= Solution
The positive centers in the supplied maps are examples of lunar <mascons>, especially associated with large impact basins. An empty excavation by itself removes mass and would not explain a positive central anomaly. Basin formation can thin the low-density lunar <crust> and raise denser <lunar mantle> beneath the floor; impact melting, collapse and later cooling can also create dense material and lock in a mass excess. Where a basin was later flooded, dense mare <basalt> adds another contribution. Mare infill is therefore one possible contributor, not a necessary explanation of every <mascon>.<NASA's GRAIL Mission Solves Mystery of Moon's Surface Gravity by National Aeronautics and Space Administration>[Mission-team account of impact excavation, collapse, cooling and the central mass excess, 30 May 2013]{ref}
The difference between the maps is the modeled topographic contribution. On a common reference surface, write schematically
$$
\Delta g_{\rm FA}=g_{\rm topo}+g_{\rm internal},\qquad
\Delta g_{\rm B}=\Delta g_{\rm FA}-g_{\rm topo}.
$$
The <free-air gravity anomaly> retains relief-related attraction. Rims, excavated floors and central peaks therefore contribute fine structure. The <Bouguer gravity anomaly> removes the attraction predicted from the measured topography at an assumed crustal <density>, making internal density and interface structure more apparent. A low basin floor has a negative topographic contribution; subtracting it can enhance an underlying positive central anomaly. Removing a positive rim contribution can weaken a rim high. The supplied lower map is correspondingly smoother at short wavelengths and shows prominent residual basin centers and surrounding rings. This is a change of gravity reduction, not a physical change of the craters.<GRGM900C: A degree 900 lunar gravity model from GRAIL primary and extended mission data by Frank G. Lemoine and others>[Sections 4.2–4.3, gravity predicted from topography and its subtraction to obtain Bouguer gravity]{ref}
\Image[/past-exam-of-the-plate-tectonics-course-of-the-university-of-oxford/2022-lunar-mascon-structure.png]
{title=Original schematic showing how dense fill and mantle uplift can outweigh an excavated basin's missing surface mass; illustrative curves are not GRAIL measurements}
For scale, a <Bouguer slab> approximation gives $\Delta g\simeq2\pi G\Delta\rho\,d$. A $5$ km layer with <geophysical density contrast> $300\,\mathrm{kg\,m^{-3}}$ produces about $63$ mGal above an ideal infinite slab. Actual basin geometry, burial, porosity and mantle uplift require a finite three-dimensional model. Smaller craters can have central lows, damaged porous interiors or more complex rings; \b[the maps do not imply that every crater has a positive anomaly or that positive anomalies measure basalt thickness uniquely].
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