近地小天体对地撞击成坑模型研究进展

刘文近; 张庆明; 马晓荷; 龙仁荣; 任健康; 龚自正; 武强; 任思远

doi:10.11883/bzycj-2021-0255

近地小天体对地撞击成坑模型研究进展

doi: 10.11883/bzycj-2021-0255

1.
北京理工大学爆炸科学与技术国家重点实验室，北京 100081
2.
北京卫星环境工程研究所，北京 100094

基金项目: 民用航天预研项目（D020304）

详细信息

作者简介:
刘文近（1993－　），男，博士研究生，lwj931@163.com

通讯作者:
张庆明（1963－　），男，教授，博士生导师，qmzhang@bit.edu.cn

中图分类号: O383；O303
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- 被引次数: 0
出版历程
- 收稿日期: 2021-06-28
- 修回日期: 2021-08-24
- 网络出版日期: 2021-10-28
- 刊出日期: 2021-12-05

A review of the models of near-Earth object impact cratering on Earth

1.
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China
2.
Beijing Institute of Spacecraft Environment Engineering, Beijing 100094, China

摘要

摘要: 近地小天体对地撞击成坑是行星研究的前沿问题之一。本文中介绍了陨石坑成坑过程与类型、实验室模拟成坑现象和陨石坑成坑模型律，分析了近地小天体对地撞击成坑机理和点源模型的不足，指出了近地小天体对地撞击成坑未来研究的发展趋势。
- 陨石坑 /
- 超高速碰撞 /
- 点源模型 /
- 相似律 /
- 耦合参数
Abstract: Near-Earth object (NEO) impact cratering is one of the frontier themes in planetary research. The cratering process and types, laboratory impact cratering phenomena, and cratering scaling are introduced. The hypervelocity impact-cratering process is conventionally divided into three successive stages: contact and compression, excavation, and modification. When large impact craters are formed in geological materials, shearing is the main deformation mode. At small scales, cratering in brittle materials is dominated by surface spalling; much of the crater volume consists of a wide, flat spall zone. According to the morphological characteristics of impact craters, impact craters are generally divided into two groups: simple and complex craters. The cratering mechanism of NEO impact cratering and the deficiency of the point -source model are analyzed. The cratering mechanism can be divided into strength regime and gravity regime. In the strength regime, the cratering results are controlled by strength, and in the gravity regime, the cratering results are dominated by gravity. Crater scaling laws have been established based on dimensional analysis, point-source approximation and the results of experimental and numerical impact. The scaling law is a specific power rate form, which describes well the scaling of crater size, ejecta, and crater growth. But the scaling law of the point-source model is not applicable to the experimental phenomena in several impactor radii. The suggestions for future research of NEO impact cratering are pointed out: (1) scaling where the point-source hypothesis is not applicable; (2) the effect of melting, gasification, atmosphere and temperature on the cratering process; (3) the scaling law and model of oblique impact; (4) momentum enhancement effect of impact; (5) experimental and numerical methods to simulate the formation of impact craters.
- impact crater /
- hypervelocity impact /
- point source model /
- scaling /
- coupling parameter

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图 1 地球撞击坑数据库世界地图

Figure 1. Earth impact cratering database world map

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图 2 简单坑和复杂坑形成过程的示意图^{[12, 19]}

Figure 2. Series of formation of simple and complex craters^{[12, 19]}

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图 3 简单的陨石坑^[12]

Figure 3. Simple impact crater^[12]

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图 4 复杂的陨石坑^[19]

Figure 4. Complex impact craters^[19]

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图 5 波音公司600g土工离心机^[35]

Figure 5. The Boeing 600g geotechnical centrifuge^[35]

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图 6 成坑表面压力与时间曲线^[42]

Figure 6. The crater surface pressure versus time ^[42]

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图 7 钢弹丸以4.8 km/s撞击干砂岩成坑过程中抛射物的演化^[45]

Figure 7. Typical evolution of ejecta at different times after a steel projectile impacting dry sandstone at 4.8 km /s ^[45]

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图 8 成坑形状与撞击速度的关系^[46]

Figure 8. The relationship between crater shape and impact velocity^[46]

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图 9 典型的半球形金属坑和剖面图^[47]

Figure 9. Typical hemispherical metal crater and profile^[47]

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图 10 岩石类陨石坑^{[48, 50]}

Figure 10. Rocky impact crater^{[48, 50]}

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图 11 不同实验拟合的经验公式曲线

Figure 11. Empirical formula curves fitted by different experiments

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图 12 成坑效率 ${\varPi }_{V}$ 与 ${\varPi }_{2}$ 大小的关系示意图^[53]

Figure 12. Schematic illustration of cratering efficiency ${\varPi }_{V}$ depends on ${\varPi }_{2}$ ^[53]

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表 1 公式(11)中参数

Table 1. The parameters value of equation (11)

m	n	v^*	注释	来源
2/3	2/3	$v/{c}_{{\rm{t}}}$		文献 [62-63]
1/2	2/3	$v/{c}_{{\rm{t}}}$		文献 [64]
1/3	0.58	$v/{c}_{{\rm{t}}}$		文献 [65]
2/3	2/3	$\sqrt{{\rho }_{\mathrm{t}}{v}^{2}/{Y}_{\mathrm{t}}}$		文献 [47, 66-67]
1/3	2/3	$\sqrt{{\rho }_{\mathrm{t}}{v}^{2}/{Y}_{\mathrm{t}}}$		文献 [68]
0.725	2/3	$\sqrt{{\rho }_{\mathrm{t}}{v}^{2}/{Y}_{\mathrm{t}}}$		文献 [69]
0.523	0.3545	$\sqrt{{\rho }_{\mathrm{t}}{v}^{2}/{Y}_{\mathrm{t}}}$		文献 [55]
0.448	0.563	$\sqrt{{\rho }_{\mathrm{t}}{v}^{2}/{Y}_{\mathrm{t}}}$		文献 [44]
2/3	2/3	$\sqrt{{\rho }_{\mathrm{t}}{v}^{2}/{H}_{{\rm{B}}}}$	${H}_{{\rm{B}}}$ 是布氏硬度	文献 [70]
0.62	0.48	$\sqrt{{\rho }_{\mathrm{t}}{v}^{2}/{H}_{{\rm{B}}}}$	2.6 km/s $\text{＜}v \text{≤}$ 5 km/s	文献 [71]
0.5	0.68	$\sqrt{{\rho }_{\mathrm{t}}{v}^{2}/{H}_{{\rm{B}}}}$	$v \text{＞}$ 5 km/s	文献 [71]

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表 2 强度和重力机理控制下成坑变量相似律

Table 2. Summary of cratering variables scaling in strength and gravity regimes

成坑结果	一般形式相似	点源，强度区间(假设 $Y\gg \rho ga$ )	点源，重力区间(假设 $\rho ga\gg Y$ )
体积 $V$	$\dfrac{\rho V}{m}=f\left(\dfrac{ga}{{U}^{2}},\dfrac{Y}{\rho {U}^{2}}\right)$	$V{\propto \dfrac{m}{\rho }\left(\dfrac{Y}{\rho {U}^{2} }\right)}^{-\frac{3\mu }{2} }{\left(\dfrac{\rho }{\delta }\right)}^{1-3\nu +\frac{3\mu }{2} }$	$V\propto \dfrac{m}{\rho }{\left(\dfrac{ga}{ {U}^{2} }\right)}^{ \frac{-3\mu }{2+\mu } }{\left(\dfrac{\rho }{\delta }\right)}^{\frac{2+\mu -6\nu }{2+\mu } }$
半径R	$R{\left(\dfrac{\rho }{m}\right)}^{{1}/{3} }=f\left(\dfrac{ga}{ {U}^{2} },\dfrac{Y}{\rho {U}^{2} }\right)$	$R{ {\left(\dfrac{\rho }{m}\right)}^{ \frac{1}{3} }\propto \left(\dfrac{Y}{\rho {U}^{2} }\right)}^{-\frac{\mu }{2} }{\left(\dfrac{\rho }{\delta }\right)}^{ \frac{1}{3}-\nu +\frac{\mu }{2} }$	$R{\left(\dfrac{\rho }{m}\right)}^{\frac {1}{3} }\propto {\left(\dfrac{ga}{ {U}^{2} }\right)}^{\frac {-\mu }{2+\mu } }{\left(\dfrac{\rho }{\delta }\right)}^{\frac{2+\mu -6\nu }{3\left(2+\mu \right)} }$
深度 $h$	$h{\left(\dfrac{\rho }{m}\right)}^{{1}/{3} }=f\left(\dfrac{ga}{ {U}^{2} },\dfrac{Y}{\rho {U}^{2} }\right)$	$h{ {\left(\dfrac{\rho }{m}\right)}^{ \frac{1}{3} }\propto \left(\dfrac{Y}{\rho {U}^{2} }\right)}^{-\frac{\mu }{2} }{\left(\dfrac{\rho }{\delta }\right)}^{ \frac{1}{3}-\nu +\frac{\mu }{2} }$	$h{\left(\dfrac{\rho }{m}\right)}^{ \frac{1}{3} }\propto {\left(\dfrac{ga}{ {U}^{2} }\right)}^{ \frac{-\mu }{2+\mu } }{\left(\dfrac{\rho }{\delta }\right)}^{\frac{2+\mu -6\nu }{3\left(2+\mu \right)} }$

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表 3 各种地质材料地质材料耦合参数指数和成坑体积相似律^[53]

Table 3. Coupling parameter exponent of various geological materials and scaling law of crater volume ^[53]

材料	相似指数 $\alpha$	相似指数 $\ \mu$	${K}_{1}$	$\overline{Y}/{\rm{MPa}}$	强度区间¹⁾	重力区间¹⁾	强度向重力机理转换的冲击器直径/m²⁾
砂	0.51	0.41	0.24	0	−	$V=0.14{m}^{0.83}{g}^{-0.51}{U}^{1.02}$	接近 0
干土	0.51	0.41	0.24	0.18	$V=0.04m{U}^{1.23}$	$V=0.14{m}^{0.83}{g}^{-0.51}{U}^{1.02}$	0.2
湿土	0.65	0.55	0.20	0.14	$V=0.05m{U}^{1.65}$	$V=0.60{m}^{0.783}{g}^{-0.65}{U}^{1.3}$	1.2
水	0.648	0.55	2.30	0	−	$V=13.0{m}^{0.783}{g}^{-0.65}{U}^{1.3}$	接近 0
软岩	0.65	0.55	0.20	7.6	$V=0.009m{U}^{1.65}$	$V=0.48{m}^{0.783}{g}^{-0.65}{U}^{1.3}$	11
硬岩	0.60	0.55	0.20	18	$V=0.005m{U}^{1.65}$	$V=0.48{m}^{0.783}{g}^{-0.65}{U}^{1.3}$	32
1) 弹丸的质量 $m$ 的单位是kg，速度 $U$ 的单位是km/s，成坑体积 $V$ 的单位是m³; 2) 地球加速度下10 km/s冲击。

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参考文献(78)

[1]	MARUYAMA S, EBISUZAKI T. Origin of the Earth: A proposal of new model called ABEL [J]. Geoscience Frontiers, 2017, 8(2): 253–274. DOI: 10.1016/j.gsf.2016.10.005.
[2]	PELTON J N, ALLAHDADI F. Handbook of cosmic hazards and planetary defense [M]. London: Springer, 2015: 5−13.
[3]	ALVAREZ W. Comparing the evidence relevant to impact and flood basalt at times of major mass extinctions [J]. Astrobiology, 2003, 3(1): 153–161. DOI: 10.1089/153110703321632480.
[4]	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.
[5]	SCHULTE P, ALEGRET L, ARENILLAS I, et al. The Chicxulub asteroid impact and mass extinction at the Cretaceous-Paleogene boundary [J]. Science, 2010, 327(5970): 1214–1218. DOI: 10.1126/science.1177265.
[6]	HESTROFFER D, SÁNCHEZ P, STARON L, et al. Small solar system bodies as granular media [J]. The Astronomy and Astrophysics Review, 2019, 27(1): 6. DOI: 10.1007/s00159-019-0117-5.
[7]	柳森, 党雷宁, 赵君尧, 等. 小行星撞击地球的超高速问题 [J]. 力学学报, 2018, 50(6): 1311–1327. DOI: 10.6052/0459-1879-18-313. LIU S, DANG L N, ZHAO J Y, et al. Hypervelocity issues of earth impact by asteroids [J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1311–1327. DOI: 10.6052/0459-1879-18-313.
[8]	SHOEMAKER E M, WEISSMAN P R, SHOEMAKER C S. The flux of periodic comets near Earth [M]. Arizona: University of Arizona Press, 1994: 313−335.
[9]	BLAND P A, ARTEMIEVA N A. Efficient disruption of small asteroids by Earth’s atmosphere [J]. Nature, 2003, 424(6946): 288–291. DOI: 10.1038/nature01757.
[10]	WANG X Y, LUO L, GUO H D, et al. Cratering process and morphological features of the Xiuyan impact crater in Northeast China [J]. Science China Earth Sciences, 2013, 56(10): 1629–1638. DOI: 10.1007/s11430-013-4695-1.
[11]	陈鸣, 谢先德, 肖万生, 等. 依兰陨石坑: 我国东北部一个新发现的撞击构造 [J]. 科学通报, 2020, 65(10): 948–954. DOI: 10.1360/TB-2019-0704. CHEN M, XIE X D, XIAO W S, et al. Yilan crater, a newly identified impact structure in northeast China [J]. China Science Bulletin, 2020, 65(10): 948–954. DOI: 10.1360/TB-2019-0704.
[12]	OSINSKI G R, PIERAZZO E. Impact cratering: processes and products [M]. Chichester: John Wiley & Sons, 2013.
[13]	GRIEVE R A F, THERRIAULT A M. Observations at terrestrial impact structures: Their utility in constraining crater formation [J]. Meteoritics & Planetary Science, 2004, 39(2): 199–216. DOI: 10.1111/j.1945-5100.2004.tb00336.x.
[14]	DYPVIK H, PLADO J, HEINBERG C, et al. Impact structures and events: a Nordic perspective [J]. Episodes, 2008, 31(1): 107–114. DOI: 10.18814/epiiugs/2008/v31i1/015.
[15]	PLADO J. Meteorite impact craters and possibly impact-related structures in Estonia [J]. Meteoritics & Planetary Science, 2012, 47(10): 1590–1605. DOI: 10.1111/j.1945-5100.2012.01422.x.
[16]	GAULT D E, QUAIDE W L, OBERBECK V R. Impact cratering mechanics and structures [M]//FRENCH B M, SHORT N M. Shock Metamorphism of Natural Materials. Mono Book Corporation, 1968: 23−24.
[17]	MELOSH H J. Impact cratering: a geologic process [M]. New York: Oxford University Press, 1989.
[18]	COLLINS G S, MELOSH H J, OSINSKI G R. The impact-cratering process [J]. Elements, 2012, 8(1): 25–30. DOI: 10.2113/gselements.8.1.25.
[19]	OSINSKI G R, TORNABENE L L, GRIEVE R A F. Impact ejecta emplacement on terrestrial planets [J]. Earth and Planetary Science Letters, 2011, 310(3−4): 167–181. DOI: 10.1016/j.jpgl.2011.08.012.
[20]	KIEFFER S W, SIMONDS C H. The role of volatiles and lithology in the impact cratering process [J]. Reviews of Geophysics, 1980, 18(1): 143–181. DOI: 10.1029/RG018i001p00143.
[21]	O’KEEFE J D, AHRENS T J. Cometary and meteorite swarm impact on planetary surfaces [J]. Journal of Geophysical Research: Solid Earth, 1982, 87(B8): 6668–6680. DOI: 10.1029/JB087iB08p06668.
[22]	PIERAZZO E, MELOSH H J. Melt production in oblique impacts [J]. Icarus, 2000, 145(1): 252–261. DOI: 10.1006/icar.1999.6332.
[23]	AHRENS T J, O’KEEFE J D. Shock melting and vaporization of Lunar rocks and minerals [J]. The Moon, 1972, 4(41): 214–249. DOI: 10.1007/bf00562927.
[24]	DENCE M R. The extraterrestrial origin of Canadian craters [J]. Annals of the New York Academy of Sciences, 1965, 123(2): 941–969. DOI: 10.1111/j.1749-6632.1965.tb20411.x.
[25]	TURTLE E P, PIERAZZO E, COLLINS G S, et al. Impact structures: what does crater diameter mean? [M]. Portland: The Geological Society of America, 2005: 1−24. DOI: 10.1130/0-8137-2384-1.1.
[26]	MELOSH H J, IVANOV B A. Impact crater collapse [J]. Annual Review of Earth and Planetary Sciences, 1999, 27(1): 385–415. DOI: 10.1146/annurev.earth.27.1.385.
[27]	PIKE R J. Control of crater morphology by gravity and target type: Mars, Earth, Moon. [C]// 11th Lunar and Planetary Science Conference. New York, USA: Pergamon Press, 1980.
[28]	PIKE R J. Size-dependence in the shape of fresh impact craters on the moon [M]. New York, USA: Pergamon Press, 1977: 489−509.
[29]	PILKINGTON M, GRIEVE R A F. The geophysical signature of terrestrial impact craters [J]. Reviews of Geophysics, 1992, 30(2): 161–181. DOI: 10.1029/92RG00192.
[30]	OSINSKI G R, BUNCH T E, FLEMMING R L, et al. Impact melt- and projectile-bearing ejecta at Barringer Crater, Arizona [J]. Earth and Planetary Science Letters, 2015, 432: 283–292. DOI: 10.1016/j.jpgl.2015.10.021.
[31]	GRIEVE R A F, GARVIN J B. A geometric model for excavation and modification at terrestrial simple impact craters [J]. Journal of Geophysical Research: Solid Earth, 1984, 89(B13): 11561–11572. DOI: 10.1029/JB089iB13p11561.
[32]	TREDOUX M, HART R J, CARLSON R W, et al. Ultramafic rocks at the center of the Vredefort structure: further evidence for the crust on edge model [J]. Geology, 1999, 27(10): 923–926.
[33]	OSINSKI G R, LEE P, SPRAY J G, et al. Geological overview and cratering model for the Haughton impact structure, Devon Island, Canadian High Arctic [J]. Meteoritics & Planetary Science, 2005, 40(12): 1759–1776. DOI: 10.1111/j.1945-5100.2005.tb00145.x.
[34]	CLARKE J, KNIGHTLY P, RUPERT S. Melt-water formed dark streaks on slopes of Haughton crater as possible Mars analogues [J]. International Journal of Astrobiology, 2019, 18: 518–526. DOI: 10.1017/S1473550418000526.
[35]	HOUSEN K R, SWEET W J, HOLSAPPLE K A. Impacts into porous asteroids [J]. Icarus, 2018, 300: 72–96. DOI: 10.1016/j.icarus.2017.08.019.
[36]	STÖFFLER D, GAULT D E, WEDEKIND J, et al. Experimental hypervelocity impact into quartz sand: distribution and shock metamorphism of ejecta [J]. Journal of Geophysical Research, 1975, 80(29): 4062–4077. DOI: 10.1029/jb080i029p04062.
[37]	GAULT D E, WEDEKIND J A. Experimental impact “craters” formed in water: gravity scaling realized [J]. Eos, Transactions-American Geophysical Union, 1978, 59(12): 1121.
[38]	KENKMANN T, DEUTSCH A, THOMA K, et al. The MEMIN research unit: Experimental impact cratering [J]. Meteoritics & Planetary Science, 2013, 48(1): 1–2. DOI: 10.1111/maps.12035.
[39]	EBERT M, HECHT L, DEUTSCH A, et al. Geochemical processes between steel projectiles and silica-rich targets in hypervelocity impact experiments [J]. Geochimica et Cosmochimica Acta, 2014, 133: 257–279. DOI: 10.1016/j.gca.2014.02.034.
[40]	HARRISS K H, BURCHELL M J. Hypervelocity impacts into ice-topped layered targets: Investigating the effects of ice crust thickness and subsurface density on crater morphology [J]. Meteoritics & Planetary Science, 2017, 52(7): 1505–1522. DOI: 10.1111/maps.12913.
[41]	HOLSAPPLE K A, SCHMIDT R M. On the scaling of crater dimensions: 1. explosive processes [J]. Journal of Geophysical Research: Solid Earth, 1980, 85(B12): 7247–7256. DOI: 10.1029/JB085iB12p07247.
[42]	SUN Y H, SHI C C, LIU Z, et al. Theoretical research progress in high-velocity/hypervelocity impact on semi-infinite targets [J]. Shock and Vibration, 2015, 2015: 265321. DOI: 10.1155/2015/265321.
[43]	李卧东, 王明洋, 施存程, 等. 地质类材料超高速撞击相似关系与实验研究综述 [J]. 防护工程, 2015, 37(2): 55–62. LI W D, WANG M Y, SHI C C, et al. Review of similarity laws and scaling experiments research of hypervelocity impact on geological material targets [J]. Protective Engineering, 2015, 37(2): 55–62.
[44]	张庆明, 黄风雷. 超高速碰撞动力学引论 [M]. 北京: 科学出版社, 2000. ZHANG Q M, HUANG F L. An introduction to the dynamics of hypervelocity collisions [M]. Beijing: Science Press, 2000.
[45]	HOERTH T, SCHAEFER F, THOMA K, et al. Hypervelocity impacts on dry and wet sandstone: observations of ejecta dynamics and crater growth [J]. Meteoritics & Planetary Science, 2013, 48(1): 23–32. DOI: 10.1111/maps.12044.
[46]	经福谦. 超高速碰撞现象 [J]. 爆炸与冲击, 1990, 10(3): 279–288. JING F Q. Hypervelocity impact phenomena [J]. Explosion and Shock Waves, 1990, 10(3): 279–288.
[47]	王马法, 周智炫, 黄洁, 等. 镁合金弹丸10 km/s 撞击铝靶成坑特性实验 [J]. 爆炸与冲击, 2021, 41(5): 053302. DOI: 10.11883/bzycj-2020-0129. WANG M F, ZHOU Z X, HUANG J, et al. Experiment on crater characteristics of aluminium targets impacted by magnesium projectiles at velocities of about 10 km/s [J]. Explosion and Shock Waves, 2021, 41(5): 053302. DOI: 10.11883/bzycj-2020-0129.
[48]	POELCHAU M H, KENKMANN T, HOERTH T, et al. Impact cratering experiments into quartzite, sandstone and tuff: The effects of projectile size and target properties on spallation [J]. Icarus, 2014, 242: 211–224. DOI: 10.1016/j.icarus.2014.08.018.
[49]	POELCHAU M H, KENKMANN T, THOMA K, et al. The MEMIN research unit: Scaling impact cratering experiments in porous sandstones [J]. Meteoritics & Planetary Science, 2013, 48(1): 8–22. DOI: 10.1111/maps.12016.
[50]	DUFRESNE A, POELCHAU M H, KENKMANN T, et al. Crater morphology in sandstone targets: The MEMIN impact parameter study [J]. Meteoritics & Planetary Science, 2013, 48(1): 50–70. DOI: 10.1111/maps.12024.
[51]	BUHL E, POELCHAU M H, DRESEN G, et al. Deformation of dry and wet sandstone targets during hypervelocity impact experiments, as revealed from the MEMIN Program [J]. Meteoritics & Planetary Science, 2013, 48(1): 71–86. DOI: 10.1111/j.1945-5100.2012.01431.x.
[52]	HOLSAPPLE K A, HOUSEN K R. Momentum transfer in asteroid impacts. Ⅰ. theory and scaling [J]. Icarus, 2012, 221(2): 875–887. DOI: 10.1016/j.icarus.2012.09.022.
[53]	HOLSAPPLE K A. The scaling of impact processes in planetary sciences [J]. Annual Review of Earth and Planetary Sciences, 1993, 21(1): 333–373. DOI: 10.1146/annurev.ea.21.050193.002001.
[54]	HOLSAPPLE K A, SCHMIDT R M. Point-Source solutions and coupling parameters in cratering mechanics [J]. Journal of Geophysical Research:Solid Earth, 1987, 92(B7): 6350–6376. DOI: 10.1029/JB092iB07p06350.
[55]	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.
[56]	HOUSEN K R, SCHMIDT R M, HOLSAPPLE K A. Crater ejecta scaling laws: Fundamental forms based on dimensional analysis [J]. Journal of Geophysical Research:Solid Earth, 1983, 88(B3): 2485–2499. DOI: 10.1029/JB088iB03p02485.
[57]	KENKMANN T, DEUTSCH A, THOMA K, et al. Experimental impact cratering: A summary of the major results of the MEMIN research unit [J]. Meteoritics & Planetary Science, 2018, 53(8): 1543–1568. DOI: 10.1111/maps.13048.
[58]	HERRMANN W, WILBECK J S. Review of hypervelocity penetration theories [J]. International Journal of Impact Engineering, 1987, 5(1−4): 307–322. DOI: 10.1016/0734-743x(87)90048-0.
[59]	SEDGWICK R T. Numerical techniques for modeling high velocity penetration and perforation processes [J]. 1980, 5: 253−272. DOI: 10.1016/B978-0-444-41928-6.50016-8.
[60]	向家琳. 金属材料可压缩性效应对超高速碰撞中厚靶成坑的影响 [D]. 北京: 中国科学院力学研究所, 1990. XIANG J L. Effect of compressibility of metal materials on craters of thick targets in hypervelocity collision [D]. Beijing: Institute of mechanics, Chinese Academy of Science, 1990.
[61]	罗忠文. 金属材料超高速碰撞的数值模拟 [D]. 北京: 中国科学院力学研究所, 1990. LUO Z W. Numerical simulation of hypervelocity impact of metallic materials [D]. Beijing: Institute of Mechanics, Chinese Academy of Science, 1990.
[62]	CHRISTIANSEN E L. Design and performance equations for advanced meteoroid and debris shields [J]. International Journal of Impact Engineering, 1993, 14(1−4): 145–156. DOI: 10.1016/0734-743x(93)90016-z.
[63]	SUMMERS J L, CHARTERS A C. High speed impact of metal projectiles in targets of various materials [C]// Proceedings of the 3rd Symposium on Hypervelocity Impact. Chicago, USA, 1958.
[64]	BRUCE E P. Review and analysis of high velocity impact data [C]// Proceedings of the 5th Symposium on Hypervelocity Impact. Denver, Colorado, USA: Defense Technical Information Center, 1961.
[65]	WALSH J. On the theory of hypervelocity impact [C]// 7th Symposium on Hypervelocity Impact. Florida, USA, 1964.
[66]	CHRISTMAN D R, GEHRING J W. Analysis of high-velocity projectile penetration mechanics [J]. Journal of Applied Physics, 1966, 37(4): 1579–1587. DOI: 10.1063/1.1708570.
[67]	CHARTERS A C, SUMMERS J L. Some comments on the phenomena of high speed impact [C]// Proceedings of the Dicennial Symposium. White Oak, Maryland, USA: US Naval Ordnance Laboratory, 1959.
[68]	EICHELBERGER R J, Gehring J. W. Effects of Meteoroid Impacts on space vehicles [J]. ARS Journal, 1962, 32(10): 1583–1591. DOI: 10.2514/8.6339.
[69]	YU S B, SUN G C, TAN Q M. Experimental laws of cratering for hypervelocity impacts of spherical projectiles into thick target [J]. International Journal of Impact Engineering, 1994, 15(1): 67–77. DOI: 10.1016/s0734-743x(05)80007-7.
[70]	HERRMANN W, JONES A. Correlation of hypervelocity impact data [C]// The Fifth Symposium on Hypervelocity Impact. Denver, Colorado, USA, 1961.
[71]	周劲松, 甄良, 杨德庄. 几种金属材料在2.6~7 km/s 弹丸撞击下的损伤行为 [J]. 宇航学报, 2000(2): 75–81. DOI: 10.3321/j.issn:1000-1328.2000.02.012. ZHOU J S, ZHEN L, YANG D Z. Damage behaviors of several metal materials under impacts of projectiles with hypervelocities of 2.6−7 km /s [J]. Journal of Astronautics, 2000(2): 75–81. DOI: 10.3321/j.issn:1000-1328.2000.02.012.
[72]	HOLSAPPLE K A, SCHMIDT R M. A material-strength model for apparent crater volume [C]// Proceedings of the 10th Lunar and Planetary Science Conference. 1979.
[73]	HOLSAPPLE K A. Material strength and explosive property effects in cratering and ground shock [C]// The Sixth International Symposium of Blast Simulation. Cahors, France: Centre D’ Etudesde Gramat, 1979.
[74]	HOLSAPPLE K A. The scaling of impact phenomena [J]. International Journal of Impact Engineering, 1987, 5(1−4): 343–355. DOI: 10.1016/0734-743X(87)90051-0.
[75]	SCHMIDT R M, HOLSAPPLE K A. Theory and experiments on centrifuge cratering [J]. Journal of Geophysical Research: Solid Earth, 1980, 85(B1): 235–252. DOI: 10.1029/JB085iB01p00235.
[76]	ÖPIK E J. Meteor impact on solid surface [J]. Irish Astronomical Journal, 1958, 5(1): 14–33.
[77]	SCHMIDT R M, HOUSEN K R. Some recent advances in the scaling of impact and explosion cratering [J]. International Journal of Impact Engineering, 1987, 5(1−4): 543–560. DOI: 10.1016/0734-743X(87)90069-8.
[78]	ASPHAUG E, MOORE J M, MORRISON D, et al. Mechanical and geological effects of impact cratering on Ida [J]. Icarus, 1996, 120(1): 158–184. DOI: 10.1006/icar.1996.0043.