Meteoritics & Planetary Science 53, Nr 4, 726–740 (2018) doi: 10.1111/maps.12895 Determination of Mars crater geometric data: Insights from high-resolution digital elevation models Peter J. MOUGINIS-MARK1* , Joseph BOYCE1, Virgil L. SHARPTON2, and Harold GARBEIL1 1Hawaii Institute of Geophysics and Planetology, University of Hawaii, Honolulu, Hawaii 96822, USA 2Lunar and Planetary Institute, Houston, Texas 77058, USA *Corresponding author. E-mail: [email protected] (Received 27 October 2016; revision accepted 10 April 2017) Abstract–We review the methods and data sets used to determine morphometric parameters related to the depth (e.g., rim height and cavity depth) and diameter of Martian craters over the past ~45 yr, and discuss the limitations of shadow length measurements, photoclinometry, Earth-based radar, and laser altimetry. We demonstrate that substantial errors are introduced into crater depth and diameter measurements that are inherent in the use of 128th-degree gridded Mars Orbiter Laser Altimeter (MOLA) topography. We also show that even the use of the raw MOLA Precision Engineering Data Record (PEDR) data can introduce errors in the measurement of craters a few kilometers in diameter. These errors are related to the longitudinal spacing of the MOLA profiles, the along-track spacing of the individual laser shots, and the MOLA spot size. Stereophotogrammetry provides an intrinsically more accurate method for measuring depth and diameter of craters on Mars when applied to high-resolution image pairs. Here, we use 20 stereo Context Camera (CTX) image pairs to create digital elevation models (DEMs) for 25 craters in the diameter range 1.5–25.6 km and cover the latitude range of 25° Sto42° N. These DEMs have a spatial scale of ~24 m per pixel. Six additional craters, 1.5–3.1 km in diameter, were studied using publically available DEMs produced from High-Resolution Imaging Science Experiment (HiRISE) image pairs. Depth/diameter and rim height were determined for each crater, as well as the azimuthal variation of crater rim height in 1-degree increments. These data indicate that morphologically fresh Martian craters at these diameters are significantly deeper for a given size than previously reported using Viking and MOLA data, most likely due to the improvement in spatial resolution provided by the CTX and HiRISE data. INTRODUCTION projectiles in the crater excavation and modification stages (Pike 1980). For individual planets, variations For more than half a century, the analysis of in target material strength may either produce impact craters on planetary surfaces has utilized the unusually shallow (Pike 1977a, 1977b) or deep craters measurement of the crater’s depth–diameter ratio (Barlow 1993; Boyce et al. 2006) as well as indicate (hereafter “depth/diameter”) as one of the key the potential role of volatiles (Cintala and Mouginis- parameters to advance understanding of the impact Mark 1980; Mouginis-Mark and Hayashi 1993) or process. For example, depth/diameter values have other subsurface properties (Stewart and Valiant been used to assess the degradation state of lunar and 2006). Martian craters (Leighton 1966; Pike 1971; Cintala The confident measurement of crater rim height et al. 1976). Comparison of depth/diameter across has importance for several planetary problems. For planets of different masses reveals the effects of example, McGetchin et al. (1973) and Settle and Head gravity and the modal impact velocities of the (1977) investigated radial variations in lunar crater © The Meteoritical Society, 2017. 726 Mars crater depth/diameter 727 ejecta topography to determine where ejecta from the APPROACHES TO CONSTRAINING DEPTH/ crater cavity might be deposited. However, these DIAMETER investigators did not consider the azimuthal variations of the rim crest or the ejecta deposit, so that only What do we mean, exactly, by crater diameter, symmetric processes were modeled. The azimuthal crater depth, and rim height? Robbins et al. (2017) variability in rim crest height was first studied for provide a detailed discussion of crater depth. Total lunar craters by Pike (1977b) and documented with depth (dt) is defined here as distance from the highest high-resolution topography only recently (Lalor and point on the rim crest to the lowest point on the crater Sharpton 2014; Sharpton 2014). Rim crest variability floor (Fig. 1), and has historically been the easiest within individual Martian craters has been crater parameter to measure by the methods described documented by Mouginis-Mark and Garbeil (2007) below. However, all craters exhibit irregularities in their and developed further by Mouginis-Mark and Boyce planforms to varying degrees due to local target (2012). property variability and/or nonnormal impact The determination of crater rim height also has trajectories. Apparent depth (da) is the depth as relevance to broader aspects of the geology of Mars. measured from a reconstructed surface that Drawing upon techniques developed for the analysis of approximates the pre-existing surface upon which the the rim height of lunar craters (De Hon 1979), De Hon crater first formed. Likewise, rim height (h) is the (1982) studied partially buried craters in the Eastern distance from the pre-existing surface to the maximum Tharsis region and inferred that the ridged plain elevation along the rim crest. materials which embay the exterior of the crater range Some of the earliest estimates of crater total depth from a 0 km thickness at their eastern limit to over (dt = da + h) on Mars were derived from data collected 1.5 km thickness westward of the Tharsis dome. by the Ultraviolet Spectrometer (UVS) flown on However, De Hon (1982) assumed that Mars craters Mariner 9, which entered orbit in November 1971 had a rim height–diameter ratio similar to fresh craters (Barth et al. 1974). The UVS technique used the on Mercury (Cintala 1979) and, because he could not absorption of the atmosphere to infer the thickness of measure the height of exposed rim crests, he only used the atmosphere at this point on Mars and, hence, the craters that are nearly completely buried. Of course, low depth of the crater floor compared to the surrounding points on the rim would be the first to be buried, so area. Using UVS measurements, dt/D values for craters that these lava thickness measurements may be in the diameter range 12–100 km were estimated, underestimates. If there is a wide variation in rim height including 38 craters which were deemed fresh or slightly around the crater, the depth–diameter estimate is an degraded (Burt et al. 1976). The deepest of these craters average for that crater size. were estimated to have depth/diameter values that were To investigate the problems inherent in crater similar to fresh craters on Mercury, which were depth/diameter, we first review the data sets and determined from shadow length measurements on approaches that have been used in the past, and Mariner 10 images (Gault et al. 1975). describe some of their potential limitations, focusing Measurements of Mars crater depths were also specifically on elevation data collected from the Mars made using Earth-based radar altimetry collected during Orbiter Laser Altimeter (MOLA) experiment. We then the 1971–1982 oppositions (Downs et al. 1975; Roth explore the value of utilizing high-resolution digital et al. 1989). The radar-ranging technique produced a elevation models (DEMs) to aid in the more accurate few (1–4) profiles around the circumference of the determination of depth/diameter and other geometric planet during each opposition. Each profile enabled a parameters of Martian impact craters. Finally, we single elevation estimate (relative to the center of Mars) present results for 31 fresh craters on Mars in the to be made at a spatial scale of ~10 km east–west and diameter range 1.5–25.6 km to suggest an approach ~80 km north–south. However, the radar ground-tracks for future depth/diameter investigations. Here, “fresh were limited to the latitude range 23° N–22° S, so high- craters” include those which possess rays or pitted latitude and polar craters were excluded from this material on the crater floor (Boyce et al. 2012; investigation. The dt/D values of 152 degraded complex Tornabene et al. 2012), but due to the limited number craters (some as small as D = 25 km) were estimated of CTX stereopairs, may also include slightly using this radar technique. A sample of 37 of the degraded craters (i.e., those which have lost their freshest craters (D = 25–475 km), which were still ejecta rays). This definition is different from the one classified as “highly degraded,” had dt/D < 0.015 (Roth of Boyce and Garbeil (2007), who further defined a et al. 1989). Measured crater depths rarely exceeded group of “pristine craters” on the basis of their very 2.5 km and depths of craters where D > 125 km showed large depth/diameter values. no obvious relationship with diameter. 728 P. J. Mouginis-Mark et al. Fig. 1. Cross section of a typical impact crater on Mars defining the attributes discussed in this analysis. A third method employed in the 1980s to measure of spacecraft altitudes and viewing geometries, very few dt on Mars was the use of “shape-from-shading” images formed stereopairs from which the topography techniques, which exploited the photometric properties could be determined, although certain large landforms, of a surface with a uniform albedo using a technique such as Olympus Mons, were imaged in stereo (Wu called photoclinometry (Pike and Davis 1984; et al. 1984). Jankowski and Squyres 1992; Barlow 1995). Jankowski Knowledge of the geometry of craters on Mars was and Squyres (1992) applied this technique to calibrated dramatically improved with the advent of the global panchromatic Viking Orbiter images to derive MOLA data set (Smith et al.