In situ fragmentation of lunar blocks and implications for impacts and solar-induced thermal stresses

Icarus 336 (2020) 113431

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In situ fragmentation of lunar blocks and implications for impacts and solar-induced thermal stresses O. Ruesch a, *, E. Sefton-Nash a, J.L. Vago a, M. Küppers b, J.H. Pasckert c, K. Khron d, K. Otto d a

ESTEC, European Space Agency (ESA), Noordwijk, the Netherlands ESAC, European Space Agency (ESA), Villanueva de la Ca~ nada, Spain c Institute of Planetology, Westfaelische-Wilhelms Universitaet, Muenster, Germany d Institute of Planetary Research, German Aerospace Center (DLR), Berlin, Germany b

A B S T R A C T

This study deals with an aspect of blocks observed on many rocky planetary surfaces: in situ fragmentation. Using LROC/NAC images, we characterized the morphology, morphometry and abundance of in-situ fractured blocks observed on the rim of six large impact craters of known emplacement age on the Moon. The relative number of disrupted blocks increases with crater-retention age of surfaces on which blocks are hosted, consistent with fragmentation post-emplacement due to impacts of small meteoroids. The type of break-up morphologies we observe appears to be independent of surface exposure age of the blocks. The inferred flux and size frequency distribution of projectiles responsible for disrupting blocks is consistent with expected lunar impact fluxes. Block fragmentation due to insolationdriven thermal stresses is subordinate to impacts. The possible effects of thermal stresses are evident as meridional cracks, which have preferred orientations in a young block population (~4 Ma), and as loose material (fillet) developing on top of surviving blocks in old populations (>800 Ma).

1. Introduction At a spatial scale from centimeters to tens of meters, blocks and rootless boulders are a major surface feature on solid planets and small bodies. The term block (including megablock) refers to the size range 1–100 m, that can be imaged from orbit, whereas the term boulder is used for the smaller size range, 0.1–1 m, visually accessible to landers and rovers (Bruno and Ruban, 2017). Observations at local scale by orbiters, landers and rovers have demonstrated that blocks and boulders are abundant on planetary landscapes at sub-km scales, compared to other ubiquitous planetary landforms such as impact craters and basins, which can populate surfaces at much larger spatial scales. A number of properties of blocks and boulders have been studied. The size frequency distribution of blocks has been extensively measured and used to infer the processes leading to block formation (e.g., Hartmann, 1969; Cintala and McBride, 1995; Thomas et al., 2001; Pajola et al., 2015; Küppers et al., 2011; Basilevsky et al., 2013). The morphology and morphometry of blocks has been characterized and compared to that obtained in laboratory experiments or encountered in Earth analogues to infer for­ mation and modification processes (e.g., Thomas et al., 2002; Noguchi et al., 2010; Yingst et al., 2013; Golombek and Rapp, 1997; Ehlmann et al., 2008). Where the source region of blocks is identified, such as in association with impact craters, the relationship between block size,

frequency and distance to the inferred source has been investigated to better understand the impact process (e.g., Bart and Melosh, 2010; Schulzeck et al., 2018). The spatial distribution and abundance of blocks measured from optical imagery and thermal inertia datasets has been used for regolith studies (Ghent et al., 2014; Basilevsky et al., 2015; Li et al., 2018; Denevi et al., 2016). An aspect that has received relatively little attention is the obser­ vation of blocks or boulders fractured in situ, reported to be present on many planetary surfaces. Fracturing in situ is considered in this work to correspond to instances of disruption without dispersion, i.e., this defi­ nition denotes a split block or boulder whose fragments have not been scattered and can thus be traced back to their original position in the parent block or boulder. On asteroids, fragmented ejecta blocks have been associated with rupture during emplacement (e.g., Thomas et al., 2001; Robinson et al., 2002), or with post-emplacement rupture by small impacts (Robinson et al., 2002; Durda et al., 2011) or by thermal stresses from thermal daynight cycling (Delbo et al., 2014; Molaro et al., 2017). On asteroid Ito­ kawa, fractured blocks in a pair or family configurations have been observed, and both rupture during low velocity impact of blocks onto the surface and rupture after emplacement by small impacts have been discussed, with the latter option being preferred (Nakamura et al., 2008). On asteroid Ryugu, a block was identified during preliminary

* Corresponding author at: ESA/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, the Netherlands. E-mail address: [email protected] (O. Ruesch). https://doi.org/10.1016/j.icarus.2019.113431 Received 11 June 2019; Received in revised form 21 August 2019; Accepted 29 August 2019 Available online 4 September 2019 0019-1035/© 2019 Elsevier Inc. All rights reserved.

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observations whose fracture systems were deemed consistent with an impact origin (Sugita et al., 2019). On asteroid Bennu, instead, initial surface observations revealed a disaggregated block with fragment pattern suggestive of thermal fatigue wasting (Lauretta et al., 2019; DellaGiustina et al., 2019), as well as a number of features consistent with both impacts and thermal fatigue effects (Walsh et al., 2019). On Mars, relatively few split boulders have been reported by rover missions. For those instances, the likely cause of fracturing was proposed to be the expansion of salt veins (Yingst et al., 2013), although the effect of meteoroid impacts has also been considered a possibility (Hoerz et al., 1999). Effects of thermal shock on Mars have been associated with boulders exhibiting cracks in a preferential orientation (Eppes et al., 2015) and thermal fatigue has been suggested responsible for enhanced erosion of crater wall outcrops (Tesson et al., 2019). On the Moon, in situ fragmentation has been reported in surface observations by Apollo as­ tronauts and from returned rocks (Gault et al., 1972; Hoerz et al., 1975). In these works, rupture was associated with impact(s) on the block by one or more high-velocity meteoroids (Gault et al., 1972; Hoerz et al., 1975). Instead, whenever blocks were seen at the foot of hills or of crater walls, rupture during roll-down was mentioned as the most likely cause (A17 Preliminary Science Report). A striking example of poor under­ standing of block fragmentation is the observation of a cracked boulder by the Surveyor 7 lander at Tycho crater, for which competing in­ terpretations were reported: thermal expansion and contraction (Sur­ veyor Program Results, 1969) and impact (Phinney et al., 1969). Indeed, there remains ambiguity about the cause of rock fracturing processes (Basilevsky et al., 2015). From a review of the literature we suggest that blocks fragmented in situ may represent an important stage in the comminution process of planetary surfaces. Thus, the study of fragmented blocks may contribute to our fundamental understanding of surface evolution, and, due to their ubiquity, would be an ideal tool for comparing processes on different planetary objects. Despite their scientific potential, the literature shows that the processes leading to in situ fragmentation have not been studied either in a systematic manner or in much detail. In particular, it is un­ clear at which moment most of the in situ fragmentation occurs: (1) during block emplacement on the surface (e.g., landing of ejecta block, roll-down, rubble pile re-accumulation) or (2) after their emplacement. In the latter scenario, which process (impacts or thermal fracturing), or which interplay of processes, drives rock breakdown, for a certain planetary body and environment. In addition, current literature studies using remote sensing data are deficient in providing a thorough description and characterization of the morphologies of fractured blocks. In this work, we focus on blocks on the Moon because of the availability and quality of observations and of ancillary information like the chronology of surface units. This study aims to address the following objectives:

mass wasting settings, such as cliff collapses and rock falls, have not been considered. For our work, it was necessary to select a well-characterized geological context in order to disentangle the various processes acting at different times or settings. The outer rims of impact craters (i.e., excluding the inner crater wall) were chosen because of three relevant properties: (i) all observed blocks are known to have formed as ejecta in a single and geologically instantaneous temporal instance (e.g., Melosh, 1989), (ii) the impact event leading to ejecta block formation can be accurately dated using crater size-frequency distribution measurements performed on the ejecta unit (e.g., Hiesinger et al., 2012; Ruesch et al., 2014), (iii) the absence of steep slopes on the rim and therefore the impossibility to have fragmented blocks by rolldown or to have clus­ tered blocks due to mass wasting (e.g., rock fall). Six lunar impact craters with known presence of blocks and well determined absolute model ages from crater size frequency distributions measurements have been uti­ lized for this work. They are: (1) Giordano Bruno, (2) Byrgius A, (3) Tycho, (4) Aristarchus, (5) Copernicus and (6) King craters. This set of craters was previously identified and studied by Ghent et al. (2014). Crater diameters range between 19 and 97 km and crater absolute model ages span the range ~4 to ~992 Ma (see Table 1). This age bracket corresponds well with the expected lifetime of lunar blocks of slightly smaller size (~2–10 m) because as estimated by Basilevsky et al. (2013), by 150–300 Ma, approximately 99% of an initial block population should have been erased. The age estimate of Aristarchus used in this €nig and study (Zanetti et al., 2011) is within previous estimates (Ko Neukum, 1976) and encompasses more recent measurements without considering self-secondary cratering (Zanetti et al., 2017). We note that the six crater block populations are characterized by high thermal inertia (Ghent et al., 2014). At each crater rim, we performed two types of measurements for addressing two objectives mentioned in the introduction. For objective (1) we examined all blocks larger than 20 m. Imposing this minimum size limit enabled us to focus on blocks that had been imaged with sufficient spatial resolution (�50 pixels/block); and thus, to characterize the morphology of their fractures. We note, however, that recognition of in situ fragmentation is possible also on smaller blocks, as discussed further below. For each block showing fracture or crack morphologies, we measured its distance to the crater wall escarpment and determined a morphometry parameter. We chose to use a morphometry parameter that can be applied to a wide range of spatial configurations of fragments: the spatial density Δ, defined as follows (Fig. 1): � Δ ¼ Alargest fragment Acluster (1)

(1) Investigate the morphologies of blocks fragmented in situ as a function of surface exposure age, by taking advantage of wellknown regions on the Moon whose chronology is known. (2) Study the abundance of lunar fragmented blocks with respect to the entire block population and as a function of surface exposure age.

Table 1 List of lunar impact craters used in this study and previously selected by Ghent et al. (2014). The absolute model ages of the craters are derived from crater sizefrequency distributions in Morota et al. (2009), Hiesinger et al. (2012), Zanetti et al. (2011), and Ashley et al. (2012). Craters Aristarchus and Copernicus impacted on mare material but excavated blocks from a depth reaching high­ lands material.

2. Method For the purpose of this study, we define the unambiguous identifi­ cation of an instance of block breakdown in situ with the observation of a fracture that separates, in planar (nadir) view, parallel facets of two or more fragments, i.e., the fracture planes must have matching facets. For other cases, where the fracture width is similar to or exceeds the size of the largest fragment and the facets are curvilinear in planar view, the genetic link can be established by the presence of loose material (fillet) and smaller fragments in a cluster configuration. We note that in this study we are not interested in gravity-driven fragmentation. Therefore, 2

Crater name

Age (Ma) ( Ghent et al., 2014)

Diameter (km)

Type of excavated bedrock

Latitude (N)

Longitude (E)

Giordano Bruno Byrgius A Tycho Aristarchus

4�1

22

Highlands

36.0

102.9

47 � 14 85 � 18 175 � 10

19 86 40

24.6 43.3 23.7

296.2 348.8 312.5

Copernicus

797 � 52

97

9.6

339.9

King

992 � 89

77

Highlands Highlands Maria/ Highlands Maria/ Highlands Highlands

4.9

120.5

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Fig. 1. Schematic representation of blocks fractured in situ. Fragmentation in situ is defined by the presence of parallel fracture planes in a cluster of fragments. The fragments are shown as black polygons and the measured area of the cluster (Acluster) is illustrated with a dashed red line (slightly larger for clarity). Here the parallel fractures planes and the ratio of the area of the largest fragment to the area of the parent body are relevant, not the fragment shape or spatial configuration. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

where Alargest fragment is the area of the largest fragment and Acluster is the total area grouping all fragments belonging to a single disrupted block. Acluster corresponds to a polygon area encompassing all fragments (mapped as polygons), where polygon edges between fragments are straight lines. For weakly disrupted blocks, Acluster more or less coincides with the area of the parent block, whereas for highly catastrophic dis­ ruptions, Acluster can be larger than the area of the parent block because fragments may have experienced some degree of dispersion. Note that it was not possible to consider the smallest (<5 m) fragments in Acluster due to poor imaging resolution—in particular for cases with many (>5) fragments. We note that for highly fractured blocks, Acluster can be estimated with less reliability compared to weakly fractured cases, and that, in general, a conservative approach was taken for mapping Acluster. The fragment spatial density is similar to the ratio of the masses between the largest fragment and the parent block, used extensively in impact studies (e.g., Benz and Asphaug, 1999; Housen and Holsapple, 1999). The measurement of the orientation of crack, i.e., narrow fractures, on blocks was performed with the following restrictions: (i) only mea­ surements on surfaces of blocks normal to the zenith, and (ii) avoidance of joints (i.e., fracture with no visible movement) or pre-existing layering. For objective (2), the approach we employed was to measure which fraction of a given block population is fractured. To obtain statistically reliable counts, we extended the measurements to blocks smaller than 20 m. Because of the smaller block size, however, not all morphological details could be captured. Thus, we limited the classification to two classes (Fig. 1). The first class includes un-fractured or partially frac­ tured blocks. The latter are blocks with Δ > 0.5. The second class groups blocks with Δ � 0.5. For this task, the estimation of Δ was performed visually without mapping the areas of the fragments as polygons. In addition to classifying blocks, the size of each fragmented block was estimated by fitting its shape to a circle. Although approximate, the use of a circle shape enabled rapid manual measurements, as previously shown by De Rosa et al. (2012). These measurements were performed within several 500 m � 500 m areas at each crater rim, up to a distance of 0.3 (distance from rim/crater radius) from the rim escarpment. Measurements on blocks were performed on map-projected Narrow Angle Camera (NAC) images acquired by the Lunar Reconnaissance Orbiter (LRO), with a pixel resolution in the range 0.5–1.5 m/pixel (Robinson et al., 2010). In the absence of 3-dimensional information, images with different incidence angles, namely with high (~60� ) and low (~20� ) angles, were used to better understand the shape and height of blocks above the surroundings, as well as the spatial configuration between fragments. To minimize potential bias caused by the original coherence of blocks, we considered only monolith blocks and did not

consider blocks with a breccia texture (i.e., block composed of varying albedo or texture), because of their different strength. The major min­ erals of blocks are expected to vary for the different craters as a function of two different bedrocks, identified in Table 1. We suspect that fragmentation by meteoroid impacts might be the dominant disruption process on the Moon (Basilevsky et al., 2015). Therefore, we test whether the flux and the size frequency distribution of the putative meteoroids responsible for disrupting blocks are consistent with estimates of the flux and size frequency distribution of meteoroids impacting the Moon. We subdivided our measurements into four bins based on the circular area of the clusters, (Acluster): 50–100 m2, 100–200 m2, 200–300 m2 and 300–400 m2. For each area bin, we defined the mean area in a bin: 75, 150, 250, 350 m2. For each of the four bins we determined the ratio: � Nfractured Ntotal � Amean bin (2) with Nfractured the number of strongly (0.3 � Alargest fragment / Aclus­ fractured blocks in the area bin and Ntotal the number of frac­ tured and un-fractured blocks in the area bin. We assume that each strongly fractured block is the result of a single impact by a projectile of size ddisrup. The energy of the impact is inversely proportional to the ratio of mass or area of the largest fragment to the mass or area of the target block: 0.3 � Mlargest fragment / Mtarget block � 0.5. The value Mlargest fragment / Mtarget ¼ 0.5 is referred to as QS* and Mlargest fragment / Mtar­ get ¼ 0.3 is ~1.6QS* (Benz and Asphaug, 1999). This general assumption is most reasonable for the youngest population because Hoerz et al. (1975) finds that catastrophic disruptions (i.e., Alargest fragment / Aclus­ ter � 0.5) from single impacts are most common for young populations. Catastrophic disruption in older populations is more likely to occur as a result of multiple impacts, each with an energy <
� �1=3 ddisrupt ¼ 2Q*S Vimp 2 Dtarget

(3)

where Q*S is the specific energy required to shatter a target into frag­ ments, the largest one having half the mass of the original target. The parameter Vimp is the velocity of the impactor (18 km/s) and Dtarget is the size of the target block. There is a lack of theoretical study that 3

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investigated the energy required to shatter a block in the gravity field of the Moon. Therefore, for estimating Q*S we take advantage of the numerous studies and simulations of asteroid disruptions. We use the estimate of a mean catastrophic disruption threshold Q*D provided by Benz and Asphaug (1999): � � �a �b Rpb Rpb þ Bρ (4) Q*D ¼ Q0 1 cm 1 cm

been thoroughly investigated yet (Benz and Asphaug, 1999; Bottke et al., 2005). We assume that the impact velocity has relatively little effect relative to the effect of porosity for the size of targets under consideration. For example, Bottke et al. (2005) find differences of factor 2–3 in Q* due to velocity variation in the range 1–10 km/s, for a 10 m large target. We compare our cumulative number of putative impacts for a given size of projectile to estimates of meteoroid flux observed on the Earth atmosphere. Actual flux measurements for projectiles in the size 0.2 to 1.0 m do not exist (e.g., Drolshagen et al., 2017). Therefore, we use the extrapolation of Brown et al. (2002) that uses measurements performed during 8.5 years of small near-Earth objects of sizes above 1 m colliding with the Earth. We also compare our measurements to the observations of fireballs in the range 0.12–0.21 m (Halliday et al., 1996). In order to use these model fluxes for the comparison with our data we assume the cumulative number of impacts yr 1 recently measured has remained constant in the past and can be used to calculate the cumulative number of impacts for 4 Ma, 47, 84 and 175 Ma (possible variations have been suggested for older surfaces, >200 Ma, Mazrouei et al., 2019). We use the estimates of Oberst et al. (2012) for the flux of objects colliding with the Moon based on the correction for the difference in gravitational acceleration between the Earth and the Moon. In general, the difference

where Rpb is the radius of the parent body (parent block in this study) and ρ the density of the parent block (in g/cm3). Q, B, a and b are pa­ rameters that have been determined for different target properties and impact speeds (Benz and Asphaug, 1999). We use the available values that more closely approximate the lunar conditions. The highest most value of velocity in the Benz and Asphaug (1999) study is 5 km/s and leads to Q ¼ 2.9e7 (erg/g), B ¼ 1.5 (erg cm3/g2), a ¼ 0.35 and b ¼ 1.29 for a basaltic non-porous target (from Jutzi et al., 2010). A non-porous material is likely for fresh lunar blocks. However, one might expect the material properties to vary depending on the type of block (competent basaltic lava, breccia, anortositic material) and surface exposure age. Therefore, we considered an additional set of parameters in Eq. (4) that reflects porous material (Jutzi et al., 2010). The de­ pendency of Q*D on the projectile velocity in the strength regime has not

Fig. 2. Typical examples of blocks fractured in situ observed on the rim of six lunar craters. The size of the blocks is in the range 20–100 m. The apparent degree of fragmentation increases qualitatively from right to left, and can be described in terms of the area of the largest fragment to the area of the parent block. The surface exposure time of the blocks increases from top to bottom. (a) Giordano Bruno, (b) Byrgius A, (c) Tycho, (d) Aristarchus, (e) Copernicus, and (f) King craters. 4

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landing (Fig. 3b) because a flow of impact melt is observed between two fragments. This morphology is much less frequent than the previous one. Aside from the rare cases described above, for which establishing the origin of the fragmentation is straightforward, there is much diversity in terms of fragment shapes and relative orientation. Nevertheless, two major types of block disruption configurations can often be recognized at several crater rims. The first configuration is characterized by a main central fragment surrounded by fragments of similar or smaller sizes, forming an annulus pattern (“core shattering”, Fig. 4a). The second configuration consists of a few fragments having a roughly triangular shape spread radially, without a central fragment (“cone shattering”, Fig. 4b). Fig. 4c illustrates another possible case of “cone shattering” where the major fragment is curvilinear. We performed size-frequency distribution measurements of frag­ ments on single disrupted blocks showing abundant fragments (Fig. 5). We find that the fragments size-frequency distributions follow a powerlaw distribution with an exponent in range 3.3 to 6.0, calculated excluding the largest fragments. We also find instances with a distinct shape of the distribution (Fig. 5b) characterized by several large frag­ ments and relatively fewer smaller fragments. In the case shown in 5b, there is no observational evidence for enhanced coverage of fragments by loose material relative to other clusters (Fig. 5c) like hummocky morphology or partial burials of fragments. This suggests that the dis­ tribution is likely pristine and that is not the result of burial of the smaller fraction of fragments by nearby ejecta. We found different types of crack systems on blocks (Fig. 6). The most morphologically simple system consists of a single linear, or curvilinear, narrow fracture running through the entire block that is otherwise intact. Where a bifurcation is present, the angle between cracks is ≲45� and can result in a radial configuration. In other exam­ ples, the crack system can display two or more bifurcation points with right angles between cracks, i.e., about 90� . In cases (b) and (d), where two bifurcations point are present, the cracks do not have the same width as in more simple systems. Instead, one wide (3 m) and several narrow (1.5 m) cracks are observed (Fig. 6b, d). We also note that several cracked (and un-cracked) blocks are partially covered by darker, loose material. In one case where pre-existing joints (layering) are observed, the crack system does not follow them (Fig. 6h). The measurements of crack orientation at Giordano Bruno reveal the presence of a preferred orientation (Fig. 7). The highest frequency of cracks is in the range 20–40� when data is binned each 20� . Binning each

in gravitational focusing for large (>0.1 m) meteoroid is minor (Pokorny et al., 2019). 3. Results 3.1. Results on morphologies, spatial densities and cracks A general morphological trend valid for fractured blocks at all six craters is observed. Most of the morphological diversity can be described in terms of the relationship between the size of the largest fragment and the size of the original target block (Fig. 2). The latter can be qualita­ tively inferred from the number and size of the fragments. Quantita­ tively, the relationship is described by the fragment spatial density, i.e., the morphometry parameter Δ. We first summarize qualitative obser­ vations and then focus on a quantitative description. Fragmented blocks with high spatial density typically consist of a large fragment and up to a few considerably smaller fragments chipped off from the perimeter of the primary (Fig. 2, right hand side). Frag­ mented blocks with low spatial density display a target size greater than the largest single fragment (Fig. 2, left hand side). In addition, the largest fragments can be of similar sizes, e.g., not necessarily a single largest fragment, and they are not always located at the center of the original target. The relative distance between the fragments is variable and can range from a crack appearance (short relative distance) to a distinguishable inner fracture plane often accompanied by distinguish­ able underlying regolith (long relative distance). We note that the distinction between crack and the recognition of an inner fracture plane is strongly dependent on the size of the shadow and change in reflec­ tance caused by the feature’s morphological expression, and thus the illumination incidence angle for a given image. At Copernicus crater, we identified the most compelling case for fragmentation post emplacement (Fig. 3a). Rays in the form of chains of fragments and associated albedo pattern are found extending radially from the target. These features strongly suggest an explosive event typical of a meteoroid impact. The fact that the albedo pattern is bright indicates a relatively recent event, and contrasts with the darker albedo of un-fractured blocks at Copernicus. The bright albedo signature (i.e., the young age) is not consistent with rupture caused during landing of a Copernicus ejecta block. Summarizing, the observations indicate rupture by an impact in relatively modern times. At crater Giordano Bruno, instead, we identified a clear case of fragmentation during ejecta

Fig. 3. (a) Example of catastrophic fragmentation post block emplacement by a meteoroid impact, on the rim of Copernicus crater. The age difference between the bright rays and the underlying darker crater-rich surface indicates that the fragmentation occurred well after the emplacement of the ejecta block by the Copernicus crater. (b) Example of fragmentation during emplacement of an ejecta block by the Giordano Bruno crater. The two largest fragments are separated by an impact melt flow of Giordano Bruno, indicating that fragmentation occurring during landing of the ejecta block. 5

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Fig. 4. Examples of fragment shape and configuration consistent with impact experiments and simulations. (a) Example of core shattering as described in Fujiwara et al. (1989). (b) Example of cone shattering with triangular-shaped fragments, as described in Fujiwara et al. (1989). (c) Example of an “onion shell” chip fragment. The curvilinear shape of the largest fragment is reminiscent of experiments in Walker et al. (2013) and Durda et al. (2015), although in this example the central core is missing.

Fig. 5. a) Typical examples of fragment size frequency distributions in fragmented blocks with Alargest-fragment / Acluster < 0.5. Black lines indicate power law slopes ranging from 3.3 to 7.0. Examples from Byrigus A (yellow and green), Giordano Bruno (blue), and Tycho (red and purple) craters. b) Fragmented block shown with purple line in a). c) Fragmented block shown with red line in a). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

10� does not change the orientation. The orientation is present in both short (3–14 m) and long (14–40 m) cracks. The population at Byrgius A shows a similar trend, although less pronounced. The preferred orien­ tation is at 40� when data is binned each 20� , whereas there are two preferred orientations at 40� and 140� when data is binned at 10� in­ tervals. Cracks of different lengths show a slightly different orientation: 20� for short (3–15 m) cracks and 60� for long (15–67 m) cracks, for binning each 20� . We tested whether the data is non-random with the Rao spacing test, which describes uniformly distributed data with pvalues > 0.05 (Fisher, 1993). Orientation of cracks at Giordano Bruno and Byrgius A have p-values < 0.001, indicating that the distributions can be considered non-random. What has not been observed are circular albedo features, or round

shadow-casting reliefs on the surface of blocks, that could have indi­ cated spallation zones or pits caused by meteoroid impacts. Although roughly the same continuum of morphologies (Fig. 2) is observed at all craters, which therefore appears to not depend on the surface exposure age, some temporal changes in morphology can nevertheless be identified. Fragmented blocks at crater Aristarchus and older (≳175 Ma) tend to be rounder, to have fewer cracks, and to be surrounded by fillets (i.e., onlap of loose fine-grained material). The older the surface is, the more pronounced are these features, i.e., larger fillets. At the oldest crater, King (~1 Ga), large fragments appear intensively brecciated. Small fragments can be found on top of extensive fillet material, indicating that their disaggregation from the block occurred after the (slow) deposition of the fillet. At old craters, we 6

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Fig. 6. (a, b, c, d, e) Examples of cracks with multiple bifurcation points. Note that the angles between fractures are often close to 90� . In (a, b) and (d) up to three orders of segments are present. Relatively wide cracks are marked as bold lines, whereas uncertain fractures are shown as dashed lines. Small circles denote points of bifurcations. (f, g, h, i, j) Examples or cracks with one or no bifurcation points. The angles between fractures are considerably <90� . Note that in all examples the major crack cuts through the entire block. Examples are from craters Giordano Bruno (e, f, g, h, i), Byrgius A (a, b, j) and Tycho (c, d).

remark that the surface surrounding fragmented blocks is punctuated by craters a few meters wide. We now turn to the description of the determinations made based on the morphometry parameter Δ. These measurements confirm the qual­ itative observations described above. Namely, that the range in Δ values across the different craters does not change significantly (Fig. 8a), which is in agreement with the similar continuum of morphologies observed for different exposure ages. There is no clear trend in the variation of Δ as a function of distance from the crater rim, nor as a function of crater diameter (Fig. 8a, Table 1). No clear morphometric variation was found as a function of the area of the original block, approximated by the area of the cluster (Fig. 8b).

with increasing size of the cluster areas. When the ratios at different cluster areas are considered together (from 50 m2 to 400 m2) a clear correlation with surface exposure time is found (Fig. 11). The trend can be described with: Surface Exposure Age ðMaÞ � f *1250

(5)

with f the fraction of highly fractured blocks in a population of size range 50–400 m2. There is a high correlation with a Pearson correlation co­ efficient of 0.98 (Fig. 11). As anticipated in the method section, the data in the format of Fig. 10 is used to estimate the flux and size frequency distribution of putative impacts responsible for the formation of highly fractured blocks. Here we also include values calculated with Acluster ¼ 0–50 m2. For facilitating the comparison of size frequency distributions, the data from the lunar blocks and two estimates of meteoroid flux are normalized to impact per year in Fig. 12. To a first order, we observe a relatively good agreement between putative impacts and the estimated meteoroid flux, taking into consideration our assumption of one single impact per block, the un­ certainty in retrieving the size of the projectile (Q*S), and the uncer­ tainty in the age of the populations. When considering only the flux, the population at Giordano Bruno crater is the least in agreement, with about a factor of 6 higher number of impacts. When considering only the

3.2. Results on abundance of fractured block The counts of highly fractured and total number of blocks as a function of the cluster area and of the population are shown in Fig. 9. The same data is represented in Fig. 10 with the ratio of number of highly fractured blocks to total number of blocks. We found that the abundance of highly fractured blocks relative to the total abundance of blocks is generally low, ranging from 0.01 to 0.20. Fig. 10 reveals how the population at Giordano Bruno crater has a constant ratio for different cluster areas. Older populations, instead, show an increase of the ratio 7

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Fig. 7. Rose diagram showing the orientation of cracks on blocks at Giordano Bruno and Byrgius A craters. The data is shown as percent of the total number of cracks measurements (n) in bins of 10� and 20� . The mean length of cracks is 14 m (standard deviation 7 m) at Giordano Bruno and 15 m (standard deviation 11 m) and Byrigus A.

Fig. 8. (a) Relationship between the morphometry of fractured blocks, the distance to the crater rim, and the exposure time. The morphometry is expressed as the ratio of the area of the largest fragment to the area of the cluster (see Fig. 1). Blocks from three craters with difference exposure times are shown: ~4 Ma, ~47 Ma and ~85 Ma for Giordano Bruno, Byrgius A and Tycho craters, respectively. (b) Relationship between the morphometry and the original block size, approximated by the area of the cluster.

size frequency distribution, the population at Byrgius A is the least in agreement with a shallower slope relative to the meteoroid distribu­ tions. We observe that none of the populations has a slope of the size

frequency distribution steeper than that of the meteoroids.

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Fig. 9. Statistics of counted blocks for each population in four bins of cluster area, approximated as a circle. Blue color denotes total blocks, red color denotes strongly fractured blocks. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 10. Ratio of number of strongly fractured blocks to total number of blocks, as a function of clusters area, approximated as a circle.

4. Discussion

(1975). Different meteoroid impact energy can be imparted to a block depending on the impactor size, its velocity, the total number of impacts, and the target size. We find that the fraction of disrupted blocks is higher when considering large blocks (>100 m2 relative to >50 m2) perhaps because larger blocks have a lower tensile strength (Housen and Hol­ sapple, 1999) or because of their larger exposed area. It is important to note that this difference with block size occurs for old populations and is not observed for the youngest population ~4 Ma in age. Therefore, the difference could also be explained by increasing burial of the smaller blocks and consequent decrease in fragmentation. It has been shown experimentally that, compared with blocks resting on the surface, buried blocks are less susceptible to fragmentation (Durda et al., 2011). Burial of blocks by fine ejecta material from nearby large impacts would in­ crease with time and preferentially protect smaller blocks. Additional observations that favour the role of meteoroid bombardment are, for blocks >20-m wide, the morphologies with low Δ; in particular, ray-pattern (Fig. 3a) and core and cone shattering mor­ phologies (Fig. 4). These morphologies are similar to those seen in impact experiments (e.g., Fujiwara et al., 1989; Walker et al., 2013; Durda et al., 2015). The minimal dispersion of fragments during impact breakdown could be due to the disruption of low tensile strengths blocks (e.g., Housen and Holsapple, 1999) by low energy impacts. Also, the

Several lines of evidence indicate that fragmentation during block emplacement plays a minor or insignificant role in the formation of blocks fractured in situ: (1) The disruption morphology diagnostic of fragmentation during emplacement (Fig. 3b) is infrequent relative to the diagnostic morphologies of impacts (Figs. 3a, 4). (2) There is no observable trend in the morphometry of shattered blocks with crater radius (Fig. 7a). (3) Highly fractured blocks constitute only a very small fraction (~1%) of a total young (~4 Ma) population, when the contri­ bution by post-emplacement fragmentation is still very low. Instead, the observed increase in the fraction of highly fractured blocks with exposure age (Fig. 9) demonstrates that most of the frag­ mentation in situ occurs after block emplacement. The above increase is consistent with simulations of meteoroid bombardment (Hoerz et al., 1975). The observed range (or continuum) of block disruption mor­ phologies (Fig. 2) and morphometries (Fig. 8) can be explained by im­ pacts having different energy, as shown in simulations by Hoerz et al. 9

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that another process is at play. Multiple bifurcation points, right angles between cracks and parallel cracks (Fig. 6) are features consistent with blocks on Earth affected by thermal shocks (Hall and Thorn, 2014). Cracks with these three properties were reported on Martian boulders and associated to thermal expansion and contraction (Thomas et al., 2005). The non-random orientation of cracks at Giordano Bruno is similar to the orientation of cracks, and in particular meridional cracks, observed on boulders of Earth deserts and associated to insolation weathering (e. g., McFadden et al., 2005; Eppes et al., 2010). Meridional cracks refer to vertical cracks within 33� of the north-south meridian and have been suggested to be due to thermal stresses arising from daily non-uniform solar heating (e.g., McFadden et al., 2005). Cracks at Giordano Bruno do display a preferred orientation but slightly offset in the range 20–40� E. This difference might be due to fact that the magnitude of the thermal stresses is dependent on a variety of factors, including geographic po­ sition, rock type, shape and size (Eppes et al., 2015). The observed preferential orientation is likely not caused by impacts of meteoroids or cracking during ejecta emplacement. Observational bias is unlikely because of using images with different illumination geometries. The more random crack orientation measured at Byrgius A can be inter­ preted by the combined effects of solar heating and meteoroid impacts. Because Byrgius A is ~43 Ma older than Giordano Bruno, this would imply a change with time of the dominant fragmentation process, first solar heating, then meteoroid impacts. This change is supported by the absence of blocks with a high density of cracks, e.g., with a well-developed polygonal pattern. Therefore, we suggest that even if thermal stresses are at play, and are severe enough to induce the onset of cracking, they are nevertheless insufficient for completely disrupting blocks. This is supported by the following observation: In populations younger than ~175 Ma, we did not find morphologies associated with fragmentation of the outermost surface of blocks that could be linked to the superficial effect of thermal fatigue (Molaro et al., 2017). Only in older populations, the presence of fillets around blocks could be interpreted to perhaps be due to thermal fatigue (Molaro et al., 2017; Basilevsky et al., 2015). In these old populations, however, most of the initial blocks have been erased, likely by impact bombardment (Basilevsky et al., 2013). These implications are supported by the outcomes presented in Fig. 12a. The results indicate that at ~4 Ma, the measured relative number of fractured blocks is slightly higher than expected from mete­ oroid impacts, whereas for populations older or equal than ~47 Ma, the measured relative number of fractured blocks matches, within uncer­ tainty, the number expected from meteoroid impacts. One explanation could be the presence of fragmented blocks during ejecta block emplacement. If the fraction of fragmented blocks sin ejecta emplacement is the same, they would dominate the youngest population and be considerable less significant for old populations. One could expect block fragmentation at ejecta emplacement to be related to the distance from the crater rim crest. However, this behaviour has not been found (Fig. 8). Therefore, another reason could be behind the mismatch between measured and expect number of fragmented blocks in the youngest population (Fig. 12a). The mismatch can be interpreted as an indication for a process in addition to meteoroid impacts. The process should be faster and more efficient than impact bombardment in the first few million years but its effects should terminate or become subordinate to meteoroid impacts after few tens of million years. We suggest thermal stresses due to daily cycles of non-uniform solar heating as an additional process. The non-porous assumption for Q*S provides a better agreement with the meteoroid flux and size frequency distribution and suggests that the properties of porous material (Fig. 12b) might be better suited for as­ teroids material (e.g., Jutzi et al., 2010) rather than for the generally non-pyroclastic igneous blocks of the Moon. The slope of the size frequency distributions of putative impacts has implication for the population of impactors. The similar slope between

Fig. 11. Relationship between the abundance of highly fractured blocks in a block population and the surface exposure time of the population. Highly fractured blocks are defined with Alf/Apb �0.5. The number of measured blocks in each population is >500 and their size range is 8–60 m. The Pearson correlation coefficient is 0.98.

smallest fraction of fragments that leave the target block with high ve­ locity may be unrecognizable after the impact event (e.g., Durda et al., 2011). We note that for old surfaces, secondary bombardments by nearby impacts possibly add to the total flux of impacts. The slopes of fragments size-frequency distributions (Fig. 5) are steeper than that of numerical simulation and experiments of collisional disruptions (e.g., Fujiwara et al., 1977; Jutzi et al., 2010) and of blocks larger than 10 m on small asteroids (Thomas et al., 2001; Saito et al., 2006; Sugita et al., 2019). The measured slopes are however comparable to the power-law exponent 4 of block size-frequency distributions around lunar impact craters for block size range ~5–20 m (Bart and Melosh, 2010) and for block size range 1–10 m (Cintala and McBride, 1995). A similar slope was also reported for high albedo regions on Bennu (DellaGiustina et al., 2019). We interpret the slopes of Fig. 5 as being the result of a single fragmentation event, namely the disruption of a block by a single impact. However, it is not clear why such distri­ butions differ from numerical simulations. The differences between the distributions in Fig. 5 could be due to different internal structures of the blocks. For example, numerical simulations have shown that the pres­ ence of pre-shattering fractures can lead to different fragments sizefrequency distributions, at least for fragmentations in the gravity regime and parent body sizes ≫10 m (e.g., Michel et al., 2003, 2004; Jutzi et al., 2010). The general interpretation that the measured distri­ butions reflect single fragmentation events has implications for the un­ derstanding of the origin and evolution of block populations. Increase in the steepness of size frequency distributions is often interpreted as representing stronger breaking processes, like a longer exposure age and increase in number of fragmentation events (e.g., Hartmann, 1969; Thomas et al., 2001; Saito et al., 2006). Although we do not disagree with this interpretation, we point out that a single fragmentation event can lead to a range of distribution shapes and a range of distributions slopes including power-law exponent about and higher than 4. Spallation zones and pits are usually observed on rocks affected by impacts (Basilevsky et al., 2015). However, we did not observe circular features of any kind that could be associated to spallation zones, not even on blocks with cracks. This absence might be only apparent because of insufficient spatial resolution. Alternatively, it may suggest 10

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Fig. 12. Cumulative number of putative impacts responsible for the formation of highly fractured blocks, as a function of the projectile size. The size frequency distribution of projectiles is normalized to impacts each m2 each year. The blue and red lines are size frequency distributions from direct (red) and extrapolated (blue) observations of meteoroids (Halliday et al., 1996; Brown et al., 2002). a) For non-porous target blocks. b) For porous target blocks. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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the putative impacts and known meteoroids suggest that small impacts (~1–3 m crater for projectiles 0.1–0.3 m) on the surface of the Moon are due to decimetre-size near-Earth objects. The absence of a steeper size frequency distribution seems to indicate a lack of secondary projectiles (formed by primary impacts). This observation could be explained by the low velocity of secondary projectiles (0.5–1.5 km/s, Costello et al., 2018) that would result in a low disruption efficiency.

Acknowledgment O.R. is supported by an appointment to the ESA Research Fellow Program at the European Space and Technology Center (ESTEC). We acknowledge the LROC team for the acquisition of the images and two anonymous reviewers for their comments. We appreciated discussions with M. Jutzi, M. Delbo, G. G. Michael and A. T. Basilevsky on the results of this study.

5. Conclusions

References

The results and implications of this study can be summarized in six broad categories. Regarding the properties of lunar blocks fragmented in situ:

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� The abundance of fragmented blocks (5–20 m wide) in a population increases with exposure age, whereas the range and type of rupture morphologies remains relatively unaffected through time. Regarding the dating of lunar local surfaces with block populations: � The fraction of blocks fragmented in situ in a surviving population on the Moon can be used to date their surface exposure age—provided the population was formed by a single temporal event. This dating technique does not require a priori knowledge of the original abundance of blocks. Regarding the processes leading to in situ fragmentation of blocks: � Unless the geologic context indicates otherwise, most blocks with a low Δ ¼ Alargest fragment / Acluster observed on the Moon, and possibly on other rocky planetary surfaces, can be interpreted as being the product of impact bombardment. We suggest that on the Moon, daily thermal stresses are responsible for additional fragmentation of blocks, and that this fragmentation varies in style and intensity with time. In the first few million years, non-uniform solar heating ap­ pears to enhance fragmentation of blocks, in particular through meridional cracking. Further fragmentation with time is not evident until several hundred million years, when fillet morphology de­ velops, possibly due to thermal fatigue. Regarding the size frequency distribution of projectiles: � We find that the slope of the size frequency distribution of projectiles forming fragmented blocks is consistent with that of the near-Earth objects (NEOs). Thus, the fraction of blocks fragmented in situ in a population records primary impacts and is not influenced by sec­ ondary projectiles. Regarding regolith formation on other planetary bodies: � Blocks fragmented in situ record an important phase in the grada­ tional process of block disruption and regolith development. The lunar morphologies and morphometric trends described here can be used for future studies on other planetary bodies observed at the mesoscale (<1 km). Regarding the surfaces of asteroids: � In order to understand deflection of an asteroid by kinetic impactors (e.g., Michel et al., 2018), it is important to understand the process of impact on a block, e.g., the momentum transfers, because the surface of small bodies can be dominated by blocks with minor coverage by regolith. The morphologies described here can be used as a reference for simulations of impact on a block.

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