Spherical Planting Inversion of GRAIL Data

In large-scale potential field data inversion, constructing the kernel matrix is a time-consuming problem with large memory requirements. Therefore, a spherical planting inversion of Gravity Recovery and Interior Laboratory (GRAIL) data is proposed using the L1-norm in conjunction with tesseroids. Spherical planting inversion, however, is strongly dependent on the correct seeds' density contrast, location, and number; otherwise, it can cause mutual intrusion of anomalous sources produced by different seeds. Hence, a weighting function was introduced to limit the influence area of the seeds for yielding robust solutions; moreover, it is challenging to set customized parameters for each seed, especially for the large number of seeds used or complex gravity anomalies data. Hence, we employed the "shape-of-anomaly" data-misfit function in conjunction with a new seed weighting function to improve the spherical planting inversion. The proposed seed weighting function is constructed based on the covariance matrix for given gravity data and can avoid manually setting customized parameters for each seed. The results of synthetic tests and field data show that spherical planting inversion requires less computer memory than traditional inversion. Furthermore, the proposed seed weighting function can effectively limit the seed influence area. The result of spherical planting inversion indicates that the crustal thickness of Mare Crisium is about 0 km because the Crisium impact may have removed all crust from parts of the basin.