The raised rims of impact craters consist of ejecta deposited onto structurally uplifted target rocks. Although it is commonly accepted that ejecta makes up 50–75% of the total rim height, no previous measurements on well-preserved, naturally occurring impact craters exist. Relying on data from the Lunar Reconnaissance Orbiter, I report the first direct measurements of the rim-forming constituents from 21 lunar craters ranging in diameter from 2.2 km to 45 km. Results show that the ejecta deposit accounts for no more than ~20% of rim relief, and structural uplift is the primary mechanism of rim development in both simple and complex craters. Thick, quasi-horizontal outcrops of coherent bedrock indicate that this uplift is the result of subsurface injection of debris or melt into the surrounding target rocks. Crater growth, at least during the latest portion of the excavation stage, therefore, proceeds mainly through injection—rather than ejection—of material. These results suggest that ejecta volumes and excavation depths may be factors of 3 to 4 less than previously considered.
The elevated rims of impact craters consist of fragmental ejecta emplaced onto target rock that is structurally uplifted from its preimpact level during the excavation stage of the cratering process [Croft, 1981; Melosh, 1989]. Constraining the relative proportions of these two rim components for craters of different sizes is essential in understanding how craters grow [e.g., Croft, 1981] and distribute their ejecta [e.g., McGetchin et al., 1973; Pike, 1974]. Due to the poor preservation state of large terrestrial craters [Grieve and Therriault, 2004] and, until recently, the lack of sufficient image resolution for pristine craters on airless bodies such as the Moon, it was not possible to directly measure these components on any natural impact craters larger than 1 to 2 km in diameter. Consequently, estimates of the relative importance of the two crater rim constituents were derived principally from craters produced by decimeter-scale impact experiments [Stöffler et al., 1975] and buried high explosives, HE [Carlson and Jones, 1965; Dillon, 1972; Cooper, 1977]. These results indicated that ejecta comprises 60–80% of the total rim height or in more general terms: only ~25% of a crater's total rim height is due to uplifted target rocks [Melosh, 1989].
High-resolution images acquired by Lunar Reconnaissance Orbiter's (LRO) Narrow Angle Camera (NAC) recently revealed layered outcrops along the steep upper walls of many fresh craters formed within the lava-filled mare basins on the lunar front side (e.g., Figure. 1). These outcrops have been used to estimate lava flow thicknesses [Enns and Robinson, 2013] and, if they represent structurally coherent target rock, they also can be used to constrain the proportions of ejecta and wall uplift that make up the crater rim.
Here I report measurements of layered outcrops observed on the upper walls of 21 morphologically fresh lunar craters, ranging in diameter from 2.2 km to 45 km. I first show the characteristics of these outcrops indicate they are bedrock that has been uplifted from its preimpact level and are not related to the overturned ejecta flap. I then discuss the implications of these outcrops for understanding the nature of material flow during the crater excavation stage. Because exposed sequences of target layers assist in differentiating outcrops from other linear features on crater walls, such as fractures and terraces, most craters showing conspicuous outcrops in their upper walls are located within the lava-flooded mare basins of the lunar near side rather than the ancient lunar highlands. These relatively young, flat-lying lava plains also provide a reliable preimpact reference surface from which crater rim heights are measured.
The uppermost exposed surface of coherent target rock was identified using high-resolution (0.5–2 m/pixel) NAC images [Robinson et al. 2010]. A total of 1637 images were downloaded, processed, and surveyed. Two classes of digital terrain models (DTM) were used: Where available, (specifically for Linné and Lichtenberg craters), I relied upon existing high-resolution (~2 m/pixel; vertical precision of a few meters) NAC stereo DTMs [Tran et al., 2010]; in all other cases the global100 m/pixel GLD100 (Global Lunar DTM 100 m topographic model) [Scholten et al., 2012] was used. For the area of interest herein, i.e., the nearside maria, the GLD100 has a mean vertical accuracy of better than 10 m [Scholten et al., 2012].
To ensure that the GLD100 data set provided the best available representation of crater rim and wall topography, I compared it with the most recent version (uploaded 24 February 2013) of 256 postings per degree (~118 m per posting) Lunar Orbiter Laser Altimeter (LOLA256) topographic data set derived by gridding the Lunar Orbiter Laser Altimeter ground tracks [Smith et al., 2010]. Typical results are shown in Figure 2 for Dawes Crater. In areas where the topographic grid cells were close to LOLA ground tracks, there was favorable comparison between LOLA256 and GLD100, with differences less than ±50 m for 95% of the postings. However, away from the ground tracks, LOLA256 data show major incongruities with prominent crater topography. This is clearly illustrated at the western rim crest of Dawes (Figure 2a). Interpolation across LOLA tracks, exacerbated at low latitudes, has introduced conspicuous linear artifacts (arrows in Figure 2a) and smoothing of crater rim topography relative to the GLD100 (Figure 2b) that in some cases exceeds 250 m (Figure 2c). Consequently, GLD100 appears to be the superior and more reliable data set for the purposes intended in this study.
After preprocessing using standard Integrated Software for Imagers and Spectrometers approaches, image and DTM data were ingested into ESRI ArcGIS® for analysis.
The reliability of rim height measurements depends critically on the ability to accurately constrain the elevation characteristics of the target surface prior to impact. Major steps required to determine the preimpact surface and reference crater topography to that surface are shown in Figure 3 using the 15.6 km Posidonius P crater. For each crater analyzed, I either used the NAC stereo DTM (if available) or extracted a local subset of the GLD100 extending, where possible, two to four crater diameters from each crater's center point (Figure 3a). Elevations within these local DTMs are referenced to the lunar spheroid with radius 1737.4 km. I then manually removed any elevation points related to the crater, its ejecta deposit, and any topographic anomalies such as other craters, their ejecta blankets, and adjacent highland topography (Figure 3b). The preimpact surface was constructed by fitting a second-order polynomial trend surface to the remaining elevation cells (Figure 3c). The final step was to subtract this preimpact surface from the local DTM in order to produce a DTM showing elevations relative to the preimpact surface, i.e., apparent elevations (Figure 3d).
A total of 299 individual bedrock exposures were measured within 21 craters. The apparent elevation of each outcrop's upper surface was recorded as the minimum height of wall rock uplift, WUmin (≤ WU, the actual value) as shown in Figure 4. The elevation of the rim crest, h, was measured directly above each WUmin measurement and the thickness of ejecta on the rim, Tmax (≥ T, the true value) was determined by subtracting WUmin from h.
3 Analysis and Results
3.1 Assessing the Effects of the Overturned Ejecta Flap
The term “overturned flap,” first coined by Shoemaker , is commonly used to describe the stratigraphically systematic nature of the continuous ejecta blanket [e.g., Roddy et al., 1975; Jones, 1978]. However, of importance here is the portion of the proximal ejecta nearest the rim that retains characteristics that are superficially similar to bedrock and, therefore, conceivably could be confused with uplifted target. This property is typically referred to as “stratigraphic coherence” and the portion of the ejecta flap exhibiting coherence has been referred to variously as the “continuous flap” [Shoemaker and Kieffer, 1974], the “rim fold” [Maloof et al., 2010] or the “coherent flap” [Jones, 1978].
Although exotic models have been proposed to account for the coherent flap [e.g., Jones, 1978], a simple ballistic emplacement model provides a sufficient and self-consistent genetic framework [e.g., Oberbeck, 1975]: At the edge of the excavation cavity, low ejection velocities lift and outwardly fold target material onto itself producing an inverted view of the near-surface target stratigraphy [Shoemaker, 1960; Roddy et al., 1975; Maloof et al., 2010]. In synthetic craters such as the Prairie Flat explosion crater [Roddy, 1977; Jones, 1978] formed in unlithified clays and sands, the flap is stretched and folded over the underlying target in a structurally coherent manner. However, in natural impacts into lithified targets, brittle failure occurs during folding so that the resulting flap forms an unconsolidated breccia.
The following observations and lines of reasoning indicate that the wall uplift measurements reported here are not corrupted to a significant degree by coherently emplaced ejecta:
1.Load-bearing capability. Pervasive brecciation of the coherent flap is observed at both the 1.2 km Barringer Crater [Shoemaker, 1960] and the 1.9 km Lonar Crater [Maloof et al., 2010]. While, near the rim, individual blocks can be quite large (i.e., up to ~20 m wide), closely spaced, and commonly retain bedding plane attitudes consistent with their heritage through folding, the overturned flap is not a cohesive rock unit and thus is not capable of supporting a vertical or near-vertical load. This is observed quite clearly at Barringer Crater, where there is a substantial decrease in slope (Figure 5) above the overturned Moenkopi Formation at the fold hinge surface.
The upper walls of many lunar craters exhibit protrusions and rock overhangs that require support from load-bearing basal rock units (Figures 1c–1j). If laterally contiguous, these foundation units reliably discriminate true cohesive wall rock from fragmental material in the overturned flap, even in the absence of conspicuous variations in image tone that otherwise would indicate layering. Furthermore, where DTM resolution permitted, the slopes of potential outcrops were assessed to determine if any significant slope reductions occurred within layered sequences. None were observed.
2.Scale. Impacting energies (i.e., velocities) of launched ejecta fragments increase with increasing range, irrespective of crater diameter. Only near the fold hinge located on the lip of the excavation cavity and where ejection velocities approach zero, can ejecta fragments retain the degree of stratigraphic consistency, structural attitudes and block proximity that could be confused with bedrock layering. As throw range increases, ejecta fragments become smaller and land with increasing energy leading to tumbling, fragmentation, bed disruption, and all-out ballistic sedimentation [Oberbeck, 1975]. Ballistic constraints, therefore, impose a strict limit to the radial extent of stratigraphic coherence. Consequently, at constant g, the width of the coherent flap, as measured from the excavation cavity rim, is independent of crater size.
The maximum extent of the coherent flap can be constrained by two terrestrial simple craters: Barringer and Lonar. While no specific width measurements of Barringer Crater's coherent flap have been published, geological cross sections [e.g., Shoemaker and Kieffer, [1974, Figure 3], indicate the flap extends less than 100 m beyond the fold hinge. At Lonar Crater, formed within the volcanic sequence of the Deccan Traps, the transition from coherence to mixed debris appears also to occur within ~100 m of the rim crest [Maloof et al., 2010]. Accounting for the Moon's lower gravity and the inverse g dependence of the ballistic equation, the elimination of coherency would therefore occur within ~600 m of the original excavation cavity rim for lunar craters. During the latest stages of crater formation, the original rim of the excavation cavity collapses into the basin, widening the final crater diameter [Melosh, 1989], and, thus destroying portions—if not all—of the coherent flap. Even simple, relatively well-preserved terrestrial craters, such as the Lonar [Maloof et al., 2010] and Barringer [Shoemaker, 1963] retain only a small proportion (i.e., 10–30%) of the original coherent flap hinge zone probably reflecting to some degree the ~20% expansion that simple craters experience during late-state modification [Melosh, 1989]. For complex craters, late-stage modification results in a final rim diameter that is ~50-100% larger than the original excavation cavity diameter [Grieve et al., 1981]. Consequently, the coherent flap would be completely consumed by late-stage modification for any lunar crater greater than ~7 km in diameter. Of the 21 craters in this analysis, all but two (the 4.9 km diameter Lichtenberg B and 2.2 km diameter Linné) have diameters exceeding this size; 19 show the classic morphological characteristics of complex craters [Pike, 1977].
3.Repeated stratigraphy, outcrop extent, and distribution. NAC images of all craters presented in this study were scoured for any indications of repeated, inverted stratigraphy. No distinct breaks or symmetries about a possible hinge surface were detected. All measured outcrops exceeded 200 m in lateral extent and were at least 50 m thick. Typically, outcrops were identified in all sectors of the crater's circumference where image coverage and appropriate illumination conditions permit. In the case of Eimmart A, elevated outcrops are observed in all portions of the crater rim but because this crater formed on the eastern rim of the larger Eimmart crater, it was not possible to determine the preimpact elevation for its western half. Consequently, only measurements along the eastern portion of Eimmart A's rim were recorded.
3.2 Target Uplift and Rim Ejecta Thicknesses
Table 1 and the plots in Figures 6 and 7 summarize the results of this study. The scaling relationships between the two rim constituents and rim height, h, are derived by linear regression of the 299 individual measurements of h, WUmin, and Tmax (Figure 6a):
Table 1. Measurements of Lunar Crater Rim Constituents
Average values ± 1 standard deviation. See text for details.
936 ± 88
768 ± 144
168 ± 68
0.186 ± 0.086
882 ± 160
722 ± 149
160 ± 109
0.179 ± 0.097
1330 ± 259
1150 ± 262
180 ± 48
0.139 ± 0.040
578 ± 142
404 ± 65
175 ± 111
0.284 ± 0.129
808 ± 117
625 ± 112
183 ± 73
0.226 ± 0.084
572 ± 99
381 ± 104
191 ± 47
0.342 ± 0.095
727 ± 263
598 ± 261
129 ± 55
0.198 ± 0.099
571 ± 55
382 ± 49
189 ± 32
0.332 ± 0.050
735 ± 174
615 ± 179
121 ± 32
0.173 ± 0.056
669 ± 127
491 ± 106
178 ± 65
0.267 ± 0.071
564 ± 94
431 ± 99
133 ± 47
0.240 ± 0.083
442 ± 104
335 ± 128
107 ± 51
0.263 ± 0.155
556 ± 85
419 ± 111
137 ± 49
0.258 ± 0.115
486 ± 82
375 ± 75
111 ± 35
0.229 ± 0.067
658 ± 116
502 ± 87
157 ± 81
0.231 ± 0.094
581 ± 75
515 ± 94
66 ± 34
0.118 ± 0.067
673 ± 30
541 ± 70
132 ± 75
0.195 ± 0.109
582 ± 56
487 ± 69
94 ± 30
0.165 ± 0.060
320 ± 55
223 ± 47
96 ± 22
0.300 ± 0.059
199 ± 37
178 ± 36
20 ± 9
0.102 ± 0.044
105 ± 5
80 ± 5
25 ± 4
0.239 ± 0.036
The near-zero slope on the linear regression of the data in Figure 4b demonstrates that Tmax/h is virtually independent of crater diameter over a wide range of crater sizes that includes both simple and complex crater morphologies. The intercept at 0.23 is consistent with the scaling relationships of equation (2).
The scatter in data plotted in Figures 6a and 6b consists of three components: measurement error that, given the mapping precision and resolution of the digital elevation data is not expected to exceed ~50 m vertically and should be symmetric about the mean values of each crater; real variations in the proportions of ejecta and uplifted target around each crater's rim; and, undetectable outcrops or buried target rocks located above the measured outcrops. For WUmin this last effect would shift the measured mean for each crater to a lower than actual value; conversely, for Tmax, the mean value would be artificially high. In combination, these results suggest that the actual T/h in the measured craters could be somewhat smaller—but likely not larger—than the calculated means shown in Table 1.
The proportion of total rim height represented by ejecta in the crater measurements presented here is 3 to 4 times less than that predicted from HE craters and small-scale impact experiments, i.e., T/h for lunar craters hovers around 0.2, whereas T/h values reported for synthetic craters range between 0.6 and 0.8 [Carlson and Jones, 1965; Dillon, 1972; Stöffler et al., 1975; Cooper, 1977]. Not only do these results refute the long-held contention that the ejecta deposit accounts for the majority of topographic relief at the rims of impact craters, they illustrate the limitations of relying on these synthetic analogs to understand some fundamental processes associated with hypervelocity impacts at larger scales. A full assessment of the potential issues surrounding the use of detonations and laboratory experiments as analogs to large-body impact is beyond the scope of this analysis. Suffice it to note, however, that crater growth (excavation) is initiated and controlled by the time-dependent pressure gradient field established by—among other things—the interactions of shock and rarefaction waves [Melosh, 1989]. Neither detonations nor small-scale impact experiments adequately replicate the conditions of large body impact in terms of impact velocities, peak shock pressures, and the characteristics of subsequent rarefactions. It should not be too surprising, therefore, that naturally formed impact craters differ in detail from their synthetic analogs.
Lunar craters smaller than ~15–20 km typically have simple bowl-shaped profiles with relatively large depth-diameter ratios (d/D ≅ 0.2) [Pike, 1977; Melosh, 1989] compared to larger craters and basins with complex morphologies. Consequently, crater depth-versus-diameter data (conventionally plotted in log-log space) show a well-defined inflection at the simple-to-complex transition [Pike, 1972, 1977]. Rim heights plotted against rim-crest diameters also display two distinct trends with a pronounced inflection at diameters of ~17 km [Pike, 1977]. Power law regressions of these two segments (converted from equations in Pike ) yield the rim height-to-crater radius, R scaling relationships:
where all units have been converted to meters. Standard errors are within ±0.008 of the mean for equation (3) and ±0.036 of the mean value for equation (4) [Pike, 1977 Table 1].
Figure 7a compares equations (3) and (4) with the average rim heights of each of the 21 craters shown in Table 1. Given that h = WU + T and T = 0.2 h (equation (1)), the scaling relationships between T and R (Figure 7b) become
where uncertainties derive from standard deviations in the Tmax population (Table 1).
The results presented above indicate that subsurface injection, rather than ballistic ejection, may be the primary mechanism of crater growth during the waning phases of the excavation stage as rim construction begins. Below, I address possible mechanisms to account for wall uplift and discuss implications concerning ejecta thickness models and excavation depth estimates.
4.1 Wall Uplift Mechanisms
Figure 7c compares the crater-averaged WUmin values with the WU(R) scaling relationships (dotted lines) derived from equation (1). The h(R) scaling laws [Pike, 1977] (solid line) are also shown for comparison. These data indicate that the elevated rims of both simple and complex craters are constructed primarily through subsurface structural processes, rather than ballistic emplacement of ejecta as conventional wisdom holds. Furthermore, the uplift does not die off rapidly (i.e., within 1.3 to 1.7R) as previously claimed [Melosh, 1989] based on an assessment of simple craters. Because gravitationally induced collapse [Melosh and Ivanov, 1999] expands complex craters by 1.5–2 times their original excavation cavity diameters [Grieve et al., 1981], such a rapid decay in WU would be revealed as a distinct rise in the T/h values of complex craters. Instead, equation (1) and the data in Figures 6 and 7c show that WUmin values of complex craters remain at the ~80% h level. Consequently, if the only distinction between the morphologies of simple and complex craters is due to the effects of late-stage modification—as the concept of proportional scaling [Melosh and Ivanov, 1999] requires—there is no indication that the proportion of structural wall uplift in simple craters diminishes at all, even to radial distances equivalent to 1.5–2 times the excavation cavity radius, i.e., equivalent to approximately halfway across the continuous ejecta blanket of a simple lunar crater.
The radially extensive structural uplift revealed by this analysis is not consistent with simple bulking or dilation of the excavation cavity wall as proposed by Melosh . As the examples in Figure 1 illustrate, bedrock exposures occur as coherent structural packages that, in several cases, exceed 3 km in length and over 500 m in thickness. Parallel to the crater wall the layers consistently appear horizontal or near-horizontal over extensive lateral distances, with only minor folding and faulting, not the jumbled, crumpled appearance that would be consistent with dilated or highly deformed wall rock. These observations are most consistent with outward, sill-like injection of impact melt and/or breccia into the target rocks surrounding the growing crater.
The interpretation that rim uplift is due to systematic near-horizontal injection into the crater wall rocks is consistent with observations at both Barringer and Lonar craters. Both craters show upper wall rocks that are consistently tilted outwardly: At Lonar 10°–30° outward dips typify the upper wall rocks [Maloof et al., 2010]. Although Barringer Crater exhibits intensified faulting at its joint-controlled “corners” (as discussed below), in more typical “linear” segments of the crater walls (Figure 8), the beds of the upper walls show 35°–40° dips away from the crater center [Kring, 2007]. Neither Lonar nor Barringer expresses the chaotic block arrangements that would support the bulking hypothesis.
If subsurface injection is a major process during the excavation stage, it seems likely that it would exploit any preexisting structural weaknesses in the target, including stratigraphic boundaries, buried regolith layers, regional jointing, and strong lithological contrasts (such as between competent mare basalt and weaker, comminuted highlands rocks). Virtually all the lunar impact craters analyzed in this study were formed in layered volcanic target sequences, likely containing regolith interfaces at some buried flow boundaries (Sharpton and Head, 1982). Such weak layers may facilitate injection and rim uplift and result in a wider excavation crater than expected of a similar impact into a more competent, massive target.
Exploitation of preexisting target weaknesses during excavation flow explains the “squarish” shape and rim characteristics of Barringer Crater (Figure 8) [Shoemaker, 1960, 1963; Roddy, 1978]. Kumar and Kring  confirmed that rim uplift at the corners was partially accommodated by impact reactivation of preexisting, orthogonally oriented joints and in a related study, Poelchau et al.  showed that rim uplift at the corners is approximately twice that observed along the more linear segments of the rim (80 ± 10 m at the corners compared to 40 m on the sides). Based on these observations, Poelchau et al.  proposed that rim uplift is due to thrusting of coherent rock material into the crater wall. The results I present here appear to support such a model and further indicate that this is the dominant mechanism of crater growth possibly throughout the excavation stage but at least during its waning phase when the transient rim is being constructed.
4.2 Ejecta Thickness Models
Assuming equation (6), like equation (4), holds for larger complex craters on the Moon, ejecta thicknesses on the rims of multiring basins such as Imbrium (D = 1160 [Spudis, 1993]) are considerably thinner than predicted by previous models. For instance, the widely used model of McGetchin et al. , i.e., T = 0.14R0.74 predicts 2577 m of ejecta on Imbrium's rim whereas by equation (6)T = 787 m (±235 m).
McGetchin et al.  derived their model by fitting a single power function to a population that included mostly simple craters (HE craters and Barringer Crater) but also included Copernicus (D = 94 km) and the Imbrium basin (even though data for the latter two features were considered speculative at the time [Pike, 1974]). While McGetchin et al. acknowledged potential uncertainties related to the effects of late-stage modification and attempted to reconstruct the “crater of excavation” for Imbrium based on its second ring (R = 485 km), several observations indicate that these authors at the time did not fully comprehend the effects of late-stage modification:
They used the final crater diameter for the Copernicus crater (which they plot at R = 47 km) rather than its smaller excavation cavity diameter.
They did not explain why the edge of the original excavation crater—which would have collapsed into the basin and disintegrated during late-stage modification—should be expressed as a topographically elevated basin ring.
As the McGetchin et al.  study preceded Pike's  morphometric documentation of lunar crater depth-diameter relationships, the effects of late-stage modification likely were not fully appreciated or incorporated into the resulting ejecta model.
These observations suggest that McGetchin et al.  believed that the topographic ring corresponding to Imbrium's “crater of excavation” is the morphological equivalent of the final rim of a smaller central peak crater such as Copernicus. Because, however, topography associated with a crater's continuous ejecta deposit decreases radially as a power function with a negative exponent (−3 according to McGetchin et al. ), collapse of the excavation cavity flanks not only widens the final crater but also reduces the final rim height proportionately. This effect is much more severe for complex craters than for simple ones. So, by combining the simple and complex populations, rather than treating them separately (as I have done in Figure 7b), their model overestimates the amount of ejecta emplaced on the rims of large lunar impact basins. And, because ejecta thickness decays exponentially with distance from the crater rim, it also overestimates the amount of ejecta distributed at great distances from large basin-forming events on the Moon.
Equation (6) seems to predict surprisingly thin ejecta blankets compared to previous estimates based on geological assessments of landscape modification. For instance, Fassett et al.  measured remnant relief on craters covered by the Orientale ejecta blanket to arrive at a maximum ejecta thickness of 2900 ± 300 m at Orientale's rim (i.e., the Cordilleran ring; R = 465 km) whereas the model presented here predicts T = 723 ± 217 m. However, the approach Fassett et al.  used measures the total thickness of the basin's ejecta blanket which comprises both basin-derived ejecta and locally incorporated material due to ballistic sedimentation [Oberbeck, 1975]. Material launched at high velocity along ballistic trajectories interacts violently with the local target surface, eroding relief and incorporating large amounts of local material in the final ejecta deposit. This would be the case even at the final rim ring of large basins such as Orientale, where ejecta throw distances would be hundreds of kilometers.
By focusing on relatively small simple and central peak craters, the effects of ballistic sedimentation are minimized (but not eliminated) in the data presented here because the launch trajectories of rim ejecta are relatively short (and therefore less energetic) compared to larger basin-forming events. Accepting the estimate of Fassett et al. , for instance, the amount of basin-derived ejected material at the Cordillera is ≤25% of the total deposit thickness, an estimate that is consistent with the results of Morrison and Oberbeck  who constrained the proportions of basin and locally derived ejecta based on a study of the 26 km lunar crater Delisle.
4.3 Excavation Depth
Three approaches have been taken to constrain crater excavation depth, de: decimeter-scale impacts into unconsolidated sand [Stöffler et al., 1975], flow-field models developed for HE craters [Croft, 1981], and evaluation of the central uplifts of certain heavily eroded terrestrial impact structures [Grieve et al., 1981]. These approaches led to the general acceptance [Melosh, 1989; Melosh and Ivanov, 1999] of
where De is the diameter of the excavation cavity. However, the discussion in section 3.2 shows that models based on the results of impact experiments and HE craters can be misleading. Furthermore, central uplifts only provide a maximum constraint on de because the uplifted rocks could (and probably do) originate from depths well below the base of the excavation cavity.
Observations presented here indicate that ejecta deposits near lunar crater rims are ~3–4 times thinner than previously thought implying that the total volume of excavated material is comparably smaller. This can be illustrated using the simple Z-model flow field (Figure 9), although the shape of the excavation cavity is not important for the purposes presented here. Consider, as did Croft [1980, 1981], that the transient crater consists of three components: (i) the excavation cavity, Ve′, equal to the total volume of ejecta, Ve; (ii) a volume Vu′ that balances the volume associated with permanent structural rim uplift, Vu; and (iii) a volume Vt′ accounting for the volume difference between the transient and final craters; this would include volume changes associated with melting (densification) and brecciation (dilation). Given that Vu/Ve is at least 3 times greater than previously thought, the additional volume of rim uplift must be due to a smaller excavation cavity volume, Ve′. Consequently, if excavation volume and depth are correlated, as commonly assumed [Croft, 1980, 1981; Melosh, 1989], then the maximum crater excavation depth would be somewhat less than one third the value of the previous estimate, i.e.,
Recent geological evidence appears to support such a shallow excavation depth: The ~2500 km South Pole-Aiken (SPA) basin [Spudis et al., 1994] is the largest known impact basin on the Moon. High-resolution gravity data from the recent Gravity Recovery and Interior Laboratory mission [Zuber et al., 2012] in combination with LRO's Lunar Observer Laser Altimeter (LOLA) [Smith et al., 2010] have shown that the lunar crust is only ~40 km thick [Wieczorek et al., 2013]. Because De = 0.5–0.75D [Grieve et al., 1981], equation (7) predicts that the impact event that generated SPA should have excavated deep (i.e., de ≥ 125 km) into the lunar mantle and ejected a significant quantity of material with mantle affinity.
Remotely acquired spectral data indicate that, with the exception of a few isolated occurrences of olivine-rich material around the periphery of SPA [Yamamoto et al., 2010], the only geological units with a possible mantle affinity are located on the basin floor of SPA [Lucey et al., 1998; Lucey, 2004; Wieczorek et al., 2006; Taylor et al., 2006] and could represent the interior melt sheet [Morrison, 1998]. The lack of continuous ejecta deposits with mantle affinities clearly demonstrates that the SPA-forming event did not excavate deeply, if at all, into the lunar mantle. Using equation (8), however, the estimated maximum depth of excavation for SPA would lie between ~35 km and ~55 km. Consequently, the shallow excavation depth model proposed here (equation (8)) is much more consistent with current geological and geophysical observational constraints on crustal composition and thickness than previous estimates.
5 Conclusions and Implications
The results presented in this paper indicate that lunar craters (and by extension larger lunar basins) formed through a growth process that was dominated by subsurface injection into the walls of the expanding crater. The rim and flank topography at these craters consist primarily (i.e., ~80%) of target rocks structurally uplifted in response to this injection process. The thickness of ejecta emplaced on the rims and flanks of these craters comprises only ~20% of the total rim topography, a value that is considerably lower than previously thought. Several important implications can be drawn from these results:
1.Because subsurface injection is less efficient than ballistic ejection, considerably greater impact energies would seem to be required in order to generate an excavation crater of a given size. Impacts into relatively weak target materials, especially those with horizontal layering, would be expected to produce larger excavation cavities than those formed in stronger, massive targets.
2.Excavation cavities constitute a smaller proportion of the transient crater than previously estimated. Because the width of the excavation cavity is constrained by the ejecta flap hinge zone (which is approximately equivalent to the rim of a simple crater), this constrains the depth of excavation to be considerably shallower than previously estimated, i.e., de ≤ 0.03De.
3.Primary material distributed from large basins to distal exploration and sample sites makes up a much smaller proportion of the total ejecta than previously thought; the remainder consists of locally derived contaminants incorporated into the distal ejecta deposits through ballistic sedimentation [Oberbeck, 1975]. For instance, following the approach of McGetchin et al.  with the revised rim ejecta thickness, T, for complex craters presented here (equation (6)), yields the equivalent thickness t of basin-derived ejecta as a function of normalized distance:
where r/R is distance from the crater center in multiples of rim radius R.
4.The results of this study strictly apply to reasonably small lunar craters formed into layered lava sequences. While extrapolations to larger, basin-sized features are made and appear well-founded, additional work is required to confirm these conclusions and implications. Further work is also required to determine to what extent these results pertain to craters formed on other planetary surfaces, particularly those with significant atmospheres and/or near-surface volatiles.
The author thanks David Kring and Paul Spudis for helpful discussions and Mark Robinson and his NAC team for providing critical data sets. The efforts of Nadine Barlow and an anonymous reviewer are gratefully acknowledged. This work was funded by the NASA Lunar Advanced Science and Exploration Research Program (grant NNX13AJ33G). LPI contribution 1770.