correlations also require a 50-m firn layer near the surface with P-wave velocity as low as 1 km s−1. Our study may also provide insight for future planetary missions that involve seismic exploration of icy satellites such as Titan and Europa. [ABSTRACT FROM AUTHOR]