Measuring the tidal deformation of Mercury through co-registration of MLA profiles

We focus on the radial deformation of planet Mercury during its orbital period due to tidal forces exerted by the Sun. Bertone et al. (2021) obtained the first measurement of the tidal Love number h2 of Mercury via least squares minimization of height discrepancies at the cross-overs of the profiles obtained by the Mercury Laser Altimeter (MLA) onboard NASA’s MESSENGER spacecraft. However, height discrepancies at cross-overs, intersection points of profiles, can suffer from significant interpolation errors when the separation of consecutive footprints is large and the underlying terrain is rough. Here, we re-analyze the MLA profiles using new techniques of co-registration analysis that also include a post-correction procedure based on pseudo cross-overs. We have successfully applied these techniques to obtain the spatio-temporal thickness variations of the seasonal deposits on Martian poles (Xiao et al., 2022a, 2022b). Provided that a reference DTM is available, any particular pair of profile segments forms a pseudo cross-over. The height misfit at a pseudo cross-over is assigned as the difference in height corrections in the co-registrations of the profile pair, that form the pseudo cross-over, to the underlying reference DTM. Pseudo cross-overs can have great advantages over real cross-overs: (1) Lateral shifts of the profiles can be naturally compensated and interpolation errors avoided through the co-registration process in forming the height misfits at the pseudo cross-overs; (2) Since the profile segments do not necessarily have to intersect, the available number of "cross-overs" is normally multiplied in number; (3) Furthermore, the profile segment pair forming a pseudo cross-over can be widely separated across the research region, offering "global" constraints on the adjustment. For the uncertainty and sensitivity quantification, we create synthetic MLA observations by adding realistic errors and tidal deformation assuming an a priori tidal h2 and invert for the tidal h2 using the proposed techniques. Our measurement of tidal h2, combined with refined determination of the tidal potential Love number k2 from radio science experiments, will be used to discuss updated bounds of interior structure parameters of Mercury, especially the inner core size, which will improve our understanding of its thermal evolution and magnetic dynamo.

Bertone et al. (2021). JGR: Planets, 126(4), e2020JE006683.
Xiao et al. (2022a). PSS, 214, 105446.
Xiao et al. (2022b). JGR: Planets, 127(10), e2021JE007158.