Imbrian-aged basalt ponds, located on the floor of South Pole-Aitken (SPA) basin, are used to provide constraints on the composition and evolution of the far side lunar mantle. We use forward modeling of the Lunar Prospector Gamma Ray Spectrometer thorium data, to suggest that at least five different and distinct portions of the far side lunar mantle contain little or no thorium as of the Imbrian Period. We also use spatial correlations between local thorium enhancements and nonmare material on top of the basalt ponds to support previous assertions that lower crustal materials exposed in SPA basin have elevated thorium abundances, consistent with noritic to gabbronoritic lithologies. We suggest that the lower crust on the far side of the Moon experienced multiple intrusions of thorium-rich basaltic magmas, prior to the formation of SPA basin. The fact that many of the ponds on the lunar far side have elevated titanium abundances indicates that the far side of the Moon experienced extensive fractional crystallization that likely led to the formation of a KREEP-like component. However, because the Imbrian-aged basalts contain no signs of elevated thorium, we propose that the SPA impact event triggered the transport of a KREEP-like component from the lunar far side and concentrated it on the nearside of the Moon. Because of the correlation between basaltic ponds and basins within SPA, we suggest that Imbrian-aged basaltic volcanism on the far side of the Moon was driven by basin-induced decompressional melting.