In this short paper the exclusion circles and vertical phase locities for gravity waves launched from the ground into a time-varying wind are studied using a ray-tracing technique. It is shown that waves with initial observed phase speeds that should place them within the local temporally varying exclusion circle, are often Doppler shifted outside of the circle. This, and the finite lifetime of some critical levels, allow waves to survive the critical layer and reach higher altitudes. Also, for slower phase-speed waves, the temporally varying wind can shift the observed frequency to negative values, so that the observed phase motions will be opposite (i.e. horizontally reversed and vertically upward), even though the energy still propagates upward. This effect can also cause the phase velocity to move inside the local exclusion circle. Due to the directional filtering of wave sources by the stratospheric wind, the percentage of such reverse-propagating waves will change systematically with local time and height in our simplified but realistic model. These results are related to ground-based systems, optical and radar, which sample the wind field and gravity waves in the middle atmosphere.