Using a point-source viscoelastic seismic wave modeling program, we simulated the seismograms that would be recorded for a system of an ice sheet floating on a water layer, the latter underlain by a solid containing a single isolated reflector. Ice and water layer thicknesses were 1.52-6.10 m. Sources were placed successively on the surface of the ice, in the water, and in the bottom; detectors (vertical geophones or hydrophones) were placed successively on the ice, in the water, and in the bottom. A source on the ice generated such strong antisymmetric modal energy that no reflections could be detected. A source buried 15-30 m below the bottom of the water resulted in clear reflections, whether the reflections were detected with surface geophones or buried hydrophones.Geophysicists have often observed data very similar to that which we modeled, but not universally. In practice, vibrators on floating ice produce usable reflections for a fixed but year-to-year variable water depth. To explain this observation, we are forced to assume that the floating annual ice of the Arctic is a strongly attenuative material.