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Morphometric Characterization and Reconstruction Effect Among Lunar Impact Craters

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Earth Moon Planets (2014) 111:139–155 DOI 10.1007/s11038-014-9431-0 Morphometric Characterization and Reconstruction Effect Among Lunar Impact Craters Weiming Cheng • Jiao Wang • Cong Wan Received: 2 January 2014 / Accepted: 11 March 2014 / Published online: 19 March 2014 Ó Springer Science+Business Media Dordrecht 2014 Abstract Impact craters on the lunar surface have a variety of morphometric charac- teristics that are very useful in understanding the evolutionary history of lunar landscape morphologies. Based on digital elevation model data and photographs from China’s Chang’E-1 lunar orbiter, we develop morphologic parameters and quantitative methods for presenting the morphometric characteristics of impact craters, analyzing their relational distribution, and estimating the relative order of their formation. We also analyze features in profile where craters show signs of having formed on the edge of previously existing craters to show that superimposed impacts affect morphologic reconstructions. As a result, impact craters have significant effects on the reconstruction of ancient topography and the estimation of relative formation ages. Keywords Morphometric characterization Á Position relationship Á Relative construction age Á Chang’E-1 1 Introduction The Earth’s Moon, it’s only natural satellite, has a potentially complete record of the 4.5- billion year evolutionary history of the solar system (Ronca 1966; Ouyang 2005). Impact craters are the most obvious and typical geomorphologic units (Ronca 1969; Neukum and Ivanov 1994; Neukum et al. 1975); they form when a planetary body (meteoro, comet, etc.) impact against the surface (King 1976). The diameters of impact craters on the lunar W. Cheng (&) Á J. Wang Á C. Wan State Key Laboratory of Resources and Environmental Information Systems, Institute of Geographic and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China e-mail: [email protected] J. Wang Á C. Wan University of Chinese Academy of Sciences, Beijing 100049, China 123 140 W. Cheng et al. surface range widely from only a few centimeters to hundreds of kilometers (Peter 1999). For most craters, their rims are higher than the center; as the diameters increase, the morphologic characteristics of specific impact craters appear to become more complex (Oberbeck et al. 1974). The morphometric characteristics of impact craters can provide much information regarding impact characteristics and processes (Hartmann et al. 1981; Cameron 1984). Asteroids or comets striking planetary surfaces generally produce circular impact craters, even when those objects hit at angles substantially off vertical (Melosh 1996). Elliptical impact craters are produced when impacting angles are low relative to the horizontal, with the transition between circular and elongated craters occurring somewhere near 10° (Bottke et al. 2000). Such results have been confirmed by laboratory experiments con- sisting of small aluminum and Pyrex spheres shot at several km/s into sand or aluminum targets (Burchell and Mackay 1998). Burchell et al. (2010) further used laboratory methods to imitate the impacting process, with the same speed and angle of incidence, combined with extrapolating to the correct size scale to match the SMART-1 impact; this predicts a highly asymmetric crater approximately 5.5–26 m long, 1.9–9 m wide, 0.23–1.5 m deep with a volume of 0.71–6.9 m3. Craters constitute rays and impact units formed by small objects (Melosh 1996; Neukum and Ivanov 1994) and this information can be used to estimate the relative geologic ages of a given lunar region (Shoemaker 1965). The National Aeronautics and Space Administration (NASA 1969) used the ratio of impact crater depth to diameter as a determination of relative age, and divided the craters into four categories: fresh, young, mature and aged. Methods of determining an estimate ages for cratered planetary surface units is to find a size-frequency distribution for observed craters of a given surface unit with a known crater production function, and to use the crater frequency for certain crater sizes together with a calibrating chronology function to obtain an estimate formation age for the impact craters (Oberbeck et al. 1974; Hartmann et al. 1981; Neukum 1984; Neukum and Ivanov 1994; Hartmann and Neukum 2001; Ivanov 2001). Neukum et al. (1975) found that the lunar impact crater size distribution is largely constant in the size range 0.3 km B D B 20 km for regions with formation ages between *3 and C4 Ga, based on a calibration size distribution curve. The relationship between cumulative crater frequency N and crater diameter D can be expressed as a logarithmic function. Moutsoulas and Preka (1982) used the ratio intervals from small- and medium-scale craters for morphological descriptions. On different planets or over different terrains of the same planet, a change in the fractal dimensions of craters appears to indicate different geological settings related to the geological age. Ouyang (2005) established a relationship between the distribution density of impact craters with diameters [4 km and lunar rel- ative geological age. As mentioned earlier, many investigations have focused on craters size-frequency distribution to derive estimates of relative formation age. However, there have been far fewer studies assessing crater statistics to include complex morphologic characteristics such as excavation shape and to explore profile morphologies and reconstruction effects for edge-intersected craters. Thus, in this paper, based on digital elevation model (DEM) data and photographs from Chang’E-1, China’s first lunar probe, we address this shortfall by developing a set of parameters for the morphometric characterization of impact craters, establishing a method to estimate the positional relationships and relative impacting orders of impact craters, and characterizing the profile morphologies of two edge-intersected impact craters. 123 Lunar Impact Craters 141 2 Morphometric Characteristics of Lunar Impact Craters The Center for Lunar Science and Exploration at the Lunar and Planetary Institute, pub- lished a database of impact craters, which was initially created as part of the Lunar Exploration Summer Intern Program at the Lunar and Planetary Institute in 2008 (http:// www.lpi.usra.edu/lunar/surface/). The database consists of 8,713 craters, of which about 1,644 have constrained ages. In this database, 51 physical characteristics of the craters are listed. The main attributes include: name, diameter, depth, location, volume, central peak height and diameter, width of central peak, ray length, and age. Many of these properties can be expanded in detail, e.g., the diameter can include simple surface diameter, crater instant diameter, complex crater instant diameter, floor diameter, etc. Of these attributes, only the crater diameter, depth, positional coordinates, central peak height and age of strata are obtained from maps and imagery; other indices are calculated by theoretical predic- tions. Of the 8,713 impact craters identified, only 1,644 have an age attribute assigned and in some cases there are multiple geological ages proposed for the same impact crater. Thus, the statistical properties of these named craters can be used to characterize the basic features of lunar craters (Fig. 1). From Fig. 1, we find that 36 % of lunar crater diameters are \10 km, and that as diameters increase the abundance of lunar craters gradually decreases. Against crater depth, with the enlargement of impact crater diameter crater, average depth of craters in each level increase gradually. This rule is also a more prominent appearance in central peak height and crater diameter. The central peak height of craters is generally\1 km and the percent of average central height in craters [60 km almost reaches to 30 %. The statistics above show that the larger the craters are, the deeper and the higher central peak the craters own (Head 1976). Based on the above analysis, this study selects the mor- phological indicators (including diameter and depth) of bowl-shaped impact craters to determine the specific numerical attributes from Chang’E-1 DEM data. This work can provide basic data for further study. 40% 35% 30% 25% 20% Percent 15% 10% 5% 0% <10 10-20 20-30 30-40 40-50 50-60 >60 Diameter (km) Percent of crater in different diameter class Percent of average depth in different diameter class Percent of average height of central peak in different diameter class Fig. 1 Histogram of lunar crater attributes 123 142 W. Cheng et al. Fig. 2 Horizontal projection and schematic profile diagram of bowl-shaped craters (after Grosse et al. 2012) Various complex morphologic relationships exist between the various impact craters on the lunar surface. Based on the morphometric parameters of the impact craters, the typical bowl-shaped crater models can be used to estimate the positional relationship and relative impact order between pairs of impact craters. A schematic diagram showing the vertical profiles and horizontal projections of two impact craters is presented in Fig. 2. Most of the impact craters on the lunar surface have a raised rim and low depression, whose dimensions depend on size, velocity from impacting object and age (Head 1976). A crater rim is defined simply as the crater boundary in this paper. Based on DEM data, 11 morphometric parameters, including radius (R), depth (Dp), area (A), perimeter (P), roundness (r), elevation (E), diameter (d), length (L), rays (Rs), latitude (Lat) and longitude (Lon) are selected
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