To understand the dynamics of ice shelves, a knowledge of their internal and basal structure is very important. As the capacity to perform local surveys is limited, remote sensing provides an opportunity to obtain the relevant information. We must prove, however, that the relevant information can be obtained from remote sensing of the surface. That is the aim of this study. The Jelbart Ice Shelf, Antarctica, exhibits a variety of surface structures appearing as stripe-like features in radar imagery. We performed an airborne geophysical survey across these features and compared the results to TerraSAR-X imagery. We find that the stripe-like structures indicate surface troughs coinciding with the location of basal channels and crevasse-like features, revealed by radio-echo sounding. HH and VV polarizations do not show different magnitude. In surface troughs, the local accumulation rate is larger than at the flat surface. Viscoelastic modelling is used to gain an understanding of the surface undulations and their origin. The surface displacement, computed with a Maxwell model, matches the observed surface reasonably well. Our simulations show that the surface troughs develop over decadal to centennial timescales.