Ejecta Blankets at Small Craters on the Moon

Impact-derived ejecta covers most of the lunar surface, originating from recent impacts through to the beginning of the geologic record. Despite how common ejecta is, accurate measurements of ejecta thickness are difficult to obtain, and existing estimates of ejecta thickness vary widely. This study uses excavation by meter-scale impacts on the fresh ejecta blankets of larger, kilometer-scale impacts to make point measurements of ejecta thickness. We estimate ejecta thickness at the rims of 73 lunar craters (0.1–4.8 km diameter) and create isopach maps of ejecta thickness for three craters. We derive an equation for ejecta thickness, t=0.14±0.062R(0.77±0.080)r/R(−B) , where r is the horizontal distance from the center of the crater, R is the center-to-rim crater radius, and B describes the rate at which ejecta thickness decays with radial distance. Our average value for B (2.8 ± 0.1) is similar to previous work, though we observe that B can vary significantly within an ejecta blanket.


Introduction
The parameters that govern the shape and thickness of ejecta blankets are poorly understood relative to the prominence of these features on planetary bodies.There have been many attempts to derive the thickness of ejecta at crater rims (McGetchin et al. 1973;Pike 1974;Sharpton 2014) as well as quantify the rate at which ejecta thickness decays with distance from a crater (McGetchin et al. 1973;Petro & Pieters 2006;Fassett et al. 2011), but these results vary widely.Measuring these parameters is not straightforward.Impacts on Earth are not well preserved and remote observations of ejecta on the Moon, Mars, or elsewhere are subject to ambiguity.In particular, impact-driven uplift, unknown preimpact topography, and ballistic sedimentation (Oberbeck 1975) are troublesome to account for remotely.We quantify ejecta thickness at 0.1-4.8km diameter lunar craters using excavation by subsequent, meter-scale craters to probe the ejecta-preimpact contact.

Approach
We use excavation by small impact craters to estimate the thickness of ejecta from larger craters.Impact events excavate material from depth as a function of crater diameter.If a crater excavates-or fails to excavate-material distinct in composition from the surface, its diameter constrains the surface layer thickness.Past studies have used crater excavation to measure the thickness of mare deposits (Budney & Lucey 1998;Thomson et al. 2009) and estimate the burial depth of cryptomare (Antonenko et al. 1997).These measurements are possible because mare and highland materials are chemically distinct.
Fresh lunar ejecta exhibits relatively high reflectance that allows for thickness estimates via crater excavation (Figure 1).Mature regolith is darkened by space weathering tens of centimeters into the subsurface (McKay et al. 1991).Impact craters larger than ∼10 m will excavate, overturn, then deposit bright regolith from the subsurface onto the surface, resulting in a distinct albedo contrast between bright ejecta and the dark preimpact surface.Thus, any subsequent impacts on the ejecta blanket that excavate dark regolith are excavating below the ejecta blanket.Similarly, small impacts that excavate bright material failed to penetrate the ejecta blanket.These dark/ bright "child" craters place maximum and minimum constraints on the thickness of the larger "parent" crater's ejecta blanket based on their excavation depth.Many child craters in aggregate can allow for reasonable estimates of the parent crater's overall ejecta thickness.
We use Lunar Reconnaissance Orbiter Camera (LROC) Narrow-Angle Camera (NAC) images (Robinson et al. 2010) to measure the characteristics of child craters on several parent ejecta blankets.We record rim-to-rim diameter from largeincidence-angle images and observations of excavated regolith reflectance (a proxy for albedo) from small-incidence-angle images.We only record the diameters of relatively freshlooking craters and assume that age-related widening of child crater rims is negligible.The dark-bright subsurface contact depth is best constrained by recording the largest brightexcavating craters and smallest dark-excavating craters at a given location (Figure 2).The diameter where the child crater ejecta transitions from dark to bright correlates to the depth of the boundary.In some instances, craters will show distinct jets of both bright and dark material at the rim, indicating a contact near maximum excavation depth.For consistency, we treat these as dark-excavating craters where observed.Craters excavating from near the boundary often appear with wellmixed grayish ejecta that cannot be definitively marked as dark or bright.We exclude any bright-excavating craters interpreted as excavating below the ejecta blanket and preimpact surface.We distinguish these because they will be much larger than nearby dark-excavating craters and will contain some dark material in their ejecta.Not all ejecta blankets are conducive to measurement via this method.Parent craters were selected based on sharp albedo contrast between ejecta and the background terrain.This limited us to near-equatorial impacts due to favorable incidence angles.Our sample is also biased toward highlands terrain because of its greater contrast and thicker mature regolith (Figure 3).An additional constraint is age.The parent ejecta blankets must be sufficiently old to accumulate child craters, but cannot be so old that the layers are churned and weathered beyond recognition (Costello et al. 2018).South Ray crater has a known absolute age of roughly 2 Ma (Eugster 1999) and is nearly too young for our method to work.Meanwhile, North Ray crater has a known age of ∼50 Ma (Drozd et al. 1974) and is far too old for our method.Based on this, we approximate 4-30 Ma as the optimal crater age, though that upper bound is more loosely constrained and will vary based on several factors, including parent crater diameter (the smaller the diameter, the faster bright ejecta fades) and background terrain albedo.

Excavation Depth
The maximum excavation depth (d e ) for meter-scale child craters is a significant parameter in our ejecta thickness estimates.The most commonly accepted value is d e = 0.1D t (Melosh 1989), where D t is the crater's transient diameter.For simple craters, D t = 0.84D (Melosh 1989), so this excavation depth will be d e = 0.084D, where D is the rim-to-rim diameter.This value is derived from small-scale impact experiments (Stöffler et al. 1975) and observations of terrestrial craters (Grieve et al. 1981).Only one simple crater on Earth has ejecta preserved well enough to derive a maximum excavation depth, which shows d e ∼ 0.08D (Osinski et al. 2011).A more recent study has suggested d e 0.03D t (∼0.025D for simple craters) based on estimates of ejecta thickness at lunar craters (Sharpton 2014).Thomson et al. (2009) sought to estimate mare thickness via a method similar to ours (ejecta contrast due to compositional differences, not variation in maturity) and assumed a value of d e = 0.084D.Their results compare favorably to canonical mare thickness values (de Hon 1979).However, the craters studied in Thomson et al. (2009) may not be relevant comparisons to what we use in this study as the craters they examined were >100 times larger and formed in layered mare deposits, rather than regolith.
Regolith cores acquired by the Apollo astronauts enable ground-truthing the maximum excavation depth for meter-scale lunar craters.Chemical maturity with depth-assumed to correlate with optical maturity-was cataloged in 1 cm increments from core samples acquired during the Apollo 15, 16, and 17 traverses (McKay et al. 1991).We examined small, fresh craters near the sample sites and recorded their rim-to-rim diameter, excavated material (dark or bright), and distance from the sample (Figure 4).The mature-to-immature transition in the core sample and the dark-to-bright crater diameter transition align well with d e = 0.085 ± 0.003D near the Apollo 15 and 17 sample sites.Thus, we will use this value in our ejecta thickness estimates.Deviation from the projected dark-tobright subsurface boundary >80 m from the cores likely indicates a change in the thickness of the mature layer rather than inaccuracies in the estimate.The Apollo 16 core does not align with the projected boundary, but this inconsistency is likely due to large local heterogeneities induced by ejecta from the nearby South Ray crater.

Isopach Maps
We derived ejecta thickness isopach maps for three parent craters (Figure 5).At all three of these, 4-16 m diameter child craters were plentiful and exhibited suitable contrast to derive 0.5 and 1 m depth contours over the entire ejecta blanket.Near the rim, where the ejecta is thickest, it is rarer to observe child craters large enough to constrain the preimpact-ejecta contact.We estimate the 0.5 and 1 m contours are accurate to within 50 m or better horizontally.As the deeper contours are more poorly constrained (fewer dark-excavating craters), we infer a more precise position via the rate of change in ejecta thickness.
Ejecta thickness is approximated by the equation where R is the crater radius, r is the horizontal distance from the center of the crater, T is the thickness of ejecta at the crater rim, and B is a decay constant (McGetchin et al. 1973;Melosh 1989). McGetchin et al. (1973) are ambiguous about the term radius, calling it the "apparent radius," which at the time was sometimes defined as the centerto-rim radius (Baldwin 1963) or as the radius at the preimpact ground elevation (Pike 1974).It is not clear to us what definition was intended by McGetchin et al. (1973).For consistency with the equations from Pike (1974), Sharpton (2014), and our own measurements, we treat this R as the center-to-rim radius.We used our high-confidence isopach contours to infer values of B and T. The overall noncircular shape of our depth  contours suggests some degree of variance for B within each ejecta blanket.We assume that T is a constant value over the crater's circumference and that B is constant radially but varies with azimuth.We use the 0.5/1 m isopach contours as known values of ejecta thickness at some distance, allow B to vary freely along the crater circumference, and examine the fit along 5°increments of azimuth.We record values of T that lead to the least divergence from the locations of the isopach contours,   then record what values of B correlate with these.Often, the vector radial to the rim will intercept 0.5/1 m isopach contours more than once.In these instances, we only consider the nearest isopach contour.
The results are best-fit values of T and the range of observed values for B (Table 1).Values for B vary from B = 2 to B = 6 (Figure 6).The highest of these B values are only present at one crater, where part of the ejecta blanket is deposited on a steep, rim-facing slope.If we discard azimuths with this steep topography, the best-fit values of B are remarkably consistent between all three craters.We thus approximate that at a typical small lunar impact B avg is 2.8 ± 0.1, B min is 2.1 ± 0.1, and B max is 4.0 ± 0.5.
We plug these values of T and B into Equation (1) and integrate using the volume of rotation to estimate the volumes of these three ejecta blankets.Ideally, these volumes should be nearly equal to the volume of the crater's excavation cavity, but in practice several factors complicate this comparison (Schroeter 1791;Pike 1967).Ejecta blankets will assimilate some material from the preimpact surface via ballistic sedimentation (Oberbeck 1975).While ballistic sedimentation is expected to be fairly minor at small craters, it is still a factor and will intensify with increasing distance from the crater rim.It is also likely that a fresh ejecta blanket will have considerably higher porosity than the preimpact material and thus a larger volume than the excavation cavity.
We observe several qualities in our isopach maps relevant to how accurately ejecta blankets are described by Equation (1).The brightness of a fresh ejecta blanket generally-but imperfectly-correlates with ejecta thickness.Blanket thickness does not appear to decay uniformly with radial distance.In other words, constant values of B along a radial vector are only an approximation.Ejecta exhibits heterogeneities most obviously at small, isolated, radially elongated deposits >3-4 radii from the crater rim (examples:

Rim Ejecta Thickness Estimates
In addition to the three ejecta blankets with isopach maps, we examined a further 70 craters that had sufficient information to estimate T, ejecta thickness at the rim.These parent craters have diameters of 0.1-4.8km.While these ejecta blankets have relatively fewer observable child craters, we can estimate T by assuming that B avg = 2.8 ± 0.1, B min = 2.1 ± 0.1, and B max = 4.0 ± 0.5 is valid at these impacts.We consider the excavation depths of dark-and bright-excavating child craters within 2.5 radii of the parent crater rim.We use Equation (1) to fit the data to values of T using the following metrics, in order of importance (an example of what this looks like graphically is given in Figure 2(E)): (1) When B = B min , nearly all (>99%) bright-excavating craters will have d e above the projected ejecta blanket base.
(2) When B = B max , nearly all (>90%) dark-excavating craters will have d e below the projected ejecta blanket base.
(3) When B = B avg , most dark-excavating craters will have d e below the projected ejecta blanket base, and most brightexcavating craters will have d e above.
We plot our estimates of rim ejecta thickness versus center-torim crater radius and then compare them to existing equations for T (Figure 7).The main source of uncertainty is that these rim  thickness estimates are inferred from child craters relatively far from the rim.Outlying T values could signify that our assumed decay constants at these ejecta blankets are incorrect-perhaps because of preimpact topography, impact angle, or other factors.
There could also be a range of possible values of T for craters of a given diameter.A power law fits our data well: This trendline is a reasonable estimate for T within ±30% where R < 5 km.Extrapolating this equation to larger craters may or may not be viable.

Ejecta Thickness Decay
In the three ejecta blankets mapped by this study (Figure 5), we observe that the ejecta thickness decay rate varies stochastically by azimuth, from B min = 2.1 ± 0.1 to B max = 4.0 ± 0.5, with an average value B avg = 2.8 ± 0.1.A major consequence of this is that even with a precise prediction of rim ejecta thickness, it is not possible to accurately predict ejecta thickness based solely on the distance from a crater.This has important implications for interpreting in situ samples or observations where ejecta is a significant part of the local geology.
Our observations are of young craters <5 km diameter, but it is worthwhile to consider whether values of B will be different at other impacts.Low-angle impacts and impacts on sloped terrain will probably have more extreme values of B min and B max .At larger impacts, greater amounts of ballistic sedimentation will have the effect of decreasing the value of B. The fresh ejecta blankets examined in this study likely have high porosity compared to older or larger impacts, though whether this changes the thickness decay rate is unclear.Finally, impact gardening will spread ejecta blankets laterally over time, leading to an apparent decrease in B, though this is less significant for very large (i.e., basin-forming) impacts.In total, these trends seem to suggest that older, larger impacts will have lower values of B, though quantifying this difference is beyond the scope of this study.
Let us compare our observations of B to past studies.McGetchin et al. (1973) synthesized data from terrestrial impact/blast experiments and estimates of ejecta thickness at large lunar craters to infer B = 3.0 for ejecta blankets of all sizes, with no reported uncertainty.The estimates from large lunar craters were speculative; there was no method to confidently distinguish relief created by ejecta deposition from uplift-driven relief.Further, comparing terrestrial crater experiments to lunar ejecta blankets is complicated by atmospheric drag, different gravitational accelerations, and several other factors.Blast crater experiments in particular may be poor analogs to impact ejecta (see discussion in Pike 1974 andSettle et al. 1974).Melosh (1989), synthesizing from these and other past works (i.e., Stöffler et al. 1975;Settle & Head 1976) describes the most widely accepted value, B = 3.0 ± 0.5, which generally agrees with our B avg .Petro & Pieters (2006) derive B = 2.61 based on single-value assumptions of impact parameters applied to the impact spatial analysis model from Housen et al. (1983).Notably, any effects of ballistic sedimentation are ignored by this method.This B value predicts slightly shallower thickness decay than our data.However, if one considers that ejection, impactor, and terrain characteristics likely vary substantially, this method might produce results comparable to ours.Fassett et al. (2011) used the topography of preimpact craters buried beneath Orientale Basin's ejecta to quantify thickness decay as B = 2.8 ± 0.5.Xie & Zhu (2016) use the same method to examine Orientale's ejecta but also attempt to account for erosion of the preimpact craters' rims, and produce a value of B = 2.8.These values of B are the same as our B avg , though this goes against our expectation that B should decrease with larger impacts due to ballistic sedimentation incorporating preimpact material into the ejecta blanket.Deposition of basin ejecta on the rims of these preimpact craters, though thought to be a minor factor, may contribute to these studies underestimating the thickness of ejecta.More consequentially, both Fassett et al. (2011) and Xie & Zhu (2016) implicitly assume the entire ejecta blanket will be described by a single value of B. However, by their methods what is actually being estimated is the maximum value of B-from the azimuths where ejecta thins out most rapidly with radial distance.Perhaps the B avg for Orientale ejecta is somewhat lower than 2.8, which would match our expectations.).Also displayed are the data points from Sharpton (2014), with their 2σ uncertainties.The best-fit trend of our data is given by Equation (2), T = 0.14 ± 0.062R (0.77 ± 0.080) , producing thicknesses intermediate to McGetchin et al. (1973) and Pike (1974).

Rim Ejecta Thickness
Our estimate of ejecta thickness at the crater rim is expressed by T = 0.14 ± 0.062R (0.77 ± 0.080) .We will compare the fit of other ejecta thickness equations to our observations of craters less than 5 km diameter.
The estimate for T from McGetchin et al. (1973) shares any potential shortcomings with their estimate of B, as these values were derived from the same sources of information.An additional concern is ambiguity in their definition or R-it may have been defined as the crater's radius at the preimpact ground elevation, which would result in a lower value of T than we consider.Regardless, if we assume their R is center-to-rim radius, their equation T = 0.14R 0.74 is reasonably consistent with our observations.Pike (1974) derived three equations for rim ejecta thickness to address perceived shortcomings in McGetchin et al. (1973) as an "academic exercise"; Pike did not believe reliable estimates were possible with the information and methods available at the time.These equations were based on adjusting the results from McGetchin et al. (1973) to account for different aspects of impact crater morphometry.The most oft-cited equation from Pike (1974) is T = 0.033R.This equation is consistent with our data set, though predicts ejecta slightly thicker than our trendline.
The most recent study to quantify rim ejecta thickness is Sharpton (2014).Sharpton measured ejecta thickness by locating a contact between cohesive rock layers and regolith on the walls of large mare craters (2.2-45 km diameter).He assumes this contact is the base of the ejecta and made photogrammetric measurements of the regolith layer's thickness.Sharpton's ejecta thickness equation for simple craters is T = 0.014 ± 0.004R 1.01 .Sturm et al. (2016) and Krüger et al. (2017) made similar measurements at Martian and lunar craters, respectively, that were consistent with Sharpton (2014).The best-fit trends from Sharpton (2014), Sturm et al. (2016), andKrüger et al. (2017) are not consistent with our data set.Further, the derived maximum excavation depth in Sharpton (2014) is not consistent with our observations at meter-scale lunar craters or in field studies of craters on Earth (Grieve et al. 1981;Osinski et al. 2011).At almost every ejecta blanket we measured, we observe a bright-to-dark regolith transition (the base of the ejecta blanket) at a depth half of Sharpton's rim thickness estimate but near a distance of 1 radii from the crater rim.In two instances, we observe a bright-todark transition at a depth that exceeds Sharpton's rim thickness estimate near ∼0.5 radii from the rim.If Sharpton's value of T were correct at these craters, it would require a decay constant B avg < 1.5 to reconcile with our data, which is not realistic.It is possible that the method in Sharpton (2014) does not correctly locate the base of the ejecta blanket, perhaps because there are substantial layers of overturned, semi-coherent rock in the ejecta that were mistaken for uplifted outcrop.Alternatively, Sharpton's trendline might simply be a poor fit for small craters, as that study measured only two craters within our data range.

Conclusions
We measured the size and reflectance contrast of meter-scale "child" craters to probe the contact between the larger "parent" crater ejecta blanket and the underlying preimpact surface.In service of ensuring accurate measurements, we independently derived maximum excavation depth as a function of rim-to-rim diameter, d e = 0.085 ± 0.003D, by correlating the transition diameter between dark-and bright-excavating craters to the depth transition of mature to immature regolith in Apollo core samples and their surroundings.We produced isopach maps of ejecta blankets at craters with 500, 800, and 1800 m diameters.We then used these isopach maps to quantify ejecta thickness decay with distance from the crater rim, B. This value varies stochastically along different azimuths within a single ejecta blanket but can nominally be described by B min = 2.1 ± 0.1, B max = 4.0 ± 0.5, and B avg = 2.8 ± 0.1.We estimated ejecta thickness, T, at the rims of 73 young lunar impacts 0.1-4.8km in diameter and derive a best-fit trend of T as a function of R, center-to-rim crater radius: T = 0.14 ± 0.062 * R (0.77±0.080) .Our data are reasonably consistent with existing equations of T from McGetchin et al. (1973) and Pike (1974), but not more recent analysis by Sharpton (2014).Future work will be necessary to test whether the parameters we derive are valid for larger impact craters.

Figure 1 .
Figure1.The stratigraphy of bright and dark layers at a fresh lunar crater.The relative scale of layers is exaggerated to emphasize thin deposits, and the proportionate thicknesses will vary with crater size.It is critical to note that the dark-to-bright boundary at the ejecta blanket base is agnostic to rim uplift and preimpact topography.Impact melt and overturned dark regolith are minor complicating factors for interpreting excavation near the crater rim.It is also possible for larger child craters to excavate bright material by penetrating both the ejecta blanket and mature preimpact surface.

Figure 2 .
Figure 2. (A) An example of a fresh ejecta blanket; the crater is 480 m diameter.(B)-(D) Examples of bright-excavating craters marked with blue arrows, darkexcavating craters marked with red arrows, and craters that simultaneously excavated dark and bright material marked with striped arrows.Note that dark-excavating craters are always larger than the nearby bright-excavating craters.(B) ∼2 radii from the rim; the transition from bright-to-dark child craters happens at relatively large diameters because the parent ejecta is thick (1-3 m depth).(C) ∼3 radii from the rim; ejecta is thinner (0.5-1 m depth) than in panel B because it is further from the crater.(D) ∼3 radii from the rim; ejecta is thinner (<0.5 m depth) than both panels (B) and (C) despite being as close as panel (C) because this part of the ejecta blanket has a higher decay constant B. (E) Child craters from this impact plotted by maximum excavation depth and distance from the crater.We plot Equation (1) with our estimate for thickness at the rim, T = 9 m, and B = 2.1, 2.8, and 4.0.Note that almost all dark-excavating craters are below the B = 4.0 line, almost all brightexcavating craters are above B = 2.1, and B = 2.8 is roughly at the average bright-to-dark subsurface transition.

Figure 3 .
Figure 3. Global context of the 73 craters where we made ejecta thickness estimates.Some points are too close to distinguish at this scale.

Figure 4 .
Figure 4. Crater excavation depth in the immediate vicinity of Apollo deep core samples.Gradients along the y-axes represent regolith maturity with depth in the core sample (dark is mature, bright is immature), inferred from I S /FeO ratios (McKay et al. 1991).Craters are plotted by rim-to-rim diameter alongside a notional excavation depth d e = 0.085D, which agrees well with the location of the dark/bright transition in the Apollo cores.

Figure 5 .
Figure5.Isopach maps with blue contours at 0.5, 1, 2, and 5 m, with a final contour at the crater rim.Dotted lines indicate inferred contour positions.Scale bars are approximately one crater radii.Background images are small-incidence LROC NAC mosaics with minimal shadows.The child craters that constrain isopach contours on these maps are too numerous to display; see supplemental material for these data points.
Figure 5(A), 3 radii southeast of the rim; Figure 5(C), 4 radii in any direction).Even on the "continuous" ejecta, there are rounded patches where the blanket is anomalously thin (examples: Figure 5(B), 2 radii north of the rim; Figure 5(C), 2 radii southwest of the rim).Additionally, ejecta interacts with preimpact topography, accumulating at pro-radial (crater-facing) slopes, and thinning out on anti-radial slopes (examples: Figure 5(B), the southern portion of ejecta is deposited on a steep crater-facing slope; Figure 5(C), 3 radii east of the rim, the ejecta interacts with a north-trending trough).The heterogeneous pattern of ejecta thickness was present in all craters, becoming more evident at the larger impact examples.

Figure 6 .
Figure 6.Inferred values of ejecta thickness decay B (concentric lines) with respect to azimuth (0 = north) at craters A, B, and C from Figure 5. B values vary between local highs and lows, correlating to places where the continuous ejecta terminates closer to or farther from the crater rim, respectively.The majority of values lie between B = 2.5 and B = 3.1.Anomalously high values at crater B from 115°to 235°azimuth are on rim-facing slopes steeper than 15°, which are not present anywhere else on these three ejecta blankets.

Table 1
Key Ejecta Thickness Parameters Inferred from the Distance between Isopach Contours and the Crater Rim a Values of B exclude azimuths with steep topography (115°-235°).