4.1. Comparisons of Past Estimates of Ejecta Thickness and Decay
[12] A wide range of estimates have been made for the thickness of ejecta at the rim crest of the transient cavity, and for the ejectathickness decay function. McGetchin et al. [1973] suggested a function for the thickness of ejecta at the transient cavity rim crest T_{TR} = 0.14 R_{TR}^{0.74}, with R_{TR} and T_{TR} in meters, on the basis of nuclear craters, Meteor Crater, and observations of lunar craters. The McGetchin et al. function, assuming the Cordillera ring as the location of the transient crater rim crest, implies ejecta thicknesses at this location of 2190 m, a value smaller than our measured ejecta thicknesses. This function implies even smaller thickness estimates if the transient cavity is significantly smaller than the Cordillera Ring, as seems likely. Pike [1974] suggested a wide range of models for T_{TR}; his equation (11), T_{TR} = 0.033R_{TR}, would imply a thickness of ejecta at the Cordillera ring of ∼15 km (assuming that the Cordillera ring was the transient cavity rim crest), at least factor of 5 larger than our measurements. If, however, the transient crater was well within the Cordillera ring, as discussed below, the thickness at the rim of the transient cavity implied by this equation is potentially consistent with our results. Petro and Pieters [2006] applied the Housen et al. [1983] scaling [see also Haskin et al., 2003] to suggest T_{TR} = 0.0078R_{TR,} which would imply a thickness of 3600 m if the Cordillera rim is the appropriate radius for the transient crater.
[13] Our ejectathickness measurements also allow derivation of a new power law for the decay of ejecta, with an exponent of B = 2.8 (±0.5); this is shallower than that estimated by McGetchin et al. [1973] (B = 3) and steeper than that determined by Petro and Pieters [2006] (B = 2.61), who applied the model of Housen et al. [1983], although it is formally consistent with both. Our measurements and inferred decay law differ significantly from the monotonic linear decay suggested by Short and Forman [1972] and the concave down profile of Cordell [1978]. Both of these profiles have thicknesses of ejecta of >2 km at r/R_{CR} ∼ 1.5, which is inconsistent with our observations and the preservation of several 7 to 10 km preOrientale craters at this range. When fresh, such craters would be expected to have relief of only 1.5 to 2 km, which would have been destroyed by deposition of >2 km of ejecta.
4.2. Ejecta Volumes and Comparisons to Estimated Transient Rim Crest Positions
[14] Using our power law description of the radial decay of ejecta, we can now integrate this function to calculate the volume of ejecta deposited in various regions, and evaluate the results in light of proposed locations of the transient cavity's rim crest for Orientale. Some ejecta was undoubtedly deposited at larger radial ranges than we measure [e.g., Spudis, 1993; Ghent et al., 2008], but it is likely to be a small percentage of the total ejecta volume because it commonly occurs in radial chains and is discontinuous.
[15] The Orientale basin consists of the Cordillera ring, which defines the topographic basin rim, the Outer Rook, a ring of continuous inward facing massifs, the Inner Rook, a ring of peaks, and an inner depression that contains Mare Orientale (Figure 1a). A variety of these rings have been suggested to approximate the location of the transient cavity's rim crest (see discussion in the work of Spudis [1993]), and our new thickness, volume, and decay law estimates permit us to assess the plausibility of these assignments (Table 1). From the Cordillera ring to one basin diameter from this topographic rim crest (r/R_{CR} = 3), we calculate an ejecta volume of 2.9 × 10^{6} km^{3} (+1.2, −0.8).
Table 1. Parameters of Possible Transient Crater Radii^{a}Mapped Ring  Transient Crater Radius, R_{TR}  Volume of Excavation Crater, V_{Ex}  R_{TC} Ejecta Thickness at Transient Rim  Volume of Ejecta From R_{TR} to R_{CR}  Volume of Ejecta From R_{CR} to 3 R_{CR} 


Inner Dep.  160 km  2.0 × 10^{6} km^{3}  57.5 km (+50.7, −27.2)  6.6 × 10^{6} km^{3} (+3.4, −2.2)  2.9 × 10^{6} km^{3} (+1.2, −0.8) 
Inner Rook  240 km  4.5 × 10^{6} km^{3}  18.5 km (+9.9, −6.6)  3.4 × 10^{6} km^{3} (+1.1, −0.9)  2.9 × 10^{6} km^{3} (+1.2, −0.8) 
Outer Rook  310 km  7.5 × 10^{6} km^{3}  9.0 km (+3.2, −2.4)  1.9 × 10^{6} km^{3} (+0.4, −0.4)  2.9 × 10^{6} km^{3} (+1.2, −0.8) 
Cordillera  465 km  17.0 × 10^{6} km^{3}  2.9 km (±0.3)  0 km^{3}  2.9 × 10^{6} km^{3} (+1.2, −0.8) 
[16] Assuming a paraboloidal shape for the excavation cavity, its volume is V_{Ex} = 0.5πd(R_{TR})^{2} for radius of the transient and excavation cavity, R_{TR}, and for depth of excavation d, which we assume to be 50 km. This assumed depth is supported by spectroscopic observations that suggest that the ejecta and ring massifs of Orientale are predominantly feldspathic and lack obvious signatures of lunar mantle material [Pieters et al., 2009; Yamamoto et al., 2010] as well as by geophysical modelling [Wieczorek and Phillips, 1999; Hikida and Wieczorek, 2007]. If the Cordillera ring radius approximates the radius of the excavation, this would imply an excavation volume of 17.0 × 10^{6} km^{3}, substantially greater than the ∼2.9 × 10^{6} km^{3} of ejecta observed within one basin diameter of the Cordillera ring.
[17] Extrapolating the power law description of ejecta inward to the current position of rings inside the Cordillera by varying radius R_{TR}, we can estimate the thickness of ejecta at the transient cavity's rim crest and the additional ejecta volume expected between R_{TR} and R_{CR}. If the transient radius is expressed as a fraction of the Cordillera radius, ρ = R_{TR}/R_{CR}, then the thickness expected at the transient crater rim is:
[18] If the next innermost ring, the Outer Rook Mountains approximates the size of the transient cavity [Head, 1974], then ρ ≈ 2/3. Thus, given B = 2.8, we would expect 3.1 times as thick an ejecta deposit at the Outer Rook (∼9000 m) than at the Cordillera ring, and ∼1.9 × 10^{6} km^{3} of additional ejecta would have been emplaced between the Cordillera ring and Outer Rook ring. This ejecta would have ended up within the final topographic depression of the basin defined by the Cordillera ring, with an average thickness of ejecta of ∼5 km in this region, known as the Montes Rook Formation [Scott et al., 1977]. The deposition of this volume of ejecta would have provided a significant load that may have influenced the modification stage of basin formation by facilitating the collapse of the transient cavity's rim [e.g., Head, 2010]. If we were to include this inferred volume of ejecta between the Cordillera ring and Outer Rook, a total ejected volume of ∼4.8 × 10^{6} km^{3} would be implied (Table 1).
[19] The Inner Rook Mountain ring has also been proposed to represent the approximate position of the transient cavity rim crest [Floran and Dence, 1976]. This smaller transient cavity would have an ejecta thickness of ∼18.5 km at the rim crest, a volume inside the Cordillera ring of ∼3.4 × 10^{6} km^{3}, and a total volume of ∼6.3 × 10^{6} km^{3}. The inner depression could also represent the transient cavity rim crest. Extrapolating our ejecta decay function to this much smaller transient cavity would imply an ejecta thickness at the rim crest of >50 km, a volume inside the Cordillera ring of ∼6.6 × 10^{6} km^{3}, and a total volume of ∼9.5 × 10^{6} km^{3}. The extremely large volume of ejecta for such a small transient cavity rules out this ring as a realistic candidate for the transient cavity's rim crest. Similarly, the extremely small volume of ejecta, relative to the excavation cavity of volume for a Cordillera ring–sized excavation cavity also suggests that it is unlikely to have been the location of the transient crater rim.
[20] These ejecta volumes can also be compared to the volume estimates for the Orientale transient cavity derived on the basis of alternative approaches. On the basis of gravity data, Wieczorek and Phillips [1999] determined a volume of 3.1 ± 0.4 × 10^{6} km^{3} for the transient cavity, with a maximum excavation depth of ∼50 km and radius of excavation of R_{TR} ∼ 200 km (midway between the Inner Rook ring and the inner depression). More recently, Hikida and Wieczorek [2007] derived similar values for the radius of the excavation cavity and slightly smaller depths using different gravityinversion techniques.
[21] The ejecta volume we infer outside the Orientale topographic basin (outside the Cordillera ring), but within one basin diameter, is ∼2.9 × 10^{6} km^{3}. This rises to ∼4.8 × 10^{6} km^{3} if the ejecta profile is extrapolated back inside the basin to the Outer Rook ring (R = 310 km). Estimates for the transient cavity volume derived from lunar gravity analyses (∼3.1 ± 0.4 × 10^{6} km^{3}) [Wieczorek and Phillips, 1999; Hikida and Wieczorek, 2007] are more comparable to the value we observe outside the Cordillera ring (R = 465 km), but the Cordillera ring radius is considerably greater than their estimated R_{TR} of ∼200 km. One possibility is that the radius of the transient cavity is simply larger than inferred in these gravity models. For example, if the current Outer Rook approximates the size of the transient cavity, then a 50 km depth of excavation would imply a volume of ∼7.5 × 10^{6} km^{3}, and a 40 km depth of excavation would yield a volume of ∼6 × 10^{6} km^{3}, consistent with predicted ejecta volumes.
[22] Four other factors may contribute to this difference: (1) the excavation cavity volume of a large basin is greater than the total ejecta volume deposited outside the crater [e.g., Schultz et al., 1981]; (2) the shape of the excavation cavity may be more realistically estimated by a nested cavity configuration than by assuming a paraboloidal geometry [Cintala and Grieve, 1998; Head, 2010; Baker et al., 2011]; (3) the ejectathickness model assumes no ‘bulking’ or net change in density or porosity of the ejecta, and does not include incorporation of local material into the ejecta; and (4) extrapolating the ejecta profile from outside the basin into its interior may not adequately reflect what would be deposited within the rim of the basin as it formed.
[23] In summary, our new ejecta measurements and inferred ejecta decay profile are consistent with a transient cavity radius approximated by the current location of the Outer Rook ring and are inconsistent with a much larger (R_{TR} > 400 km) or smaller (R_{TR} < 200 km) transient cavity.