5.2. Density of Large Craters on Mercury and the Moon
 Our data show that the density of craters with diameters in the range ∼128–512 km is similar on Mercury and the Moon. This conclusion differs somewhat from that reported from Mariner 10 observations by Strom and Neukum  (Strom and Neukum [1988, Figure 9] show fewer craters in the heavily cratered terrain on Mercury than the lunar highlands, although their statistics for diameters > 100 km on Mercury were poor). Two possible explanations for the similarity between the Moon and Mercury at large sizes are: (1) cratering of both surfaces reached saturation equilibrium at these crater sizes, or (2) neither body was saturated and both surfaces have the same time-integrated cratering flux (to within error).
 Saturation equilibrium is reached when accumulating craters (and their ejecta) are effectively obliterating as many pre-existing craters as are formed [Gault, 1970; Marcus, 1970]. However, whether saturation is actually observed on solar system surfaces is a subject of sustained debate [Marcus, 1970; Woronow, 1977; Hartmann, 1984; Chapman and McKinnon, 1986; Strom and Neukum, 1988; Hartmann, 1995; Hartmann and Gaskell, 1997].
 Recent modeling of how crater populations accumulate has added new evidence that craters are at saturation levels in the lunar highlands, with densities occurring at R values of ∼0.1 to 0.3 [Richardson, 2009]. Because our data suggest that (1) Mercury has the same density of large craters as the Moon, and (2) both the Moon and Mercury have R values > 1 for ∼100-km-diameter craters over more than 80% of their surfaces, we suggest that saturation was reached on Mercury as well as the Moon. As we discuss in the following section, however, craters at small diameters are more readily removed, and they appear to have experienced a different history.
 A further implication of Richardson's  modeling study is that the shape of the crater size-frequency distribution can continue to reflect the accumulating population even in saturation, as originally suggested by Chapman and McKinnon . This result implies that it may be impossible to rely on the shape of the size-frequency distribution alone to decide whether saturation has been reached. Thus, the Moon and Mercury may both have been saturated at large crater diameters (Figure 2), although models suggest that preservation of a saturated population may be inconsistent with the steepness of the production function in this size-range [Chapman and McKinnon, 1986; Richardson, 2009].
 Alternatively, the similar crater size-frequency distributions for the Moon and Mercury at large crater diameters may simply be a result of both planetary bodies having had the same time-integrated flux at these crater sizes. This explanation is plausible because the shape of the production function on ancient terrains of the Moon and Mercury was similar [Strom et al., 2005, 2008]. However, for this explanation to be correct in the absence of saturation, the product of the period of surface exposure and rate of large crater formation must be the same for both surfaces, which would constitute a remarkable coincidence, especially given that models for the rate of crater formation on Mercury imply faster crater accumulation than on the Moon [Marchi et al., 2009; Massironi et al., 2009].
 An additional factor that may have been important in reaching similar crater densities on the Moon and Mercury is crater removal by processes other than later cratering. It is possible that both planetary bodies reached saturation by large craters, but the crater size-frequency distribution on both bodies subsequently was modified by volcanism or other geological processes to approximately the same degree. This explanation is consistent with the similar fractional areas of young terrain on both bodies (R < 0.1) (Figure 3b).
 In sum, our observations are consistent with the hypothesis that crater saturation was reached for craters of diameter D > 128 km on both Mercury and the Moon. Deciding whether this or another explanation is correct will require new observations of crater density and improvements in modeling of how crater populations accumulate.
5.3. Deficit of Craters on Mercury and the Moon at Diameters 20 to 128 km
 The deficit in crater density at diameters 20 to 128 km on Mercury compared with the Moon was recognized from Mariner 10 data [Strom, 1977; Spudis and Guest, 1988; Strom and Neukum, 1988]. Hypotheses that might explain this deficit on Mercury include: (1) differences in the population of impactors on the two bodies; (2) differences in scaling related to differences in surface gravitational acceleration, strength of the target, or impact velocity; (3) differences in how secondary versus primary craters contributed to the surface population, particularly secondary craters from basin formation; and (4) differences in resurfacing that affected how crater populations accumulated and were preserved on the two surfaces. However, because models suggest Mercury has the same impactor population and a similar cratering efficiency to the Moon [Strom et al., 2005; Marchi et al., 2009], the first two explanations are unlikely. Variations in the secondary cratering process are also unlikely to explain this difference, because secondary craters are more common on Mercury than the Moon [Strom et al., 2008, 2011], not less, and most secondaries are smaller than the size range of craters considered here.
 The hypothesis that the deficit of small craters on Mercury is a result of resurfacing is thus preferred. Such a difference is plausibly the result of widespread emplacement of intercrater plains on Mercury early in its history [e.g., Trask and Guest, 1975; Murray et al., 1975; Malin, 1976; Strom, 1977; Leake, 1982]. Superposition relationships and crater statistics both provide evidence that such emplacement was not a short-lived episode but rather a complex sequence of resurfacing events during the period when rates of impact cratering were high [Malin, 1976; Woronow and Love, 1987].
 From images of terrains with the highest N(20) values on both the Moon and Mercury (Figure S1), it is clear that the most densely cratered regions on Mercury have smoother inter-crater surfaces than the most densely cratered regions of the Moon. Heavily cratered areas on Mercury tend to be intimately interspersed with intercrater plains that are not readily separable stratigraphically [Trask and Guest, 1975]. Thus, we favor the hypothesis that the difference in crater densities between the Moon and Mercury at these crater sizes is due to plains formation concomitant with early cratering [e.g., Strom, 1977], and that even the most densely cratered terrains on Mercury have experienced significant erasure of craters. This hypothesis implies that Mercury experienced crustal resurfacing early in its history on essentially a global basis, in contrast with the Moon, which has crater-saturated highlands regions that were never resurfaced. If intercrater plains on Mercury are volcanic in origin, this interval of global resurfacing has important implications for the thermal evolution of Mercury. Such a view is consistent with the idea [e.g., Denevi et al., 2009] that the upper crust of Mercury is dominated by volcanic sequences of various ages and that no “primary” crust [Taylor, 1989] is exposed at the surface today.