Shape of Boulders Ejected from Small Lunar Impact Craters

Planetary and Space Science 145 (2017) 71–77

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Planetary and Space Science

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Shape of boulders ejected from small lunar impact craters

Yuan Li a,*, A.T. Basilevsky b, Minggang Xie a, Wing-Huen Ip a,c a Space Science Institute, Macau University of Science and Technology, Macau b Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, Moscow 119991, Russia c Institute of Astronomy, National Central University, 32054 Chung-Li, Taiwan

ARTICLE INFO ABSTRACT

Keywords: The shape of ejecta boulders from 7 lunar impact craters <1 km in diameter of known absolute age was measured Moon to explore whether it correlates with the crater age and the boulder size. The boulders were mapped and then Shape of boulders measured by rectangular fitting and the shape was represented by the axial ratio or aspect ratio (A) of the Axial ratio rectangle. The main conclusions from the analysis of our measurement results are: 1) the percentages of the Crater age number of boulders of studied craters decrease with the increase of the axial ratio. Most (~90%) of the boulders have the axial ratio in the range of 1–2; no boulder with axial ratio larger than 4 was found. 2) the axial ratios of mare ejecta boulders decrease with their exposure time, whereas that for highland ones show unchanged trend. This difference may be probably due to target properties. 3) The shape of ejecta boulders are influenced by mechanical strength of bedrocks and space erosion. 4) surface peak stresses caused by thermal fatigue maybe play a significant erosion role in the shape of boulders of various diameter.

1. Introduction micrometeoroid and meteoroid bombardment and thermal stresses due to diurnal temperature changes (e.g., Clark et al., 2002). Solar wind, Impact craters and rocks/boulders are the predominant features on cosmic ray and electromagnetic radiation change the optical properties the lunar surface. In most cases, rocks appear on the lunar surface as a of the exposed materials within the rather thin surface layer. Microme- result of ejections from impact craters and come from the regolith layer teoroid bombardment was found to work mostly in the form of and bedrock basement underlying the regolith. The bedrocks in lunar sand-blasting without destroying the rocks (Horz€ et al., 1975, 1977; maria are composed of various basalts. In highlands these are impact McDonnell, 1977). Only meteoroid bombardment and thermal stresses breccias, which can be essentially fragmental breccias or contain are considered as the major factors for the destruction of boulders on the different contents of solidified shock melt (e.g., Florensky et al., 1981; airless body surface (see e.g., Basilevsky et al., 2013, 2015; Cintala and Heiken et al., 1991). Accordingly, lunar rocks/boulders studied by us are Horz,€ 2008; Delbo et al., 2014; Horz€ et al., 1975; Molaro et al., 2016). fragments of basalts or impact breccias. It should be noted that catastrophic rupture of exposed rocks on the The shape of ejecta boulders may provide an insight into the impact airless body by meteoroid bombardment has a stochastic character with fragmentation process (e.g., Melosh, 1989; Senthil Kumar et al., 2014). some boulders destroyed very soon after their appearance on the surface Krishna and Kumar (2016) described shapes of boulders by rectangular while some other that may stay untouched for very long time (e.g., Horz€ fitting, and defined the axial ratio (or aspect ratio) between long and et al., 1975). Meanwhile the destruction process by thermal stress should short axes of rectangular as a measure of the boulder shape. They sug- be more uniform in time if given the same mass and similar gested that the axial ratio (or aspect ratio) of boulders depends on ejec- thermo-mechanical properties, as all sun-illuminated rocks are univer- tion velocity, and an increase in the ejection velocity leads to a decrease sally subjected to the same process. of the axial ratio for boulders. In the following, the axial ratio or aspect Generally, the larger rocks demand the higher impact energy to be ratio will be abbreviated as A. destroyed, thus the longer survival time could be expected for them (e.g., After their formation, boulders exposed on the airless body surface Horz€ et al., 1975). However the larger rocks are mechanically weaker due are affected by a number of agents: solar wind ion implantation and to the increased number and size of intrinsic flaws (Housen and Hol- sputtering, cosmic-ray bombardment, electromagnetic radiation, sapple, 1999). Moreover, the larger rock has the higher probability to be

* Corresponding author. E-mail address: [email protected] (Y. Li). http://dx.doi.org/10.1016/j.pss.2017.07.014 Received 8 June 2017; Accepted 21 July 2017 Available online 26 July 2017 0032-0633/© 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Y. Li et al. Planetary and Space Science 145 (2017) 71–77

Table 1 The list of location, terrain type, size and absolute age of the craters studied in this work.

Crater Location Terrain Crater Crater Age name (Lat., Lon.) type size age determination (m) (Ma) technique and references

South Ray 9.15,15.38 Highland 680 ~2 Radiometric (1,2) Unnamed 12.25, 62.24 Mare 200 5–10 Morphologic (3) A Unnamed 3.61,336.51 Mare 400 20–30 Morphologic (4) B Cone 3.63,342.57 Highland 340 ~26 Radiometric (5) North Ray 8.80,15.49 Highland 950 ~50 Radiometric (1,6) Unnamed 3.02,336.58 Mare 560 70 ± 30 Morphologic (7) D Camelot 20.21,30.73 Mare 650 ~100 Radiometric (7)

(1) - Arvidson et al. (1975), (2) - Eugster (1999), (3) - Basilevsky and Head (2012), (4) - Basilevsky (1976), (5) - Turner et al. (1971), (6) - Borchardt et al. (1986), (7) - Li et al. (2017), (8) - Kirsten et al. (1973). Fig. 1. This image gives an illustration for the nominal diameter and A of identiﬁed boulders which located at the part of study area of North Ray crater. The boulder Table 2 encompassed by rectangle with width of ~5 m and length of ~6.5 m, has A of 1.3 and The basic information on images selected for the boulder counting for each of study craters. nominal diameter of ~5.7 m.

Crater Image Id Pixel scale Local solar time Incidence name (m/pixel) (24-h clock) angle boulders with exposure time on the lunar surface. (degree)

South Ray M119754107RE 0.45 15.70 56.15 2. Previous studies on the rock/boulder shape Unnamed M119449091RE 0.48 15.97 60.22 A The observed rocks can be represented as cuboid-shaped objects Unnamed M120005333LE 0.48 15.46 52.09 having three mutually perpendicular axes: the long axis a, medium axis b, B M144775952RE 0.44 8.64 50.39 Cone M168319885RE 0.29 14.49 37.40 and short axis c. It is obvious that in most cases a rock ejected to the lunar M175388134LE 0.28 9.01 44.87 surface should lie with its short axis upward. So, when we observe rocks Unnamed M142495666RE 0.51 10.45 44.88 from above, as in the case of the present study, most probably we see the C M166072850LE 0.49 16.14 69.03 long a and medium b dimensions of it (e.g., Demidov and Basilev- North Ray M144524996LE 0.45 8.88 47.18 Borya M127159138LE 0.40 9.95 46.42 sky, 2014). M135418902RE 0.51 15.81 65.29 Fujiwara et al. (1978) reported an impact experiment in which ~5 cm Unnamed M104662862LE 1.09 15.29 49.37 basalt blocks were shot with polycarbonate cylinders 0.8 cm in diameter D M1121393925E 0.98 9.13 43.13 with masses of 0.37 g at a velocity of 1–4 km/s. Statistical processing of Camelot M134991788LE 0.48 16.17 64.60 the geometry of the fragments yielded average values of b/a ¼ 0.73, and M162107606LE 0.43 7.14 73.85 ¼ Spook M144524996LE 0.45 8.89 47.18 c/a 0.5. Capaccioni et al. (1984) used a 1 g aluminum projectile shot at a velocity of ~10 km/s at triaxial ellipsoids with dimensions 30 21 15 cm and composed of specific concrete and obtained values impacted due to their larger area. The interplay of these factors are not of b/a ¼ 0.72 and c/a ¼ 0.49 which are similar to the result of Fujiwara well understood by now. Therefore, the issue of how meteoroid impacts et al. (1978). If to consider the a/b ratio (A), these experiments showed affect the survival times of boulders of various sizes demands addi- the average value to be ~1.4. tional studies. Demidov and Basilevsky (2014), as part of their study, measured 40 By modeling boulder/rock response to diurnal thermal forcing, relatively large boulders in six rocky areas of lunar surface using Lunar Molaro et al. (2017) concluded that lunar exposed boulders have weak Reconnaissance Orbiter Camera (LROC) Narrow Angle Camera (NAC) outer layer that is susceptible to surface disaggregation, so this disag- images and found that b/a ratio is 0.78 for highland rocks with a standard gregation should be the primary mechanism for thermal breakdown, deviation of 0.16 and 0.83 for mare rocks with a standard deviation of while the formation of large cracks that splits a boulder would 0.18. The Welch test showed that the distributions of the b/a parameters be secondary. are similar for highland and mare rocks, and hence the two samples can In reality, the erosion processes of thermal stress and meteoroid be regarded as one with an average value and standard deviation are 0.8 impact are worked on the lunar boulders simultaneously. The outer layer and 0.16, respectively. This gives an average value of a/b (A)tobe of boulders are weakened by thermal fatigue (Molaro et al., 2017) which 1.25 ± 0.05 (95% confidence interval). should assist destruction of material by impacts. On the other hand, The study on the ejecta boulders of Censorinus crater (3 Ma) by impacts could create micro-cracks that thermal fatigue could then take Krishna and Kumar (2016) indicates that A for the boulders vary from 1 advantage of it, thus hastening granular disintegration. to 4. It was found that the boulders near the crater rim are characterized As the rocks/boulders are exposed to the airless surface the meteoroid by larger range of A, between 1 and 4, whereas for boulders near the edge impacts and thermal fatigue destroy them by breakup and/or exfoliation of ejecta blanket, dominated by the range of 1–2. (Ghent et al., 2014). One may expect that these two processes either completely destroy the exposed boulders or influence their shape. The 3. Methodology present study examines how the shape of the ejecta boulders changes with their exposed time on the lunar surface and with the boulder size, 3.1. Craters under study and the image data respectively. This work is complementary to the work of Li et al. (2017), whose main topic is about the changing of the spatial density of ejecta In this study we used the same populations of craters as in the study of

72 Y. Li et al. Planetary and Space Science 145 (2017) 71–77

Li et al. (2017): South Ray, Unnamed A, Unnamed B, Cone, Unnamed C, North Ray, Borya, Unnamed D, Camelot, Spook. Li et al. (2017) found that in association with craters Unnamed C, Spook and Borya, boulders larger than 3 m were not observed, so these three craters were excluded from further study. The basic information on the study craters is listed in Table 1. More detailed descriptions can be found in Basilevsky et al. (2013) and Li et al. (2017). The Lunar Reconnaissance Orbiter Camera Narrow Angle Camera (LROC NAC) images (Robinson et al., 2010) with mean pixel scale of ~0.5 m were employed in this study for the boulder identiﬁcation and shape measurement. We downloaded the original experimental NAC data record from the website of Arizona State University (http://www.lroc. asu.edu/archive); then processed the data with radiometric calibration and map projection using ISIS3.4 software. In the end, the processed images were imported into ArcGIS desktop 10.0 software for digital mapping and shape measurement.

3.2. Criteria for selection of LRO images and counting areas

Boulders in the images with significantly oblique sunlight are bright on the sunward side and a shadowed region exists on the opposite side making it non-measurable. In order to observe boulder completely in shape, the criteria for the LRO NAC image selection are the same as in Li et al. (2017): 1) Two images with the opposite Sun-illumination geom- etries to present the boulders completely. 2) The images with incidence angle in the range of ~45–~55 which are good compromise for the boulders identification and their shape and size determination. 3) Images with a pixel scale of ~0.5 m. Sometimes, the image set could not satisfy all above three criteria for a complete observation of boulders, so we had to make compromise. Examples (Li et al., 2017) are: 1) The only one image was selected when there is no image with opposite incidence angle; 2) The images with most proximal to ~45–~55 incidence angle were selected when there is no image with incidence angle exactly in the mentioned range; 3) Images with the highest available pixel scale were selected even if their pixel scale is worse than 0.5 m/pixel. Table 2 provides a list of the images we selected for each of study craters, as well as their pixel scale, local solar time and incidence angle. The study area for each considered craters was selected in the crater ejecta blanket to be inside a concentric annulus within a crater radius distance away from the crater rim crest. For some craters, in order to avoid the influence of ejecta from surrounding large craters and the effect of overexposed areas in the used images, the counting areas are only parts of that concentric annulus (see Fig. 2). More detailed descriptions can be found in Li et al. (2017).

3.3. Shape measurement of boulders

We follow the process of the boulder shape measurement of Krishna and Kumar (2016) in which the boulder outline was digitized as a rectangle. The shape was described as the ratio of lengths of long (a) and apparent short (b) axes of rectangle. The isometric shape results in values of A about 1. An increase in the A of a boulder indicates an increase of boulder elongation. This A defines only two sides of the boulder visible from above while its third dimension (the boulder height) remains un- known. As was mentioned above this hidden side is generally believed to be corresponding to the minimum axis c. The boulder outline is digitized as a rectangle following the work of Krishna and Kumar (2016), and its nominal diameter is defined as the geometric mean of long and short axis of the digitized rectangle. An example of this procedure is shown in Fig. 1. The boulder encompassed by red rectangle in Fig. 1 has a width of 5 m and a length of 6.5 m, which resulting in a nominl diameter of ~5.7 m and a A of 1.3. Fig. 2. Counting areas (radial sectors) and examples of identified boulders (right images) Because various pixel scales and the buried or/and low-relief corresponding to the black rectangular areas in the study area for crater South Ray, Un- named A, Unnamed B, Cone, North Ray, Unnamed D and Camelot, respectively. The red appearance of relatively small size boulders may lead to incomplete circles in the left images are the crater rims. statistics in boulder study, we mapped and measured boulders only larger

73 Y. Li et al. Planetary and Space Science 145 (2017) 71–77

Fig. 3. Histogram plots of A of identiﬁed boulders. The number at the upper location on top of a bar indicates the percentage of number of boulders in the given bar; the number at the lower location indicates the number of boulders in this bar. The data were binned from 1 with the increasing interval of 0.5 for A value. The mean values of A for each of the studied craters are also given in the ﬁgures.

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Table 3 Percentages of number of boulders distributed in the various A ranges.

A range 1–1.5 1.5–22–2.5 2.5–33–3.5 3.5–4 Percentage range (%) 40–73 27–41 0–17 0–1.5 0–0.4 0–0.1

Fig. 6. The plots of values of A of each of the studied craters plotted against boulder diameter. The diameter ranges are presented in Table 4. The horizontal positions of A symbols correspond to median values of corresponding size bins. The errors bars correspond to 95% conﬁdence level.

Fig. 4. Percentages of numbers of identified boulders in various A ranges (color data) for is defined as the ratio of lengths of long (a) and apparently short (b) axes each of the studied craters versus the crater age with crater names were shown (names of of rectangle. Histogram plots of the A for identified boulders (D > 3m)in mare and highland craters are marked in red and black, respectively) and its corre- the study areas of study craters are shown in Fig. 3. It is seen that about sponding data were linked in vertical grey lines. ‘UA’ indicates the crater Unnamed A and half (~50%) of boulder populations have the A in the range of 1–1.5; ‘UB’ indicates the crater Unnamed B. Noted that the data of Unnamed A for A ranges of – 1–1.5 and 1.5–2 overlap together. The error were determined by Possion error that in the most (~90%) of the boulders have A in the range of 1 2 and only a small form of (√n)/N, where n indicates the number of boulders in each of A ranges for a fraction of them has the larger values (>2). Boulders from the oldest studied crater, N indicates the total number of boulders for a studied crater. (For inter- studied crater Camelot (~100 Ma) do not have A larger than 2 in value. fi pretation of the references to colour in this gure legend, the reader is referred to the web Data listed in Table 3 show the percentage of number of boulders version of this article.) distribution of A for the studied craters. It is noted that the percentages gradually decrease as the A increase. Because of absence of boulders with than 3 m in nominal diameter. A larger than 2 for crater Camelot, the lower limit of percentage range for A larger than 2 is zero as shown in Table 3. If the crater Camelot is 4. Results excluded, the percentage range is 5–17 for A's range of 2–2.5. Never- theless, the percentages still gradually decrease as the A increase. Very Fig. 2 shows the study areas for seven study craters: South Ray, Un- small fraction of boulders has A to be 2.5–4 and no boulders with A > 4 named A, Unnamed B, Cone, North Ray, Unnamed D and Camelot in were observed that is consistent with the results of Krishna and Kumar > fi which 253, 138, 258, 109, 232, 981, 11 boulders ( 3 m) were identi ed, (2016) who studied crater Censorinus (D ¼ 3.8 km). respectively. Fig. 4 presents the relationship between the percentages of number of As described in Section 3.3, the boulder shape is described as A which identified boulders in various A ranges of each of studied craters and their ages. At the first glance, for the A interval of 1–1.5, 1.5–2 and 2–2.5 they seem unchanged with violation by data from Unnamed A. If we look into the trend for mare and highland crater separately, for the A range of 1–1.5, mare craters increase with crater age; for 1.5–2, they are generally unchanged; for 2–2.5, they decrease with crater age. While for highland craters, the trends keep constant with crater age. Therefore, in general, one may conclude that for mare craters with the increase of exposure time on the lunar surface the percentage of the most isometric boulders (A ¼ 1–1.5) slightly increases, less isometric/more elongated (A ¼ 1.5–2) ones remain constant, and more elongated (A ¼ 2–2.5) ones slightly decrease instead. Highland craters seem to keep constant with crater age around mean value of A of ~1.45. For larger aspect ratios (2.5–4) the corresponding numbers are too small (0–1.5) to show a clear trend for both mare and highland craters. Fig. 5 plots that the mean values of A of boulders for each of studied craters with the crater age, showing that the mean values of A decreases with crater age for mare craters, while it is almost unchanged with mean value of ~1.45 for highland craters. Fig. 6 shows the relationship between the mean value of A in various diameter intervals of boulders of each of the studied craters and the Fig. 5. Distribution of the mean values of the A of boulders for each of studied craters versus crater age with the mare and highland terrain type shown. The error bars corre- boulder size. Their values are listed in Table 4. To obtain reasonably good spond to 95% confidence level. statistics, the bin sizes are not constant but increase with the boulder size.

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Table 4 Mean values of A of boulders in different diameter interval for each of the studied craters.

The boulder size ranges South Ray Unnamed A Unnamed B Cone North Ray Unnamed D Camelot

3–3.5 1.42 ± 0.03 1.51 ± 0.04 1.56 ± 0.04 1.41 ± 0.05 1.42 ± 0.04 1.29 ± 0.02 1.34 ± 0.10 3.5–4 1.47 ± 0.04 1.59 ± 0.06 1.55 ± 0.04 1.46 ± 0.06 1.46 ± 0.04 1.42 ± 0.02 1.54 ± 0.23 4–5 1.41 ± 0.04 1.77 ± 0.07 1.50 ± 0.04 1.40 ± 0.07 1.49 ± 0.05 1.50 ± 0.02 1.42 ± 0.3 5–7 1.53 ± 0.07 1.79 ± 0.09 1.44 ± 0.06 1.44 ± 0.09 1.48 ± 0.05 1.55 ± 0.02 – 7–12 1.45 ± 0.10 1.67 ± 0.26 1.40 ± 0.13 1.34 ± 0.17 1.41 ± 0.08 1.53 ± 0.04 – 12–18 ––––1.29 ± 0.20 1.48 ± 0.11 – 18–24 ––––1.37 ± 0.29 1.26 ± 0.27 –

we have got for mare boulders in Fig. 5: mean value of A decreases with crater age. Meanwhile the highland boulders show almost unchanged trend as shown in Fig. 4 which is consistent with the generally unchanged trend for mean value of A of boulders from highland craters as shown in Fig. 5. Besides, the mean value of A of ~1.45 for highland boulders is consistent with the results of Fujiwara et al. (1978) and Capaccioni et al. (1984). Because most of the boulders for each of studied craters are in the A range of 1–2(Fig. 4 and Table 3), we inferred that erosion process is more effective in reducing A when A > ~2, however has little effect on the changing of A when A is ~2 or smaller. The difference trends between mare and highland boulders in Fig. 5 may be probably due to target property: the values of A for boulders produced from fractured highland bedrock are generally less than ~2 (see Fig. 3), because breccias of the highland bedrock experienced frac- turing as part of their formation. It was also found that the value of A depends on the boulder size: it increases within the size intervals of 3–7m(Figs. 6 and 7), but decreases for larger size. The important observation is that the values of A for mare Fig. 7. The plot of mean values of A in various boulder size ranges versus boulder boulders are generally larger than that of highland boulders for given diameter for all of the studied highland craters and mare craters, respectively. The hori- size. We attributed this variation trend to the target property and space zontal positions of A symbols correspond to median values of corresponding size bins. The erosion. In other words, the values of A for boulders produced from less errors bars correspond to 95% confidence level. fractured mare basalt is expected to be larger than that from fractured highland bedrock; then the space erosion worked on them, thus shows Fig. 6 shows that the values of A of boulders sharply increased within the the values of A decreases. first two size intervals (from 3 to 4 m), except Unnamed B, but the var- The thermomechanical modeling to the lunar boulders by Molaro iations appear in the larger-size boulders. This trend is presented for both et al. (2017) indicates that the surface peak stresses has a concave roll- boulders associated with craters located in mare terrain (unnamed A, over (weak thermal erosion) at the boulders diameter of 7 m (Fig. 10 in unnamed B, unnamed D and Camelot) and in highland (South Ray, Cone Molaro et al., 2017) which correspond to convex rollover (less erosion and North Ray). rate) in Fig. 7 at 7 m. Moreover, small size of boulders could experience Fig. 7 shows the values of A of boulders combined in two sub- thermal stress throughout their entire volume, leading to severe thermal populations: mare craters and highland ones. It is seen in Fig. 7 that for breakup and granular disintegration. Therefore, surface peak stresses the first four size intervals (from 3 to 7 m) the mean values of A increase from thermal fatigue at various boulder diameters probably the main both for mare and highland craters (although there is a overlap between explanation for the convex rollover distributions both for mare and 4 m and 7 m for highland craters) and in this generalized plot it is more highland craters. obvious than in Fig. 6. For the larger boulders, united subpopulation of mare craters displays a decrease trend. While for united subpopulation 6. Conclusions highland craters, the mean values of A show prominent decreases until the diameter location of 15 m, then shows a moderately increase till 21 m In this study, the shape measurements on the boulders in the ejecta with large error. Therefore, the subpopulation of highland craters shows blankets of seven lunar craters <1 km in diameter were performed. decrease trend as boulder size increasing, although the constancy trend Because the ejecta boulders are produced simultaneously with the cor- can not be rejected due to the large uncertainties of these data points. responding crater formation (Melosh, 1989), we treat the crater forma- Another important observation is that almost all the data points of mare tion ages as the exposure time of its ejecta boulders. For the study craters boulders are larger than those of highland ones. the absolute age of their formation were estimated in the previous works; so we know how long these populations of boulders were exposed to the 5. Discussion potential destructing agents: meteoroid impacts and day-night temperature variations (thermal fatigue). It is necessary to mention that the It was found in Fig. 4 that for mare craters with the increase of the considered changes in the boulder shape occurred on the background of exposure time on the lunar surface, the percentage of the most isometric their destruction and general decrease of the boulder populations boulders (A ¼ 1–1.5) slightly increases, less isometric/more elongated (Basilevsky et al., 2013, 2015). At each time stage we deal with the (A ¼ 1.5–2) ones remain constant, and more elongated (A ¼ 2–2.5) ones boulders which survived from the moment of their appearance on the slightly decrease instead. This suggests that, on average, mare boulders in surface until this stage and their shapes and sizes were modified by the the considered populations become more isometric with increasing destruction processes during this time interval. exposure time, that is to say, the mean value of A of mare boulders will The main conclusions obtained as below: decrease as their exposure time. This conclusion is consistent with what

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