Integral inversion of GRAIL inter-satellite gravitational accelerations for regional recovery of the lunar gravitational field

Abstract

We present an integral-based approach for high-resolution regional recovery of the gravitational field in this article. We derive rigorous remove-compute-restore integral estimators relating the line-of-sight gravitational acceleration to an arbitrary order radial derivative of the gravitational potential. The integral estimators are composed of three terms, i.e., the truncated integration, the low-frequency line-of-sight gravitational acceleration, and the high-frequency truncation error (effect of the distant zones). We test the accuracy of the integral transformations and of the integral estimators in a closed-loop simulation over the Montes Jura region on the nearside of the Moon. In this way, we determine optimal sizes of integration radii and grid discretisation. In addition, we investigate the performance of the regional integral inversion with synthetic and realistic GRAIL observations. We demonstrate that the regional inversion results of the disturbing gravitational potential and its first order radial derivative in the Montes Jura mountain range are less contaminated by high-frequency noise than the global spherical harmonic models.

Antarctic Time-Variable Regional Gravity Field Model Derived from Satellite Line-of-Sight Gravity Differences and Spherical Cap Harmonic Analysis

“…(16) in which b θ , b λ , and b r are the components of b SCH A in the SCHA coordinate system. Considering Equations ( 14)-( 16) and the LOS gravitational differential operator, the following equation is established [42].…”

“…Equation ( 18) can be solved by the conventional least-square inversion. Since the local gravity field modelling is often an ill-posed problem characterized by the instability of the normal equation matrix, some regularization methods should be used to tackle the ill-conditioning nature of the normal equations [42]. In this case the solution is sought in such a way that the following objective function is minimized.…”

Patched Local Lunar Gravity Solutions Using GRAIL Data

“…GRAIL KBRR data are ideally suited for estimating local parameters: each KBRR measurement is approximately directly proportional to the difference in gravity potential at the two satellite locations, making them well-suited to estimate local parameters (Rowlands et al, 2005). Several analyses have thus used GRAIL data for regional gravity field estimation (e.g., Han, 2013;Han et al, 2014;Šprlák et al, 2020). In Goossens et al (2014), we utilized this and produced a local map of gravity at the south pole of the Moon using GRAIL extended mission data.…”