Spatially and temporally static crustal magnetic anomalies are contaminated by static core field effects above spherical harmonic degree 12 and dynamic, large-amplitude external fields. To extract crustal magnetic anomalies from the measurements of NASA's Magsat mission, we separate crustal signals from both core and external field effects. In particular, we define Magsat anomalies relative to the degree 11 field and use spectral correlation theory to reduce them for external field effects. We obtain a model of Antarctic crustal thickness by comparing the region's terrain gravity effects to free-air gravity anomalies derived from the Earth Gravity Model 1996 (EGM96). To separate core and crustal magnetic effects, we obtain the pseudo-magnetic effect of the crustal thickness variations from their gravity effect via Poisson's theorem for correlative potentials. We compare the pseudo-magnetic effect of the crustal thickness variations to field differences between degrees 11 and 13 by spectral correlation analysis. We thus identify and remove possible residual core field effects in the Magsat anomalies relative to the degree 11 core field. The resultant anomalies reflect possible Antarctic contrasts due both to crustal thickness and intracrustal variations of magnetization. In addition, they provide important constraints on the geologic interpretation of aeromagnetic survey data, such as are available for the Weddell Province. These crustal anomalies also may be used to correct for long wavelength errors in regional compilations of near-surface magnetic survey data. However, the validity of these applications is limited by the poor quality of the Antarctic Magsat data that were obtained during austral Summer and Fall when south polar external field activity was maximum. Hence an important test and supplement for the Antarctic crustal Magsat anomaly map will be provided by the data from the recently launched Ørsted mission, which will yield coverage over austral Winter and Spring periods when external field activity is minimal.