Quantifying the size of impact basins on the Moon and Mars.
Authors: Buoninfante Salvatore , Wieczorek Mark A. , Galluzzi Valentina , Ferranti Luigi , Milano Maurizio , Fedi Maurizio , Palumbo Pasquale 
Published: July 2024

Introduction:The surface and crustal structure of the terrestrial planets in the inner solar system have been influenced by large and energetic impact events. Impact basins have long been recognized and studied through satellite images, topographic data, and gravity data.Peak-ring basins are characterized by a rim crest and an interior peak ring, while multi-ring basins are larger and defined by having additional concentric topographic rings (e.g., [1]). Peak-ring and multiring basins are widespread on the terrestrial planets and can be characterized by their gravity signature. GRAIL data showed that large lunar basins are characterized by a central gravitational anomaly. The size of this gravitational anomaly corresponds closely to the diameter of the inner peak-ring of a basin, while the main ring is approximatively twice the diameter of the peak ring [2]. This allowed to confirm the existence of previously proposed basins, to correctly identify which ring is the main crater rim, and to detect new basins that were not yet identified.In this work we present an improved techniques based on the analysis of gravity and crustal thickness data to estimate the inner ring and rim crest diameters. This technique expands upon the work of [2] and allows us to better identify highly degraded basins. From this analysis, we quantify how lower resolution gravity and crustal thickness datasets (such as for Mars and Mercury) might bias the peak ring and main rim diameter estimates.Methods:In our approach, we first quantify the regional value of the Bouguer gravity anomaly and crustal thickness, which is defined as the average value obtained from azimuthally averaged profiles in the radius range 1.5D to 2D, where D is the crater diameter. The diameter of the Bouguer gravity high, as well as the diameter of the crustal thickness anomaly, were then estimated as the radius where the profiles first intersect the background regional values. After the initial estimate of D was obtained, the procedure was iterated until there was no change in the obtained diameters.We tested this method using Bouguer gravity data for certain lunar peak-ring and multi-ring basins (see table 1 in [2]), by considering the spherical harmonic degree range from 6 to 540 (which removes the effect of the hemispheric asymmetry and the South Pole&#8211;Aitken impact). We then filtered the data using the spherical harmonic degree range 6-49 in order to simulate the lower resolution of the Mars gravity models (e.g., GMM-3, [3],[4]). We then used the same approach using crustal thickness maps derived after GRAIL [5], both for the degree ranges 6-310 and 6-46, to simulate the loss of spatial resolution of Mars. Uncertainty estimates were obtained for the crustal thickness and the Bouguer anomaly diameter by considering the &#177;1&#963; values for the background values in the spatial range of 1.5D to 2D.In Figure 1 we show an example for the Humboldtianum basin, which has a peak-ring diameter of 322 km (5.3&#176; in angular radius). Our method gives a result of 323.1 &#177; 4.4 km from the Bouguer gravity data (using the degree range 6-540), and 316.3 km &#177; 4.9 km from crustal thickness data (using the degree range 6-310).Conclusions and future work:When considering the highest spatial resolution of the Bouguer gravity data and crustal thickness maps, our method properly detects peak-ring or inner ring sizes for lunar basins with main rim diameter greater than 250 km (i.e., for inner ring diameters greater than about 110 km). Nevertheless, when considering filtered versions of these datasets that correspond to the effective spatial resolution of the Mars gravity models, only basins with rim crest diameters greater than about 450 km can be detected with acceptable accuracy. Regardless, these results confirm a roughly one-to-one relationship between the Bouguer anomaly diameter and the inner peak-ring diameter of lunar basins, as well as between crustal thinning size and peak-ring size (Figure 2).We first plan to apply this approach to the Moon in order to reassess the impact basins database of [2]. Following this, we will apply the same methodology to Mars to provide a consistent database of Martian basin sizes. Previous databases for Mars suffer from a difficulty of detection as a result of sedimentary and erosive processes, and also an imperfect understanding of their crustal thickness and gravity signatures that was only elucidated by the GRAIL mission. Future analyses will be applied to the planet Mercury. Results from these analyses will allow one to better constrain the impact rate during the early solar system.Figure 1. Bouguer gravity anomaly (left) and crustal thickness (right) of the Humboldtianum impact basin.&#160; Images of these datasets are shown in the top row, and azimuthally averaged profiles are shown in the bottom row. Black dashed lines represent the peak-ring or inner ring radius (km), while black solid lines denote the main rim radius (km). Regional values of the Bouguer gravity anomaly and crustal thickness are indicated by red dashed lines, while Bouguer anomaly and crustal thinning diameters are shown with red solid lines.&#160;Figure 2. Bouguer anomaly diameter (left) and crustal thinning diameter (right) versus peak-ring or inner-ring diameter (km) for certain lunar peak-ring and multi-ring basins. Basins include Schwarzschild, d&#8217;Alembert, Milne, Bailly, Planck, Schr&#246;dinger, Mendeleev, Birkhoff, Lorentz, Vaporum, Korolev, Moscoviense, Cr&#252;ger-Sirsalis, Grimaldi, Apollo, Hertzsprung, Freundlich-Sharonov, Humboldtianum, Coulomb-Sarton, Humorum, Smythii, Nectaris, Orientale, Crisium, Imbrium. Red dashed lines indicate a 1:1 ratio.&#160;References:[1] Baker D. M. H., et al. (2011). Planet. Space Sci.[2] Neumann G. A., et al. (2015). Sci. Adv.[3] Genova A., et al. (2016). Icarus.[4] Wieczorek M. A., et al. (2022). JGR: Planets.[5] Wieczorek M. A., et al. (2013). Science.&#160;Acknowledgements: We gratefully acknowledge funding from the Italian Space Agency (ASI) under ASI-INAF agreement 2017-47-H.0.