3-D inversion of gravity data in spherical coordinates with application to the GRAIL data

Three-dimensional (3-D) inversion of gravity data has been widely used to reconstruct the density distributions of ore bodies, basins, crust, lithosphere, and upper mantle. For global model of 3-D density structures of planetary interior, such as the Earth, the Moon, or Mars, it is necessary to use an inversion algorithm that operates in the spherical coordinates. We develop a 3-D inversion algorithm formulated with specially designed model objective function and radial weighting function in the spherical coordinates. We present regional and global synthetic examples to illustrate the capability of the algorithm. The inverted results show density distribution features consistent with the true models. We also apply the algorithm to a set of lunar Bouguer gravity anomaly derived from the Gravity Recovery and Interior Laboratory (GRAIL) gravity field and obtain a lunar 3-D density distribution. High-density anomalies are clearly identified underlying lunar basins, a wide region of the lateral density heterogeneities that exist beneath the South Pole-Aitken basin are found, and low-density anomalies are distributed beneath the Feldspathic Highlands Terrane on the lunar far-side. The consistency of these results with those obtained independently from other existing methods verifies the newly developed algorithm.