Passive seismology allows measurement of the structure of glaciers and ice sheets. However, most techniques used so far in this context are based on horizontally homogeneous media where parameters vary only with depth (1-D approximations), which are appropriate only for a subset of glaciers. Here, we analyze seismic noise records from three different types of glaciers (plateau, valley and avalanching glacier) to characterize the influence of the glacier geometry on the seismic wavefield. Using horizontal-to-vertical spectral ratios, polarization analysis and modal analysis, we show that the plateau glacier and the valley glacier can be seen as 1-D, whereas the relatively small avalanching glacier shows 3-D effects due to its bed topography and the deep crevasses. In principle, the techniques proposed here might allow monitoring such crevasses and their depth, and thus to constrain a key parameter of avalanching and calving glacier fronts.