Crater Size-Frequency Distribution Measurements and Age Determination of Sinus Iridum
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摘要: 撞击作用是行星形成和表面重塑的重要地质过程，记录和揭示了行星的演化历史.撞击作用形成的撞击坑可用于研究天体表面地质单元形成的时间.依据内太阳系天体表面的撞击历史，总结了通过对撞击坑的直径和频率分布进行统计，计算天体表面模式年龄的原理和方法.在此基础上，利用美国“月球勘测轨道器(LRO)”广角相机获得的图像，对月球虹湾地区的撞击坑进行了直径-频率分布统计研究，获得其3个主要地质单元的绝对模式年龄分别为3.33 Ga、3.21 Ga和2.60 Ga，有效限定了本区主要地质事件发生的时间.Abstract: Impact cratering is an important process in planet formation and surface modification.It creats impact craters on the surface, which records and reveals the geological history of the planet. It is known that the younger a surface is, the less amount and smaller diameters the craters on that surface are. Therefore, model ages of a surface region of a solid celestial body can be estimated by measuring the crater size-frequency distribution. We summarized the principles and its application, and applied the method to the age determination of Sinus Iridum on the Moon using images obtained by Lunar Reconnaissance Orbiter Wide Angle Camera. Our results show that this region has three main geological units with model ages of 3.33 Ga, 3.21 Ga and 2.60 Ga, respectively.
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Key words:
- the Moon /
- Sinus Iridum /
- crater size-frequency distribution /
- absolute model age /
- planetary geology /
- geochronology
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图 1 NPF(1)与HPF(2)曲线对比(Ivanov, 2008, 有改动)
图中D为撞击坑直径，R为利用公式(4)获得的R(D)值.图中曲线：1.NPF(Neukum et al., 2001)；2.HPF(Hartmann，2005)；3.饱和平衡曲线(Hartmann，1984)
Fig. 1. Comparison of NPF(1) and HPF(2)
图 2 月球撞击年代曲线(据Hiesinger et al., 2000, 有简化)
图中A代指Apollo，L代指Luna，横坐标T为月球表面绝对模式年龄，纵坐标Ncum(D＞1 km)为单位面积上直径大于1 km的撞击坑总量
Fig. 2. Lunar Cratering Chronology Curve
图 3 虹湾的位置及虹湾地区LRO广角相机图像
a.虹湾在月球表面的位置，底图为LRO广角相机图像；b.虹湾LRO广角相机图像，图中点线区内为虹湾的范围，白色方框内为二次撞击坑集中分布区
Fig. 3. Location of Sinus Iridum and LRO Wide Angle Camera mosaic of Sinus Iridum
图 4 虹湾地区地质单元划分与各地质单元定年结果
a.虹湾地区地质单元划分与各单元绝对模式年龄.图中黑色虚线内为虹湾范围，黑色实线为各地质单元界限，白色虚线内为进行撞击坑直径-频率分布测量的区域，底图为利用Clementine不同波段比值合成的假彩色图像；b.地质单元A的定年结果；c.地质单元B1的定年结果；d.地质单元B2的定年结果；e.地质单元C的定年结果.图b~e中横坐标为撞击坑直径，纵坐标为累积撞击坑频率
Fig. 4. Geologic units in Sinus Iridum and their absolute model ages
图 5 熔岩流覆盖对撞击坑直径-频率分布曲线的影响(据Neukum et al., 1976, 有改动)
图中横坐标为撞击坑直径，纵坐标为累积撞击坑频率.t1表示t1时刻撞击坑直径-频率分布曲线；t2指t2时刻撞击坑直径-频率分布曲线；D0为t1时刻熔岩流所覆盖的撞击坑的直径上限
Fig. 5. Effects of lava flow on crater size-frequency distribution curve
表 1 Neukum撞击坑产率函数的系数(Neukum et al., 2001)
Table 1. Coefficients in NPF (Neukum et al., 2001)
ai 旧数值 新数值 a0 -3.076 8 -3.087 6 a1 -3.626 9 -3.557 528 a2 +0.436 6 +0.781 027 a3 +0.793 5 +1.021 521 a4 +0.086 5 -0.156 012 a5 -0.264 9 -0.444 058 a6 -0.066 4 +0.019 977 a7 +0.037 9 +0.086 850 a8 +0.010 6 -0.005 874 a9 -0.002 2 -0.006 809 a10 -5.181 0-4 +8.251 0-4 a11 +3.971 0-5 +5.541 0-5 
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表 2 各区域不同直径单元的累积撞击坑频率
Table 2. Ncum of different diameter units in each area
区域 面积(km2) 各直径单元的累积撞击坑频率(km-2) 0.5 km 0.6 km 0.7 km 0.8 km 0.9 km 1.0 km 1.2 km 1.5 km 2.0 km 2.5 km A 4 238.967 2.97e-2 2.17e-2 1.23e-2 8.73e-3 6.84e-3 5.43e-3 3.30e-3 7.08e-4 2.36e-4 0 B1 7 418.919 3.48e-2 1.70e-2 1.05e-2 8.36e-3 5.26e-3 2.97e-3 1.89e-3 6.74e-4 4.04e-4 1.35e-4 B2 3 855.643 3.55e-2 1.89e-2 1.14e-2 8.30e-3 5.19e-3 3.11e-3 1.82e-3 2.59e-4 2.59e-4 0 C 6 288.833 2.56e-2 1.18e-2 8.11e-3 5.41e-3 3.98e-3 3.02e-3 1.59e-3 7.95e-4 3.18e-4 1.59e-4
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表 3 各区域二次撞击坑剔除情况
Table 3. Number of eliminated secondary craters in each area
区域 撞击坑总数 二次撞击坑数 有效撞击坑数 A 165 39 126 B1 319 61 258 B2 173 36 137 C 192 28 164
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表 4 虹湾地区地质年龄(所属地层)对比(单位：Ga)
Table 4. Comparison of ages and stratigraphy for Sinus Iridum in billion years
地质单元 年龄(本文) 所属地层 Hiesinger(2000) Schaber(1969) A 3.33 Im1 3.26 Im1/Im2 B 3.21 Im2 3.01/3.39 Im1/Im2 C 2.60 EIm 2.96 EIm Hiesinger(2000)的研究结果据 Hiesinger et al.(2000) ；Schaber(1969)的研究结果据Schaber(1969).
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