基于有限元分析的月球撞击坑初始形态对月表退化作用机制研究*

doi:10.7523/j.ucas.2026.017

摘要/Abstract

摘要： 月球表面缺乏大气和水蚀作用,是撞击坑演化研究的理想场所。基于地形扩散理论,本研究构建一维轴对称理想模型与1.5 m高分辨率数字高程模型约束的二维模型,分析初始几何参数对撞击坑形貌退化的动力学控制机制。以直径800 m撞击坑为例,建立水平坑底、尖锐坑缘及宽缓坑缘三种剖面,量化3 Ga演化周期内形变特征：水平坑底模型沉降量最大值达88.7 m,尖锐坑缘外扩最快,宽缓坑缘退化最慢。二维模拟揭示其经历边缘钝化、物质迁移与坑底堆积过程,最大撞击坑3 Ga后坑深减少50 m。模型维度对比显示,一维与二维模型在前200 Myr形态参数一致,200 Myr后受横向扩散主导的剥蚀-堆积耦合机制影响,二维模型坑深衰减更剧烈。证实直径<200 m撞击坑在3 Ga后完全退化为低起伏地貌,导致撞击坑尺寸-频率分布定年法（CSFD）在古老月面应用时存在计数遗漏风险。本研究通过多维度模型与真实地形验证,为完善月表撞击坑年代学框架及优化月面工程选址提供定量依据。

关键词: 月球撞击坑, 月貌退化, 有限元模拟, 撞击坑定年, 高性能数值模拟

Abstract: The unique environmental features of the lunar surface, characterized by the absence of atmosphere and aqueous erosion, provide an ideal setting for studying crater evolution. Based on topographic diffusion theory, this study constructs 1D axisymmetric ideal models and 2D models constrained by real topography to systematically clarify the dynamic control mechanisms of initial geometric parameters on crater morphological degradation. By establishing 800-meter-diameter crater profiles with three typical initial morphologies: flat crater floor, sharp crater rim, and gently sloped crater rim, we quantitatively characterize their morphometric decay over a 3-billion-year evolutionary cycle. The flat-floor model exhibits maximum cumulative floor subsidence of 88.7 meters, the sharp-rim model shows the highest rim expansion rate, while the gently-sloped-rim model maintains optimal morphological stability. Two-dimensional simulations using a 1.5-meter-resolution digital elevation model (DEM) reveal characteristic processes including rim rounding, mass wasting, and floor deposition, with representative craters displaying up to 50-meter depth reduction after 3 billion years. Comparative model dimensionality analysis demonstrates strong consistency in morphometric parameters between 1D and 2D models during the initial 200 million years. Beyond this period, transverse diffusion-dominated erosion-deposition coupling mechanisms result in more significant crater depth reduction in two-dimensional models compared to their one-dimensional models. Impact craters with diameters below 200 meters completely degrade into low-relief terrain after 3 billion years, introducing omission risks in crater size-frequency distribution (CSFD) chronology for ancient lunar terrains. Through multidimensional modeling and real-terrain validation, this research establishes novel dynamic constraints for refining lunar crater chronological frameworks and optimizing engineering site selection.

Key words: lunar crater, lunar landscape degradation, finite element simulation, crater chronology, high-performance numerical simulation

中图分类号:

穆希瑶, 胡才博, 曾兴国, 石耀霖. 基于有限元分析的月球撞击坑初始形态对月表退化作用机制研究^*[J]. 中国科学院大学学报, DOI: 10.7523/j.ucas.2026.017.

MU Xiyao, HU Caibo, ZENG Xingguo, SHI Yaolin. Mechanisms of initial crater morphology impacting lunar surface degradation: A finite element modeling study[J]. Journal of University of Chinese Academy of Sciences, DOI: 10.7523/j.ucas.2026.017.

参考文献

[1] 姜衍, 徐长仪, 陈凌. 月球撞击坑识别的研究现状与展望[J]. 中国科学: 地球科学, 2024, 54(5): 1411-1435.
[2] Huang Y H, Soderblom J M, Minton D A, et al.Bombardment history of the Moon constrained by crustal porosity[J]. Nature Geoscience, 2022, 15(7): 531-535.
[3] Wang Y R, Wu B, Xue H O, et al. An improved global catalog of lunar impact craters (≥1 km) with 3D morphometric information and updates on global crater analysis[J]. Journal of Geophysical Research: Planets, 2021, 126(9): e2020JE006728. DOI:10.1029/2020JE006728.
[4] 岳宗玉, 史珂, 邸凯昌, 等. 撞击坑研究进展与展望[J]. 中国科学: 地球科学, 2023, 53(11): 2482-2493.
[5] Yang C, Zhao H S, Bruzzone L, et al.Lunar impact crater identification and age estimation with Chang'E data by deep and transfer learning[J]. Nature Communications, 2020, 11(1): 6358. DOI:10.1038/s41467-020-20215-y.
[6] Baker D M H, Head J W, Fassett C I, et al. The transition from complex crater to peak-ring basin on the Moon: New observations from the Lunar Orbiter Laser Altimeter (LOLA) instrument[J]. Icarus, 2011, 214(2): 377-393. DOI:10.1016/j.icarus.2011.05.030.
[7] Collins G S, Melosh H J, Marcus R A.Earth Impact Effects Program: A Web-based computer program for calculating the regional environmental consequences of a meteoroid impact on Earth[J]. Meteoritics & Planetary Science, 2005, 40(6): 817-840. DOI:10.1111/j.1945-5100.2005.tb00157.x.
[8] Sun S J, Yue Z Y, Di K C.Investigation of the depth and diameter relationship of subkilometer-diameter lunar craters[J]. Icarus, 2018, 309: 61-68. DOI:10.1016/j.icarus.2018.02.031.
[9] Wang J T, Kreslavsky M A, Liu J Z, et al. Quantitative characterization of impact crater materials on the Moon: Changes in topographic roughness and thermophysical properties with age[J]. Journal of Geophysical Research: Planets, 2020, 125(10): e2019JE006091. DOI:10.1029/2019JE006091.
[10] Watters T R, Weber R C, Collins G C, et al.Shallow seismic activity and young thrust faults on the Moon[J]. Nature Geoscience, 2019, 12(6): 411-417. DOI:10.1038/s41561-019-0362-2.
[11] Arvidson R E, Boyce J, Chapman C, et al.Standard techniques for presentation and analysis of crater size-frequency data[J]. Icarus, 1979, 37(2): 467-474. DOI:10.1016/0019-1035(79)90009-5.
[12] Hiesinger H, Jaumann R, Neukum G, et al.Ages of mare basalts on the lunar nearside[J]. Journal of Geophysical Research: Planets, 2000, 105(E12): 29239-29275. DOI:10.1029/2000JE001244.
[13] Fassett C I, Beyer R A, Deutsch A N, et al. Topographic Diffusion Revisited: Small Crater Lifetime on the Moon and Implications for Volatile Exploration[J]. Journal of Geophysical Research: Planets, 2022, 127(12): e2022JE007510. DOI: 10.1029/2022JE007510.
[14] 郭弟均, 刘建忠, 张莉, 等. 月球地质年代学研究方法及月面历史划分[J]. 地学前缘, 2014, 21(6): 45-61. DOI: 10.13745/j.esf.2014.06.006.
[15] Fa W Z, Liu T T, Zhu M H, et al.Regolith thickness over Sinus Iridum: Results from morphology and size-frequency distribution of small impact craters[J]. Journal of Geophysical Research: Planets, 2014, 119(8): 1914-1935. DOI:10.1002/2013JE004604.
[16] Neukum G, Ivanov B A, Hartmann W K.Cratering records in the inner solar system in relation to the lunar reference system[J]. Space Science Reviews, 2001, 96(1): 55-86. DOI:10.1023/A:1011989004263.
[17] Cui Z X, Yang Q, Zhang Y Q, et al.A sample of the Moon's far side retrieved by Chang'e-6 contains 2.83-billion-year-old basalt[J]. Science, 2024, 386(6728): 1395-1399. DOI:10.1126/science.adt1093.
[18] Yue Z Y, Di K C, Wan W H, et al.Updated lunar cratering chronology model with the radiometric age of Chang'e-5 samples[J]. Nature Astronomy, 2022, 6(5): 541-545. DOI:10.1038/s41550-022-01604-3.
[19] Wang J, Meng X M, Han X H, et al.18-Months operation of Lunar-based Ultraviolet Telescope: A highly stable photometric performance[J]. Astrophysics and Space Science, 2015, 360(1): 10. DOI:10.1007/s10509-015-2521-2.
[20] Yang Y Z, Lin H L, Liu Y, et al. The effects of viewing geometry on the spectral analysis of lunar regolith as inferred by in situ spectrophotometric measurements of Chang'E-4[J]. Geophysical Research Letters, 2020, 47(8): e2020GL087080. DOI:10.1029/2020GL087080.
[21] Kneissl T, van Gasselt S, Neukum G. Map-projection-independent crater size-frequency determination in GIS environments: New software tool for ArcGIS[J]. Planetary and Space Science, 2011, 59(11/12): 1243-1254. DOI:10.1016/j.pss.2010.03.015.
[22] Liu J N, Yue Z Y, Di K C, et al.New lunar crater production function based on high-resolution images[J]. Remote Sensing, 2023, 15(9): 2421. DOI:10.3390/rs15092421.
[23] Di K C, Li W, Yue Z Y, et al.A machine learning approach to crater detection from topographic data[J]. Advances in Space Research, 2014, 54(11): 2419-2429. DOI:10.1016/j.asr.2014.08.018.
[24] Settle M, Head J W.Radial variation of lunar crater rim topography[J]. Icarus, 1977, 31(1): 123-135. DOI:10.1016/0019-1035(77)90075-6.
[25] Mahanti P, Robinson M S, Humm D C, et al.A standardized approach for quantitative characterization of impact crater topography[J]. Icarus, 2014, 241: 114-129. DOI:10.1016/j.icarus.2014.06.023.
[26] Yang X, Fa W Z, Du J, et al. Effect of topographic degradation on small lunar craters: Implications for regolith thickness estimation[J]. Geophysical Research Letters, 2021, 48(22): e2021GL095537. DOI:10.1029/2021GL095537.
[27] Ross H P.A simplified mathematical model for lunar crater erosion[J]. Journal of Geophysical Research (1896-1977), 1968, 73(4): 1343-1354. DOI:10.1029/JB073i004p01343.
[28] Culling W E H. Analytical theory of erosion[J]. The Journal of Geology, 1960, 68(3): 336-344. DOI:10.1086/626663.
[29] Pike R J.Size-dependence in the shape of fresh impact craters on the Moon[C/OL]//Roddy D J, Pepin R O, Merrill R B, eds. Impact and Explosion Cratering: Planetary and Terrestrial Implications: Proceedings of the Symposium on Planetary Cratering Mechanics, Flagstaff, Arizona, September 13-17, 1976. New York: Pergamon Press, 1977[2026-04-02]. https://ntrs.nasa.gov/citations/19780060140
[30] Wünnemann K, Ivanov B A.Numerical modelling of the impact crater depth-diameter dependence in an acoustically fluidized target[J]. Planetary and Space Science, 2003, 51(13): 831-845. DOI:10.1016/j.pss.2003.08.001.
[31] Fassett C I, Thomson B J.Crater degradation on the lunar maria: Topographic diffusion and the rate of erosion on the Moon[J]. Journal of Geophysical Research: Planets, 2014, 119(10): 2255-2271. DOI:10.1002/2014JE004698.
[32] 李春来, 刘建军, 任鑫, 等. 基于嫦娥二号立体影像的全月高精度地形重建[J]. 武汉大学学报(信息科学版), 2018, 43(4): 485-495. DOI:10.13203/j.whugis20170400.
[33] 张君策. 月球地貌退化过程与月表温度时空演化的数值模拟:对月表环形山定年和热月震机制的启示[D]. 北京: 中国科学院大学, 2024.
[34] Zhao F Y, Zuo W, Li C L.Improvement of lunar surface dating accuracy utilizing crater degradation model: A case study of the Chang'e-5 sampling area[J]. Remote Sensing, 2023, 15(9): 2463. DOI:10.3390/rs15092463.
[35] Stopar J D, Robinson M S, Barnouin O S, et al.Relative depths of simple craters and the nature of the lunar regolith[J]. Icarus, 2017, 298: 34-48. DOI:10.1016/j.icarus.2017.05.022.
[36] Rosenburg M A, Aharonson O, Sari R.Topographic power spectra of cratered terrains: Theory and application to the Moon[J]. Journal of Geophysical Research: Planets, 2015, 120(2): 177-194. DOI:10.1002/2014JE004746.
[37] Courant R, Friedrichs K, Lewy H.Über die partiellen Differenzengleichungen der mathematischen Physik[J]. Mathematische Annalen, 1928, 100(1): 32-74. DOI:10.1007/BF01448839.
[38] Rüsch O, Wöhler C.Degradation of rocks on the Moon: Insights on abrasion from topographic diffusion, LRO/NAC and Apollo images[J]. Icarus, 2022, 384: 115088. DOI:10.1016/j.icarus.2022.115088.
[39] Kring D A. Guidebook to the Geology of Barringer Meteorite Crater, Arizona (a.k.a. Meteor Crater)[M]. 2nd ed. Houston: Lunar and Planetary Institute, 2017. [2026-04-02]. https://www.lpi.usra.edu/publications/books/barringer_crater_guidebook/
[40] Ding C Y, Xiao Z Y, Wu B, et al. Fragments delivered by secondary craters at the Chang'E-4 landing site[J]. Geophysical Research Letters, 2020, 47(7): e2020GL087361. DOI:10.1029/2020GL087361.
[41] Melosh H J.Impact Cratering[M]. Oxford: Oxford University Press, 1989.
[42] Holsapple K A, Schmidt R M.On the scaling of crater dimensions: 2. Impact processes[J]. Journal of Geophysical Research: Solid Earth, 1982, 87(B3): 1849-1870. DOI:10.1029/JB087iB03p01849.
[43] Soderblom L A.A model for small-impact erosion applied to the lunar surface[J]. Journal of Geophysical Research (1896-1977), 1970, 75(14): 2655-2661. DOI:10.1029/JB075i014p02655.

基于有限元分析的月球撞击坑初始形态对月表退化作用机制研究^*

Mechanisms of initial crater morphology impacting lunar surface degradation: A finite element modeling study

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 3

编辑推荐

Metrics

本文评价

访问统计

联系我们

[1]	尹迪, 董培育, 石耀霖. 顾及下地壳拖曳力的川滇地区地表形变有限元数值模拟[J]. 中国科学院大学学报, 2021, 38(1): 1-8.
[2]	李蔚琳, 程惠红, 张怀, 石耀霖. 河西走廊系列盆地构造演化的三维数值模拟[J]. 中国科学院大学学报, 2019, 36(2): 196-207.
[3]	兰姣霞王志甲洪友士. 高能气动喷丸致纯铜细晶化的实验与模拟[J]. 中国科学院大学学报, 2008, 25(2): 172-176.