Titan's impact crater population after Cassini

Journal Pre-proof Titan's impact crater population after Cassini

Joshua E. Hedgepeth, Catherine D. Neish, Elizabeth P. Turtle, Bryan W. Stiles, Randolph Kirk, Ralph D. Lorenz PII:

S0019-1035(19)30045-4

DOI:

https://doi.org/10.1016/j.icarus.2020.113664

Reference:

YICAR 113664

To appear in:

Icarus

Received date:

15 January 2019

Revised date:

3 January 2020

Accepted date:

26 January 2020

Please cite this article as: J.E. Hedgepeth, C.D. Neish, E.P. Turtle, et al., Titan's impact crater population after Cassini, Icarus(2020), https://doi.org/10.1016/j.icarus.2020.113664

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© 2020 Published by Elsevier.

Journal Pre-proof Titan’s Impact Crater Population After Cassini

Joshua E. Hedgepetha*, Catherine D. Neisha, Elizabeth P. Turtleb, Bryan W. Stilesc, Randolph Kirkd, Ralph D. Lorenzb

The University of Western Ontario, Department of Earth Sciences, London, ON N6G 2V4,

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United States Geological Survey, Astrogeology Science Center, Flagstaff, AZ, 86001, USA

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Corresponding author, Email address: [email protected] (J.E. Hedgepeth)

Paper resubmitted to Icarus

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Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA

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The Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA

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Canada

01/03/2020

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Abstract Titan is Saturn’s largest moon and has a dynamic surface with methane rivers carved by an active hydrological cycle and sand seas shaped by aeolian processes. One way to study the rates of these processes is by examining Titan’s impact craters, because they provide quantitative constraints on the level of degradation. With the end of the Cassini Mission in September 2017,

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we have reassessed the crater population using the entire Cassini Synthetic Aperture Radar (SAR) dataset, including 30 additional craters since the last assessment in 2012, for a total of 90

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certain to possible impact craters on Titan. We adjust for incomplete coverage (~69%) of the

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moon by SAR imaging using a Monte-Carlo approach, and find no major change in Titan’s

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inferred surface age from prior studies. We then used the SARTopo and stereo topography data

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sets to measure crater depths and diameters. For the first time, rim heights for twelve craters were also reported. On average, Titan’s craters are shown to be shallower, with lower rims, than

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those observed on similarly sized icy moons (e.g. Ganymede). This suggests that the observed

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modification is due to a combination of sand and sediment infilling onto the crater floor and fluvial erosion of the rims with fluvial erosion playing a larger role than previously thought in

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crater degradation on Titan.

Keywords: Titan, surface; Impact processes; Radar observations; Geological processes

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1. Introduction The Cassini spacecraft orbited Saturn from 2004 to 2017 (Edgington and Spilker, 2016). It uncovered vast amounts of new information about Saturn, its rings and moons. In particular, Saturn’s moon Titan was revealed to have extensive surface-atmosphere interaction, facilitating erosional and depositional processes that alter the surface (Lorenz et al., 2006; Lorenz et al., 2008; Lorenz and Radebaugh, 2009; Burr et al., 2013; Hörst, 2017). During the Cassini mission,

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the surface of Titan was observed principally by the Imaging Science System (ISS), the Visual

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and Infrared Mapping Spectrometer (VIMS), and the Radio Detection and Ranging (RADAR)

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instrument (Porco et al., 2004; Brown et al., 2004; Elachi et al., 2004, respectively). ISS studied

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Titan’s clouds and haze and was used to perform large scale geologic studies of the surface (Porco et al., 2004). VIMS also studied atmospheric processes and constrained the composition

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of Titan’s surface (Brown et al., 2004). RADAR measured the topography and roughness of the

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surface, studied surface properties and composition, and constrained the depths of the lakes and seas (Le Gall et al., 2011; Janssen et al., 2016; Corlies et al., 2017; Mastrogiuseppe et al., 2018).

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By the end of the Cassini mission, Titan was revealed to have a diverse geologic landscape

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shaped by a variety of processes similar to those that modify the surface of the Earth (Lopes et al., 2010) Linear sand dunes cover thousands of kilometers of Titan’s surface (Lorenz et al., 2006), and Neish et al. (2013) found that aeolian processes play a dominate role in the degradation of Titan’s surface. However, this is likely through aeolian infill rather than aeolian erosion (Lorenz and Lunine, 1995). Aeolian erosion is directly related to the grain sizes and transport velocity of sand (Greeley and Inversen, 1985), and the wind speeds on Titan are suspected to be far too small for abrasion to occur (Lorenz et al., 1995; Burr et al., 2015). Erosion on Titan is mainly controlled by Titan’s methane cycle (Atreya et al., 2006). Methane on

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Titan acts like water on Earth, forming clouds and rain (Turtle et al., 2011). Fluvial features have been observed all over Titan’s surface by Cassini RADAR (Lorenz et al., 2008; Burr et al., 2013), and near the poles there are methane lakes and seas (Stofan et al., 2007). Recent evidence suggests that these regions may be a “wetlands”, a region of saturated soils which could account for the limited crater population observed in the higher latitudes (Neish et al., 2012; 2014). One mode of constraining how Titan’s surface is changing is by studying its crater

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morphologies (Neish et al., 2013, 2016). Impact cratering forms distinct circular depressions

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during impact as material is melted, vaporized, and ejected outward (Melosh, 1989). Material is

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folded back onto itself to form an elevated rim around the crater while other material is ejected

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out around the crater (Melosh, 1989). The observations of the airless worlds of the solar system provide clear constraints on the shapes craters form (Schenk, 2002; Bray et al., 2012) . As a

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result, the morphologies of Titan’s craters, including depth, diameter, and rim height, provide

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quantitative constraints by which to assess the degree of degradation compared to “fresh” counterparts on airless icy satellites. “Fresh” does not assume age; it represents craters that are

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representative of what a crater would look like immediately after crater formation free of

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degradation or long-term relaxation (Robbins et al., 2018). Neish et al. (2013) used Ganymede and Callisto as analogues for pristine Titan craters because these moons are similar to Titan in size and density, and thus have similar surface gravity (𝑔~1.35 m/s2 on Titan, 𝑔~1.4 m/s2 on Ganymede, and 𝑔~1.25 m/s2 on Callisto). They therefore provide a template for well-preserved craters, which is needed to quantitatively constrain how degraded Titan’s impact craters are. However, there are some differences that may alter the crater morphologies on Titan vs. Ganymede/Callisto. The average impact velocity of Titan is half that of Ganymede with Callisto impact velocities in between the two (Zahnle et al.,

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2003; Neish et al., 2013). Another key factor in crater morphology is the thermal gradient of impacted ice (Schenk, 2002; Bray et al., 2014; Silber and Johnson, 2017). Each satellite appears to have an outer ice layer ~100 km thick overlaying a 𝐻2 𝑂 − 𝑁𝐻3 ocean (Spohn and Schubert, 2003; Iess et al., 2010; Nimmo and Bills, 2010). The major difference between Titan and the other two moons is the presence of hydrocarbons on the surface (Stofan et al., 2007). Marine environments alter the morphology of impact craters (e.g. Collins and Wünnemann, 2005), and

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are present on Titan in the form of lakes, seas, and possible “wetlands” of liquid hydrocarbons

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(e.g., Stofan et al., 2007; Neish and Lorenz, 2014). Clathrates in the ice may alter the

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morphology as well. Clathrates on Titan are composed of hydrocarbons trapped within the

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molecular structure of the ice. These may significantly strengthen the ice (Durham et al., 2003), altering the physical structure of the impact craters (Senft and Stewart, 2011).

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Using the known population of craters at that time, Neish et al. (2013) showed that Titan’s

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craters were shallower than craters on Ganymede and Callisto. The freshest craters on Titan came close to, but never exceeded, the depths observed on Ganymede or Callisto. This

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quantitatively showed that Titan has undergone varying amounts of surface modification, and

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Titan’s crater population reflected this. Neish et al. (2013) suggested that degradation was dominated by aeolian infill. The levels of degradation observed in Titan’s impact craters are uniformly distributed from very deep to very shallow. Unlike aeolian infilling, which slowly fills in craters continuously over time, fluvial modification decreases with time as slopes decrease, leading to a plateauing of degradation (Forsberg-Taylor et al., 2004; Neish et al., 2013). We would therefore expect most craters to be shallow if fluvial degradation was the dominant mechanism.

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These results are supported by geomorphological observations of Titan’s crater population, which also suggest that erosion and burial are the dominant mode of crater modification (Lorenz et al., 2007; Wood et al., 2010; Neish and Lorenz, 2012). Dark crater floors are likely indicative of infilling by fine grained organic sand and sediment, which appear smooth at Cassini's radar wavelength of 2.2 cm. Note that sand does not refer to any specific composition, but rather a particle grain size that ranges between 1/16 mm – 2 mm, i.e., the size at which a particle can be

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saltated across a surface (Lorenz and Zimbelman, 2014). There is also ample evidence that

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fluvial erosion is taking place across Titan’s surface, and in its impact craters (Collins, 2005;

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Lorenz et al., 2008; Soderblom et al., 2010; Neish et al., 2016). Furthermore, Titan’s low population of craters is consistent with a heavily modified surface that has a young crater

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retention age (~0.2-1.0 Gyr) (Neish and Lorenz, 2012). Previous assessments of Titan’s crater

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population identified a total of 60 craters from a combination of RADAR and VIMS data

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through 2010 (Lorenz et al., 2007; Wood et al., 2010; Buratti et al., 2012; Neish and Lorenz, 2012). However, there have been substantial additions to these datasets since these studies were

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completed. Cassini ended its mission with ~69% of Titan’s surface mapped by synthetic aperture

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radar (SAR). This is more than double the amount of coverage (~33%) available at the time of the previous assessment of Titan’s craters (Neish and Lorenz, 2012). Furthermore, the older data have been updated with improved georeferencing that has shifted the position of previously known features. The amount of topography data has also grown but still only covers ~9% of Titan’s surface, with ~5% coming from SARTopo with improved elevation values (Stiles et al., 2009; Corlies et al., 2017) and only ~2% coverage from stereo topography (Kirk et al., 2012). SARTopo is a method developed to extract topography data from SAR images, using information from the regions where the five beams of the SAR swath overlap. The highest

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resolution SAR images of the surface of Titan are 175 m/pixel (Elachi et al., 2004). SARTopo has a resolution of 10 km in the horizontal and 75 m in the vertical. The vertical error in each SARTopo measurement was determined by Stiles et al. (2009) using radar instrument noise and viewing geometry. Neish et al. (2013) showed how the majority of the error that exists in the Titan crater depth measurements are from natural variations within the crater itself. The 10 km horizontal resolution may impede the measurement of the crater rims, being averaged down by

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the surrounding walls, but the SARTopo topography is determined over 300 m increments to

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translate the topography in finer detail.

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Stereo topography data suffers from less coverage but better resolution. Stereogrammetry

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(stereo) is a data set derived by using two overlapping images and information about camera positioning to determine the topography over the entire 2D region of coverage (Robbins et al.,

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2018). Titan stereo data has a resolution of ~1.4 km/pixel (Kirk et al., 2012). The stereo data is

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assumed to have a systematic error of ~5% which is significantly lower than the natural variation observed in crater morphometry measurements (Neish et al., 2013; Bray et al., 2012). This

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resolution makes it more comparable to the stereo data of other icy moons (0.3-1.5 km/pixel).

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Neish et al. (2013; 2018) calculated the stereo crater depths on Titan and found most crater depths to be nearly the same (< ±100 𝑚) as measured in SARTopo; however, two craters were observed to be significantly more shallow than SARTopo measurements. They posited that these differences related to a lack of features within the crater floor that are necessary to select tie points for stereo measurements. It is important to note that the technique Neish et al. (2013; 2018) used to calculate the stereo depths was not the same as the technique used to measure the Ganymede depths (Bray et al., 2012). Bray et al. (2012) used the same profile approach that Neish et al. (2013) used when measuring SARTopo data by finding the maximum and minimum

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points along a profile, but Neish et al. (2013; 2018) used the average rim to average floor elevation to calculate the stereo results (Robbins et al., 2018). There are now 44 more flybys of RADAR and SARTopo data to investigate in order to complete Cassini's dataset of Titan’s crater population. In this work, we seek to provide as complete an assessment of Titan’s crater population as is possible at the end of the Cassini mission. We reanalyze all previously known craters and make note of any additional craters that

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have been identified in the final data set. We then analyze Titan’s crater morphologies to

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constrain the extent of erosion and deposition on Titan. We identify all craters with topographic

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data and compare the depths of Titan’s craters with similarly sized craters on Ganymede and

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Callisto. We also measure Titan’s rim heights for the first time to study the effect of fluvial erosion independently of sand and sediment infill (which primarily fills in the crater floors,

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leaving the rims unmodified). However, we recognize the potential limitations of using

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SARTopo data so set out to determine whether the rim heights derived from this data set are reliable. Our goal is for this work to serve as a complete review of Titan’s crater population post

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2. Methodology

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Cassini until more data becomes available (e.g. Lorenz et al., 2018).

2.1 Crater Mapping

We constructed a global mosaic using the SAR and High-Altitude SAR (HiSAR) image swaths through the last close flyby of Titan, T126. These images are sampled at resolutions that range between 64 ppd and 256 ppd (pixels per degree). Before mosaicking, each file was manually evaluated, and those with the highest resolution and relative quality were stacked on top. We also utilized a global ISS mosaic constructed at ~11 ppd (4 km/pixel) (Cassini ISS

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Team, 2015). This mosaic is considerably lower in resolution than the RADAR mosaic, but the increased coverage can reveal craters that were not observed by the RADAR instrument. We used a simple approach for identifying crater candidates. Craters are often circular, but there are a great number of suspiciously circular features on Titan that may have formed through other geologic processes. We therefore focused our search on circular features with rough (bright) ejecta surrounding smooth (dark) interiors. Crater ejecta is commonly radar bright due to

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the blockiness of the ejected material – see Thompson et al. (1981) for examples from the Moon.

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Most craters on Titan have been infilled by fine-grained sediments, leading to a smooth crater

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floor. We assign a level of certainty to each crater identified, using the certainty scale developed

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by Wood et al. (2010). We rated craters as Certain (C1), Nearly Certain (C2), Probable (C3), and a new fourth category of Possible (C4) (Wood et al., 2010). These classifications roughly relate

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to the number of lines of evidence any putative crater has pointing to its origin as an impact

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structure (i.e., circularity, ejecta blanket, obvious rim, dark crater floor, etc.) (Figure 1). It also considers a judgment of how confident we are in each line of evidence. For example, candidate

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Crater #8 H (Figure 1) exhibits a roughly circular radar dark interior with a bright ejecta blanket.

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Therefore, candidate Crater #8 H is given a certainty of C2 because it has three supportive lines of evidence. Where SARTopo data exist over a putative crater, we used that dataset to differentiate between a circular mound and a circular depression. Most SARTopo data only exist for previously identified craters (Wood et al., 2010; Neish and Lorenz, 2012; Neish et al., 2013), so this is not as useful at identifying additional craters. The lack of SARTopo for the new craters is attributed to the identification of many craters in the lower resolution data set (HiSAR), where SARTopo data is not available, and the prevalence of gaps or holes in the SARTopo data similar to what was observed in Forseti by Neish et al. (2018).

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Figure 1: From left to right, craters are listed in order of certainty (1 to 4): Momoy (𝑪 = 𝟏), Crater #8 H (𝑪 = 𝟐), Crater #1 H (𝑪 = 𝟑), and Crater #29 H (C4). The crater diameters are listed in the bottom left designated by a ‘D’ and in kilometers. Below each crater are the four key characteristics used to identify a crater with an indication of if that crater meets that qualification. Crater certainty is measure of how many qualifications it meets. C1 meets all the qualifications, C2 meets at least 3 to a reasonable degree, C3 has only two clear indicators are met, and C4 is clearly circular with one other qualification suspected to be a remnant feature of the crater. A green check indicates the qualification is clearly is met, a question mark indicates a feature is suspected to be a remnant of the crater but may be caused by a different geological phenomenon, and a red x indicates it is clearly missing.

We modified these rules when searching the ISS global mosaic for new impact craters. The

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benefit of using the ISS mosaic is that it has global coverage, but the lower resolution and lack of

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topographic shading prevent identification of Titan’s smallest craters (< ~10 km). In addition,

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instead of using roughness differences to identify impact craters, we looked for material differences to distinguish the key indicators. For example, the organic sands are darker in the near-infrared wavelengths, so we looked for evidence of dark infilling in a circular feature. However, this relationship is limited to areas where there is sand nearby. Alternatively, too much sand might hide a narrow, degraded rim. A new ISS mosaic is being developed at higher resolution that may reveal additional craters, but the numbers are likely to be small and should not change our overall conclusions. Beyond identifying additional craters, we also reanalyzed previously known craters to identify any errors in the existing dataset (Figure 2). We determined that the georeferencing

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utilized in Wood et al. (2010) and Neish and Lorenz (2012) no longer matches the existing georeferencing assigned to RADAR and SARTopo data; improvements in the Titan rotation model used to assign geographical coordinates to RADAR features have shifted some crater centers westward (e.g., Figure 2) by a few kilometers to tens of kilometers (Stiles et al., 2008; Stofan et al., 2012; Meriggiola et al., 2016). These types of changes highlight the importance of systematically identifying each crater, including the known population, to ensure they are

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accurately and fully up-to-date with the now complete Cassini dataset.

Figure 2: Selk crater (Certainty=1, D=80km) observed in Cassini RADAR data. The current geo-position of Selk crater is mapped with a red circle. Overlain on the RADAR image is the available SARTopo elevation data measured in meters. The black dashed circle denotes the location reported in Wood et al. (2010) and Neish and Lorenz (2012) in a now superceded reference frame. After identifying each crater, we measured their diameters. The diameter of the crater rim is observed to vary at different locations, so the rim to rim diameter was measured along the

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north-south axis and the east-west axis of the crater. The average of the two measurements was used as the diameter listed in Table 1, and the variance between the two was used as an approximate error in the diameter. It should be noted that without topography, identifying the rim is more difficult. The rim position must be estimated using the RADAR image to identify the bright rim and ejecta and the dark crater floor it surrounds. Therefore, the error in crater diameter is larger for those craters without corresponding topography data. SARTopo Topography

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2.2

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The topographic dataset for Titan is far less complete than the RADAR, ISS, and VIMS

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coverage. Only 14 unique craters have usable topographic data available, and Crater #1 H is the

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only crater among them that has not been studied before. Twelve craters are covered by SARTopo, eight have associated RADAR stereo pairs, and none are covered by the RADAR

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altimeter. Six craters have both SARTopo and stereo data. For this study, we first analyze the

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SARTopo data. The SARTopo dataset consists of two-dimensional profiles that follow the beam overlaps of the Cassini RADAR instrument, and as a result, the profiles cross the craters at

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somewhat random locations. We use the topographic profiles available for each crater to derive

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crater diameters and depths relative to the local topography and relative to the rim topography; as a result, we are also able to derive the first ever measurements of crater rim heights on Titan (Figure 3). Rim positions are identified using the peak in topography at the edge of the crater, and the crater floors are identified as the lowest point in the crater. With these points defined, we can derive each of the desired crater measurements. Crater diameter is defined as the distance between the opposite sides of the crater rim (Pike et al., 1967; Turtle et al., 2005). Modeling has shown that erosion often creates an apparent diameter that is slightly larger than the diameter when the crater formed but not more than the

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existing level of error in our results (Forsberg-Taylor et al., 2004). The limited topography profiles that are available rarely go directly through the center of the crater, so additional steps must be taken to derive the actual diameter. The simplest approach is to measure the distance between each rim to the center of the crater found through radar mapping. The radius is then the average of these distances, but there is error in this estimate arising from the assumption that the crater is perfectly circular. We use the difference between the maximum and minimum

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measurements from the average as the observed error, and these errors can be up to ~20% at

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times; it is important to be aware of these errors when doing diameter-dependent studies (e.g.

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depth-to-diameter comparisons, Bray et al., 2012; Neish et al., 2013). This error was propagated,

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where necessary, to determine the error in the relative depths of Titan craters to Ganymede craters.

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Past studies of Titan’s craters have shown that their depths are generally shallower than those

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on similar icy moons (Neish et al., 2013). Our results need to take into consideration the effects of resolution when comparing the two data sets (Titan vs. Ganymede). SARTopo averages

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topography over ~10 km wide profiles in ~300 m increments along the track of the profile (Stiles

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et al., 2009). The horizontal resolution of topographic data on other icy moons is much higher than in SARTopo (typically 0.3-1.5 km/pixel). In addition, topography on Ganymede and Callisto was derived from a combination of stereo photogrammetry and shadow length measurements, in contrast to the SARTopo technique which is derived from the calibration of the overlapping SAR data. In the SARTopo data, small, steep features like crater rims may be artificially reduced in height because they are being averaged with nearby lower elevations of the crater wall and ejecta blanket. Therefore, in contrast to previous Titan studies, we measured depth from the surrounding terrain to the crater floor, removing rim heights from the calculation.

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In this way, we constrain the level of degradation independent of erosion of the rim and, by extension, we avoid artificially lower rim-height values biasing the measurements. We utilize the profile technique used by Bray et al. (2008, 2012) to ensure that our measurements are comparable to those acquired for Ganymede craters while adapting modern nomenclature for broader clarity across impact crater studies (Robbins et al., 2018). Bray et al. (2008; 2012) use a eight profile approach to account for variance in the crater rim and floor

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(Stewart and Valiant, 2006; Neish et al., 2013; Robbins et al., 2018). However, SARTopo is

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often limited to one profile, and rarely do these pass directly through the center of the crater.

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However, we think this is unlikely to be a major issue in the determination of our crater

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measurements. Complex craters are significantly flatter than bowl like simple craters (Melosh, 1989), and this is especially true for craters on icy satellites (Schenk, 2002; Neish et al., 2013).

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We suspect Titan transitions from simple to complex around the same point as Ganymede and

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Callisto (𝐷 ≈ 3 km; Schenk, 2002). All of the craters (12) analyzed here are large enough to assume near-edge profiles are as reliable as one directly through the center. This does not negate

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the problems of being limited to a one profile approach, but these problems are unavoidable but

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must be taken into account.

A large part of rim variance can be attributed to natural variation in the existing topography prior to impact, so we begin by subtracting out any regional slope in the topographic profile. In an ideal situation, this produces topographic profiles with the surrounding terrain elevation at ~0 m; the crater topography is represented by the large-scale fluctuations that remain (Figure 3). A line is fit to the profile between 1.5𝑟 to 5.0𝑟 from each rim, where r is the radius of the crater. We exclude values < 1.5𝑟 to prevent the topography of the crater and its ejecta blanket from biasing the results, and 5𝑟 is the distance used by Bray et al., (2008; 2012). We found a linear fit

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best describes the large-scale variations of the local topography that vary 100s of meters at times; attempts to fit to higher-order equations (order 2, 3 and 4) produce fits that are essentially linear. When we subtract the regional slope, the terrain becomes centered at ~0 m, but the surrounding topography still had an average standard deviation of ~65 m among the craters studied. Crater measurements are taken once the topography is adjusted in the manner described

𝐻𝑟𝑖 = 𝐻𝑟𝑖𝑚 − 𝐻𝑡𝑒𝑟𝑟𝑎𝑖𝑛

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above. The rim heights (𝐻𝑟 ) are then measured with respect to the local terrain, (1)

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where 𝐻𝑟𝑖𝑚 is the SARTopo elevation measurement at the rim, 𝐻𝑡𝑒𝑟𝑟𝑎𝑖𝑛 is the elevation of the

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surrounding terrain (0 after slope removal), and i represents a specific profile through the crater

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(Figure 3). This measurement is done on the left and right of the profile, then averaged to derive a final rim height that accounts for fluctuations in crater topography. This is repeated if more

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profiles are available and the total average of all measurements is used. The error in these results

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is determined using the intrinsic error reported in each measurement along the SARTopo profile, as well as natural variations in rim topography. For example, the average rim height of Selk

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crater (Figure 2) is 283 m. This is the average height of the rim on the left (294 m) and right

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(272 m) of the topographic profile. Each point has a defined intrinsic error (±40 m on the left and ±34 m on the right). We use the intrinsic error at each point to find the maximum and minimum height possible for each measurement. Then we use the absolute maximum and absolute minimum heights between them to approximate the error bounds in the rim height measurement (334 m and 238 m, or

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m).

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Figure 3: A) Sinlap crater (𝑪𝒆𝒓𝒕𝒂𝒊𝒏𝒕𝒚 = 𝟏, 𝑫 = 𝟖𝟖 𝐤𝐦) and B) Soi crater (𝑪𝒆𝒓𝒕𝒂𝒊𝒏𝒕𝒚 = 𝟏, 𝑫 = 𝟖𝟒 𝐤𝐦) as observed by Cassini SAR with SARTopo data overlain. The crater centers and rims are identified with a black 'x'. Below is the topography profile that goes through the crater, plotted along the distance (km) of the profile going through the crater. The rim to floor depth (𝒅𝒓 ) is shown in black, and the terrain to floor depth (𝒅𝒕 ) is shown in green. Sinlap demonstrates how the topography measurements of a less degraded crater compare to the heavily eroded terrain of Soi crater where 𝒅𝒕 ~𝟎 𝐤𝐦. We used the same method to derive average depths, also determining the maximum and minimum errors using the intrinsic error in each height measurement. The terrain-to-floor depth (𝑑𝑡 ) (Figure 3) is the change in elevation from the terrain (𝐻𝑡𝑒𝑟𝑟𝑎𝑖𝑛 ~ 0 km) to the floor (𝐻𝑓𝑙𝑜𝑜𝑟 ), where 𝐻𝑓𝑙𝑜𝑜𝑟 is the SARTopo elevation at the lowest point of the crater floor. This value is <0 after the regional slope is removed, producing a positive depth value of 𝑑𝑡𝑖 = 𝐻𝑡𝑒𝑟𝑟𝑎𝑖𝑛 − 𝐻𝑓𝑙𝑜𝑜𝑟

(2)

The rim-to-floor depth (𝑑𝑟 ) (Figure 3) is the change in elevation from the rim (𝐻𝑟𝑖𝑚 ) to the floor (𝐻𝑓𝑙𝑜𝑜𝑟 ),

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(3)

The value 𝑑𝑟 is the crater depth defined using the profile technique of measuring from the rim to the floor. (e.g. Williams and Zuber, 1998; Bray et al., 2012). Our approach breaks it down into its two main components: rim height above the surrounding terrain and interior depth below the surrounding terrain. Rim-to-floor depths are the combination of these two measurements (i.e. 𝑑𝑟 = 𝑑𝑡 + 𝐻𝑟 ), where 𝐻𝑟 has been shown to be modified mainly by fluvial erosion and 𝑑𝑡 shown

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to be modified mainly by infill and deposition (Grant et al., 1997; Forsberg-Taylor et al., 2004).

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combination of aeolian infill and some alluvial infill from rim erosion (Lorenz et al. 1995;

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Forsberg-Taylor et al., 2004).

This approach allows us to quantify impact crater degradation. However, even the most well-

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preserved craters present noisy profiles. In trying to constrain degradation on Titan, we must

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interpret data that is often stochastic (Figure 3B). Sinlap (Figure 3A) presents a best-case scenario where the crater and its surroundings are relatively undegraded, subtracting out the

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regional slope is straightforward, and the rim and crater floor are easily distinguishable. Soi

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(Figure 3B), on the other hand, is much more degraded, and the data are more difficult to interpret. For example, on the east side of Soi, the data are skewed to the point where the terrain elevation becomes negative. Realistically, the crater depth is assumed to be ~0 m, but it illustrates the limitations in trying to determine crater depth in significantly modified terrain. 2.1 Stereo Topography Next, we compare the rim-to-floor depths to those derived from SAR stereo topography, which is similar in resolution (~1.4 km/pixel, Kirk et al., 2012) to the Ganymede data. Five craters have both SARTopo and stereo data. A sixth has SARTopo and autostereo, which is a

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technique that assumes the profile across a crater is perfectly symmetric and compares the foreshortening of the near and far crater walls (Neish et al., 2013). Overlapping SARTopo and stereo data allow direct comparison between the two data sets, so we can assess whether previous depth estimates (Neish et al., 2013) are a robust representation of crater topography on Titan. Previous work has derived crater morphometry using the stereo data (Kirk et al., 2012; Neish et al., 2013, 2015, 2016, 2018). No new stereo data have been obtained since these studies

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were published. However, we have reanalyzed the stereo results because Neish et al. (2013,

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2015, 2016, 2018) used the average rim to average floor elevation approach rather than the

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profile approach (Robbins et al., 2018) used here and by Bray et al. (2008; 2012). The average

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rim to average floor approach uses a statistical analysis that averages a traced region of the crater rim and floor (e.g. Figure 4a). This approach gives a more representative view of fluctuations in

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crater morphology, but in doing so, it can artificially degrade the rim and floor measurements by

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averaging them with nearby terrain. Here we use an eight profile approach to ensure the stereo results are comparable with the SARTopo results by finding the maximum and minimum

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elevations of eight individual profiles through the crater. For Ganymede, Bray et al. (2012) used

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an eight Profile approach to account for fluctuations in the local topography without artificially degrading the measurements. The limited data coverage for SARTopo restricts the number of profiles and their orientations, but with the stereo data we can take eight radial profiles for each crater (e.g. Figure 4b). We extract profiles at equally spaced azimuths and extending up to five crater radii from the center when possible. (In some cases, stereo coverage is truncated prior to this distance.) As with SARTopo, rim and floor heights are measured by finding the maximum and minimum position on each side of the profiles. More measurements are available than with SARTopo (up

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to 16 vs 2-6), and the error is presented as the standard deviation in the measurements. The assumed systematic error (~5%) in the stereo data is significantly lower than the natural topographic variation observed (Neish et al., 2013; Bray et al., 2012), so it is not included in the

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3. Results

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Figure 4: a) Ksa crater (𝑫 = 𝟒𝟓 𝐤𝐦) seen in Cassini SAR overlain by stereo topography (Kirk et al., 2012). A region (white) around the rim (R) and floor (F) are defined to statistically derive the rim and floor heights in past works (Neish et al. 2013; 2015; 2016; 2018). (Note the regions defined in the figure are hypothetical, shown to describe the method). b) Ksa crater in stereo topography split into eight profiles, spaced equally at azimuths between 0 and 180 degrees from the north-south axis. Each profile is analyzed like the SARTopo profiles, to find the maximum and minimum on each side of the crater; then the values are averaged.

3.1 Crater Population in the complete Cassini dataset Thirty additional craters have been discovered since the analysis of Neish and Lorenz (2012) and are presented here (designated H in Table 1) (Figure 5). Nearly half of these craters were observed in HISAR images, the rest were observed in SAR images. It is more difficult to confidently identify craters in the lower resolution HiSAR data set, so most of these craters were classified as C3 (probable) or C4 (possible). No new craters were identified in the ISS mosaic.

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One of the most recently identified craters, Paxsi (115 km), was discovered using the VIMS dataset (Buratti et al., 2012). However, now that 69% of Titan’s surface is imaged by RADAR, many of the craters that we see in ISS and VIMS data are now also covered by RADAR data. In fact, many of the HISAR observations were planned based on interesting features observed in the ISS data; that is probably why no new craters were identified in the ISS map. The largest newly identified crater is 70 km in diameter, and the smallest is 9 km. Most of the

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craters have a dark interior and a bright, rough rim and ejecta blanket, but this is not true in all

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rough rim around the entire crater. Crater #3 H (C3) is one of the few cases that has a radar

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bright interior; this may be a function of its location in the radar-bright labyrinth terrains (Lopes et al., 2016; Malaska et al., 2017, 2014). Crater #9 H (C3) is not completely mapped in SAR, and

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its rim is less distinct. However, the interior is moderately darker than the surroundings with

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areas of moderately brighter ground that may be an ejecta blanket. Craters #15 H (C4), #19 H (C3), and #20 H (C3) show distinctly darker interiors with possible bright ejecta blankets; the

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ejecta blanket is more akin to labyrinth terrain which distorts the shape of the dark terrain as well

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as making it slightly less circular than expected. Crater #13 H (C3) lacks a distinct rim, but there is a hint of an ejecta blanket surrounding a distinctly darker circular interior. Crater #18 H (C3) highlights the difficulty of identifying smaller (<30km) craters in the HiSAR data set because the crater features begin to become too small to identify in the lower resolution data set. Crater #14 H (C3) is distorted by encroaching sand dunes from the east but still retains a bright rim and ejecta to the west. Craters #22 H (C4), #23 H (C3), #29 H (C4), and #30 H (C3) all lack clear ejecta blankets and only show slight evidence of bright rough rims.

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Figure 5: Thirty additional candidate craters have been identified and are shown in Cassini SAR data, each image scaled to be 5 crater diameters in width. These images are sampled from a global mosaic that is stretched to the same backscatter greyscale. Craters are listed in descending diameter (D, bottom left, in km). The certainty is denoted by C (bottom right). The Crater # for this study (designated H in Table 1) are shown in the top left. Official names are at the top right (where applicable).

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Combining the additional craters with those that have been reanalyzed, Titan’s known population is now 90 potential impact craters (50% larger than previously recorded). The entire population of 90 craters has been updated to reflect their corrected center latitudes and longitudes and their diameters (Table 1). There is a clear bias of craters in the equatorial region (Figure 6). When split into equal areas (±30° from the equator), 65% of the craters are found in the equatorial region. This is not a result of coverage biasing (Figure 7); only 55% of the SAR

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coverage resides within the equatorial region. Therefore, there are 10% less craters in the poles

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than we would expect assuming an equal cratering rate across the surface. This distribution may

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be a result of the increased fluvial and lacustrine activity in the higher latitudes, or the presence

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of a former polar ocean (Burr et al., 2013; Neish and Lorenz, 2014; Neish et al., 2016).

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Figure 6: A global Cassini SAR mosaic of Titan mapping the 30 additional craters (red) and the original 60 (yellow). Circle size is scaled to four times the crater diameter. (The circles are projected and appear more elliptical at larger latitudes.)

Figure 7. The amount of surface area not covered (missing %) along Titan’s latitudinal axis. There is a significant portion of the poles that is mapped in SAR Radar, and it does not account for the lack of craters in Titan’s poles.

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Table 1: The complete list of Titan's craters at the end of the Cassini mission. Craters are classified by ID, ordered from largest to smallest diameter, with an asterisk indicating available SARTopo data. The craters are defined by the publication where they were first identified or the name they have been officially assigned. Unnamed craters are labeled with a W (Wood et al. 2010), NL (Neish and Lorenz 2012), and H for those presented here. Latitude and longitude are reported based on the latest spin model used for RADAR data (e.g. from Stofan et al., 2012). Certainty: 1=certain, 2=nearly certain, 3=probable, 4=possible. ID Crater Name Longitude Latitude Diameter Certainty SAR Swath (°W) (°N) (km) 1* Menrva 87.0 20.0 1 T003, T077, T108 400+25 −30 2 Paxsi 341.5 5.5 2 T104 130 ± 5 3* Forseti 10.7 25.9 1 T023, T113 125 ± 40 4* Afekan 200.3 26.0 1 T043, T083 115 ± 5 +10 5* Hano 345.0 40.5 1 T016, T084, T104 105−20 6* Sinlap 16.0 11.5 1 T003, T108, T113 88 ± 1 7* Soi 140.9 24.3 1 T016, T055, 85 ± 15 T056, T120 8* Selk 199.1 6.9 1 T036, T095, 84 ± 2 T098, T120, T121 9 Guabonito 151.7 -11.3 2 T013, T048 72 ± 3 10* Crater #1 H 240.3 31.9 3 T084, T104 70 ± 25 11 Crater #26 W 86.0 -8.1 2 T013, T029 69 ± 1 12 Nath 7.8 -30.6 2 T050 68 ± 0.5 13 Crater #3 H 110.8 -6.2 3 T113 67 ± 1 14 Crater #4 H 347.8 1.5 2 T104 67 ± 0.5 15 Crater #49 W 188.9 -10.9 3 T008, T036, 63 ± 1 T041, T121 16 Crater #5 H 164.4 31.3 3 T120 63 ± 1.5 17 Crater #6 H 129.2 14.5 3 T120 59 ± 1 18 Crater #7 H 138.4 1.8 2 T091 55 ± 55 19* Ksa 65.3 13.7 1 T017, T077, 45 ± 2 T113, T083 20 Crater #8 H 205.1 -14.7 2 T113 43 ± 0.5 21 Crater #47 W 184.5 -7.6 3 T008, T120, T121 42 ± 1 22 Crater #25 W 88.7 -11.5 2 T003, T013, T113 42 ± 2 23* Crater #24 W 165.1 -7.8 1 T013, T048, T12 41 ± 1 24 Crater #9 H 293.1 52.1 3 T084, T104, T016 40 ± 0.5 25 Momoy 44.6 11.7 1 T017, T077, T113 40 ± 1 26 Crater #11 H 340.8 -8.8 3 T104 38 ± 3 27 Crater #6 NL 147.6 2.1 1 T044, T056 34 ± 3 28 Crater #45 W 18.6 8.2 3 T003, T121 34 ± 1.5 29 Crater #12 H 154.0 19.8 3 T049 34 ± 1 30 Crater #13 H 188.4 21.2 3 T098 34 ± 1 31 Crater #5 NL 140.5 12.1 2 T056 32 ± 1 32 Crater #43 W 50.2 10.6 3 T017, T077, T083 32 ± 1

Journal Pre-proof Diameter (km) 31 ± 3 29 ± 1.5 29 ± 1 29 ± 1 27 ± 2 27 ± 0.5

SAR Swath

2 3 3 3 4 3

39 40 41* 42 43 44 45 46 47 48* 49 50

Beag Crater #22 W Crater #10 NL Crater #18 H Crater #4 NL Crater #42 W Crater #19 H Crater #40 W Crater #21 W Crater #3 NL Crater #20 H Crater #8 NL

169.5 30.0 129.7 207.8 141.8 166.9 127.0 67.3 84.3 150.7 121.5 194.8

-34.7 11.4 -30.6 -13.1 11.0 -10.6 -3.1 -12.4 -10.5 -16.3 -15.6 0.1

26 ± 1 25 ± 2 25 ± 2 23 ± 3 23 ± 0.5 23 ± 1 23 ± 1.5 21 ± 0.5 20 ± 1.5 20 ± 5 20 ± 0.5 20 ± 0.5

1 2 3 4 2 3 3 3 2 2 3 3

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

Crater #41 W Crater #9 NL Crater #21 H Crater #22 H Crater #20 W Crater #23 H Crater #24 H Crater #17 W Crater #39 W Crater #25 H Crater #13 W Crater #18 W Crater #19 W Crater #38 W Crater #26 H Crater #7 NL Crater #37 W Crater #27 H Crater #15 W Crater #48 W

260.2 162.7 149.2 62.5 77.9 170.7 353.8 75.9 129.7 73.3 309.9 250.1 74.9 24.5 175.6 160.2 349.5 235.3 249.3 173.4

29.9 19.2 -68.7 -9.8 -8.0 21.8 36.6 -13.2 33.4 12.3 83.3 39.4 -13.3 -57.1 -6.7 -38.3 42.0 -60.1 38.2 22.7

18 ± 0.5 18 ± 0.5 17 ± 1 17 ± 0.5 17 ± 0.5 16 ± 0.5 16 ± 0.5 16 ± 1 16 ± 1 16 ± 1 15 ± 1 14 ± 1.5 14 ± 1 13 ± 0.5 12 ± 0.5 11 ± 0.5 11 ± 0.5 11 ± 0.5 10 ± 0.5 10 ± 0.5

3 3 4 2 2 4 3 2 3 4 2 2 3 3 3 3 3 3 2 3

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Crater #28 H

-37.8

10 ± 1

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Ta T36 T017, T077 T071 T083, T098 T023, T104, T113, T120 T098 T029 T041 T058, T064, T095 T056, T020 T013, T121 T058, T057, T020 T013, T113, T121 T013, T041, T113 T048, T058, T057 T021 T036, T061, T098, T121 T043, T083 T057, T056 T058, T077 T113 T013 T056, T098 T084 T013 Ta T104 T029 T021, T084, T092 T013 T039 T048, T077 T057, T120 T018 T021, T084, T091 T084, T092 T021, T029, T083, T120 T021, T049

171.0

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33 34 35 36 37 38

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Latitude (°N) 48.0 -49.6 12.5 0.0 54.2 -6.3

Certainty

Crater #23 W Crater #46 W Crater #44 W Crater #14 H Crater #15 H Crater #16 H

Longitude (°W) 50.3 40.4 62.1 280.4 353.9 349.0

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Crater Name

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ID

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SAR Swath

4

Crater #16 W Crater #35 W Crater #36 W Crater #30 H Crater #34 W Crater #7 W Crater #33 W Crater #11 W Crater #32 W Crater #9 W Crater #14 W Crater #10 W Crater #6 W Crater #8 W Crater #30 W Crater #29 W Crater #12 W Crater #31 W

238.9 266.9 105.1 171.4 227.8 39.4 324.1 343.3 229.0 254.0 350.1 43.4 38.4 17.1 43.2 261.9 12.9 45.4

82.6 23.9 63.8 -40.0 34.8 -18.9 105.1 25.3 83.0 39.0 44.2 18.6 -17.1 14.0 -18.9 30.9 -54.5 -28.3

9 ± 0.5 9 ± 0.5 9 ± 0.5 9 ± 0.5 9 ± 0.5 9±1 8 ± 0.5 8 ± 0.5 8 ± 0.5 7 ± 0.5 7 ± 0.5 5 ± 0.5 5 ± 0.5 4 ± 0.5 4 ± 0.5 4 ± 0.5 3 ± 0.5 3 ± 0.5

2 3 3 3 3 3 3 3 3 3 2 2 2 2 3 3 2 3

T043, T113, T020, T083, T098 T029 T098 T056, T098 T018 T025 T025 T71 T016 T025 T030 T018 T003 T025 T003 T025 T021 T007 T025

3.2 Crater Counts

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Latitude (°N) 67.4

Certainty

Crater #29 H

Longitude (°W) 104.6

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We have produced a total crater count, corrected for the incomplete coverage of Titan by Cassini SAR, following the same approach as Neish and Lorenz (2012). We use a Monte-Carlo

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approach to determine the probability of detecting craters of different sizes on Titan. We begin by constructing two 360×180 arrays where each cell represents a 1°×1° area of Titan’s surface. The first array represents the SAR coverage where each “active” (1) cell represents areas with coverage and all other cells are “inactive” (0) areas without coverage. The second array represents the random position of a crater of a specific size. A random center latitude and longitude are assigned, and each cell along the rim and within the interior of the crater is mapped as "active" (1) with all cells outside the crater mapped as "inactive" (0). If any cell is active in both arrays, then the crater is classified as “discovered”. As 𝑛 → ∞, where n is the number of

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times the experiment is done, the frequency of discovering the crater approaches the probability of discovering it. We repeat this process 1,000 times for diameters between 30-1200 km in diameter bins of √2 km. The probability is the number of times the crater is “discovered” divided by the total number of experiments (1,000). When Neish and Lorenz (2012) assessed Titan’s crater population, only ~33% of the surface was mapped in SAR. With ~69% of the surface now mapped, the probability of missing a crater

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has decreased. The effect is reduced with increasing crater diameter as the probability of

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detecting larger craters approaches 100%, as there are fewer coverage gaps in which a large

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crater could ‘hide’ (Lorenz, 1995). Given the distribution of Cassini SAR swaths and the

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potential of higher visibility of large craters in the global ISS and VIMS datasets, it is more likely that one would see at least a portion of the largest craters. The crater count is adjusted to

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included possibly undetected craters,

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𝐶 = 𝐶𝑎𝑐𝑡𝑢𝑎𝑙 ∗ 𝑃−1

(4)

where 𝐶 is the corrected crater count, 𝐶𝑎𝑐𝑡𝑢𝑎𝑙 is the actual crater count, and 𝑃 is the probability of

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being detected (Table 2).

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Table 2: Titan’s crater count corrected for incomplete coverage.

68.9 68.9 68.9 68.9 68.9 68.9 68.9 68.8 73.3 76.8 80.1 95.3

Corrected Number of Craters 4.4 5.8 5.8 21.8 8.7 21.8 14.5 21.8 9.5 7.8 5 1

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2√2 − 4 4 − 4√2 4√2 − 8 8 − 8√2 8√2 − 16 16 − 16√2 16√2 − 32 32 − 32√2 32√2 − 64 64 − 64√2 64√2 − 128 256√2 − 512

Probability of Detection

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Number of Diameter (km) Craters

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We find that the final crater count follows the same general trend as previous assessments (Figure 8a). Neish and Lorenz (2012) observed more small craters than predicted based on

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Titan's atmosphere which should prevent very small craters (< ~5 km) from forming

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(Artemieva and Lunine, 2005; Korycansky and Zahnle, 2005); however, in this analysis there are

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fewer smaller craters, so the updated value is more consistent with model predictions. The population still follows the predicted crater population for large diameters (Artemieva and Lunine, 2005; Korycansky and Zahnle, 2005), suggesting the crater retention age derived by Neish and Lorenz (2012) remains a plausible estimate for Titan (i.e., 0.2 to 1.0 Ga; Figure 8b). We also find Lorenz et al. (2007) were surprisngly accurate given the limited surface coverage (10%). However, Menrva remains the outlier. At 400 km in diameter, it is unlikely to have formed in the last billion years, yet morphologically it looks relatively fresh. It is possible that Menrva is simply an unlikely impact event. However, a recent model suggests there may have been a catastrophic event that produced Saturn’s youngest rings, and Menrva may be one of the

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by-products of this event (Ćuk et al., 2016). One other explanation is that the nature of degradation in this region of Titan is different than in other regions, but we have yet to reconcile why that would be. There would have to be a difference in the material strength and/or the rate of

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erosion.

Figure 8: (a) The corrected crater count for Titan given the total SAR coverage through the end of the Cassini Mission (through flyby T126) with √𝑵 error bars (shown with a solid line), compared to the corrected crater count produced by Lorenz et al. (2007) (through flyby T18) (shown with red dots) and the corrected crater count produced by Neish and Lorenz (2012) (through flyby T65) (shown with a dashed line). (b) The corrected crater count for Titan (shown with a black solid line) compared to the predicted impact distribution for a 1 Ga surface from

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Korycansky and Zahnle (2005) (shown with a red dotted line) and a 200 Ma surface from Artemieva and Lunine (2005) (shown with a blue dashed line). 3.3 Crater Morphometry from SARTopo Only ~30 craters have SARTopo data within three crater radii of the crater center, and only 15 have SARTopo passing over the crater itself. Three of these profiles are too stochastic or are missing too much of the interior to be interpreted. All three of these craters are < 20 km in diameter – for these smaller crater sizes, it is more difficult for a profile with such coarse

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resolution to be usable. This leaves 12 craters with high enough quality SARTopo data to

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analyze. Stereo results have been reported for 8 craters, only two of which are unique from the

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12 observed in SARTopo. Here, we update crater depths using the SARTopo data (Table 3);

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Titan’s craters can be compared to similarly sized craters on Ganymede and Callisto. Impact

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body (e.g., Schenk, 2002). For example, on Europa the transition to complex crater morphology occurs at smaller diameters than for its larger siblings Ganymede and Callisto because of its

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Callisto because there are more data available for the former.

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Rim Height 𝑯𝒓 (m)

Rim Depth 𝒅𝒓 (m)

Terrain Depth 𝒅𝒕 (m)

Relative Depth Ra

Relative Depth Rb

Menrva

400+25 −30

150+95 −120

430+130 −115

280+170 −210

0.64+0.10 −0.11

0.54+0.13 −0.14

Forsetic

125+40 −40

285+125 −115

> 405+145 −185

> 120+185 −120

< 0.66+0.10 −0.12

< 0.56+0.20 −0.16

Afekan

115+5 −5

235+115 −120

530+160 −165

295+75 −80

0.56+0.14 −0.13

0.43+0.18 −0.16

Hano

105+10 −20

230+75 −105

400+100 −80

170+135 −145

0.67+0.07 −0.08

0.57+0.09 −0.11

Sinlap

88+1 −1

375+175 −150

790+255 −245

410+175 −145

0.31+0.21 −0.22

0.17+0.26 −0.27

Soi

85+15 −15

220+45 −45

220+80 −80

0+95 −0

0.77+0.09 −0.08

Selk

84+2 −2

280+50 −54

470+125 −105

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0.81+0.07 −0.07

190+155 −130

0. 58+0.09 −0.11

0.51+0.11 −0.13

Crater #1 H Crater #24 W

70+25 −25

200+125 −110

290+165 −155

90+105 −75

0.73+0.15 −0.16

0.70−0.16 +0.17

41+1 −1

255+60 −65

300+90 −80

45+65 −45

0. 66+0.09 −0.10

0.72+0.07 −0.08

Ksa

45+2 −2

395+50 −60

795+85 −100

400+75 −90

0.12+0.11 −0.10

0.24+0.09 −0.08

Crater #10 NL Crater #3 NL

25+2 −2

0+20 −0

105+45 −45

140+65 −60

0.86+0.06 −0.06

0.88+0.05 −0.05

20+5 −5

130+100 −105

250+170 −175

120+155 −120

0.63+0.26 −0.25

0.69+0.21 −0.21

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Table 3: Rim heights, rim-to-floor depths, and terrain-to-floor depths of Titan craters measured with SARTopo. Rim-to-floor depths are compared to Ganymede crater depths using relative depths (R).

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Using Ganymede depths measured by Bray et al. (2012). Using Ganymede depths measured by Schenk (2002). c SARTopo is missing data in the floor of the crater. Therefore, the depth measurements are minimum values. b

We use the Ganymede crater parameters from Bray et al. (2012) and Schenk (2002) to compare with those of Titan (Figure 9). Comparing crater depths between the two moons allows us to constrain the level of erosion occurring on Titan. We present this comparison in terms of relative depths (𝑅), where 𝑅(𝐷) = 1 −

𝑑𝑇𝑖𝑡𝑎𝑛 (𝐷) 𝑑𝐺𝑎𝑛𝑦𝑚𝑒𝑑𝑒 (𝐷)

and d is the depth of the crater measured

from rim to floor for a crater of a set diameter (Table 3). The freshest craters will have 𝑅 → 0 indicating no difference between the Titan depths and the “pristine” Ganymede depths. The most degraded craters will have 𝑅 → 1, indicating a Titan crater with no topography. Qualitatively, the

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depths of craters on Titan appear shallower than the depths of fresh craters on Ganymede (Figure 9), suggesting erosion and infill by aeolian and fluvial processes, as proposed by Neish et al. (2013). In the next section, we quantify this relationship through a statistical approach. 3.3.1

SARTopo Crater Depths

To test the likelihood that Titan’s craters represent fresh Ganymede craters that have been altered by infill and erosion (Figure 9a) we used the goodness-of-fit Kolmogorov-Smirnov test

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(KS-test) to judge whether the two depth distributions come from the same population or not.

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The technique finds the maximum difference (KS) between the observed and modeled

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distribution functions, 𝐹𝑛 (𝑥) and 𝐹(𝑥) respectively (Trauth, 2015):

where n is the number of measurements.

(5)

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𝐾𝑆 = max|𝐹𝑛 (𝑥) − 𝐹(𝑥)|

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The null hypothesis states that the SARTopo measurements are part of the same distribution

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as the modeled distribution. It is rejected if the calculated KS exceeds the critical KS value or if the probability, p, of observing a statistic this extreme if the null hypothesis is true is less than

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the significance factor (O’Connor and Kleyner, 2012). The probability and critical value relate to

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predefined tabulated values that change as a function of sample size. Here, the null hypothesis is that Titan’s craters in their present form have similar depths to craters on Ganymede (i.e., they are drawn from the same population). Using the average SARTopo measured crater depth distribution for Titan gives KS = 0.70 (KScritical = 0.449) and p = 0.0111%. Even when we use the upper limits of Titan’s crater depths, we find KS = 0.475 and p = 1.9%. These results suggest that we can reject the null hypothesis that Titan’s current crater depths are a part of the same distribution as fresh Ganymede crater depths. Even in the upper-

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limit scenario, there is only a 2% probability of observing a statistic this extreme if the craters

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come from the same population.

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Figure 9: a) Crater depths, measured from rim to floor, of Ganymede craters (Bray et al., 2012 black diamonds; Schenk 2002 dashed black line) and Titan craters as measured by SARTopo (red circles). b) Rim heights of Ganymede craters as measured by Bray et al. (2012) (data black diamonds, trend black dashed line) compared to those measured on Titan (red circles). The error in the Ganymede data is an upper limit, using the error in the depth measurements which considers the error in the rim and floor measurements (see a). c) Crater depths, measured from local terrain of Ganymede craters (Bray et al., 2012 black diamonds) compared to Titan craters (red circles).

Therefore, we deem it likely that Titan’s craters represent a modified population of craters from Ganymede. On average, Titan’s rim-to-floor crater depths are 51% shallower than craters on Ganymede. Smaller (𝐷 < 75 km) craters are slightly less degraded than larger craters

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(𝐷 > 75 km) overall at 53% and 57% respectively. Crater degradation is a combination of infill

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and erosion (Forsberg-Taylor et al., 2004), but infill is likely the most significant modifier of smaller craters (Neish et al., 2013). However, as we discuss in the next section, our results

larger craters. SARTopo Rim Heights

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3.2.1

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suggest erosion of the rim may still be a significant factor in crater degradation, especially for

Measuring rim heights provides constraints on fluvial erosion, because aeolian erosion is

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unlikely to significantly erode crater rims or alter their heights (Forsberg-Taylor et al., 2004).

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Fluvial erosion, on the other hand, preferentially erodes crater rims, as the erosion rate is directly

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proportional to slope (Neish et al., 2016). In addition, measuring crater depths from the surrounding terrain removes potential effects of rim erosion from the calculation, providing more accurate constraints on the amount of crater infill (Figure 9b and 9c). Titan’s rim heights are not as a high as those on Ganymede, suggesting that not only does infill play a significant role in modifying crater depths on Titan, but fluvial erosion of the rims does too. A KS-test of the rim height distributions on Ganymede and Titan gives similar results to the KS-test of crater depth distributions (KS = 0.645, KScritical = 0.449, and p = 0.0201%). Therefore, we reject the null hypothesis that the rim heights on Titan follow the same distribution

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as those on Ganymede. We find that Titan’s rims are even more degraded than the overall depths (72%). The rim-to-floor depths are affected by both infill (changes in 𝑑𝑡 ) and rim erosion (changes in 𝐻𝑟 ). By using terrain-to-floor depths we can begin to constrain how much of the degradation is caused by infill, which may be caused by aeolian or fluvial deposition. First, we perform a KStest and are unable to reject the hypothesis that the terrain depths on Titan and Ganymede

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populations are the same (KS = 0.406, KScritical = 0.449, and p = 5.2%). However, the terrain-to-

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floor depths on Titan are still 39% shallower than those on Ganymede on average. Smaller

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craters (𝐷 < 75 km) are much shallower than larger craters (𝐷 > 75 km) at 48% and 26%

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shallower, respectively. This suggests infill has played a more significant role for the smaller (𝐷 < 75 km) craters consistent with the findings of Neish et al. (2013). Modeling of fluvial infill

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suggests that it operates more quickly on smaller craters with the rate of infill decreasing with

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time (Forsberg-Taylor et al., 2004; Neish et al., 2016). Therefore, it may seem surprising that the rims exhibit more degradation than the terrain-to-floor depths, but our results illustrate that infill

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is still the predominate modifier of smaller craters. It suggests erosion of the rims through fluvial

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activity also plays a significant role in the degradation of larger craters despite previous works suggesting aeolian infill is the predominant modifier of the surface (Neish et al., 2013; 2016). The significance of rim erosion in our results is likely due to the inherent bias towards identifying the largest craters. The most eroded rims do not show any spatial relationships, but the two most preserved rims (least amount of erosion) are consolidated at ~20∘ latitude and within the first 100∘ of longitude. It is possible clathrates strengthen Titan’s crust (Durham et al., 2003), but stronger ice would produce deeper craters than those observed on Ganymede (Senft and Stewart, 2011). Clathrates

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would also lower the thermal conductivity of the ice leading to a warmer interior (Bray et al., 2014; Silber and Johnson, 2017). The higher thermal gradient would lead to shallower craters (Schenk, 2002; Senft and Stewart, 2011). The precise effect of either of these are difficult to constrain. However, we doubt that the increase in thermal gradient would rival that of the tidal heating Ganymede experiences. Furthermore, the existence of craters (e.g. Sinlap or Ksa) that are the predicted depth of a fresh crater on Ganymede suggests any significant effect would have to

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be localized.

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Finally, there is a bias in our dataset that must be acknowledged. We are limited to craters (a)

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that can be readily identified in Cassini SAR data, and (b) that have topography data. Given the

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difficulties in identifying more degraded craters on Titan using the Cassini data, it should be stressed that the degradation we observe is undoubtedly a lower limit. Future missions may

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improve our estimates, but it is clear there is significant degradation of Titan’s surface by both

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infill and erosion even among some of the most well-preserved craters on Titan. 3.3 Stereo Crater Measurements

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As described above, we must consider whether SARTopo measurements are reliable

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indicators of rim heights or if the spatial sampling could artificially reduce the rim heights measured compared to craters on Ganymede. The topography on Ganymede has much better resolution (0.05-1.0 km, Schenk and Ridolfi, 2002; Schenk 2002; Bray et al., 2012) than SARTopo data of Titan (~10 km, repeated over 300 m increments; Stiles et al., 2009). The lower resolution results in averaging longer wavelength signals while rims peak over shorter wavelengths. The resultant averaging of topography in SARTopo could result in artificially lower rim heights measured on Titan, such that crater depths would also be decreased. Stereo observations, on the other hand, provide topographic resolutions more comparable to Ganymede

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(~1.4 km, Kirk et al., 2012). Previous measurements of Titan stereo data suggest they are comparable to the SARTopo measurements (Neish et al., 2013; 2015; 2016; Table 4), with some notable exceptions (Neish et al., 2018). We wish to determine if the different methodology of measuring crater morphometry with SARTopo on Titan compared to measuring crater morphometry on Ganymede with stereo measurements might bias the data. Our results demonstrate that stereo measurements using the average rim to average floor

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approach of Neish et al. (2013, 2015, 2016, 2018) matches with our stereo depths using the eight

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profile method used by Bray et al. (2012; Figure 10) within the error of each measurement

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(Table 4). Furthermore, the depths we measured with stereo also match up with SARTopo

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results within error, with two exceptions (Forseti and Hano). Neish et al. (2018) explores the possible reasons for this marked difference. They suggest the lack of features in the crater

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interiors may bias the stereo interpolation of the rim height, thereby decreasing the actual depth

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of the crater and artificially raising the elevation of the crater floor. The incomplete stereo coverage for Hano and Forseti may also play a role here, but the only other crater with

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incomplete coverage, Crater #6 NL, does not appear to be anonymously shallow.

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Table 4: Comparing Titan crater diameters and rim to floor depths measured with SARTopo and stereo, following stereo methodologies in this work (H Stereo) and previous work (N Stereo). Diameter (km)

Rim Depth 𝒅𝒓 (m)

Technique

Source

Menrva

400+25 −30

430+130 −115

SARTopo

This work.

Forseti

125+40 −40

>405+145 −185

SARTopo

This work1

140+10 −10

180+60 −60

N Stereoa

Neish et al. (2018)

145+30 −30

110+45 −45

H Stereob

This work

Afekan

115+5 −5

530+160 −165

SARTopo

This work.

Hano

105+10 −20

400+100 −80

SARTopo

This work.

100+5 −5

~0

N Stereo

Neish et al. (2018)

Crater

130+35 −35

70+30 −30

H Stereo

b

This work

Journal Pre-proof 790+255 −245

SARTopo

This work.

82+2 −2

700+100 −100

Autostereoc

Neish et al. (2015)

85+15 −15

220+80 −80

SARTopo

This work.

78+2 −2

240+120 −120

N Stereoa

Neish et al. (2015)

95+20 −20

300+95 −95

H Stereob

This work

Selk

84+2 −2

470+125 −105

SARTopo

This work.

Crater #1 H

70+25 −25

290+165 −155

SARTopo

This work.

Crater #24 W

41+1 −1

300+90 −80

SARTopo

This work.

42+5 −5

340+80 −80

N Stereoa

Neish et al. (2016)

50+15 −15

390+145 −145

H Stereob

This work

45+2 −2

795+85 −100

SARTopo

This work.

39+2 −2

750+175 −175

N Stereoa

Kirk et al. (2012)

50+10 −10

805+145 −145

H Stereob

This work

Momoy

40+1 −1

680+100 −100

Autostereoc

Neish et al. (2013)

Crater #6 NL

40+5 −5

340+70 −70

N Stereoa

Neish et al. (2015)

55+10 −10

385+85 −85

H Stereob

This work

105+45 −45

SARTopo

This work.

250+170 −175

SARTopo

This work.

25+2 −2

Crater #3 NL

20+5 −5

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Crater #10 NL

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Ksa

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Soi

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88+1 −1

Sinlap

a

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Averaging measurements taken from up to 8 transects of the stereo data (as in Bray et al., 2012). Statistically averaging the stereo topography of the entire crater as in Neish et al. (2013; 2015; 2016; 2018). c Measurements taken by comparing foreshortening of the near and far walls, discussed in Neish et al. (2013). b

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Figure 10: Titan crater depths derived from three different techniques: SARTopo measurements are shown with circles; stereo results using the method defined here are shown with triangles and using the method in previous work (Neish et al. 2013, 2015, 2016, 2018) are shown with squares. Craters with stereo data are color coded by crater, and those without stereo data are shown in gray. The craters are plotted using the diameter measurements reported in Table 2.

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We have shown that stereo and SARTopo measurements give similar results using both the method defined in this work and the method used previously (Neish et al., 2013; 2015; 2016; 2018). We demonstrate this quantifiably with a KS-test of the stereo depths compared to the SARTopo depths. It gives p = 96.9% with KS = 0.208 (KScritical = 0.410), so the null hypothesis (that the two represent the same population) cannot be disregarded. Given the similarities in depths between SARTopo and stereo, we therefore consider it reasonable to use SARTopo data to compare depths to those of craters on other icy moons, substituting stereo where SARTopo is not available. Furthermore, we trust SARTopo-derived depths over stereo-derived depths given the issues observed in the stereo measurements of Forseti and Hano.

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Since the Titan stereo results are comparable to the SARTopo results, we can consider the results of the different methods as a whole population. In total, 14 craters are covered by some type of topography data: twelve are covered by SARTopo topography, six are covered by stereo topography, and two more are covered by autostereo. Earlier we demonstrated that there was a near 0% chance (p = 0.0153%) that the average rim-to-floor depths on Titan are the same distribution as Ganymede’s craters. Combining results using all three methods, the chance of

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Titan’s crater depths being the same distribution becomes even slimmer (p = 0.00463%, KS =

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0.5682, KScritical = 0.3524). This further strengthens our evidence that Titan is undergoing

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significant degradation.

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4. Conclusions

We have endeavored to compile the complete post-Cassini crater population for Titan, and

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report 50% more craters than the previous compilation (Neish and Lorenz, 2012). When we

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adjust for the increased coverage, the population is in line with previous assessments (Lorenz et al., 2007; Wood et al., 2010; Neish and Lorenz, 2012). Our results are therefore consistent with

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previously reported crater retention ages between 200 Ma to 1.0 Ga. Although this work found a

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slightly lower number of small craters (D < 10 km) than Neish and Lorenz (2012), this is in line with predictions of this population of craters based on models of the atmospheric disruption of impactors (Korycansky and Zahnle, 2005). Identifying craters of this size range is limited by the resolution of the Cassini instruments, and the resulting modification of these features on its surface, so the values presented have increased error compared to larger crater counts. An updated ISS map has been released that has remarkably increased resolution and signalto-noise ratio (https://photojournal.jpl.nasa.gov/catalog/PIA22770) (Karkoschka et al., 2018).

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Our results suggest there are still a few craters that have yet to be identified, and this new map may help to better constrain Titan’s crater population. We used the compiled data to further characterize 14 of Titan’s craters with available SARTopo and stereo topography data. Comparing these results with craters on Ganymede shows that Titan’s craters are 51% shallower, driven by a combination of crater infill (39% have shallower terrain-to-floor depths) and rim erosion (72% have more degraded rims). This suggests

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fluvial erosion may play a much larger role than previously thought in crater modification on

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Titan. Previous expectations were that fluvial erosion contributed less than infill to degradation

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due to the distribution of crater depths (Neish et al., 2013), but our results suggest this is not the

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case. Indeed, initial modeling efforts show that even Sinlap, one of the least degraded craters on Titan, has undergone notable fluvial erosion (Neish et al., 2016). Both fluvial erosion and aeolian

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infill appear to be important contributors to the modification of Titan’s surface.

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Rim heights could also be artificially reduced due to low resolution averaging inherent to the SARTopo technique, but comparisons between the higher-resolution stereo data and SARTopo

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data show similar results. This indicates that comparisons between SARTopo data on Titan and

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higher-resolution stereo topography on Ganymede are robust, and the differences are likely due to erosion on Titan and not a result of the different measurement techniques.

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Acknowledgments The authors would like to thank the Cassini team for acquiring the data utilized in this work, and to thank J. Lunine for helpful comments on the manuscript. J. H. would also like to thank the Technologies for Exo-Planetary Science (TEPS) NSERC CREATE program for funding that supported this work. E. T. is supported by Cassini-Huygens grant NNX13AG28G. A portion of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology,

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under a contract with the National Aeronautics and Space Administration.

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Highlights  A post-Cassini crater assessment for Titan observes 90 total craters  Topography data used to determine crater depths and for the first time, rim heights  Titan’s craters are shallower than pristine craters on Ganymede  Crater rim heights are 72% more degraded and crater depths are 39% shallower  This suggests that fluvial erosion plays a significant role in crater modification

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