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. 1999). The close (~300 m) topographic profiles across 86 craters on Mars in order along-track spacing of the individual laser to investigate the degree of terrain softening that may measurements and the ~160 m footprint of the have affected the geometry of the crater due to viscous individual laser shots enabled geometric data to be flow of the rim materials caused by entrained ice. The derived from individual topographic MOLA profiles spatial resolution of each topographic profile was across the crater (Garvin and Frawley 1998; Garvin defined by the spatial resolution of the Viking images, et al. 2000; Mouginis-Mark and Garbeil 2007; which typically ranged from ~40 to 200 m per pixel and Tornabene et al. 2013). Other investigations have assumed that the crater cavity was symmetric. The utilized a global topographic data set with MOLA data Jankowski and Squyres (1992) sample craters were in gridded at a scale of 128th-degree (i.e., 463 m postings the diameter range of 1.3–80 km, including 52 at the equator). For example, Robbins and Hynek “unsoftened” craters that were believed to lack this ice (2012) used the gridded MOLA topography to (hence, no viscous flow and so they represented typical determine the depth of craters as small as ~3kmin craters) and 34 “softened” craters (where the presence diameter to develop the largest Mars crater database. of ice may have led to shallower than normal craters due to viscous relaxation), with the objective of POTENTIAL LIMITATIONS quantifying the greater degree of shallowing experienced by the ice-rich craters. Each data set and associated method described in Photographic prints (typically 8″ 9 10″) of Viking the Approaches to Constraining Depth/Diameter Orbiter images were used in the late 1970s and early section has intrinsic limitations, many of which were 1980s to measure the length of the shadows that fell on identified by the authors at the time. For example, the crater floors (Cintala et al. 1976; Pike 1980). With shadow length measurements (Cintala et al. 1976; Pike known lighting geometry (i.e., solar azimuth and 1980) assumed a symmetric rim crest, and therefore inclination), the rim shadow on the crater floor could be assumed that any single rim height measurement measured from the print and thus provide an estimate accurately captured the true value. In addition, these of the total depth of the crater. It was assumed that the authors recognized that the shadow may not fall on the shadow of the highest point on the rim crest fell on the deepest part of the crater floor because the floor is not deepest part of the crater floor. This technique was flat. Other technical issues were associated with the subsequently improved by Chappelow and Sharpton early (pre-1990s) measurement of shadow length (2002), who developed a measurement technique for measurements. For example, Pike (1980) described in constraining the morphology of simple (i.e., small) detail his criteria for image selection as a function of craters by considering three basic shape variations of solar illumination, but still relied on the manual the crater: paraboloidal, conical, and flat-floored. measurement of shadow lengths on the photographic Stereomeasurements were also potentially possible from prints (and so counted on the darkroom skills of their Viking Orbiter images. However, due to the wide range technical help). Only with the advent of easy access to Mars crater depth/diameter 729 digital versions of Viking Orbiter images could the gridded to a spatial scale of 1/128th degree (a degree on edges of the shadows be determined (e.g., Mouginis- Mars is ~59 km at the equator), which provides a Mark and Hayashi 1993). Attempts to use spatial resolution of 463 m per pixel at the equator photoclinometry for impact craters on Mars (Jankowski (Smith et al. 2001). This interpolation is essentially a and Squyres 1992; Barlow 1995) assumed a uniform smoothing algorithm which averages the original albedo for the surface (Davies and Soderblom 1984). individual altimetric values to generate a regional trend Pike and Davis (1984) utilized radiometrically calibrated to fill voids with an average of the surrounding points. Viking Orbiter 1 images and employed a Minnaert However, in certain instances, both smoothing the function to approximate the phase function of the topographic highs on the rim crest (producing lower rim surface. Due to dust on the surface, or geologic elevations) as well as averaging of the crater depth diversity of the crater floor, this assumption will not be (giving shallower depths) can result (Stewart and the case for most impact craters on Mars. Valiant 2006; Robbins and Hynek 2012, 2013). Resolution effects also introduce uncertainties when In Fig. 3 we present a comparison of the geometry calculating dt/D for craters on Mars. For example, of 31 craters (D = 1.52–25.57 km) measured using the Earth-based radar-derived altimetric data suffered to the PEDR MOLA data and measurements made from the greatest extent from the spatial resolution of the radar 128th-degree DEM using the Interactive Measurement, footprint. Because each radar-ranging measurement was Profiling, and Analysis of Crater Topography averaged over a footprint ~10 km in longitude and (IMPACT) program (Mouginis-Mark et al. 2004) for ~80 km in latitude, an underestimation of the depth was the same craters. We use this limited data set of 31 often the result of each measurement including local craters because these are the same craters which we high points at this scale, such as the inner wall and investigate in the High-Resolution Digital Elevation central peak of the crater (Roth et al. 1989). Other Models section, and so can maintain a consistent measurements of crater geometry, such as the comparison across data types. The PEDR estimation of rim height, were even more susceptible to measurements of depth were made through visual the low spatial resolution of the radar footprint because inspection of all the laser profiles which cross the crater, each rim height estimate was an average of elevations using coregistered Thermal Emission Imaging System within the entire radar cell. (THEMIS) visible (VIS) images as the base. The Garvin and Frawley (1998) and Garvin et al. (2000) average of all of the measurements of rim height was recognized that individual MOLA profiles (known as used along with the deepest measure of the crater depth. the Precision Engineering Data Record data or Typically, it was found that there are 1–3 profiles which “PEDR” data) across craters would most likely miss the cross craters where D < 5 km, 10–12 profiles for craters highest point on the rim and the lowest point on the where D = 8 – 14 km, and >15–18 profiles for D = 15 – crater floor (Fig. 2). Depths (and diameters) measured 20 km. For the gridded MOLA data set, rim height was for craters a few kilometers in diameter are most the average of ~10–30 points around the crater rim for susceptible to the exact location of the laser profile D = 3–8 km, and ~40–140 points where D > 10 km. across the crater. Figure 2a illustrates the fortuitous IMPACT is an interactive technique that facilitates situation where multiple MOLA profiles cross the floor the easy collection of geometric data for Mars craters. It of the crater, thereby allowing a reasonable estimate of allows the estimation of the elevation of the preimpact rim height and crater diameter to be determined. This is topography. In the IMPACT program, this is done using not, however, always the case, as is illustrated in a second-order polynomial fit to at least 8 points visually Fig. 2b where only a single topographic profile crosses selected to encompass the crater and lie beyond the ejecta the interior of the crater, and even then the MOLA blanket, and surround as much of the crater as possible shots fall entirely on the inner wall. Thus, no accurate (Mouginis-Mark et al. 2004). Using either an image or a estimate of the crater depth can be obtained. The shaded relief version of the gridded MOLA data set, a severity of this estimation of diameter is directly related user can then trace the rim crest to determine the highest to the size of the crater, as larger craters (Fig. 2c) have point on rim, lowest point on rim, average rim height multiple profiles crossing the crater floor. In these above preimpact surface, and standard variation in rim instances, the profiles allow for an estimation of the rim height measurements. IMPACT uses this trace around height at multiple places, thereby allowing the average the rim crest to determine rim height measurements in 1- rim height to be estimated. degree increments of azimuth. From the latitude/ In an attempt to fill the data gaps in the PEDR longitude of each point measurement on rim, the center MOLA data set, an interpolated MOLA data set has of the crater is determined from the trace of the rim crest often been used (Garvin et al. 2003; Stewart and (which provides multiple estimates of the crater radius) Valiant 2006). Here, the MOLA PEDR data have been and the best-fit circle is used to define the crater radius. 730 P. J. Mouginis-Mark et al.

Fig. 2. Examples of individual Mars Orbiter Laser Altimeter (MOLA) tracks across craters of different diameters. Faint dots indicate all of the MOLA shots in the area, and black dots indicate data used for each profile. “Distance” is measured from the top of each image. a) A 3.9 km diameter crater (15.1° N, 98.2° E) where four profiles cross the central part of the crater floor. Base image is Thermal Emission Imaging System (THEMIS) V28627019. b) A 4.1 km diameter crater (8.8° N, 181.3° E) where only one MOLA profile crosses the interior of the crater, with the data falling on the inner wall rather than the crater floor. Base image is THEMIS V53698016. c) Multiple MOLA profiles cross this 9.3 km crater (29.6° N, 116.5° E), allowing both dt/D and 29 point measurements on the rim crest to be measured. Base image is THEMIS V28876009. d to f) MOLA-derived profiles across the three craters illustrated in (a) to (c). MOLA-derived crater geometric parameters are also shown.

Fig. 3. Comparison of crater geometry using the raw Precision Engineering Data Record (PEDR) Mars Orbiter Laser Altimeter (MOLA) shots and the 128th degree gridded MOLA data. a) Crater diameter, showing that the gridded data generally produces larger estimates of diameter. b) Total crater depth, showing that deeper craters are associated with the PEDR data. c) Depth/ diameter, with larger values associated with the PEDR data set. Mars crater depth/diameter 731

This allows the total crater depth to be calculated by subtracting the lowest point of the crater floor from the highest of all points on the rim crest. Maximum and average rim heights are determined by subtracting each elevation point on the rim from the best-fit preimpact surface. In each case, “true” crater diameters for the gridded MOLA data were measured from the CTX image. The craters included here range in diameter from 1.5 to 25.6 km (as measured from the PEDR data), all lie within 50° of the equator, and 13 are within 20° of the equator. We selected craters found only near the equator or in the midlatitudes of Mars in order to avoid high-latitude craters affected by climate-driven processes. Some of the resolution effects associated with the cross-track spacing of the MOLA tracks are evident in these data. Crater diameter is frequently underestimated with the PEDR data because the profile does not cross the crater center (Fig. 3a). Conversely, the PEDR measurements often suggest deeper craters (Fig. 3b), which is most likely due to the smoothing effect in the gridded topography. We note that Robbins and Hynek (2013) performed a similar comparison with Fig. 4. Two examples of perspective views derived from digital elevation models of impact craters on Mars. a) Very fresh a much larger data set but did not find any significant appearing 4 km diameter crater. Digital elevation models difference between the two measurement techniques, (DEM) produced from Context Camera (CTX) images although for craters D =~5 km they noted that craters D22_035823_1870 and F02_036522_1869. b) Toconao crater are deeper in PEDR compared to gridded data. (16.9 km dia.) shows some signs of modification, including However, similar trends in our measurements are also only a very small central peak which has most likely been almost totally buried by eolian material. DEM produced from evident in the estimation of dt/D (Fig. 3c), where the CTX images D04_028844_1583 and D04_028699_1583. PEDR data give higher values for all crater sizes than the gridded topography. 2016). It is now possible to generate DEMs from either HIGH-RESOLUTION DIGITAL ELEVATION CTX or HiRISE stereoimage pair using Ames Stereo MODELS Pipeline (Moratto et al. 2010) (Fig. 4) or from the SOCET Set software (Kirk et al. 2008). Watters et al. All data sets used for measuring crater depth and (2015) have taken this approach for small diameter have limitations, principally due to the spatial (25 m < D < 5 km) craters to investigate size and resolution and (in many instances) the single terrain dependencies. Context Camera-derived DEMs topographic profile across the crater used for rim height typically have a spatial scale of ~24 m (four times the and depth estimation. We now present our pixel scale of the input images), while HiRISE-derived recommendations for the next generation of analysis of DEMs have a postspacing of 1–2 m with a vertical the topography of Martian impact craters through the precision in the tens of cm (Kirk et al. 2008). It is likely analysis of digital elevation models (DEMs) at a spatial that the CTX DEMs have a vertical precision of ~2m, resolution of ~2–25 m per pixel, and highlight some although we have not undertaken a quantitative preliminary results. Based on the ability to produce analysis of this attribute. We have created 20 new DEMs from stereo high-resolution CTX images, with DEMs from CTX stereopairs, from which 25 craters ~6 m per pixel resolution (Malin et al. 2007) and (D > 4.0 km) are studied in detail. In most cases, only HiRISE at ~0.25 m per pixel (McEwen et al. 2007) one crater is included in each DEM, so that this new images, we set the stage not only for the analysis of data set is inherently limited in the number, size, and Martian craters but also for lunar craters (using Lunar degradation state of the measured craters. Figure 5 Reconnaissance Orbiter Camera data), the minor illustrates the spatial distribution of these craters. planets (e.g., Vesta from DAWN High Altitude There are limitations to the use of these DEMs Mapping Orbit data; Vincent et al. 2014) and Mercury because (currently) only craters that fit entirely within a (from the Mercury Laser Altimeter; Susorney et al. single CTX image are included. Realistically, this limits 732 P. J. Mouginis-Mark et al.

Fig. 5. Distribution of craters measured in this analysis. Black dots indicate craters studied using Context Camera (CTX)- derived digital elevation models (DEMs). Red dots with white rims indicate craters studied with High-Resolution Imaging Science Experiment (HiRISE)-derived DEMs. Base image is the global topographic map of Mars (Mercator projection) derived from MOLA observations (Smith et al. 2001). (Color figure can be viewed at wileyonlinelibrary.com.) the diameter of the crater that can be measured to also applied the same analysis techniques to six publically ~25 km. A further issue is that most CTX DEMs for available DEMs produced by the HiRISE Science Team. craters D >~20 km contain the distal portions of the These DEMs are available at the University of Arizona ejecta blanket and so a measure of rim height may be Web Site (http://www.uahirise.org//dtm/). The use of lower than reality. However, these ejecta blankets are these HiRISE DEMs includes three craters within the typically only a few meters in thickness at a radial Southern Highlands and one on the floor of Valles distance of a few (2–5 km) from the rim crest Marineris. All six HiRISE craters lie equatorward of 50°. (Mouginis-Mark and Baloga 2006; Mouginis-Mark and There is a range of elevations where all of the craters Boyce 2012), so we do not expect the ejecta to formed, from ~À4kmto+2.5 km relative to the MOLA significantly affect estimation of crater rim height or datum (Smith et al. 2001). Thus, we have not explored crater total depth. In addition, the limited albedo craters at higher elevations, where the role of volatiles in variation within small (<5 km diameter) craters, where influencing crater geometry may be less apparent bright Sunward facing inner wall slopes saturate the (Mouginis-Mark 1979). image, often conspire to make stereomatching a difficult Our new measurements from the CTX DEMs are task. Thus, the DEMs are rarely adequate for studying presented in Table 1. Craters included in this study small craters (D < 3 km). This is unfortunate because formed on a diversity of terrains, including the northern numerous investigators (e.g., Cintala and Mouginis- plains (Utopia Planitia), Chryse Planitia, lava flows Mark 1980; Pike 1980; Boyce et al. 2006) have associated with the Tharsis, and Elysium volcanoes, as demonstrated that there is a transition from relatively well as ridged plains materials in Lunae Planum and deep simple craters to relatively shallow complex craters Syria Planum (Fig. 5). over the diameter range ~3–5 km. From the CTX DEMs, we have measured D and dt ANALYSIS AND OBSERVATIONS for all the craters included in Fig. 3 by using the IMPACT program (Mouginis-Mark et al. 2004). To To estimate the inherent differences between the augment the population of craters D < 5 km, we have data sets frequently used in dt/D estimation, we present Table 1. Database derived from analysis of the DEMs used in this analysis. Av. SD Av. Max Min dia. dia. Depth ht SD ht ht. ht. Latitude Longitude (km) (km) (km) (km) (km) (km) (km) HiRISE 1 HiRISE 2 CTX 1 CTX 2 38.1 191.6 1.503 0.253 0.365 0.046 0.021 0.075 0.020 ESP_025735_2185 ESP_025801_2185 14.64 198.96 1.520 0.034 0.418 0.060 0.007 0.083 0.047 D16_033317_1944 D16_033462_1944 50.2 184.5 1.620 0.203 0.438 0.089 0.012 0.122 0.062 ESP_025366_2306 ESP_025498_2305 À11.5 290.3 2.179 0.238 0.500 0.093 0.010 0.116 0.071 ESP_027802_1685 ESP_028501_1685 À28.7 226.9 2.618 0.269 0.638 0.150 0.021 0.197 0.110 PSP_002118_1510 PSP_003608_1510 23.81 175.77 2.700 0.064 0.514 0.049 0.018 0.104 0.039 G19_025828_2033 G20_025973_2033 À45.9 9.5 2.811 0.362 0.626 0.104 0.032 0.178 0.049 ESP_012991_1335 ESP_013624_1335 À48.1 242.4 3.087 0.426 0.653 0.125 0.028 0.184 0.063 ESP_014011_1315 ESP_014288_1315 8.77 181.34 4.000 0.106 0.980 0.159 0.015 0.194 0.125 733 D22_035823_1870 F02_036522_1869 depth/diameter crater Mars 14.70 98.19 4.800 0.156 0.971 0.095 0.038 0.153 0.030 G11_022376_1946 G16_024288_1946 24.45 107.45 8.100 0.274 2.212 0.302 0.047 0.393 0.202 G19_025514_2048 G20_025870_2048 31.80 114.31 8.620 0.178 1.744 0.313 0.052 0.422 0.222 P12_005814_2120 P15_007093_2119 29.65 116.55 9.200 0.128 2.484 0.409 0.036 0.506 0.327 P15_007027_2099 P15_006816_2100 7.70 166.18 10.100 0.308 1.805 0.416 0.037 0.501 0.309 G05_020211_1877 F06_038250_1877 31.49 116.25 10.360 0.118 2.621 0.404 0.071 0.533 0.224 P15_007027_2099 P15_006816_2100 18.57 293.05 10.450 0.176 1.393 0.238 0.049 0.320 0.038 B05_011754_1998 B06_011820_1998 14.28 199.25 12.000 0.390 1.979 0.166 0.127 0.533 0.002 D16_033317_1944 D16_033462_1944 14.53 98.46 12.520 0.354 3.042 0.242 0.073 0.457 0.086 G11_022376_1946 G16_024288_1946 8.27 181.58 13.010 0.410 2.346 0.376 0.082 0.580 0.227 D22_035823_1870 F02_036522_1869 17.94 272.25 13.040 0.278 1.825 0.263 0.069 0.437 0.132 G04_019917_1981 G03_019561_1977 14.17 202.34 13.190 0.370 2.129 0.316 0.080 0.518 0.130 F02_036508_1944 P20_009041_1949 À20.29 285.35 13.230 0.596 1.748 0.179 0.042 0.287 0.041 D04_028844_1583 D04_028699_1583 27.98 116.71 15.100 0.486 2.633 0.323 0.086 0.503 0.073 P15_007027_2099 P15_006816_2100 28.42 319.55 15.700 0.386 2.306 0.388 0.067 0.568 0.259 G12_022869_2086 P15_006980_2087 À25.15 223.36 16.050 0.664 1.685 0.198 0.061 0.333 0.070 D13_032301_1560 D14_032591_1560 À20.86 285.33 16.900 0.438 1.931 0.302 0.074 0.321 0.009 D04_028844_1583 D04_028699_1583 30.80 297.62 19.000 0.624 2.975 0.388 0.107 0.572 0.045 G12_022817_2110 G14_023740_2110 14.57 155.61 20.390 0.498 2.298 0.421 0.084 0.602 0.247 B19_016849_1935 B20_017627_1934 32.98 118.60 20.980 0.610 2.921 0.555 0.108 0.770 0.080 P15_006750_2133 P16_007462_2133 42.41 345.00 24.630 0.592 3.258 0.599 0.085 0.800 0.400 G23_027259_2226 P13_006267_2227 12.43 89.22 25.570 0.359 3.215 0.251 0.119 0.544 0.003 D17_033743_1925 D20_035233_1925 734 P. J. Mouginis-Mark et al.

Fig. 6. Comparison of crater depth estimates from different data sets. These plots demonstrate that the gridded Mars Orbiter Laser Altimeter (MOLA) topography give the lowest estimates of depth, and the Context Camera (CTX) and High-Resolution Imaging Science Experiment (HiRISE), digital elevation models (DEMs) the highest values. a) MOLA Precision Engineering Data Record (PEDR) depth versus CTX depth. b) MOLA gridded depth versus CTX depth. c) MOLA PEDR depth measurements, comparing two different ways of calculating diameter (from PEDR data versus CTX and HiRISE DEMs). d) dt/D values derived from PEDR data versus CTX and HiRISE DEMs. The two outliers where the DEMs show smaller dt/D values are due to underestimation of the crater diameter from the PEDR data. the geometric data for the Mars craters also measured et al. 2004). First in Fig. 6c, we show that there is a from the MOLA PEDR, the gridded data, and the difference in dt/D due to the underestimation of D when CTX-derived DEMs (Fig. 6). Figure 6a demonstrates using the PEDR data set. Here, we assume that the that the MOLA PEDR data produce smaller depth value of D determined from the CTX image is the estimates than the CTX DEMs, and that this difference accurate measure of the diameter because at the ~24 m compared to CTX values is even greater when per pixel scale of the DEM a more accurate and precise measurements are made from the gridded MOLA data rim crest can be identified from the topographic (Fig. 6b). These results are consistent with the data contours. Smaller values of dt/D are derived when the presented in Fig. 3, namely that use of the PEDR true crater diameter is used rather than the PEDR measurements is likely to give deeper estimates of dt value. This is a result of the topographic profile not compared to the 128th-degree gridded data set. crossing the crater center (Fig. 2b). The consequences of We have also explored the differences between underestimating dt, as well as the inclusion of less MOLA-derived dt/D values and CTX DEM-derived accurate estimates of D, are shown in Fig. 6d, which dt/D using the IMPACT technique (Mouginis-Mark presents dt/D derived from the PEDR and CTX data Mars crater depth/diameter 735

Fig. 7. At left are examples of the azimuthal variation in crater rim height (measured at 1° intervals) for five craters, measuring between 4.0 and 16.9 km in diameter. North is at the left and right sides of each plot, and south is in the middle. All crater rim heights are referenced to the elevation of the surrounding terrain. Average (solid horizontal line) and 1 standard deviation values (dashed horizontal lines) for the 360 individual rim height measurements are also shown. The craters are shown at right. North is toward the top in all images. The red lines show the trace of each measured rim crest. Note that there is no uniform variation in rim height around the perimeter of the crater, so that each example is unique. All images of the craters are CTX scenes. a) D22_035823_1870. b) P15_007027_2099. c) P15_007027_2099. d) P15_007027_2099. e) D22_035823_1870. (Color figure can be viewed at wileyonlinelibrary.com.) 736 P. J. Mouginis-Mark et al.

sets. It is evident from Fig. 6d that almost all dt/D values are significantly larger when using the CTX- derived elevation data, at times being ~29 that of the PEDR values. A further aspect of the determination of dt/D can be addressed when using the DEMs. In the 1970s– 1990s, it was assumed that the rim crest has a constant elevation. However, a new analytical approach for rim height determination was developed for Mars craters (Robbins and Hynek 2012) and by Sharpton (2014) for the analysis of DEMs of lunar impact craters, and allows the azimuthal variations in crater rim height to be investigated (Fig. 7). Some earlier investigations of dt/D used a single value of rim height if the shadow length technique was used (e.g., Cintala and Mouginis- Mark 1980; Pike 1980), two values of MOLA PEDR data were used (Garvin et al. 2000), or measurements from the gridded MOLA data set (Boyce and Garbeil 2007). Figure 7 illustrates that rim height may vary by several hundred meters for craters in the diameter range Fig. 8. Diameter (D) versus average rim height (h). Because ~9–17 km diameter. In addition to providing a more there is no obvious transition between small (D < 5 km) and accurate measure of dt, we envision that this detailed large (D > 8 km), all craters are included in the single analysis of the azimuthal variation in rim height might relationship. Note that there is no reduction in the size of the be of particular value, for instance, in assessing the rim error bars as crater diameter increases. Error bars are presented for all data points, but are not visible for some topography in relation to the observed structural uplift craters because they are too small. See Table 1 for raw data of the rim (Sturm et al. 2016); the same stratigraphic values. unit might have different elevations relative to the surrounding terrain (i.e., the preimpact surface). Each crater can be seen to have a unique pattern of rim craters. While all of the craters studied here have an height variations, but the smallest crater (D = 4.0 km) ejecta blanket, some craters lack morphologic features in our CTX sample of five craters in Fig. 7 displays the suggestive of very fresh craters (e.g., ejecta rays or least variation, while Toconao crater (D = 16.9 km) has pitted materials on the crater floor; Tornabene et al. large azimuthal variations resulting from the very low 2012; Boyce et al. 2012). Inspection of the craters SE rim. One might expect that variability in the rim studied here confirms that all of the deepest craters have height might be due to differences in target material (or prominent central peaks, hummocky floors, and/or fine- impact angle), but Fig. 7 illustrates that for the craters scale morphologies, suggesting that they are not heavily studied here there is no correlation between crater modified. However, other craters studied may also diameter and the variability in rim topography. possess these attributes, and so there is the possibility Specifically, two craters (D =~10 km) formed in the that these deepest craters are simply outliers in a single same region (Utopia Planum) and, hence, the same population. The craters studied here are not the target material show a similar average rim height but youngest craters on Mars and so may still have there is a twofold difference in the standard deviation of experienced some infilling (reducing crater depth) and rim height. Thus, it is probably unwise to assume that erosion (lowering the crater rim). Once additional all craters of a given size have the same geometric DEMs become available, it would be valuable to test if characteristics when, for example, trying to re-create the these craters are outliers or represent a set of craters pristine structure of degraded Martian craters such as comparable to the “pristine” craters identified by Boyce that attempted by Arvidson et al. (1978), Forsberg- and Garbeil (2007). With the caveat of this potential Taylor et al. (2004), and Grant et al. (2016). In Fig. 8 limitation of the young age of the craters studied, we we present all of our measurements for rim height from provide the dt/D relationship derived from our DEMs, the CTX and HiRISE DEMs. The best-fit relationship as well as a comparison to some of the other 0.688 2 is h = 0.050 D (D = 1.5–25.6 km, N = 31, R = estimations of the dt/D relationship (Fig. 9). 0.75). Adopting the analysis of the crater geometry using In the production of the DEMs, we made no the conventional approach (e.g., Pike 1980) we separate attempt to select image pairs of only the freshest impact simple bowl-shaped craters (~<5 km diameter) from Mars crater depth/diameter 737

Fig. 9. Left) Comparisons of crater parameters, as measured with the CTX and HiRISE DEMs. Error bars are one standard deviation of the crater diameter, crater total depth, or rim height as measured at 360 1-degree increments around the crater rim. Diameter (D) versus total depth (dt). Three relationships are identified for craters <5 km dia., the deepest four large craters, and the remaining craters >7 km dia. Error bars are presented for all data points, but are not visible for some craters because they are too small. Right) Comparison of these least squares fits to earlier estimates of dt/D. a) Small (D < 4 km) craters (Watters et al. 2015). b) Small craters from this study. c) Small (D < 3.6 km) craters (Cintala and Mouginis-Mark 1980). d) The four deepest large craters, this study. e) Other large craters, this study. f) Pristine large craters (D = 12–49 km) (Boyce and Garbeil 2007). g) Fresh craters (D = 12–49 km) (Boyce and Garbeil 2007). h) Large craters (D = 4–80 km) (Cintala and Mouginis-Mark 1980). larger flat-floored craters. For the 10 simple craters DEMs derived from CTX data represents the current 2 (D = 1.5–4.8 km, R = 0.93), the best fit is dt = 0.276 optimal situation for crater geometric studies. Rarely D0.808 (in kilometers). This is similar, but produces are such craters on Mars imaged completely by HiRISE slightly deeper craters, than the relationship dt = 0.205 (although numerous rim segments are covered in the D1.012 (in meters) determined by Watters et al. (2015). publically available HiRISE DEMs) so that meter-scale For flat-floored craters, there appears to be two crater studies could be conducted. However, the derivation of populations with some craters deeper than others at a a large crater database using CTX stereopairs is also given diameter. The relationship for the craters with the challenging. Not only is it laborious to identify image 0.711 largest dt/D values (i.e., least filled) is dt = 0.504 D pairs but the production of the DEM using either (N = 4, D = 8.1–12.5 km, R2 = 0.99) and for those SOCET SET or the Ames Stereo Pipeline also takes craters which appear to be partially infilled craters is several hours per crater. For example, it would be very 0.649 2 dt = 0.375 D (N = 17, D = 8.6–25.6 km, R = 0.65), time consuming to produce a CTX-based database that with measurements in kilometers. From Fig. 9, it is could rival the data set of 2,269 craters (D = 6–216 km) evident that Watters et al. (2015) determined a slightly discussed by Boyce et al. (2005) from MOLA data in deeper relationship for small (D < 4 km) craters than order to search for spatial variations in dt/D over an the one we have estimated from a much smaller data entire geographic region such as Utopia Planitia. Thus, set. In contrast, for larger craters (D =~10–80 km), our it is more likely that measurements made from CTX- values of dt/D are deeper than those of Watters et al. derived DEMs could best be used as calibration points (2015) and other estimates (e.g., Cintala and Mouginis- against which PEDR MOLA-derived results can be Mark 1980; Garvin et al. 2000; Boyce and Garbeil compared. Databases that rely on measurements made 2007), presumably because we can measure greater from the gridded MOLA topography should be used depths (and higher rim heights) from the DEMs. with caution, particularly when large data sets of craters <5 km diameter are required. It is, therefore, hoped that IMPLICATIONS, CONCLUSIONS, AND the stereosoftware becomes increasing widely used as RECOMMENDATIONS well as increasingly easy to use. Our preliminary observations from this analysis can As illustrated by Watters et al. (2015), HiRISE be summarized as follows. DEMs for craters where D < 1 km are the current best 1. Early methods of estimating depth (e.g., data for the analysis of crater geometry. For craters measurements of the rim’s shadow on the crater where D >~5 km, we believe that using high-resolution floor) did not have the ability to identify the lowest 738 P. J. Mouginis-Mark et al.

point of the crater floor or the highest point on the data sets (e.g., Cintala and Mouginis-Mark 1980; crater rim, so that craters were frequently reported Garvin et al. 2000; Boyce and Garbeil 2007). as being shallower than they really are. 2. Use of gridded 128th-degree MOLA DEM Acknowledgments—The authors appreciate the consistently underestimates the maximum depth of comprehensive review provided by Guest Editor Stuart the crater, and suggests shallower craters than Robbins, and the detailed comments by Nadine Barlow, measured with the PEDR data set. In some which significantly improved this manuscript. We thank instances (Fig. 6d), the MOLA depth estimate can the Autonomous Systems and Robotics Group, be only 50% the measurement from the CTX Intelligent Systems Division, NASA Ames Research DEM. Center for the production of the Stereo Pipeline 3. We agree with Robbins and Hynek (2013) that software which we used to generate all of the CTX raw data from individual MOLA profiles must DEMs. Our research was supported by NASA’s only be used with caution when D < 10 km. Solar System Workings Program through grant Inspection of the exact location of each profile NNX15AH24G to V. L. Sharpton and grant NASA/ with respect to the crater rim must be done before ASU 1282441 to J. M. Boyce from the THEMIS Team confident estimates of depth and rim height can be at Arizona State University. This is HIGP Publication made. For craters where D < 5 km, the crater 2255, SOEST number 9995, and LPI Contribution No. diameter will almost certainly be underestimated 2020. 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