In August 1990, the U.S. Navy declassified all Geodetic Mission (GM) radar altimeter data acquired by the Geosat satellite over oceanic regions south of 60¿S. We have used these GM data in conjunction with the unclassified, lower-resolution Geosat Exact Repeat Mission (ERM) altimeter data to construct high-resolution gravity fields on a 5-km grid covering the annular region of the southern ocean, which lies between 60¿S and 72¿S and encircles Antarctica. During the GM a complete mapping of the marine geoid (between 72¿S and 72¿N) was accomplished. The GM produce more densely spaced ground tracks (typically 2 or 3 km at 60¿S) than those of either the ERM or Seasat. Consequently, we were able to use the GM data to map the marine gravity field at a higher resolution than was previously possible using satellite altimeter data. This paper describes the techniques we used to derive these gravity fields and image them. These techniques involve (1) computing along-track sea surface height slopes, (2) gridding of these ascending and descending slopes, (3) converting the slopes to conventional deflections of the vertical, (4) transforming the deflections to gravity anomalies in the frequency domain, and (5) imaging. The resulting images of the marine gravity field reveal much that is new about the seafloor and the tectonic fabric of the southern ocean: a region which includes large expanses of seafloor that have never been surveyed by ships.