Effects of incidence angle on observations of equilibrium crater diameter

Determining the equilibrium crater diameter for a crater population is important in lunar regolith depth estimates as the equilibrium diameter represents the steady-state between the formation of new craters and the removal of older craters [1]. [2] hypothesized that the number of craters identified in an image is dependent on the incidence angle and showed that for three different young mare regions, fewer craters are visible at lower incidence angles, affecting reliable estimates of the equilibrium diameter of the counted crater population. [3] disputed this hypothesis and the presence of an equilibrium crater population in the data from [2]. Testing the hypothesis from [2], we chose four Apollo Metric images of the same area with different incidence angles to examine the effects of resolution on apparent equilibrium diameter estimates. We selected a 100 km2 area centered at 27.3°N, 18.2°W in Mare Imbrium east of Lambert crater with data at 87°, 82°, 71°, and 50° incidence angles, and scan resolutions of 6.6 to 7.6 m/pixel. To compare the craters visible at different illuminations, we resampled the images to 10 m/pixel and employed three individuals to count craters. The cumulative histograms for the four Apollo Metric frames exhibit the effects of different incidence angles on reliably counting craters. Current results show that the crater counts for the 82° incidence angle image are the most consistent between different observers, finding a production function slope of -4.1 and an apparent equilibrium diameter of 200 m. Deviation from the small crater trends (equilibrium population?) and the production function slope observed at 82° incidence is found at the higher (87°) and lower (71°, 50°) incidence angles. We attribute some of this deviation to the effects of incidence angle on crater detection; at crater diameters >~300 m, we find similar production functions, an observation consistent with our identification of these large craters in all four illuminations. However, the small crater trends vary significantly among observations at different illuminations. An important question is whether the small crater slope and rollover we observe are representative of the equilibrium crater population or whether these observations are due to resolution limits of the images, a too-small count area, or shadow effects (e.g., loss of small craters in the shadows of larger craters). To test if the observed rollover in the cumulative histograms is due to resolution effects or to the observation of the equilibrium crater population, we will use substantially higher resolution images. Images from the Lunar Reconnaissance Orbiter Camera Narrow Angle Camera (resolution increasing during the nominal mission from ~1.5 to ~0.5 m/pixel) at incidence angles ranging from 50° to 87°, focusing on higher incidences (70° to 87°), will be used to maximize the identification of small craters. [1] L. A. Soderblom (1970) JGR, 75, 2655. [2] B. B. Wilcox et al. (2005) Meteoritics & Plan. Sci., 40, 695. [3] V. R. Oberbeck (2008) Meteoritics & Plan. Sci., 43, 815.