Abstract 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 ∼ 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.

中文翻译：

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基于GRAIL和LOLA卫星数据的月球地壳密度和全球重力场估计

摘要 我们在谱域中使用牛顿积分来解决月球的两个大地测量/地球物理任务。首先，我们确定月壳内的 3D 体积密度分布（逆问题）。为此，我们开发了一个线性数学模型，该模型通过表面球谐函数对横向可变密度分量进行参数化。我们利用 GL1500E GRAIL 引力场模型和 LOLA 地形模型来确定三种类型函数的体积密度：1) 常数，2) 横向变量，和 3) 3D 空间变量（假设径向线性变化）。其次，我们计算了由这三种地壳成分（前向问题）推断出的月球引力场模型，球谐度为 2519，对应于月球赤道约 2.2 公里的空间分辨率。这些模型的有效性根据 GRAIL 2 级引力场模型进行评估。我们的空间可变地壳模型代表了全球和高原地区局部的最佳拟合。我们还针对 1B 级 GRAIL 卫星到卫星跟踪数据测试了 GRAIL 模型、近期和独立前向模型以及我们的新模型的性能，重点是对 2 级数据以外的评估（即球谐度数大于 650）。这些来自我们模型的中频和高频信号与 1B 级观测相关，是所有测试的全球引力场模型中最好的。我们具有优化的 3D 地壳密度变化的高分辨率位势模型应该是未来月球着陆器导航和地球物理探索的资产。