Survival Times of Meter-Sized Boulders on the Surface of the Moon

Planetary and Space Science 89 (2013) 118–126

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Planetary and Space Science

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Survival times of meter-sized boulders on the surface of the Moon

A.T. Basilevsky a,b,n, J.W. Head b, F. Horz c a Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, Moscow 119991, Russia b Department of Geological Sciences, Brown University, Providence, RI 02912, USA c LZ Technology Inc., 1110 NASA Parkway, Houston, TX 77058, USA article info abstract

Article history: Analysis of the abundance of ejecta boulders Z2 m in diameter on the rims of twelve lunar craters (150– Received 6 May 2013 950 m in diameter) of known formation ages (2–300 Ma) led to estimates of the survival times of meter- Received in revised form sized boulders against collisional destruction on the Moon. The median survival time, when 50% of the 9 July 2013 original rock population 42 m was destroyed, is about 40–80 Ma, while the 99% survival time (99% of Accepted 23 July 2013 rocks destroyed) is about 150–300 Ma. These estimates are a factor of 5 shorter than the survival times Available online 31 July 2013 that one would extrapolate from the calculations of Horz et al. (1975a) for surface rocks o20 cm in Keywords: diameter. However, recent experimental insights into the effective strength of different sized targets The Moon (Housen and Holsapple, 1999) suggest that meter-sized boulders have effective strengths a factor of 2–3 Boulder life time less than 10 cm sized rocks, thus reducing the survival times of meter-sized boulder by similar factors. Collisional destruction Additionally, Horz et al. (1986) demonstrated that the cumulative effects of multiple impacts are more severe than assumed in the 1975 paper, thus decreasing the survival times of all surface rocks, regardless of size, by an estimated 20–30%. Also, typical crater ejecta are fractured at macroscopic and microscopic scales, and thus most likely weaker than the “pristine” crystalline rocks used in laboratory “calibration” experiments. These considerations bring the model calculations into much better agreement with our actual boulder observations. As a consequence we suggest that the new estimates are more realistic than those of Horz et al. (1975a). Accounting for the differences in impact velocities and impact rates for the Moon and Mars, our survival times of lunar rocks Z2 m in diameter may also apply, within a factor of 2, to the surface boulders of Phobos and Deimos. & 2013 Elsevier Ltd. All rights reserved.

1. Introduction cause some surface abrasion akin to sand blasting. The dominant process on the Moon is collisional disruption. Rock boulders are frequently observed on the surfaces of Horz et al. (1975a) speciﬁcally calculated the survival of hand planetary bodies and their residence times at the surface can specimen-sized rocks using Monte Carlo methods to simulate the reveal the nature and rates of small scale erosion and weathering impact environment (location and magnitude of impact events), processes. In this paper we consider the survival times of meter- and the experimental insights into the collisional destruction sized boulders on the surface of the Moon. As shown by Gault and process available at that time, substantially relying on unpublished Wedekind (1969), Shoemaker (1971), Gault et al. (1972), Horz et al. experiments by Gault on granites and basalts (see Horz et al., (1975a), and McDonnell et al. (1977), the destruction of lunar 1975a). These model-calculations produced good agreement with surface boulders is largely accomplished by collisional disruption measured exposure ages of the Apollo rock suite. Accordingly, the due to a single or a small number of relatively energetic impact median survival time at which 50% of original 10 cm diameter 7 events that deliver the critical rupture energy (ER); a surface rock rocks were destroyed is on the order of 10 years, yet the 99% is deemed destroyed when the largest fragment remaining after survival time (where 99% of the original rock population is some energetic collision is o0.5 the original rock mass (Gault and destroyed) is on the order of 3.5 107 years. A large number of

Wedekind, 1969). Relatively small (o0.001 ER) yet numerous subsequent collisional fragmentation experiments on various impacts are unable to generate penetrative fractures and merely geologic materials, including meteorites, and conducted by a number of experimental groups, are summarized by Cintala and Hӧrz (2008). These subsequent investigations conﬁrmed the n Corresponding author at: Vernadsky Institute of Geochemistry and Analytical results of Gault on crystalline rocks and substantiated the experi- Chemistry, Russian Academy of Sciences, Moscow 119991, Russia. mental basis of the Horz et al. (1975a) model calculations. Tel.: +7 499 137 4995; fax: +7 095 2054. E-mail addresses: [email protected], The present paper pursues a totally different approach to [email protected] (A.T. Basilevsky). estimate the survival times of lunar surface boulders. It takes

0032-0633/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.pss.2013.07.011 A.T. Basilevsky et al. / Planetary and Space Science 89 (2013) 118–126 119 advantage of the superb spatial resolution of the LROC NAC images calculations are summarized in Table 1, including extrapolations (Robinson et al., 2010) which reveal the presence of numerous to meter-sized boulders which were done by graphical extension surface boulders on the rims and ejecta deposits of relatively fresh, of Figure 11 of Horz et al. (1975a). small (o1 km diameter) impact craters. The smallest boulders Table 1 contains estimates of the time required to destroy 50% that can be recognized with confidence in these images are on the (median survival time) of the rocks of a given size and the time order of 2 m. Suitable LROC images are available for the Apollo required to destroy 99% of the rocks (1% survival level). The survival landing sites, including 6 craters for which the absolute formation times calculated by Horz et al. (1975a) are consistent with measured ages are known from the measured exposure histories of returned exposure ages of returned Apollo rocks, the reason why their Figures Apollo samples. Additionally, Basilevsky (1976) detailed the gen- 11–14 are limited to spherical rocks o20 cm in diameter. Linear eral morphologic evolution and degradation of similar-sized cra- extrapolation of these figures suggests that rocks with diameters 2 ters and proposed some relative timescale for craters o1kmin to 4 m, which are seen with confidence in the LROC NAC images, diameter. LROC images include many such craters and an addi- have median survival times of 250 to 500 Ma and their 99% tional 6 such craters were selected in this study to complement destruction level is reached at some 700 to 1500 Ma. the dated Apollo craters. The boulder population of these 12 craters ranged from some maximum at the youngest crater to essentially zero at the most degraded structure. The progressive decrease of the boulder-population can thus be traced with time, 3. Survival times of lunar rock fragments of meter size and estimates for the survival times of meter-sized boulders can be derived. One can test the above survival times for meter-sized lunar rocks by observing the evolution of boulder populations on the rims of relatively small lunar craters of different, absolute forma- 2. Survival times of lunar rock fragments of tion ages. Penetration through the unconsolidated regolith into – centimeter decimeter size bedrock and ejection of the meter-size boulders is typical for lunar craters 100 m in diameter and larger, the reason why we The erosion and collisional destruction of lunar surface rocks by consider only craters with diameters Z150 m. We also analyzed hypervelocity impact at a wide variety of scales became evident the local geological setting of each candidate crater to verify that with the return of Apollo surface images and samples in the early morphologically fresh craters, akin to the candidate or smaller, had 1970s (Shoemaker, 1971)(Fig. 1). The returned rocks especially rocky ejecta. We are thus confident that we selected twelve craters displayed evidence of surface abrasion by micrometeorites, but for this investigation that penetrated through the regolith and also of penetrative fracturing, and eventual disruption by more originally had rocky ejecta on their rims. energetic events (Gault et al., 1972; Neukum, 1973; Horz et al., In our approach we assume that all boulders observed on the 1974, 1975a; Horz, 1977; McDonnell et al., 1977). crater rims are produced or exposed in the initial cratering event Two mechanisms of erosion became evident: (1) abrasion of and then evolve on the surface. Possible excavation of boulders by rocks by relatively small micrometeorite impactors and (2) cata- newly formed, smaller craters is not significant, as such craters are strophic destruction of rocks by relatively energetic events. It was rare in our test areas, as detailed in the discussion. Also, none of found that the dominant process of lunar rock destruction is their the test areas contained large, fresh craters in the vicinity that catastrophic disruption by the impact of one or a few energetic could have buried meter-sized boulders under its ejecta. particles capable of producing penetrating fractures at the dimen- The LROC NAC images used in our study have a spatial sional scale of the entire target rock; the much less energetic small resolution 0.5 m per pixel and we can see reliably all rock “ scale impact environment merely causes abrasion akin to sand- fragments Z2 m in diameter. The website http://apollo.mem- ” blasting and plays a minor role with hand specimen sized rocks tek.com/LRO_NAC_Apollo_Images.html was very helpful in search- (Horz et al., 1975a; McDonnell et al., 1977; Horz, 1977). This ing for the appropriate images. Within the rim of each of these conclusion was based on impact experiments with glass, basalt twelve craters, a 100 100 m2 area was selected and it was within and granite spheres and cubes, as well as with bonded sand this (high-resolution) square where we studied and counted the 2 targets, between 5 and 10 cm in size, and at impact velocities 1 abundance of surface boulders. The locations of the 100 100 m to 7 km/s (Gault and Wedekind, 1969; Gault et al., 1972 and as areas within the crater rims considered were carefully selected to detailed by Horz et al., 1975a). Horz et al. (1975a) describe the ensure that we had a typical area representative of the terrain. critical rupture energy (ER) per gram target material (ergs/g) as Fig. 2 illustrates two examples of this approach. : : Using high-resolution LROC NAC images, a total of twelve E ¼ 8:4 106 δ0 075 m0 925; R craters were studied and the results are summarized in Figs. 3–5 where δ is the target density (3 g/cm3) and m is the target mass (in and Table 2. The diameters of these twelve craters vary from 180 to grams) for targets of spherical geometry. 950 m. In principle, the difference in the crater diameters could Calculations of survival times require the use of a projectile- somehow affect our results. But because among the twelve and ultimately energy flux at the lunar surface. Horz et al. (1975a) considered craters the smaller and the larger ones are both used the microcrater production rates estimated by Hartung and morphologically fresh and subdued to very subdued, this influence Storzer (1974) and Horz et al. (1975b), and assumed these rates to seems not to result in a systematic error, but rather leads to some be constant over recent geologic history. The results of their “noise”.

Table 1 Estimates of the rock survival time (Ma) from Hӧrz et al. (1975a, Figure 11) and linear extrapolations (italics) to boulders a few meters in size.

1 Rock mass (g) 101 102 103 104 107 108 2 Rock diametera (cm) 1.85 4.0 8.6 18.5 185 400 3 Survival time median, 50% level (Ma) 1.9 4.6 10.3 22 234 497 6 Survival time 1% level, (99% destroyed) (Ma) 6 14.5 32 68 690 1550

a assuming that the rock is of spherical shape. 120 A.T. Basilevsky et al. / Planetary and Space Science 89 (2013) 118–126

The absolute formation ages of six craters were determined by clusters in between areas almost free of boulders (Fig. 3d). cosmic ray exposure studies of samples collected by the Apollo A few superposed craters, 3 to 10 m in diameter, are seen in astronauts on the rims or ejecta deposits of these craters (Arvidson Fig. 3d. et al., 1975; Borchard et al., 1986; Eugster, 1999; Funkhauser, 1971; 3) North Ray Crater, 950 m in diameter, dominates the Northern Kirsten et al., 1973a, 1973b; Stettler et al., 1973; Turner et al., 1971; portion of the Apollo 16 site (Muehlberger et al., 1972). The Waenke et al., 1971). These are: South Ray, North Ray, Cone, astronauts reached its eastern rim; they sampled its ejecta on Camelot, Surveyor and Elbow. Following is a brief summary of the rim and at some distance to the east. Based on these their characteristics: samples it was possible to estimate its age as 50 Ma (Arvidson et al., 1975; Borchard et al., 1986; Fernandes et al., 1) The morphologically very prominent South Ray Crater is 2013). In the LROC images and in situ Apollo surface photo- 680 m in diameter and dominates the southern Apollo 16 graphy it is seen that the crater rim and inner slopes are landing site (Muehlberger et al., 1972). The astronauts did not covered with numerous rock fragments with diameters from visit this crater but they could identify and sample its ejecta at 1–2to5–10 m, forming clusters among areas almost free of some distance from the crater. Its age of 2 Ma is based on the boulders (Fig. 3f). A number of craters, 3 to 10 m in diameter, cosmic ray exposure time of numerous samples (Arvidson et al., are superposed on the ejecta. 1975; Eugster, 1999). The LROC images show that the rim and 4) The morphologically degraded Camelot Crater, 650 m in inner slopes are covered with numerous rock fragments with diameter, is located at the Apollo 17 landing site (Muehlberger diameters from 2to15–20 m (Fig. 3a) and areas devoid of et al., 1973). Astronauts traversed its rim and sampled remnants boulders are rare. Several small impact craters, a few meters in of its ejecta. Based on these samples it was possible to estimate diameter, are superposed on the ejecta blanket. its age as 85 to r140 Ma (Kirsten at al., 1973b)andwe 2) The morphologically very prominent Cone Crater, 340 m in assume 100 Ma. The images taken from orbit and in situ show diameter, is located at the Apollo 14 site (Swann et al., 1971). the crater rim and inner slopes to possess clusters of rock The astronauts climbed up close to the rim crest and sampled fragments with diameters from 2 to 5 m, yet much of the test its ejecta. Based on these samples it was possible to estimate area is free of boulders (Fig. 3h). Superposed craters, 3 to 10 m in the age of Cone Crater as 26 Ma (Turner et al., 1971). In the diameter, commence to become numerous here. LROC images and in situ surface images by Apollo it is seen that 5) Surveyor Crater, 200 m in diameter, is even more degraded the crater rim and inner slopes are covered with numerous than Camelot (Shoemaker et al., 1970); the Apollo 12 lunar rock fragments with diameters from 1–2 to 10 m, forming module landed on its N-rim. The astronauts sampled remnants

Fig. 1. (a) Millimeter-sized impact crater with spallation zone (arrow) on the surface of impact melt breccia sample 73,155 (image NASA S73-2323887B). (b) Fragmented rock at The Terrace, at the edge of Hadley Rille on the Apollo 15 landing site (image NASA AS15-8211140). (c) Partially fragmented 20-m boulder at the end of its rolling and bouncing track on the slope of central peak complex of lunar crater Schiller (image LROC NAC M109502471LC). A.T. Basilevsky et al. / Planetary and Space Science 89 (2013) 118–126 121

of its ejecta and these samples yielded age estimates of 180 to but also including smaller craters that were eliminated from the 240 Ma. (Funkhauser, 1971; Waenke et al., 1971); we assume present study, because there was no assurance that they had a 200 Ma to be representative. The images taken from orbit and substantial boulder population initially. More recently, Basilevsky in situ by Apollo show rare clusters of rock fragments with and Head (2012) demonstrated that this morphologic approach to diameters from 2 to 3 m on the rim and inner slope, but most relative and absolute crater ages agrees well with dating by crater of the area is free of boulders (Fig. 3j). Superposed craters of counting methods (Morota et al., 2009). However, its accuracy is 3to15–20 m in diameter are numerous here. difﬁcult to estimate and lies probably within 750% of the 6) The morphologically degraded Elbow Crater, 400 m in dia- determined age value. meter, is located at the Apollo 15 site (Swann et al., 1972). The group of six additional craters included: Astronauts reached its rim and sampled remnants of its ejecta. Its age is estimated at 280 to 330 Ma (Stettler et al., 1973; 1) A morphologically fresh crater, 200 m diameter, 13 km south Kirsten et al., 1973a), and we assume 300 Ma. The images taken of the Luna 24 landing site, penetrating the basaltic plains of from orbit and in situ show only rare rock fragments, with Mare Crisium (Fig. 3b). It is probably a secondary crater by diameters of a few decimeters, but most of the area is boulder- ejecta from the farside crater Giordano Bruno. The morphologic free (Fig. 3l). Superposed craters of 3 to 15–20 m in diameter age of these secondaries was estimated to be between 5 and are abundant. A boulder 2 m in diameter is seen in the study 10 Ma (Basilevsky and Head, 2012). Abundant rocks of 2 to area inside a crater of about 10 m in diameter; this boulder may 10 m in diameter are seen in the study area. be not a remnant of the primary rock population of Elbow 2) A morphologically fresh 400 m crater 18 km north of the Apollo crater, but one that was excavated later by this small crater. 12 site, superposed on the basaltic plains of this region of Oceanus Procellarum (Fig. 3c). Judging from shadow measurements on The absolute ages of the other six craters are based on their image M120005333LC, the western inner slope is very steep, morphologic appearance and size, as suggested by Basilevsky about 351. This implies that this crater belongs to the morpholo- (1976). This method compares the degradational state of a crater gically prominent class A of Basilevsky (1976) and suggests that its with that of dated Apollo craters, including the above 6 structures, age is close to that of Cone Crater at the Apollo 14 landing site, i.e.

Fig. 2. (a) South Ray Crater at the Apollo 16 landing site 1 (white square outlines the area shown in Fig. 2b); (b) 100 100 m2 study-area on the rim of South Ray Crater, revealing numerous ejecta fragments of 2 to 15 m in diameter; (c) Elbow Crater at the Apollo 15 landing site (white square refers to Fig. 2d); (d) 100 100 m2 study-area on the rim of Elbow Crater; note the general absence of rock fragments (arrow points at one questionable rock fragment), and the presence of numerous craters superposed on the ejecta deposit. (parts of LROC NAC images M144524996RC and M117467833RC, respectively). 122 A.T. Basilevsky et al. / Planetary and Space Science 89 (2013) 118–126

between 20 and 30 Ma (Basilevsky, 1976). Abundant rocks of 2 to is 22 m. This diameter/depth ratio identiﬁes this crater as 10 m in diameter are seen in the study area. morphologic class B, yet close to the AB boundary of Basilevsky 3) The third member is a 180 m crater near the Lunokhod 1 site in (1976).Weestimateitsagetobe30to40Ma.Blocks2to5min Mare Imbrium (Fig. 3e). It is 350 m west of the small crater Albert diameter with a few larger ones are seen in the study area, but (http://planetarynames.wr.usgs.gov/). Its depth, as measured on signiﬁcant parts are almost free of them. Several craters smaller the topographic map of this area (Karachevtseva et al., 2012, 2013), than 10 m in diameter are seen in the study area.

Fig. 3. The 100 100 m2 analysis areas on the rims of twelve lunar craters for which absolute formation ages were known or estimated: (a) South Ray Crater at the Apollo 16 site, (b) 200 m crater in the vicinity of Luna 24 site, (c) 400 m crater in the vicinity of Apollo 12 site, (d) Cone Crater at the Apollo 14 site, (e) 180 m crater in the area of Lunokhod 1, (f) North Ray Crater at Apollo 16, (g) 450 m crater Borya in the area of Lunokhod 1, (h) Camelot Crater at Apollo 17, (i) Spook Crater close to the Apollo 16 lander, (j) Surveyor Crater 1 at Apollo 12, (k) 300 m crater at the Apollo 14 site, (l) Elbow crater at the Apollo 15 site. Upper right hand of each framelet identiﬁes the target terrain: H – highland, M – mare; the lower left shows the estimated crater age. White arrows show rock fragments. Parts of images M144524996RC, M119449091RE, M120005333LC, M114064206LC, M175502049RC, M129187331LC, M175502049RC, M134985003LC, M126825870LC, M117650516RC, M131765772LC, and M117467833RC, respectively.

Fig. 4. Cumulative number of rocks 42 m in each of the 100 100 m2 analysis areas of the 12 lunar craters labeled (a–l) in Fig. 3. Gray symbols designate highland sites and black symbols represent mare sites. Note the systematic decrease of boulder populations with increasing crater age (a–l). A.T. Basilevsky et al. / Planetary and Space Science 89 (2013) 118–126 123

4) The fourth crater is the 450 m crater Borya (http://planetary Analyzing the shadow geometries of images M132943081RC names.wr.usgs.gov/); it is also located in the Lunokhod 1 area of and M131765772LC, the depth/diameter ratio of this crater is Mare Imbrium (Fig. 3g). Its depth is 52 m. (Karachevtseva 1/10. This places it at the boundary between morphologic et al., 2012, 2013). This identifies this structure as morphologic classes B and BC of Basilevsky and Head (2012) and suggests class AB, close to the boundary with B of Basilevsky (1976). that its age is close to 300 Ma (Basilevsky, 1976). A few We estimate its formation age to be 50 to 60 Ma. Blocks 2 to boulders of 2–4 m in diameter are seen in the study area. 5 m in diameter with a few larger ones are seen dispersed in Numerous craters smaller than 10 m in diameter occur in the the study area. Craters smaller than 10 m in diameter are seen study area. in the study area. 5) The morphologically degraded crater Spook, some 700 m in As can be seen in Figs. 3–5, and Table 2, the rims of the first diameter, is located 500 m west of the Apollo 16 lunar three craters having ages of 2, 5–10 and 20–30 Ma, respectively, module (Fig. 3i). Judging from shadow measurements of image have very rocky, pristine surfaces. Rims of the next three craters M102064759RC taken at the Sun elevation 91, the depth/ with the ages 26, 30–40 and 50 Ma have moderately rocky diameter ratio of this crater is about 1/7. This places it at the surfaces and it appears that 50% or more of their primary rock boundary between morphologic classes AB and B. We suggest a population has been destroyed. Rims of the next two craters, formation age of 150–200 Ma. Several craters 10–20 m in having ages 50–60 and 100 Ma, show the presence of the rock diameter are seen in the study area. A boulder 2m in clusters, but most of the rim area is devoid of rock fragments. diameter is seen in the study are on the rim of the 20 m crater. Referring to Figs. 4 and 5, typical spatial densities for 42m It may be not a remnant of the primary rock fragment field of boulders in fresh craters such as South Ray are 300–400 per test Spook crater, but excavated by this relatively small crater. area of 100 100 m (0.01 km2). The spatial densities for boulders 6) This morphologically degraded crater, 300 m in diameter, 410 m in Fig. 4 compare favorably with earlier boulder counts on occurs 150 m NNE of the Apollo 14 lunar module (Fig. 3k). fresh craters by e.g. Cintala and Mc Bride (1995), yet the improved

Fig. 5. Number of boulders 42 m observed in a 100 100 m2 analysis area of 12 lunar craters 4 of known or estimated formation age; letters refer to craters in Fig. 3.

Table 2 Characteristics of craters of known absolute age and whose rims were used to study the population of boulders 42m.

Key to Site Crater Crater size Crater age References Rock abundance Superposed crater Fig. 3 name (m) (Ma) abundance

a Apollo 16, H South Ray 680 2 Arvidson et al. (1975), Eugster (1999) Very high Low b Luna 24, M Unnamed 200 5–10 Basilevsky (1976), Basilevsky and Head (2012) Very high Low c Apollo 12, M Unnamed 400 20–30 Basilevsky (1976) Very high Low d Apollo 14, H Cone 340 26 Turner et al. (1971) High Low e Lunokhod 1, M Unnamed 180 30–40 Basilevsky (1976) High Moderate f Apollo 16, H North Ray 950 50 Arvidson et al. (1975), Borchard et al. (1986) High Moderate g Lunokhod 1, M Borya 450 50–60 Basilevsky (1976) High Moderate h Apollo 17, M Camelot 650 100 Kirsten et al. (1973b) Locally high Moderate i Apollo 16, H Spook 700 150–200 Basilevsky (1976) Rare High g Apollo 12, M Surveyor 200 200 Funkhauser (1971), Waenke et al. (1971) In some locations High k Apollo 14, H Unnamed 300 300 Basilevsky (1976) Rare High l Apollo 15, M Elbow 400 300 Stettler et al. (1973), Kirsten et al. (1973a) One quest-ionable rock High 124 A.T. Basilevsky et al. / Planetary and Space Science 89 (2013) 118–126 resolution of LROC yields substantially more meter-sized boulders objects. It is thus possible that we overestimated the 99% destruc- in our study. The spatial density of boulders 42 m drops to tion time for m sized boulders and that the latter may be as short typically o100 samples/test area for craters between 40 and as 150 Ma. The latter would bring the ratio of observed 99% and 100 Ma. This seems approximately the time frame within which 50% destruction times (some 150/50 Ma) in much better agree- some 50% of the original boulder population was destroyed. One ment with the modeled ratio of 3.1 by Horz et al. (1975a, 1975b). may also conclude that up to 70–90% of the rock population was At otherwise constant impact conditions, this ratio depends only destroyed at craters some 120–150 Ma old. The rims of the 3 oldest on the size frequency of the impactors. craters (4 200 Ma) have o10 boulders/test area, if not no5, In our consideration we assumed that all boulders observed on suggesting that 495% of all boulders were destroyed. The oldest the crater rims are produced or exposed in the initial cratering structure investigated is the 400 m Elbow Crater and it had had event and then evolved on the surface. We do not think that such only one marginally visible boulder 42 m on its rim and ejecta processes as excavations of boulders by newly formed smaller blanket. It is important to note that on the rims of relatively young craters or burial of boulders by ejecta could significantly distort (o100 Ma) craters (cases a through h in Figs. 3 and 4) boulders of our results. Such cases certainly can happen (Fig. 3i and l), but as it 10–20 m across are present although rare, but on the rims of is seen in Figs. 3 and 5 and in Table 2 the most significant changes relatively old (4150 Ma) craters (cases i through l in Figs. 3 and 4) in the areal densities of boulders on the rims of the considered only boulders 2–4 m across are seen. craters happened within the first 50 Ma. Calculations using the Rounding the crater formation ages and preserved rock popu- lunar crater production curve by Neukum (1983) show that during lations as shown in Fig. 5, we estimate the survival times of this time period within the considered 100 100 m2 areas, only boulders 2–4 m in diameter to be as follows: the median survival several small (10–20 m in diameter) craters are expected to be time is about 40–80 Ma and the time needed to destroy 99% of the formed. Also the regolith growth rate is only approximately 1 mm/ original boulder population is about 150–300 Ma. Fig. 5 also Ma (Quaide and Oberbeck, 1975) during the Moon′s recent past illustrates that the destruction of surface boulders is relatively and we avoided contamination of the study sites by fresh ejecta fast initially, as long as such boulders occupy large fractions of the from any “large” crater, thus making burial of meter-sized boulders surface area; destruction of the last few boulders takes consider- unlikely. able, absolute time, consistent with impact as a stochastic process. We note that the experimental basis for the MC model of Horz These are general rock destruction estimates for the twelve et al. (1975a) related to collisionally destroyed targets in the kg craters investigated, seven of which formed on mare surfaces and mass range, mostly spheres and cubes of crystalline rocks o10 cm five in highland terrains. The mare target rocks are basalts which in size (Gault and Wedekind, 1969; Gault et al., 1972). As empha- are mechanically strong, while the highland targets may vary from sized and tested, the model seems consistent with diverse obser- friable breccias to mechanically strong melt-bearing breccias if not vations about the exposure history of Apollo rocks of similar sizes pure impact melts. The noticeable decrease in the rock abundance as shown in Figures 12–14 in Horz et al. (1975a). Although it was on the rim of the 26 Ma old Cone Crater (Fig. 3d) compared to the suspected that much larger targets may be mechanically weaker, 20–30 Ma old unnamed mare crater (Fig. 3c) is most likely due to a due to the increased number and sizes of intrinsic flaws (e.g. Grady systematic difference in mechanical strength of mare basalts and and Kipp, 1980, Pusch et al., 2013), it was not fully appreciated typical highland lithologies. Similar strength effects may also until Housen and Holsapple (1999) conducted appropriately scaled apply to the rocks illustrated in Fig. 3i and k. impact experiments and developed some general understanding In summary, our photogeologic approach yields values of 40– of these size-dependent strength effects. As summarized in their 80 Ma for the median survival time of lunar surface boulders some Figure 12, the effective target strength of a 20 cm object increases 2–4 m in size, and we estimate some 150–300 Ma to collisionally by a factor of 3–4 relative to a 200 cm object. Since Horz et al. destroy some 99% of these boulders. These times are significantly (1975a) used a constant strength regardless of target size, inclu- shorter than those extrapolated from the MC of Horz et al. (1975a): sion of a size-dependent strength term would reduce the survival 250–500 Ma for the 50% probability and 700–1500 Ma for the 99% times of meter-sized boulders by similar factors. Accounting for probability of destruction for 2 m diameter boulders. Our observa- this size-dependent target strength would bring the modeled tions therefore suggest that the residence times of meter-sized survival times into much closer agreement with the actual boulders are a factor of 4–5 shorter than extrapolated from Horz observations. et al. (1975a). Additional insights into the collisional destruction of surface rocks were also offered by Horz et al. (1986). The critical rupture

energy (ER) in Eq. 1 may not only be delivered by a single event of 4. Discussion magnitude ER, but also by a small number of events, eaoER; the critical rupture energy is acquired in cumulative fashion and the We demonstrated that ejecta boulders, 2–4 m in size, are question arises: what is the smallest event that contributes? The abundant on the rims of “young” (o30 Ma) lunar craters MC model of Horz et al. (1975a) integrated over all energies 0.1 ER o1 km in diameter, yet similar sized craters 4200 Ma have rims and larger, but the later experimental work by Horz et al. (1986) and ejecta deposits essentially devoid of such boulders. Using suggests that impacts as small as 0.05 ER, possibly still smaller, will these observations, we estimate the times at which 50% and 99% of contribute to the collisional destruction of finite sized objects. these boulders are destroyed, to be some 40–80 Ma and some More work is needed to determine the smallest event that 150–300 Ma, respectively. These survival or destruction times are contributes to the collisional destruction of surface boulders, but some factor of 5 shorter than those extrapolated from Horz et al. the implications are obvious: the smaller this event, the shorter (1975a, 1975b). The photogeologic observations suggest that large the surface residence times compared to the existing model of boulders are destroyed much more rapidly than one would predict Horz et al. (1975a). We estimate this effect to lead to surface from data for the decimeter-size rocks. The above observation that residence times some 20–30% shorter than modeled in 1975. the boulders of 10–20 m in diameter are observed on the rims of Additionally, the actual micrometeorite flux used by Horz at al. craters younger than 100 Ma and not seen on the rims of the older (1975a) could be in error and is known to no better than a factor of craters may suggest that the larger (10–20 m) boulders are 2–3 (see e.g. Gruen et al., 1985; Love and Brownlee, 1993). Also, the destroyed very efficiently as well. Some of the 2 m size boulders role of thermal cycling is unknown and possibly contributes to the observed occur in clusters and attest to the destruction of larger destruction of lunar surface rocks, especially of relatively large size A.T. Basilevsky et al. / Planetary and Space Science 89 (2013) 118–126 125

(e.g., Dombard et al., 2010; Capek and Vokrouhlicky, 2012; Molaro 3. The photogeologically determined estimates can provide addi- and Byrne, 2012; MacKenzie-Helnwein et al., 2009). Also, typical tional insights into the rates of surface processes on the Moon ejecta boulders may be internally fractured und of weaker rheol- and can potentially be used to estimate the formation ages of ogy than the ideal, pristine rocks used in the experimental relatively large (1–20 km), morphologically fresh, lunar craters. “calibration” studies. 4. The differences in the impact environment of the Moon and Based on the above considerations, the MC model of Horz et al. Mars suggest that the survival times of the rock fragments (1975a) must be modiﬁed and it does not apply to meter-sized Z2 m in diameter on the surface of Phobos and Deimos are lunar surface boulders. Much shorter life times for such boulders within a factor of 2 of that of the Moon. should be expected. The above estimates, approximate as they are, provide insights into the rates of surface processes on the Moon, including the correlation with the morphologic degradation of pristine craters o1 km in diameter. Our observations may also be Acknowledgments used to estimate the ages of some relatively large craters whose age is old enough to have their original rocky ejecta obliterated, We acknowledge the stimulating discussions and help of but at the same time too young to have suffered noticeable B.A. Ivanov, A.V. Ivanov, M.J. Cintala and J.L. Dickson. Work by changes in the overall crater morphology, especially rim sharpness JWH was funded by JPL Grant 1237163 for participation in the and steepness of its inner slopes. Morphologically fresh lunar High Resolution Stereo Camera Team on the Mars Express Mission, craters of 1–20 km in diameter may be candidates for such boulder which is gratefully acknowledged. FH was supported by Planetary studies. Geology and Geophysics Grant 12-PGG12-0017. Our results may also be extrapolated to estimate the survival times of rock fragments on the surface of other atmosphereless References bodies, for example, Phobos and Deimos (Thomas et al., 2000).

In the vicinity of Mars and thus on its satellites, the average impact Arvidson, R., Crozaz, G., Drozd, R.J., Hohenberg, C.M., Morgan, C.J., 1975. Cosmic ray velocity is 8.62 km/s, but on the surface of the Moon it is 16.2 km/s exposure ages of features and events at the Apollo landing sites. The Moon 13, (Ivanov, 2001). Also, the Mars/Moon crater production rate ratio, 255–276. averaged over time, has a value 2.04 for impactors originating in Basilevsky, A.T., 1976. On the evolution of small lunar craters. In: Proceedings of the 7th Lunar Science Conference, pp. 1005–1020. the asteroid belt that are responsible for craters larger than a few Basilevsky, A.T., Head, J.W., 2012. Age of Giordano Bruno crater as deduced from the tens of meters (Hartmann and Neukum, 2001). As a consequence, morphology of its secondaries at the Luna 24 landing site. Planetary and Space – the energy flux per unit time and unit surface area onto Phobos Science 73, 302 309. Borchard, R., Stoeffler, D., Spettel, B., Palme, H., Waenke, H., Wacker, K., Jessberger, (and Deimos) is approximately a factor of 4 less than that of the E.K., 1986. Composition, structure, and age of the Apollo 16 subregolith Moon, yet the impact rate is a factor of 2 higher and thus basement as deduced from the chemistry of post-Imbrium melt bombs. increasing the energy flux to within a factor of 2 of the lunar flux. Proceedings of the 17th Lunar and Planetary Science Conference. Journal of Geophysycal Research 91 (B13), E43–E54. The rate of rock disruption by meteorite impacts on the surface of Capek, D., Vokrouhlicky, D., 2012. Thermal stresses in small meteoroids. II. Effects of Phobos and Deimos should thus be a factor 2 lower compared to an insulating surface layer. Astronomy and Astrophysics 539, A25, http://dx.doi. the Moon and the rock survival times should be twice as long. But org/10.1051/0004-6361/201117697. Cintala, M.J., Mc Bride, K.M., 1995. Block distribution on the lunar surface: a other potentially important factors may also contribute, such as comparison between measurements obtained from surface and orbital photo- impacts by the low-velocity crater ejecta returning to Phobos graphy. NASA Technical Memorandum 104804, 46. after their escape to near-Mars space (Ramsley and Head, 2013), Cintala, M.J., Hӧrz, F., 2008. Experimental impacts into chondritic targets, part I: disruption of an L6 chondrite by multiple impacts. Meteoritics and Planetary and thermal stresses due to the rather large and frequent Science 43 (4), 771–803. diurnal temperature changes (from 130 to 300 K; Kuzmin and Dombard, A.J., Barnouin, O.S., Prockter, L.M., Thomas, P.C., 2010. Boulders and ponds Zabalueva, 2003). on the Asteroid 433 Eros. Icarus 210, 713–721. Eugster, O., 1999. Chronology of dimict breccias and the age of South Ray crater at the Apollo 16 site. Meteoritics and Planetary Science 34, 385–391. Fernandes, V.A., Fritz, J., Weiss, B.P., Garrick-Bethell, I., Shuster, D.L., 2013. The 5. Conclusions bombardment history of the Moon as recorded by 40Ar–39Ar chronology. Meteoritics and Planetary Science 48, 241–269. Z Funkhauser, J., 1971. Noble gas analysis of KREEP fragments in lunar soils 12033 1. Analysis of the abundance of rock fragments 2 m in diameter and 12070. Earth and Planetary Science Letters 12, 263–272. on the rims of twelve craters (150–950 m in diameter and Gault, D.E., Hӧrz, F., Hartung, J.B., 1972. Effects of microcratering on the lunar known ages of 2–300 Ma) led to estimates of the survival times surface. Proceedings of the Third Lunar Science Conference 3, 2713–2744. Gault, D.E., Wedekind, J.A., 1969. The destruction of tektites by micrometeoroid of such rocks on the surface of the Moon. It was found that the impact. Journal of Geophysycal Research 74, 6780–6794. median survival time (50% of the original rock population Grady, D.E., Kipp, M.E., 1980. Continuum modeling of explosive fracture in oil shale. destroyed) is about 40–80 Ma, while 99% of such rocks are International Journal of Rock Mechanics and Mining Science Abstracts 17, – – 147 157. destroyed in about 150 300 Ma. Gruen, E., Zook, H.A., Giese, R.H., 1985. Collisional balance of the meteoritic 2. These observed survival times are approximately a factor complex. Icarus 62, 244–272. 5 shorter than those extrapolated from Horz et al. (1975a). Hartmann, W.K., Neukum, G., 2001. Cratering chronology and the evolution of Mars. Space Science Reviews 96, 165–194. This apparent disagreement is due to a number of factors. Hartung, J.B., Storzer, D., 1974. Lunar microcraters and their solar flare track record. As demonstrated by Housen and Holsapple (1999) the effective In: Proceedings of the 5th Lunar Science Conference, pp. 2527–2541. strength of meter sized boulders is less than that of decimeter- Horz, F., 1977. Impact cratering and regolith dynamics. Physycs and Chemistry of – sized targets used in the experimental basis of the Horz et al. the Earth X, X, 3 15. Horz, F., Schneider, E., Hill, R.E., 1974. Micrometeoroid abrasion of lunar rocks: a model; also, numerous less energetic events than those Monte-Carlo simulation. Proceedings of the 5th Lunar Science Conference 3, employed by Horz et al. (1975a) will contribute in cumulative 2397–2412. fashion to the catastrophic disruption of surface rocks (Horz Horz, F., Schneider, E., Gault, D.E., Hartung, J.B., Brownlee, D.E., 1975a. Catastrophic rupture of lunar rocks: a Monte-Carlo simulation. The Moon 13, 235–238. et al., 1986). Diurnal temperature cycling and associated stres- Horz, F., Brownlee, D.E., Fechtig, H., Hartung, J.B., Morrison, D.A., Neukum, G., ses may also contribute to the destruction of lunar surface Schneider, E., Vedder, J.F., Gault, D.E., 1975b. Lunar microcraters—Implications rocks (e.g. Molaro and Byrne, 2012). Additionally, the original for the micrometeoroid complex. Planetary and Space Science 23, 151–172. Horz, F., Cintala, M.J., See, T.H., Cardenas, F., Thompson, T.D., 1986. Collisional ejecta boulders may be fractured and weakened relative to the fragmentation of granodiorite targets by multiple impact events, The 26th pristine rocks employed in the experimental impact studies. Lunar and Planetary Science Conference, Abstract # 364. 126 A.T. Basilevsky et al. / Planetary and Space Science 89 (2013) 118–126

Housen, K.R., Holsapple, K.A., 1999. Scale effects in strength-dominated collisions of Neukum, G., 1973. Micrometeoroidal ﬂux, microcrater population development and rocky asteroids. Icarus 142, 21–33. erosion rates of lunar rocks. Lunar Science IV. Abstracts. The Lunar Science Ivanov, B.A., 2001. Mars/Moon cratering rate ratio estimates. Space Science Reviews Institute. Houston, pp. 558–560. 96, 87–104. Neukum, G., 1983. Meteoritienbombardement und Datierung planetarer Oberﬂa- Karachevtseva I.P., Konopichin А.А., Shingareva K.B., Cherepanova E.V., Gusakova E.N., chen, Habilitation Dissertation for Faculty Membership. Ludwig-Maximilians- Baskakova M.A. (2012) Atlas of Lunokhod-1: GIS Mapping and Analysis of the University, Munich p. 186. Region Landing Site “Luna-17” Based on Lunar Reconnaissance Orbiter. Modern Pusch, R., Weston, R., Knutsson, S., 2013. Impact of scale on rock strength. Journal of Problems of Remote Sensing of the Earth from Space, Moscow. Space Research Earth Sciences and Geotechnical Engineering 3 (2). Institute, pp. 292–304 (in Russian). Quaide, W.L., Oberbeck, V.R., 1975. Development of the mare regolith: some model Karachevtseva, I., Oberst, J., Scholten, F., Konopichin, А., Shingareva, K., Cherepa- considerations. The Moon 13, 27–55. nova, E., Gusakova, E., Haase, I., Peters, O., Plescia, J., Robinson, M., 2013. Ramsley, K.R., Head, J.W., 2013. Mars impact ejecta in the regolith of Phobos: bulk Cartography of the Lunokhod-1 landing site and traverse from LRO Image and concentration and distribution. Planetary and Space Science, in press. Stereo topographic data. Planetary and Space Science, http://dx.doi.org/10.1016. Robinson, M.S., Brylow, S.M., Tschimmel, M., Humm, D., Lawrence, S.J., Thomas, P.C., j.pss.2013.06.002, in press. Denevi, B.W., Bowman-Cisneros, E., Zerr, J., Ravine, M.A., Caplinger, M.A., Kirsten, T., Horn, P., Kiko, J., 1973a. Ar40-Ar39 Dating of Apollo 16 and Apollo 15 Ghaemi, F.T., Schaffner, J.A., Malin, M.C., Mahanti, P., Bartels, A., Anderson, J., Rocks and Rare Gas Analysis of Apollo 16 Soils. Lunar Science IV. Abstracts. The Tran, T.N., Eliason, E.M., McEwen, A.S., Turtle, E., Jolliff, B.L., Hiesinger, H., 2010. Lunar Science Institute. Houston, 3, pp. 438–440. Lunar reconnaissance orbiter camera (LROC) instrument overview. Space – – Kirsten, T., Horn, P., Heinemann, D., 1973b. Chronology of the Taurus–Littrow region Science Reviews 150 (1 4), 81 124. Shoemaker, E., 1971. Origin of Fragmental Debris on the Lunar Surface and the I: ages of two major rock types from the Apollo 17 site. Earth and Planetary History of Bombardment of the Moon. Instituto de Investigones Geologicas de Science Letters, 125–130. la Deputacion Provincial, vol. XXV. Universidad de Barcelona. Kuzmin, R.O., Zabalueva, E.V., 2003. The temperature regime of the surface layer of Shoemaker, E.M., Batson, R.M., Bean, A.L., et al., 1970. Preliminary geologic the Phobos regolith in the region of the potential Fobos-Grunt space station investigation of the Apollo 12 landing site, Part A, Geology of the Apollo 12 landing site. Solar System Research 37 (6), 480–488. landing site, Apollo 12 Preliminary Science Report. NASA SP-235, Washington Love, S.G., Brownlee, D.E., 1993. A direct measurement of the terrestrial mass D.C., pp. 113–156. accretion rate of cosmic dust. Science 262, 550–553. Stettler A., Eberhardt P., Geiss J., Grogler N., Maurer P., 1973 Ar39–Ar40 ages and MacKenzie-Helnwein, P., Hallet, B., Hankins, K., 2009. Solar-induced thermal Ar37–Ar38 exposure ages of lunar rocks. In: Proceedings of 4th Lunar Science stresses in surface rocks. AGU Fall Meeting 2009. Abstract #EP51A-0580. Conference, pp. 1865–1888. McDonnell, J.A.M., Ashworth, D.G., Flavill, R.P., Carey, W.C., Bateman, D.C., Jennison, Swann, G.A., Bailey, N.G., Batson, R.M., et al., 1971. Preliminary geologic investiga- R.C., 1977. The characterization of lunar surface impact erosion and solar wind tion of the Apollo 14 landing site, Apollo 14 Preliminary Science Report. NASA sputter processes on the lunar surface. Philosophical Transactions of the Royal SP-272, Washington, D.C., pp. 39–85. Society of London Series A: Mathematical and Physical Sciences 285 (1327), Swann, G.A., Bailey, N.G., Batson, R.M., et al., 1972. Preliminary geologic investiga- – 303 308. tion of the Apollo 15 landing site, Apollo 15 Preliminary Science Report. NASA Molaro, J, Byrne, S., 2012. Rates of temperature change of airless landscapes and SP-289, Washington, D.C., pp. 5-1–5-112. implications for thermal stress weathering. Journal of Geophysical Research Thomas, P.C., Veverka, J., Sullivan, R., et al., 2000. Phobos: regolith and ejecta blocks 117, E10011, http://dx.doi.org/10.1029/2012JE004138. investigated with Mars orbiter camera images. Journal of Geophysical Research Morota, T., Haruyama, J., Miyamoto, H., Honda, C., Ohtake, M., Yokota, Y., Matsu- 105, 15091–15106. naga, T., Hirata, N., Demura, H., Takeda, H., Ogawa, Y., Kimura, Y., 2009. Turner, G., Huneke, J.C., Podosek, F.A., Wasserburg, G.J., 1971. 40Ar–39Ar ages and Formation age of the lunar crater Giordano Bruno. Meteoritics and Planetary cosmicray exposure ages of Apollo 14 samples. Earth and Planetaery Science Science 44 (8), 1115–1120. Letters 12, 19–35. Muehlberger, W.R., Batson, R.M., Boudetter, E.L., et al., 1972. Preliminary geologic Waenke, H., Wlotzka, F., Baddenhausen, H., Balacescu, A., Spettel, B., Teschke, F., investigation of the Apollo 16 landing site, Apollo 16 Preliminary Science Jagoutz, E., Kruze, H., Quinjano-Rico, M., Rieder, H., 1971. Apollo 12 samples: Report. NASA SP-315, Washington, D.C., pp. 6-1–6-81. Chemical composition and its relation to sample locations and exposure ages, Muehlberger, W.R., Batson, R.M., Cernan, E.A., et al., 1973. Preliminary geologic the two component origin of the various soil samples and studies on lunar investigation of the Apollo 17 landing site, Apollo 17 Preliminary Science metallic particles. In: Proceedings of the 2nd Lunar Science Conference, pp. Report. NASA SP-330, Washington, D.C., pp. 6-1–6-91. 1187–1208.