On the information contents and regularisation of lunar gravity field solutions

Till the present day the recovery of the lunar gravity field from satellite tracking data depends in a crucial way on the level and method of regularisation. With Earth-based tracking only, the spatial data coverage is limited to only slightly more than 50% and the inverse problem remains severely ill-posed. The development of global gravity models suitable for precise orbit modeling as well as geophysical studies therefore requires a significant level of regularisation, limiting the solution power over the far-side where no gravity information is available. Unconstrained solutions, within the framework of global harmonic base functions, are only possible for very low degrees (< 10). Any significant change to this situation is only to be expected when global satellite-to-satellite tracking data of high quality becomes available early in the next decade. Yet, a rigorous analysis of the impact of the chosen method and level of regularisation is lacking. Most gravity models employ a Kaula-type signal smoothness constraint of 15 × 10⁻⁵ /l², which allows a good overall data fit as well as a smooth field over the far-side. Furthermore, a geographical type of constraint has been suggested, where surface accelerations have been introduced in areas of no data coverage. Modern numerical methods, on the other hand, offer direct tools and search mechanisms for the optimal level of regularisation. This paper presents a study of Tikhonov-type regularisation of lunar gravity solutions, with emphasis on the so-called L-curve and quasi-optimality methods for regularisation parameter estimation. Furthermore, new quality measures of lunar gravity solutions are presented, which account for the bias introduced by the regularisation.