Maps of relatively strong crustal magnetic field anomalies detected at low altitudes with the magnetometer instrument on Lunar Prospector are presented. On the lunar nearside, relatively strong anomalies are mapped over the Reiner Gamma Formation on western Oceanus Procellarum and over the Rima Sirsalis rille on the southwestern border of Oceanus Procellarum. The main Rima Sirsalis anomaly does not correlate well with the rille itself but is centered over an Imbrian-aged smooth plains unit interpreted as primary or secondary basin ejecta. The stronger Reiner Gamma anomalies correlate with the locations of both the main Reiner Gamma albedo marking and its northeastward extension. Both the Rima Sirsalis and the Reiner Gamma anomalies are extended in directions approximately radial to the center of the Imbrium basin. This alignment suggests that Imbrium basin ejecta materials (lying in many cases beneath the visible mare surface) are the sources of the nearside anomalies. If so, then the albedo markings associated with the stronger Reiner Gamma anomalies may be consistent with a model involving magnetic shielding of freshly exposed mare materials from the solar wind ion bombardment. Two regions of extensive magnetic anomalies are mapped in regions centered on the Ingenii basin on the south central farside and near the crater Gerasimovic on the southeastern farside. These regions are approximately antipodal to the Imbrium and Crisium basins, respectively. The Imbrium antipode anomaly group is the most areally extensive on the Moon, while the largest anomaly in the Crisium antipode group is the strongest detected by the Lunar Prospector magnetometer. A consideration of the expected antipodal effects of basin-forming impacts as well as a combination of sample data and orbital measurements on the nearside leads to the conclusion that the most probable sources of magnetic anomalies in these two regions are ejecta materials from the respective impacts. In both regions the strongest individual anomalies correlate with swirl-like albedo markings of the Reiner Gamma class visible on available orbital photography. ¿ 2001 American Geophysical Union