Crustal density and global gravitational field estimation of the Moon from GRAIL and LOLA satellite data

We employ Newton's integral in the spectral domain to solve two geodetic/geophysical tasks for the Moon. Firstly, we determine 3D bulk density distribution within the lunar crust (inverse problem). For this purpose, we develop a linear mathematical model that parameterises the laterally variable density component by surface spherical harmonics. We exploit GL1500E GRAIL gravitational field model and LOLA topography model to determine bulk density in three types of function: 1) constant, 2) laterally variable, and 3) 3D spatially variable (assuming a linear change in the radial direction). Secondly, we calculate lunar gravitational field models inferred by these three crustal compositions (forward problem) up to spherical harmonic degree 2519 corresponding to a spatial resolution of similar to 2.2 km at the lunar equator. Efficacy of these models is assessed with respect to the GRAIL Level 2 gravitational field models. Our spatially variable crustal model represents the best fit globally and also locally in highland areas. We also test the performance of GRAIL models, recent and independent forward models, and our new models against Level 1B GRAIL satellite-to-satellite tracking data focusing on evaluation beyond Level 2 data (i.e., spherical harmonic degrees greater than 650). These medium- and high-frequency signals from our models correlate with the Level 1B observations the best among all global gravitational field models tested. Our high resolution geopotential model with the optimized 3D crustal density variation should be an asset to future lunar lander navigation and geophysical exploration.