Probing Lateral Density Variations in the Crust from Gravity and Topography: Applications to the Moon and Mars

We present a constraint matrix to be used in the determination of gravity field models from spacecraft tracking data that uses information from topography and that allows for the direct determination of lateral variations in crustal density. Our approach is based on a matrix formulation of Bouguer corrections using a spherical harmonics expansion for density. This formulation also allows to directly determine the spherical harmonics coefficients for density in the crust from a set of gravity coefficients. We validate this by comparison with an approach using localization and show that both methods result in comparable density maps. We then apply the constraint matrix on a test case using lunar data from before the Gravity Recovery and Interior Laboratory (GRAIL) mission, and compare this with results from GRAIL, showing that we can obtain density results similar to those from GRAIL data. We also apply this constraint to the determination of the gravity field of Mars. While our results for Mars tentatively suggest a hemispherical density contrast separated by the north-south dichotomy, the resolution of Martian gravity is currently too low to robustly determine large-scale density variations.