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ma=86400 Obliteration of ancient impact basins on the Moon by viscous relaxation | Nature Astronomy
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Obliteration of ancient impact basins on the Moon by viscous relaxation

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Abstract

The widely accepted accretion scenario of planet formation suggests that the Moon experienced a violent bombardment in its early history. The accretion scenario predicts that a total of ~300 basins with sizes greater than 300 km formed throughout its bombardment history; however, only ~40 basins of this size are identified on the Moon. The cause for this notable discrepancy is unknown. Here we investigate the viscous relaxation of impact basins formed within ~150 Myr after the completion of lunar magma ocean (LMO) solidification, as only impacts that happened afterwards could be retained by the crust. We find that, owing to the high temperature of the lower crust, basins formed within ~100 Myr after the LMO solidification could have been sufficiently relaxed by lower crustal inflow to escape detection in gravitational and topographic data. By contrast, basins formed afterwards should have limited relaxation, as the cooler temperature of the lower crust inhibits the inflow. Our results show that, to have ~40 retained basins, the Moon would have had ~300–1,000 basin-forming impacts throughout its history and the LMO would have solidified ~4.3 Gyr ago. The temperature-dependent viscous relaxation of post-LMO basins provides a realistic explanation for the low number of basins observed on the Moon. The substantial relaxation of early basins suggests that terrestrial planets, which experienced crustal cooling after magma ocean solidification, may have suffered far more impacts than the basin records indicate.

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Fig. 1: Temperature and crustal thickness variations with time for a 800-km-diameter basin formed ~50 Ma after tLMO on the lunar nearside and farside.
Fig. 2: Temperature and crustal thickness variations with time for a 800-km-diameter basin formed ~100 Ma after tLMO on the lunar nearside and farside.
Fig. 3: Variations of relaxation factor for the simulated and observed lunar basins as a function of their formation ages.
Fig. 4: Expected number of basins (D > 300 km) estimated from two chronology systems and the relationship between the time of the Moon that started to retain the basins and the time of LMO solidification.
Fig. 5: Post-relaxed crustal thickness variations as a function of distance from the basin centre for the SPA basin with the thin initial crust in the basin interior.

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Data availability

The lunar crustal thickness and topography models used in this study are retrieved from GRAIL crustal thickness archive (https://zenodo.org/records/997347) and the Planetary Data System Geosciences Node (https://pds-geosciences.wustl.edu/missions/lro/lola.htm), respectively. The parameters for the iSALE, Abaqus and CitcosS models are all included in the Supplementary Information. The raw data for figures and Extended Data figures are available via Zenodo at https://doi.org/10.5281/zenodo.13893293 (ref. 120).

Code availability

The iSALE code is distributed on a case-by-case basis to academic users in the impact community, strictly for non-commercial use. Scientists interested in using or developing the iSALE should see https://github.com/isale-code for a description of application requirements. The Abaqus (www.simulia.com) and COMSOL (www.comsol.com) used in this work are commercial software.

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Acknowledgements

We acknowledge the developers of iSALE (https://isale-code.github.io), including G. Collins, K. Wünnemann, T. Davison, B. Ivanov and J. Melosh, and the pySALEPlot visualization package developer, T. Davison. We thank G. Michael and C. Orgel for the discussions of lunar crater ages. M.-H.Z., M.D. and L.X. are supported by the Science and Technology Development Fund of Macau (0064/2022/A2, 0020/2021/A1 and 0012/2023/RIA1) and National Natural Science Foundation of China (12173106 and 12303064).

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Author notes

  1. These authors contributed equally: Meng-Hua Zhu, Min Ding.

Authors and Affiliations

  1. State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau, China

    Meng-Hua Zhu & Luyuan Xu

  2. Department of Earth and Space Sciences, Southern University of Science and Technology, Shenzhen, China

    Min Ding

  3. Institut de Physique du Globe de Paris, Université Paris Cité, CNRS, Paris, France

    Mark Wieczorek

  4. Département Lagrange, University of Nice–Sophia Antipolis, CNRS, Observatoire de la Côte d’Azur, Nice, France

    Alessandro Morbidelli

  5. Department of Earth and Planetary Sciences, University of California at Davis, Davis, CA, USA

    Qing-Zhu Yin

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Contributions

M.-H.Z., A.M., M.D. and M.W. conceived and discussed the idea. M.-H.Z. performed the impact simulations. M.D. performed the thermal evolution modelling and viscous relaxation simulations. M.D., M.-H.Z., M.W. and A.M. discussed the viscous relaxation results. L.X. and M.-H.Z. simulated the topographic diffusion of basin ring structures. M.-H.Z. and Q.-Z.Y. discussed the geochemical evidences for early impacts of the Moon. The manuscript was written by M.-H.Z. and M.D. with detailed reviews and contributions by all authors.

Corresponding author

Correspondence to Meng-Hua Zhu.

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Nature Astronomy thanks Christian Riedel and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Impact-induced crustal structure and temperature anomaly for initial crustal thicknesses (Tc) of 30 km (left) and 40 km (right).

The basin diameters are about 400 (a, b), 800 (c, d), and 1,500 km (e, f) that are generated by vertical impacts with a velocity of 17 km s−1 for impactor diameter of 20, 40, and 80 km, respectively. In each plot, the left panel shows the basin structure, in which the yellow and blue colors represent the crustal and mantle material, respectively; the right panel shows the impact-induced temperature anomaly. These impact-induced structures and temperature anomalies are used in the subsequent modeling of long-term viscous relaxation. The triangles in each plot represent the inner ring (yellow) and rim (orange) of the basin, respectively. The model time is shown in each plot.

Extended Data Fig. 2 Schematic illustration of the thermal conduction model setup and modeled temperature profiles on the Moon’s nearside and farside hemisphere.

a shows the model setups with different Th contents and megaregolith thickness of nearside and farside hemisphere. The crust of the nearside or of the PKT region (dark red) has a thickness of 30 km with Th concentration of 5.5 ppm, covered by an ejecta layer (see refs. 88,89,90,93) with a thickness (hr) of 1 km. The farside crust (light blue) of case 1 has an upper crustal thickness of 30 km with a Th concentration of 0.5 ppm and a lower crustal thickness of 10 km with a Th concentration of 5 ppm, with the top of crust being covered by an ejecta layer with a thickness of 1 km; for case 2, the farside has a Th concentration of 0.5 ppm for the entire crust of 40 km, covered by a megaregolith layer with thickness of 5 km (see refs. 14,101,102,122). In a, the numbers in orange represent the Th content of lower crust and megaregolith thickness for farside crust of case 2. The thermal conductivities of the ejecta/megaregolith layer (kr), crust (kc), and mantle (km) are assumed to be 0.3, 2, and 3 W k−1 m−1, respectively. b shows the modeled temperature profiles of the upper 100 km of the Moon for the nearside at 50 (cyan), 100 (green), and 150 (red) Myr after tLMO. c and d show the modeled temperature profiles of the farside at 50 (cyan), 100 (green), and 150 (red) Myr after tLMO for case 1 and case 2 scenario, respectively. The horizontal dashed line in b, c, and d marks the crust-mantle boundary; the vertical dashed line marks 1,200 K, the critical temperature above which the lower crust may viscously flow; the black solid lines are solidus for the crust and mantle that are used as the initial temperature profiles for our simulations. The gray dashed-dot line in b and c represents the temperature profile of 10 K km−1 used for impact cratering simulations in this work; the blue dashed line in c represents the temperature profile of 50 K km−1 used for the SPA-forming impact simulation in Trowbridge et al.41.

Extended Data Fig. 3 Pre- and post-relaxation temperature and crustal thickness variations for 400 and 1,500 km-diameter basins formed at 50 Myr after tLMO on the lunar nearside and farside.

The crustal thickness (Tc) is assumed to be 30 km for the nearside (left panel) and 40 km for the farside (right panel), respectively. a and b shows the basin with diameter of 400 km while c and d shows the basin with diameter of 1,500 km. In each plot, the left part represents the initial (pre-relaxation) state while the right part represents the post-relaxation state at the modeling time as shown in the corner. The black lines represent the crustal boundaries. The cyan and gray dashed line represents the temperature contour of 1,200 K and 1,450 K, respectively, in which the latter could represent the boundary of melt pool.

Extended Data Fig. 4 Horizontal displacement of the crust material during the post-impact viscous relaxation process for basins (D = 800) formed at 50 Myr after tLMO.

The lower crust has an average thickness of ~10 km with temperature higher than 1,200 K, forming a flow channel. The top panel depicts the post-relaxation crustal structure of the basin with initial crustal thickness of 30 km after ~8 Myr since the impact event and the bottom panel is for the case with initial crustal thickness of 40 km after ~9 Myr since the impact. In each panel, the green profiles represent the initial topographic surface and crust-mantle interface (Moho) from the impact cratering simulations; the black dashed lines represent the post-relaxation topographic surface and crust-mantle interface. The arrow shows the flow direction. The color represents the horizontal displacement of materials from their initial positions, where a negative value represents a displacement towards the basin center and a positive value represents a displacement away from the basin center. The crust annulus, formed by the collapse of central peak during impact cratering process77, disappears after the relaxations for both basins (see Supplementary Movies 3 and 4 for details).

Extended Data Fig. 5 Pre- and post-relaxation temperature and crustal thickness variations for 400 and 1,500 km-diameter basin formed at 100 Myr after tLMO on the lunar nearside and farside.

The crustal thickness (Tc) is assumed to be 30 km and 40 km for the nearside (left panel) and the farside (right panel), respectively. a and b shows the basin with a diameter of 400 km while c and d shows the basin with a diameter of 1,500 km. In each plot, the left part of vertical black line represents the initial (pre-relaxation) state while the right part represents the post-relaxation state at the modeling time as shown in the bottom right corner. The black curves represent the crustal boundaries. The cyan and gray dashed curve represents the temperature contour of 1,200 K and 1,450 K, respectively, with the latter representing the boundary of the melt pool.

Extended Data Fig. 6 Temperature and crustal thickness variations with time for 800 km-diameter basins formed at 150 Myr after tLMO on the lunar nearside and farside.

The figure is similar to Figs. 1 and 2, but for basins formed at 150 Myr after tLMO. The initial temperatures of both the nearside and the farside crusts are all below 1,200 K (cyan line in a). The heated lower crusts from the upwelling of impact-induced melt pools (gray line) are very limited (see b). The crusts in the basin interiors are not fully thickened before their temperatures drop below 1,200 K (cyan line in c).

Extended Data Fig. 7 Pre- and post-relaxation temperature and crustal thickness variations for 400 and 1,500 km-diameter basins formed at 150 Myr after tLMO on the lunar nearside and farside.

The figure is similar to Extended Data Figs. 3 and 5, but for basins formed at 150 Myr after tLMO. a and b shows the basin with a diameter of 400 km while c and d shows the basin with a diameter of 1,500 km. The pre-relaxed temperatures of both the nearside and the farside crusts are all below 1,200 K (cyan line, left part of vertical black line in each plot). The heated lower crusts from the upwelling of impact-induced melt pools (gray line, right part in each plot) are very limited. The crusts in the basin interiors are not fully thickened before their temperatures drop below 1,200 K (cyan line, right part in each plot). Note that for basin with D ~ 1,500 km formed at 150 Myr after tLMO on the nearside, we consider the crust thickness of zero in the basin interior (see c) because such a large impact may not easily form the thick crust within the basin (see refs. 68,69,72).

Extended Data Fig. 8 Initial and post-relaxed crustal structures for basins with different formation times.

Each plot presents the initial (dashed line) and post-relaxation topographies and crust-mantle interface profiles (solid lines) for basins formed 50 (red), 100 (blue), and 150 Myr (green) after tLMO. The numbers at the bottom of each plot report the relaxation factor. The upper panel shows the basins on the nearside (Tc=30 km) while the lower panel shows the basins on the farside (Tc=40 km). The pre-relaxed basin structures (dashed line) are from the impact simulations. a and d show the pre- and post-relaxed structures for basins with a diameter of 400 km, while b and e depict the structures for basins with a diameter of 800 km, and c and f represent the structures for basin with a diameter of 1,500 km. We note that for basin with D ~ 1,500 km formed at 150 Myr after tLMO on the nearside, we consider the crust thickness of zero in the basin interior (see c). The number in bracket at the bottom of c represents the relaxation factor for this case.

Extended Data Fig. 9 Topographic diffusion for basins with different formation times.

The topographic profiles from the young and well-preserved Schrödinger and Orientale basin are used as the initial profiles for basins of 300 km (a) and 800 km (b) in diameter. For D ~ 1,500 km basins, we stretch the topographic profile of Orientale by a factor of ~1.6 in diameter to represent the initial topographic structure (c). Assuming these basins formed 4.30, 4.25, 4.20, and 3.85 Gyr ago, their topographies are modified by subsequent impact events.

Extended Data Fig. 10 Post-relaxed temperature and crustal structure for the SPA basin with thick crust (Tc = 20 km) in the basin interior.

The initial impact-induced crustal structure is from Trowbridge et al.41. a shows the post-relaxed temperature and crustal thickness variations after ~10 Myr of viscous relaxation, in which the cyan curve represents the temperature contour of 1,200 K, and the purple- and black-dashed curves represent the topography and crust-mantle interface, respectively. The triangle represents the rim of the basin (~1,000 km radial distance from the basin center). b presents the crustal thickness variations as a function of the distance from the basin center; the black and blue curves represent the pre- and post-relaxed crustal boundaries in our simulations; the gray curves show the topography and crust-mantle interface variations; the light gray bands represent 1-sigma errors derived from the LOLA DEM Model121 and the crustal thickness model from the GRAIL observations14.

Supplementary information

Supplementary Information

Supplementary Figs. 1–8, Tables 1–3 and captions of Supplementary Movies 1–21.

Supplementary Movie 1

The viscous relaxation simulations for basins D ≈ 400 km formed at 50 Myr after tLMO on the nearside. In the video, the left panel shows the crust (yellow) and mantle (blue) material; the right panel shows the temperature variations; D represents the basin diameter, and Tc represents the pre-impact crustal thickness. The number in the left corner of each snapshot represents the model time.

Supplementary Movie 2

The viscous relaxation simulations for basins D ≈ 400 km formed at 50 Myr after tLMO on the farside. In the video, the left panel shows the crust (yellow) and mantle (blue) material; the right panel shows the temperature variations; D represents the basin diameter, and Tc represents the pre-impact crustal thickness. The number in the left corner of each snapshot represents the model time.

Supplementary Movie 3

Similar to Supplementary Movie 1, but for basin of D ≈ 800 km formed at 50 Myr after tLMO.

Supplementary Movie 4

Similar to Supplementary Movie 2, but for basin of D ≈ 800 km formed at 50 Myr after tLMO.

Supplementary Movie 5

Similar to Supplementary Movie 1, but for basin of D ≈ 1,500 km formed at 50 Myr after tLMO.

Supplementary Movie 6

Similar to Supplementary Movie 2, but for basin of D ≈ 1,500 km formed at 50 Myr after tLMO.

Supplementary Movie 7

The viscous relaxation simulations for basins D ≈ 400 km formed at 100 Myr after tLMO on the nearside. In the video, the left panel shows the crust (yellow) and mantle (blue) material; the right panel shows the temperature variations; D represents the basin diameter, and Tc represents the pre-impact crustal thickness. The number in the left corner of each snapshot represents the model time.

Supplementary Movie 8

The viscous relaxation simulations for basins D ≈ 400 km formed at 100 Myr after tLMO on the farside. In the video, the left panel shows the crust (yellow) and mantle (blue) material; the right panel shows the temperature variations; D represents the basin diameter, and Tc represents the pre-impact crustal thickness. The number in the left corner of each snapshot represents the model time.

Supplementary Movie 9

Similar to Supplementary Movie 7, but for basin of D ≈ 800 km formed at 100 Myr after tLMO.

Supplementary Movie 10

Similar to Supplementary Movie 8, but for basin of D ≈ 800 km formed at 100 Myr after tLMO.

Supplementary Movie 11

Similar to Supplementary Movie 7, but for basin of D ≈ 1,500 km formed at 100 Myr after tLMO.

Supplementary Movie 12

Similar to Supplementary Movie 8, but for basin of D ≈ 1,500 km formed at 100 Myr after tLMO.

Supplementary Movie 13

The viscous relaxation simulations for basins D ≈ 400 km formed at 150 Myr after tLMO on the nearside. In the video, the left panel shows the crust (yellow) and mantle (blue) material; the right panel shows the temperature variations; D represents the basin diameter, and Tc represents the pre-impact crustal thickness. The number in the left corner of each snapshot represents the model time.

Supplementary Movie 14

The viscous relaxation simulations for basins D ≈ 400 km formed at 150 Myr after tLMO on the farside. In the video, the left panel shows the crust (yellow) and mantle (blue) material; the right panel shows the temperature variations; D represents the basin diameter, and Tc represents the pre-impact crustal thickness. The number in the left corner of each snapshot represents the model time.

Supplementary Movie 15

Similar to Supplementary Movie 13, but for basin of D ≈ 800 km formed at 150 Myr after tLMO.

Supplementary Movie 16

Similar to Supplementary Movie 14, but for basin of D ≈ 800 km formed at 150 Myr after tLMO.

Supplementary Movie 17

Similar to Supplementary Movie 13, but for basin of D ≈ 1,500 km formed at 150 Myr after tLMO.

Supplementary Movie 18

Similar to Supplementary Movie 14, but for basin of D ≈ 1,500 km formed at 150 Myr after tLMO.

Supplementary Movie 19

The viscous relaxation simulations for the SPA basin with crust thickness in the basin interior of 0 km.

Supplementary Movie 20

The viscous relaxation simulations for the SPA basin with crust thickness in the basin interior of 10 km.

Supplementary Movie 21

The viscous relaxation simulations for the SPA basin with crust thickness in the basin interior of 20 km.

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Zhu, MH., Ding, M., Wieczorek, M. et al. Obliteration of ancient impact basins on the Moon by viscous relaxation. Nat Astron (2025). https://doi.org/10.1038/s41550-024-02444-z

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