This is a proposal to process the GRACE satellite range, range-rate, and range-acceleration data with a goal to obtain a map of the geoid over the Antarctic with spatial resolution between 35 and 100 km. The free-air gravity derived from this geoid should fundamentally change our view on geological structure and history of the Antarctic continent in much the same way that the GEOSAT mission impacted our understanding of plate tectonics in the world's oceans. Due to resource limitations, however, the GRACE project team will not use the range and its derivatives to generate high spatial resolution estimates of the gravity field along the satellite ground track. The new geoid and derived free-air gravity field will require development of an algorithm to process the range, range-rate and range acceleration data and convert them to a self-consistent geoid. The GRACE-derived gravity field will be compared with marine, airborne gravity and land-based surveys as well as with major geological features of the Antarctic continent to assess wavelength resolution. This comparison will require the integration of the airborne and marine data sets and determination of the subglacial topography for some of the airborne surveys. Once the new geoid and derived fee-air gravity have been generated, the continent-wide subglacial topography could be estimated via an optimal co-kriging interpolation of the available bedrock measurements and the geoid, joint with the statistical relationships describing the spatial variation of topography, and the spatial correlation of the geoid and topography. The subglacial topography will be also determined using an alternative approach, the Parker inversion method. These products will be made available to the ice sheet modeling community. The new continent-wide subglacial topography will be used in combination with altimetric ice surface elevations to calculate a new estimate of Antarctic ice sheet volume, which can be used to calibrate the eustatic sea-level curve from oxygen isotope data for the present and maximum possible variations of the global sea level curve. The new subglacial topography estimates will also be used to interpret geologic structures of the Antarctic and the processes responsible for their formation. This research will have several areas of broader impact and intellectual merit: (a) the map of subglacial topography, together with an improved estimate of the Antarctic ice volume, will be an important contribution to the science goals of the Antarctic Climate Evolution initiative (ACE). Modeling the nucleation of the East Antarctic ice sheet relies on high-quality subglacial topography models, as well as modeling the drainage of the entire ice sheet. (b) The proposed GRACE-derived gravity approach, if proven to be successful, can be applied to the Arctic region and indeed to the entire world. While the Arctic gravity field is of high quality south of 82 N (ERS-1 orbit coverage), a large polar gap remains. Mapping the main geological features in these hard-to-reach parts of the world from satellite measurements would be a significant step forward in understanding the plate tectonic features of the Artic and Antarctic and should extend significantly recent marine geological and tectonic studies of the region.