A review of the models of near-Earth object impact cratering on Earth
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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。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.
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Key words:
- impact crater /
- hypervelocity impact /
- point source model /
- scaling /
- coupling parameter
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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
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 $ v \text{＞} $5 km/s 
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表 2 强度和重力机理控制下成坑变量相似律
Table 2. Summary of cratering variables scaling in strength and gravity regimes
成坑结果 一般形式相似 点源，强度区间(假设$ 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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