The apparent density distribution of the lunar crust revealed by the spherical coordinate-based mapping method

As an important physical property of the Moon, the lunar crustal density provides evidence for the early evolution process of the Moon, such as the asymmetry of its nearside and farside. The apparent density is the average value of the bulk density at a certain depth. The gravity inversion method is an effective tool of determining the apparent density distribution of the lunar crust. Benefiting from the lunar GRAIL mission's high-precision gravity field models, it is theoretically possible to establish a global high-resolution apparent density model through the gravity inversion. However, there are two major problems, namely, the accuracy and efficiency of the inversion. To solve these problems, different from the admittance methods, we develop a high-precision apparent density mapping method in the spherical coordinate. The improved 2D Gauss-Legende formula and adaptive subdivision algorithm are adopted to calculate the high-precision gravity anomalies of the Tesseroid cells. The parallel algorithm based on OpenMP is involved to improve the calculation efficiency of the global data. And the Cordell iterative algorithm is utilized to derive the apparent density model fitting the real gravity anomalies. The synthetic data tests verify the accuracy and efficiency of our method. Subsequently, we use LOLA topographic data to correct the gravity anomalies obtained from GRAIL and derive the global lunar Bouguer gravity anomalies. The lunar crust thickness model given by Wieczorek et al (2013) is chosen as the bottom interface of the density layer. As a result, we obtain a global high-resolution lunar crust apparent density model with a resolution of about 20 km by the presented mapping method. Our model shows that the apparent density of the lunar crust ranges from about 2200 - 2900 kg/m³ with a mean value of about 2600 kg/m³. The Procellarum KREEP Terrane (PKT) and the large impact basins present higher apparent density, while the Feldspathic Highlands Terrane (FHT) varies around the mean apparent density, and there is a significant variation within the South Pole-Aiken Basin Terrane (SPAT). Our apparent density distribution around the PKT and FHT is significantly relevant to the surface grain density model derived from the current FeO and TiO₂ abundance map. However, our apparent density distribution around the SPAT differs from the surface grain density, suggesting a more complex density structure in this region.