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Gravity waves (GWs) transport momentum and energy in the atmosphere, exerting a profound influence on the global circulation. Accurately measuring them is thus vital both for understanding the atmosphere and for developing the next generation of weather forecasting and climate prediction models. However, it has proven very difficult to measure the full set of GW parameters from satellite measurements, which are the only suitable observations with global coverage. This is particularly critical at latitudes close to 60° S, where climate models significantly under-represent wave momentum fluxes. Here, we present a novel fully 3-D method for detecting and characterising GWs in the stratosphere. This method is based around a 3-D Stockwell transform, and can be applied retrospectively to existing observed data. This is the first scientific use of this spectral analysis technique. We apply our method to high-resolution 3-D atmospheric temperature data from AIRS/Aqua over the altitude range 20–60 km. Our method allows us to determine a wide range of parameters for each wave detected. These include amplitude, propagation direction, horizontal/vertical wavelength, height/direction-resolved momentum fluxes (MFs), and phase and group velocity vectors. The latter three have not previously been measured from an individual satellite instrument. We demonstrate this method over the region around the Southern Andes and Antarctic Peninsula, the largest known sources of GW MFs near the 60° S belt. Our analyses reveal the presence of strongly intermittent highly directionally focused GWs with very high momentum fluxes (∼ 80–100 mPa or more at 30 km altitude). These waves are closely associated with the mountains rather than the open ocean of the Drake Passage. Measured fluxes are directed orthogonal to both mountain ranges, consistent with an orographic source mechanism, and are largest in winter. Further, our measurements of wave group velocity vectors show clear observational evidence that these waves are strongly focused into the polar night wind jet, and thus may contribute significantly to the “missing momentum” at these latitudes. These results demonstrate the capabilities of our new method, which provides a powerful tool for delivering the observations required for the next generation of weather and climate models.