Size‐frequency distribution of crater populations in equilibrium on the Moon

Abstract

Overprinting of craters by subsequent impacts and topographic degradation complicates crater statistics, especially for old surfaces and small‐diameter crater populations. A crater population is regarded as in equilibrium at a particular crater size when smaller craters are being produced at the same rate at which they are being destroyed. Evaluating the equilibrium state of crater populations is challenging, and empirical equilibrium densities are frequently inferred. By performing careful crater counts and cross comparisons on several lunar surfaces, we study the size‐frequency distributions (SFD) for the crater populations, which have portions in equilibrium. The results are one of the few observational constraints on the SFD of crater populations in equilibrium, showing that referring to empirical equilibrium densities is not safe for evaluating the equilibrium states of crater populations. Equilibrium densities are not positively correlated with the ages of crater populations, and some populations in equilibrium have crater densities less than those previously believed to represent equilibrium conditions. Besides the SFD of the production population, different crater removal rates at different diameters also affect the SFD of crater populations in equilibrium. The equilibrium onset diameter (Deq) of a crater population can be translated to model ages because older populations have larger Deq, and those for same‐aged surfaces are comparable. We show that the crater populations studied here are in equilibrium at much smaller diameters than those predicted for same‐aged surfaces by crater degradation models, thus indicating lower crater degradation rates on the Moon, and/or younger ages of the counting areas.

Geological Characterization of the Ina Shield Volcano Summit Pit Crater on the Moon: Evidence for Extrusion of Waning‐Stage Lava Lake Magmatic Foams and Anomalously Young Crater Retention Ages

“…We identify 542 impact craters ≥10 m in diameter on the Ina mounds, which is more than twice the number (i.e., 232) reported by Braden et al (). The cumulative SFD of these mound impact craters (Figure c) does not show clear evidence of a crater population in the equilibrium state (e.g., Xiao & Werner, ). Fitting of these mound impact craters using the Neukum lunar CF and PF produces an absolute model age of 59 ± 3 Ma, compared with 33.2 ± 2 Ma of Braden et al ().…”

Size-frequency distribution of different secondary crater populations: 1. Equilibrium caused by secondary impacts

“…If equilibrium is caused only by continuous impact cratering and mass wasting, and no other resurfacing effects (e.g., fluvial, aeolian, and lava erosion) exist, equilibrium is also frequently termed as steady state [ Shoemaker et al ., ], empirical saturation [ Chapman and Jones , ], and saturation equilibrium [ Richardson , ], e.g., equilibrium of most crater populations on homogeneous lunar and Mercurian surfaces. Preliminary laboratory experiments of repeated impact cratering in sandbox [ Gault , ], detailed analyses of crater size‐frequency distribution (i.e., SFD) on the Moon [ Xiao and Werner , ], and sophisticated numerical models [ Richardson , ] have characterized the equilibrium process of different crater populations. The SFD of crater populations that are in equilibrium is primarily dependent on that of production crater population [e.g., Marcus , ; Chapman and McKinnon , ; Richardson , ]: production populations with ≤ ~ −4 differential SFD slopes (see section 2.2 about the introduction on SFD slopes) yield about −3 differential SFD slopes for the equilibrium populations, e.g., the rim‐to‐rim diameter D < 4 km crater population on the lunar mare [e.g., Basaltic Volcanism Study Project , ]; those with ≥ ~ −3 differential SFD slopes cause similar SFD for the equilibrium populations, but no single equilibrium density exists for such cases, because the equilibrium density oscillates depending on when the last large impact was formed, e.g., the D ≥ 10 km crater population older than ~3.8 Ga on the Moon [ Strom et al ., ].…”

“…The SFD of crater populations that are in equilibrium is primarily dependent on that of production crater population [e.g., Marcus , ; Chapman and McKinnon , ; Richardson , ]: production populations with ≤ ~ −4 differential SFD slopes (see section 2.2 about the introduction on SFD slopes) yield about −3 differential SFD slopes for the equilibrium populations, e.g., the rim‐to‐rim diameter D < 4 km crater population on the lunar mare [e.g., Basaltic Volcanism Study Project , ]; those with ≥ ~ −3 differential SFD slopes cause similar SFD for the equilibrium populations, but no single equilibrium density exists for such cases, because the equilibrium density oscillates depending on when the last large impact was formed, e.g., the D ≥ 10 km crater population older than ~3.8 Ga on the Moon [ Strom et al ., ]. Besides this first‐order principle, it has been recently found that the onset diameter where equilibrium occurs ( D eq ) is approximately the same on different places of same‐aged lunar surfaces [ Xiao and Werner , ], but both the crater SFD and density at D < D eq exhibit subtle variations at different locations of coeval surfaces [ Schultz et al ., ; Xiao and Werner , ]. These variations are caused by a combination of changed crater production and removal rates for different‐sized craters [ Xiao and Werner , ].…”

On the importance of self-secondaries

“…It has been suggested that populations of small craters on the normal ejecta deposits of Tycho, which are dominated by self-secondaries have achieved the equilibrium state at D < ~15 m in diameter, but crater populations on the melt pools of Tycho have not been in equilibrium at D ≥ 5 m (Shoemaker et al 1969;Xiao 2016). Likewise, crater populations on the impact melt pools of the King crater is in equilibrium at D ≤ 40-50 m (Ashley et al 2012), those on surfaces ~ 220 Myr old are in equilibrium at D ≤ 20 m , and those on melt pools of the Copernicus crater are in equilibrium at D ≤ ~100 m (Xiao and Werner 2015). Therefore, both the gradual accumulation of younger crater populations and crater degradation should be considered when studying the evolution of crater populations on continuous ejecta deposits.…”

“…For example, Fig. 3 shows a recent revisit to the landing site of the Surveyor 7 mission (Xiao and Werner 2015;Xiao 2016), where the self-secondaries scenario was first proposed. Around the landing site, the different facies of Tycho's ejecta deposits (Shoemaker et al 1969) can be classified into 3 types based on their surface textures: normal ejecta deposits that have minor modification by subsequent melt flows, melt veneer that cover normal ejecta deposits, and melt pools that are located at low-relief areas (Fig.…”