Submillimeter-scale topography of the lunar regolith

We have applied computer stereophotogrammetry to Apollo Lunar Surface Close up Camera (ALSCC) pictures of the lunar surface to construct the first-ever digital topographic relief maps of undisturbed lunar soil over spatial sca les from 85 mu m to 8.5 cm. Using elevation histograms, fractal analysis, a nd Hapke's photometric roughness model we show that Apollo 14 (Fra Mauro) I mbrium ejecta is rougher than average Apollo 11 (Mare Tranquilitatis) and A pollo 12 (Oceanus Procellarum) mare surfaces at submillimeter to decimeter size-scales. We confirm the early result of K. Lumme et al. (1985, Earth Mo on Planets 33, 19-29) that the cumulative distribution of elevations for lu nar soil is typically well described by Gaussian statistics. However, cumul ative distributions are insensitive to asymmetries in the shapes of elevati on histograms: Of 11 discrete elevation histograms we measured, about half exhibit significant deviations from Gaussian behavior. We also confirm Lumm e et al.'s finding that the roughnesses of all lunar surfaces increase with decreasing size-scale. We further show that the scale dependence of roughn ess is well represented by fractal statistics. The rates of change of rough ness with size scale, represented by fractal dimension D, are remarkably si milar among terrians. After correcting for the contribution of large-scale roughness, our average value of D = 2.31 +/- 0.06 falls within the range 2. 0 less than or equal to D less than or equal to 2.4 reported from lunar rad ar studies. The amplitude of roughness, which we characterize with the rms slope angle at l-mm scale, varies significantly among terrains. For lunar m are, the average rms slope angle is 16 degrees +/- 43 degrees and that for Fra Mauro regolith is 25 degrees rt 1 degrees. By comparison to radar data, we suggest that the roughness of Fra Mauro (Imbrium ejecta) regolith is si milar to that of lunar highland terrains. We find that the Gaussian slope d istribution assumed in B. W Hapke's model (1984, Icarus 59, 41-59) adequate ly describes typical lunar regolith surfaces. A revised form of Hapke's equ ation that models realistic particle phase functions and the coherent backs catter opposition effect was fitted to disk-resolved lunar photometric obse rvations and yields estimates of <(theta)over bar> = 27 +/- 1 degrees for h ighland and a = 24 =/- 1 degrees for mare regolith. These values of <(theta )over bar> as well as the implied relative highland:mare photometric roughn ess ratio are best matched in our elevation data by the cummulative contrib utions of surface topography covering all scales greater than 0.1 mm. Less than 5% of the photometrically detected roughness of lunar regolith is cont ributed by surface relief at scales larger than 8 cm. This conclusion impli es that values of 8 derived from whole-disk and disk-resolved photometry, r espectively, may be taken to represent the same physical quantity. In addit ion, particulate samples used in goniophotometric measurements should not b e assumed to be photometrically smooth (i.e., 8 = 0 degrees), as is often d one in laboratory applications of Hapke's photometric model. The predicted photometric roughness at size scales of 0.1 mm and less significantly excee d photometric estimates and suggests that there exists a measurable size sc ale below which topographic relief either is not photometrically detectable or is not represented in the Hapke model as macroscopic roughness. (C) 199 9 Academic Press.