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Unscrambling crater modification on : timescales and processes.

For submission to ROSES – Mars Data Analysis Progam 2015 (NNH15ZDA001N-MDAP)

1. Table of contents...... 0 2. Scientific/Technical/Management...... 1 2.1 Summary...... 1 2.2 Goals of the Proposed Study...... 1 2.3 Scientific Background...... 1 2.3.1. Noachian-crater topography constrains pre-3.8 Ga surface processes on Mars...... 1 2.3.2. Retrieving crater-modification processes and timescales is enabled by a statistically representative survey of craters ...... 4 2.4 Technical Approach and Methodology...... 6 2.4.1. Determine timescale of crater modification through analysis of crosscutting craters...... 7 2.4.2. Constrain fluvial erosion through analysis and modeling of isolated craters .....9 2.4.3. Synthesis: crater modification to crater obliteration...... 13 2.4.4. Assumptions and caveats...... 13 2.5 Perceived Impact of Proposed Work...... 14 2.6 Relevance of Proposed Work...... 15 2.7 Work Plan...... 15 2.8 Personnel and Qualifications...... 15 3. References...... 16 4. Biographical sketches...... 24 5. Current and Pending Support...... 27 6. Budget Justification...... 28 6.1. Budget narrative...... 28 6.1.1. Personnel and Work Efforts...... 30 6.1.2. Facilities and Equipment...... 30 6.2 Budget Details...... 30 Unscrambling Noachian crater degradation on Mars.

2. Scientific/Technical/Management:

2.1 Summary. Noachian crater modification records pre-3.8 Ga surface processes on Mars (e.g. Craddock & Howard 2002). However, because Noachian crater modification has never been subjected to a statistically-representative survey, the potential of crater modification to constrain the rates and processes of Noachian landscape evolution remains largely untapped. Summarizing decades of research, Irwin et al. (2013) state “Fluvial erosion around the Noachian/ transition is better constrained than […] landscape evolution throughout the Noachian Period.” Basic open questions include: (1) For how long did crater modification continue? (2) Was pre-3.8 Ga crater modification dominated by fluvial erosion, or was fluvial erosion subordinate to processes that did not require surface liquid ? Previous work suggests, but does not confirm, that fluvial erosion was indeed the dominant crater-modification process and that it operated over an interval spanning ≥108 yr. However, crater infilling by , aeolian infilling, infilling, or diffusion, have also been suggested, and a brief time-window of crater modification has not been ruled out. Testing these hypotheses will require systematic analysis of a statistically- representative database of modified craters. We will test the prolonged-fluvial-erosion hypothesis by: (1) constraining crater modification versus time during the pre-3.8 Ga interval using crosscutting craters, an approach that is independent of uncertainties in the crater production function; (2) using the morphometry of isolated craters to quantify the relative contributions of fluvial versus nonfluvial processes and their regional variations. Combining these results, we will (3) synthesize the crater modification constraints and the crater size- frequency distribution, which has been argued to contain a record of crater obliteration. In summary, we will quantify previous qualitative arguments about Noachian surface processes, distilling these constraints to a form that can be used to inform climate models and climate evolution models for Early Mars.

2.2 Goal of the proposed study. The goal of the proposed work is to use topography data and simple forward models to make quantitative inferences about the history and processes of crater modification during the Noachian on Mars. We will make measurements on craters selected from the latest publicly- available crater database (Robbins et al. 2012), and use these to do the following:-

• (§2.4.1) Determine the duration of crater modification on Noachian Mars using the statistics of modification of crosscutting craters. ( 1 and 2; ~40% of total effort). • (§2.4.2) Test the hypothesis of fluvial backwasting, and constrain the fluvial-erosion contribution to crater infilling (Years 1, 2 and 3; ~45% of total effort). • (§2.4.3) Link crater-modification data to crater size-frequency distributions (~15% of effort).

In order to define a focused, well-posed investigation of appropriate scope for a three- study, we make several simplifying assumptions, which are explained and justified in §2.4.4.

2.3 Scientific background. 2.3.1. Ancient-crater topography constrains pre-3.8 Ga surface processes on Mars. Most closed-basin craters in low- Noachian terrains are anomalously shallow, anomalously flat-floored, lack visible ejecta blankets, and have subdued rims relative to craters on the and relative to younger craters on Mars (e.g. Murray 1971, Soderblum 1974,

1 Unscrambling Noachian crater degradation on Mars.

Mangold et al. 2012, Craddock et al. 1993); yet the ancient craters retain relatively steep inner walls. These observations suggest that the craters are degraded. The degraded state of these ancient craters is consistent with widespread fluvial erosion on Mars pre-3.8 Ga (e.g. Malin 1976, Craddock & Howard 2002, Irwin et al. 2013). Noachian crater modification suggests ~1 km terrain-averaged resurfacing (Howard 2007), much more than the <1m terrain-averaged erosion corresponding to the Late Noachian/Early Hesperian peak in incision, which may have been as brief as 105 yr (Fassett & Head 2008, Barnhart et al. 2009, Hoke et al. 2011, & Head; see also Hoke & Hynek 2009). (Here and throughout, we refer to crater modification that may have extended into the earliest Hesperian as “Noachian”). Noachian crater size-frequency distributions are consistent with ≫ 100m resurfacing ( 1974), or alternatively a change over time in the impactor size-frequency distribution (Strom 2005, Fassett et al. 2012).

Figure 1. Multiple processes have modified Mars highlands craters, and the dominant process has not been determined. Left panel: Rim-retreat by fluvial-erosion is indicated by dendritic, branching sinuous ridges interpreted as inverted channels (43°E, 20°S) (Irwin et al. 2012). Middle panel: Prolonged erosion is suggested by crosscutting relations showing that later- forming craters are commonly deeper than earlier-formed craters (Craddock & Howard 2002). White box indicates location of image in left panel. Right panel: Infilling, not rim-retreat, appears to have resurfaced Suata, a 24km-diameter closed-basin crater close to Tyrrhena with a shallow floor. The 300-400m high rim indicates little or no rim-retreat and only minor diffusion.

Direct evidence for fluvial erosion in the form of topographically-inverted, radial drainage networks has been found, but only at a few craters (e.g., Irwin et al. 2012). confirmed that one shallowed-crater floor (<3.8 Ga) contains fluviodeltaic sediments (Grotzinger et al. 2014). Leaching by persistent, top-down liquid water is suggested by Noachian- stratigraphic sequences of Al-clays overlying Fe/Mg-rich clays that are distributed globally (Carter et al. 2015). Many features of the Noachian landscape (steep inner walls, flat floors, easily-eroded crater fills, and sharp-sided isolated mesas) are difficult to explain other than by fluvial erosion, although no systematic fitting of data to models has been done (Craddock & Howard 2002, Mest & Crown 2005). Crater-infilling states have a bimodal distribution (Fig. 2) that is better explained by fluvial erosion than by other processes (Forsberg-Taylor et al. 2004, Grant 1987). This is because fluvial erosion rapidly fills deep craters but only slowly fills shallow craters (Howard 2007), so that a rapid shut-off of fluvial erosion would leave few craters with <50% infilling (Forsberg-Taylor et al. 2004). Post-fluvial accumulation of little-modified craters builds

2 Unscrambling Noachian crater degradation on Mars. up the other “mode” in the distribution (Fig. 2). Finally, the relative rarity of integrated channel networks can be understood in terms of impacts competing with erosion/sedimentation (Collaborator Howard, 2007; Malin & Edgett 2001; Edgett & Malin 2002). These data establish the plausibility of a runoff contribution to >3.8 Ga crater modification, but they do not constrain its relative importance, nor its duration. Non-runoff explanations for crater modification have been suggested (e.g. Soderblum 1974) (Fig. 1). For example, (1) low-viscosity has flooded craters on , the Moon, and Mars (e.g. Kreslavsky & Head 2002, Fassett et al. 2011, Marchi et al. 2013, & Head 2002, Hurwitz et al. 2010). Lava infilling has affected Noachian craters, which commonly show evidence for at least a veneer of volcanic fill, and perhaps more (Wilhelms & Baldwin 1989, et al. 2005, Korteniemi et al. 2005, Fig. 2. Strongly bimodal crater distribution in Noachian McDowell & Hamilton 2007, Fassett terrains (MC-20; Robbins et al. 2012 database). Young, & Head 2008, Warner et al. 2010, sharp-rimmed deep craters (a small number of which of Goudge et al. 2012,). Recently, which contain alluvial fans and/or mountains), analysis of rocky, blocky, and are younger and fewer in number than smooth-floored -rich floor fills for many craters (Mangold et al. 2012, Forsberg-Taylor et al. shallow-floored Noachian craters led 2004). Depth is normalized to relative to the complex- Edwards et al. (2014) to advocate crater depth scaling of Tornabene et al. (2013a). Red impact-induced volcanism as an line shows the cleanest cut between the two classes, infilling mechanism. (2) Both fine- which is used in §2.4. This proposal focuses on the grained impact ejecta and volcanic “heavily modified” class. ash would have been more common early in Mars history (Bandfield et al. 2013). As airfall, this material could have mantled and infilled craters. A thicker past would have dispersed more dust, sand, and ash, favoring aeolian infilling (Hartmann 1971, Grant & Schultz 1993, Malin & Edgett 2000, Kerber et al. 2013). (3) Diffusion lowers crater rims on the Moon (Fassett & Thomson 2014) and on Mars (Watters et al. 2015). (4) A role for infilling by distal ejecta is suggested by the impact. Hale’s volatile-bearing, low-viscosity ejecta smoothed and infilled topographic depressions out to ~2 crater radii (Jones et al. 2010; El-Maary et al. 2013). Infilling by volatile- bearing low-viscosity distal ejecta may have been more important in the Noachian because Mars has lost volatiles since the end of the Noachian (Villaneuva et al. 2015, Webster et al. 2015). The relative contribution of these non-fluvial mechanisms to Noachian crater modification is not understood. In summary, crater modification is one of the few available probes of surface processes and timescales during the Early and Middle Noachian, a period of great interest to planetary evolution (Clifford et al. 2014).

At , results confirm that airfall, volcanic, and water-requiring processes all had some role in crater modification, but do not constrain the relative importance of these processes. Gusev’s surface is lava (Greeley et al. 2005), but inliers show volcaniclastic materials draped over an ancient core; the structure and composition of the are consistent with airfall later altered by water (Crumpler et al. 2011). Spirit also found -rich rocks,

3 Unscrambling Noachian crater degradation on Mars. suggestive of and runoff (Ruff et al. 2014). Spirit’s findings illustrate the need for a statistically representative crater survey to determine whether fluvial degradation was a major or minor player.

2.3.2. Retrieving crater-modification timescales and processes is enabled by a statistically representative survey of craters. To break the degeneracy between fluvial erosion and non-fluvial processes, crater rims are crucial. Runoff erosion and debris-flow erosion cause scarp retreat (backwasting) while maintaining steep inner-wall slopes (Craddock & Maxwell 1993, et al. 2001). By contrast, non-fluvial processes (diffusion, infilling) subdue scarps while reducing inner-wall slopes. These qualitative differences between process signatures are well-understood. This is because of extensive work on terrestrial scarp retreat that has been checked against absolute exhumation histories recorded by cosmogenic nuclides and thermochronology (e.g. Collaborator Howard 1994, Tucker et al. 2001, et al. 2000). Previous morphologic work on Noachian craters did not carry out a formal fit of models to data, focused on individual craters, used pre-MGS data, or all three (e.g. Öpik 1965, Murray 1971, Craddock et al. 1997). One previous morphometric study of Noachian craters fit modern data to models (Mangold et al. 2012), but they did not make a process interpretation for the Noachian. Therefore, the relative importance of fluvial versus non-fluvial processes has not been quantified. We propose to take Fig. 3. Our proposal in the context of (a small the next step (Fig. 3), by using MOLA subset of) published Noachian crater modification data and a volume-balance model to studies, showing that the proposed work extends a determine the relative contribution of long-standing effort towards globally distributed different crater-degradation processes to process studies. volumetric infilling for a statistically- representative ensemble of Noachian craters. Our work leverages the new global crater database (Robbins et al. 2012) (Fig. 3) and builds on previous work (Fig. 3), much of it by Collaborator Howard and his students and colleagues. For example, our work leverages the earlier finding that the distribution of crater-infilling states is bimodal (e.g. Forsberg-Taylor et al., 2004) (Fig. 2). We also make use of the new global of Mars (Tanaka et al. 2014, Irwin et al. 2013), which we use to demarcate the Noachian (Fig. 6).

Noachian craters exhibit a range of degradation states (Fig. 2), but this does not require that modification during the Noachian was time-progressive: spatial variation in target properties (Weiss & Head 2015; Boyce & Garbeil 2007) or in the availability of snow/ice for melting (Kite et al. 2013, Wordsworth et al. 2015) would produce a range of degradation states.

4 Unscrambling Noachian crater degradation on Mars.

Constraining the duration of modification would be easy if individual craters carried time-stamps visible from orbit. With such time-stamps, we could aggregate craters by age, plot age against degradation/infilling, and infer the course of degradation (Fassett & Thomson 2014, Golombek et al. 2014). Suppose infilling was instantaneous. Then, all craters predating that instant would show equal infill (after correcting for crater size, and setting aside geologic noise). Craters that came after the infilling event would be little modified. Now consider the other extreme – that infilling processes operated with constant efficiency, but then suddenly stopped. In that case, heavily-modified craters of different ages would show progressive increase in the degree of infilling.

The needed time-stamps are provided by crosscutting relationships among ancient craters (Craddock & Howard 2002; Fig. 1). Crosscutting relationships unambiguously record relative time, and probabilistically record absolute time (assuming a model) (Fig. 4). A late- forming crater is more likely to crosscut another than to be crosscut itself. A large population of crosscutting craters will have a mean age that is younger than the craters they crosscut (Fig. 4). A population of craters that neither crosscut nor are crosscut will have an intermediate mean age (Fig. 4). Assuming a constant crater flux and that the crater density is not close to saturation, the population of crosscutting craters is given by incomplete beta functions (Fig. 4). Aggregating hundreds of crosscutting crater-pairs (this proposal) leads to strong constraints on the duration of crater modification, even in the presence of geologic noise (§2.4.1).

Better constraints on Noachian crater- modification resurfacing processes and timescales (from analysis of many individual surviving craters) will help to make sense of the Noachian highlands crater size-frequency distribution (CSFD) (Jones 1974, Figure 4. Time kernels and observed relative depths for heavily- & Jones 1977, Barlow modified craters in MC-20. Among heavily-modified craters, 1988). Noachian CSFDs relatively old craters are more-modified. show a shallower slope between 4-32 km diameter, with steeper slopes at >32 km and <4 km diameter (Fig. 5) (Chapman & Jones 1977, Irwin et al. 2013). We refer to this relative lack of 4-32 km diameter craters as the “S-” (Fig. 5). Is the S-curve caused by production (a change in the impactor size-frequency distribution with time; Oberbeck 1977, Barlow 1988, Strom 2005)? Or is it caused by destruction (an episode of incomplete resurfacing that preferentially destroyed smaller craters, leaving the largest craters; Jones 1974, Hynek & Phillips 2001, Irwin et al. 2013, Robbins et al. 2013, Quantin et al. 2014)? Did both processes play a role? The “S-curve” question has persisted for more than 40 years (e.g., compare Strom & Whitaker 1976 and Jones 1974), but remains unresolved, because there are strong arguments on both sides. On one hand, Mars CSFD slopes are similar to lunar highlands CSFD slopes, favoring a production-function explanation (although the Mars crater density is lower.) On the other hand, the large proportion

5 Unscrambling Noachian crater degradation on Mars. of greatly degraded craters on Mars suggests an additional, unseen population of craters that formed but were obliterated. The answer matters, because to remove m! ost of the 4 km diameter craters (Fig. 5), ~1 km of areally-averaged resurfacing is required. This is >103 times the resurfacing represented by valley network incision (Robbins et al. 2013). In §2.4.3, we synthesize crater mechanisms with CSFD data. We will also use spatial statistics to test the obliteration hypothesis for the CSFD.

Figure 5. Left panel: Crater size-frequency distribution for 0-135°E, 0-30°S, showing the “S- curve” relative to Hartmann’s (2005) isochrons. Error bars are √N. Right panel: (panel by J. Riggs, Northwestern). Pairwise correlation function for craters with depth/diameter ≤0.05 (heavily-modified); these are significantly more clustered than craters with depth/diameter ≥0.05.

2.4 Technical Approach and Methodology. We focus on craters >10 km diameter, that form topographically closed basins, and are located in the MC-20 (Sinus Sabeuus), MC-21 (Iapygia), MC-22 (Mare Tyrrhenum), and MC-16 (Memnonia) quadrangles (i.e., 0-135°E and 135-180°W, 0-30°S). These quads span a range of elevations (and a range of proximities to volcanic centers) within the low-latitude band where obvious evidence for glaciation is uncommon (e.g. Berman et al. 2009, Conway & Mangold 2013). Together, they sample ~30% of Noachian-aged ice-free terrain – a statistically- representative ensemble (Fig. 6). >10 km craters are predominantly Noachian (Ward 1974, Irwin et al. 2013, Forsberg-Taylor et al. 2004) and easy to resolve and measure with MOLA data (Robbins et al. 2012). Using the Tanaka et al. (2014) global GIS, we will mask out post- Noachian materials from these quads, and craters that partly overlap post-Noachian materials. After masking, ~1000 craters remain, allowing visual inspection of each crater and each model output, while still comprising sufficient statistical power to probe Noachian surface processes.

We will use only topographically closed basins in our analysis (craters for which the maximum drainage area within the crater of crater-pair is not much larger than the area of that crater or crater-pair). This is because gravity-driven transport of sediment into or out of the crater would complicate the interpretation of the volume balance.

6 Unscrambling Noachian crater degradation on Mars.

Figure 6a. Study area. Open triangles correspond to crosscutting craters. dots correspond to isolated craters. Grayed-out regions correspond to post-Noachian materials; dark gray for volcanics.

Fig. 6b. Filtering of crater populations. For MC-21, ~150 isolated craters and ~300 crosscutting- pairs survive all checks.

2.4.1. Determine timescale of crater modification through analysis of crosscutting craters. We hypothesize that crater modification occurred over a >107 yr period during the Noachian.

Our starting point for determining the timescale of crater modification is the Robbins database (Robbins et al. 2012). We identify intersections among the Robbins craters using an ArcGIS buffer equal to 133% of the crater radius. For each intersection, we note which crater is younger (if a clear crosscutting relationship can be established) by visual inspection of controlled THEMIS global mosaics, MOLA topography, and CTX images. Because our interest is only in Noachian processes and timescales, we exclude the “less modified” craters in Fig. 2. We do this by normalizing observed crater depth d by the depth of a (geologically-young) pitted-floor crater of equivalent diameter (d = 0.357 D0.52 by regression of fresh complex craters; Tornabene et al. 2013a). Next, by visual inspection of the 2-D histogram of crater infilling states and crater

7 Unscrambling Noachian crater degradation on Mars. diameters (Fig. 2), we assign craters with normalized (relative) depth > (0.5 + 0.3(log10(D)-1)) to the “less-modified” class and exclude them. Because these less-modified craters are Hesperian or Amazonian, our dataset now contains only degraded (mostly Noachian) craters (Mangold et al. 2012). We also exclude crater-intersections for which no crosscutting relationship could be determined. These craters are more heavily-degraded on average, so their inclusion would bias the results.

Among the remaining crosscuts, the matrix of pair-wise crosscutting relationships is checked for logical consistency (e.g., if A cuts B and B cuts C, then C cannot cut A). Using the matrix, craters are assigned to one of four groups: “crosscutting,” “is crosscut,” “both crosscuts and is crosscutting,” or “unconstrained relative age.” In preliminary work, we determined the depth:diameter (a measure of infilling) using DEPTH_RIMFLOOR_TOPOG/ DIAM_CIRCLE_TOPOG in the Robbins database. In the full model we will use the radial profiles described in §2.4.2 to determine crater diameter, and relative crater depth. “Crosscutting” craters were (43±11)% deeper on average than craters that “are crosscut”. Bootstrapping (scrambling of depth:diameter ratios) confirmed that this result was not due to chance (at the 99.9% significance level). The result is not an artifact of big craters preferentially crosscutting small craters, because the depth/diameter ratio of small ancient craters in our database follows a similar cdf to the depth/diameter ratio of large ancient craters in our database. This result suggests, independent of uncertainties in how the crater production function changed with time (e.g. Strom et al. 2005), that Noachian crater modification was a prolonged process. For how long?

To determine the duration of Noachian crater modification, we use the difference in relative infilling state (1 – relative depth) between overlapping craters (correcting for original depth using the Tornabene et al. 2013a scaling) (Fig. 7). The relative infilling state of the younger member of the pair is less than in the older member of the pair in 100 out of 138 crater-pairs for the MC-20 quad. To quantify the chronological implications, we carried out a simple inversion. The inversion has two free parameters: (1) the duration of Noachian crater modification Δm, (2) the amplitude of geologic noise, c. We generated forward models by scanning systematically through the grid defined by these two parameters. For each parameter combination, we found the relative-infilling state for many crater pairs by (a) randomly assigning timestamps to craters, (b) assigning a “relative modification” stamp to each crater using the following formula:

E = (min(Δm, 1- t)/Δm)n + cε where (1-t) is the amount of time the crater is exposed to erosion, and ε is drawn randomly from a normal distribution with mean 0 and variance 1. We then compared the relative modification of the true MC-20 crater-pairs to the relative modification of the synthetic crater-pairs (Fig. 7). The best fits are for high values of Δm and moderate values of c. (The conclusion is insensitive to n; we use n = ½, which is reasonable for fluvial infilling - Forsberg-Taylor et al. 2004). Combining our preliminary results with existing crater-chronology models (Lillis et al. 2013, Robbins et al. 2014), and marginalizing over the unknown amplitude of geologic noise, implies crater- modification continued for >30 Myr. This is 30-300 times longer than the interval of surface erosion required to explain the valley networks (e.g. Barnhart et al. 2009, Rosenberg & Head 2015, Hoke et al. 2011).

8 Unscrambling Noachian crater degradation on Mars.

Figure 7. Showing how crater crosscuts constrain the duration of Noachian crater modification. Left & middle panel: 100 out of 138 crosscuts among ancient craters have the younger crater more eroded, more than would be expected if erosion was brief. This figure also shows that ~100 crater-pairs are sufficient to get interesting timescale constraints even in the presence of natural geologic noise. Right panel: The black contours enclose the 68% (inner) and 99% (outer) probability regions (based on χ2-squared errors). Note that χ2 calculation used 8 bins, fewer than the ~20 plotted in left panels. Topographically open craters are included in this plot but will be excluded in the proposed work. (Shown: preliminary work on MC-20 quad).

We propose to apply this protocol to all four quads, with refinements. These refinements are:

• Ejecta corrections. Using the Maxwell-Z model (Maxwell 1977, Barnhart & Nimmo 2011) that we have previously implemented (Mangold+Kite et al. 2012b) we will subtract the areally-averaged ejecta contribution to the relative infill of mutually crosscutting craters. We do not expect that this will be a large correction. • Exclude topographically-open craters, by visual inspection. This will include removal of crater-pairs where the shared rim has eroded away (allowing mass transfer between craters). • Analysis and simulation of triplets and quadruplets of overlapping ancient craters, using analytical functions for the time kernel (Fig. 4).

In addition to the aggregate and quad-by-quad results, we will map out the duration of erosion as a function of global elevation, regional elevation (MOLA detrended), by geologic unit, and by proximity to volcanic centers. Given that ~100 crater pairs are sufficient to constrain timescale (Fig. 7), our ~500-pair analysis will have the power to detect strong correlations between timescale and these parameters (should they exist). Finally, we will compare the timescale of crater-obliteration required by crosscutting craters to the timescale suggested by the overall crater degradation (§2.4.3).

2.4.2. Constrain contribution of fluvial erosion through analysis and modeling of isolated craters. In the words of Murray et al. (1971), “Mars crater morphologies reflect crater modification processes; therefore, they can supply insight into the of those processes.” This task has

9 Unscrambling Noachian crater degradation on Mars. two parts. In the first part, we will subject fluvial backwasting to a strict test, by identifying shallow-floored, isolated, closed-basin craters whose rim heights are inconsistent with fluvial backwasting. In the second part, we will calculate the relative contributions of fluvial backwasting, infilling, and diffusion.

Our topographic data is obtained as follows. We identify craters with diameters >10 km from the Robbins database that are separated from other similar craters by a buffer-distance of at least 1 crater radius (rim-to-rim buffer distance). For these isolated craters, we locally detrend the topography, and then use a Python script to extract radial profiles. The number of radial profiles (typically >50) is set to avoid oversampling MOLA grid resolution. We use MOLA because MOLA gridded data have been shown to yield basic morphometric measurements that are similar to those obtained with the aid of higher-resolution stereo topography for crater size >10 km (Robbins & Hynek 2013). Furthermore, MOLA topography allows generating a larger crater dataset than does HRSC or CTX stereo topography.

Part A. Fingerprinting closed-rim craters where mass was sourced from outside the crater. We hypothesize that shallow-floored craters far from volcanic provinces have shallow rim heights consistent with rim backwasting, while shallow-floored craters within or near volcanic provinces have tall rims that require mass input from beyond the crater. (For this sub-task only, we will consider craters on Hesperian volcanic terrains within the quads of interest, because these provide a reference point for the influence of volcanism.)

Fluvial erosion in topographically closed basins leads to rim retreat. Rim retreat can be straightforwardly tested through rim survival. If rim relief is large but the crater is shallow- floored, then shallowing involved major mass input from outside the rim (Fig. 1). This is because crater rims are narrow, so a small amount of rim retreat greatly reduces rim relief. If the rim- removing process is coupled to the floor-shallowing process (i.e. erosion), then the shallower the floor, the more muted the crater rim should be. Alternatively, if the Early Mars craters are shallow due only to mass input from outside the rim, then there should be no correlation between rim height and depth:diameter ratio (after correcting for size dependencies in depth:diameter ratio, removing topographically open basins, and after removing post-Noachian craters that don't show much modification of rim height or floor depth) (Fig. 2). Therefore, we will analyze the correlation between rim degradation and crater infilling using our radial profiles

Rim height is “notoriously difficult to estimate” (Robbins et al. 2012), and because previous rim height estimates are not precise enough for our purposes, we will re-determine rim height for all isolated craters >10 km in the quads of interest. The most comprehensive global crater database (Robbins et al. 2012) includes a rim height field corresponding to the difference between the mean elevation of a small number of manually selected points on the rim peak and the mean elevation of a small number of manually selected points on the crater floor. Instead, using all the data points in our radial profiles, we will fit power-law rim shapes (e.g. Barnhart & Nimmo 2011, Stewart & Valiant 2006) to each profile of each crater, and record the 50th, 90th and 99th percentile rim heights implied by the power-law fit. To determine the crater depth, we will use our detrended profiles to determine the lowest points inside that do not correspond to small nested craters, relative to detrended background terrain.

10 Unscrambling Noachian crater degradation on Mars.

We will then bin our crater-depth and rim-height data by diameter (10-20 km, 20-40 km, 40-80 km), identify craters in each bin with large rim relief (inconsistent with having achieved their infilling state via rim retreat), and look for systematic trends with distance measured from the geologic boundary of volcanic provinces mapped in ArcGIS (Tanaka et al. 2014). Finally, we will aggregate our data into a single bin, by normalizing crater-depth by the expected initial crater-depth for craters of that size (Tornabene et al. 2012, 2013a). The hypothesis that volcanic influence should increase close to a volcanic center is reasonable because dikes on Mars span ~103 km (Head et al. 2006), simulations and observations indicate that mantle-plume heads can span 103 km (d’Acremont et al. 2003), and it is observed that intact-rimmed craters in volcanic areas typically have lava floors (e.g. Fig. 2).

In addition to backwasting, crater-rim height can be reduced by diffusion. This means that our test is conservative: craters with rims too tall for fluvial backwasting definitely require mass sourced from outside the rim.

Part B. Volume-balance modeling. We hypothesize that among Noachian craters, fluvial erosion transported >50% of the volume involved in crater modification.

Crater modification processes can be divided into infilling, diffusion, and backwasting (Table 1). Infilling adds material to the crater floor without modifying the wall or rim. Backwasting chews into the rim, infilling the floor, conserving mass within the crater region. Diffusion softens the rim and ejecta (Table 1).

Mass redistribution within crater rim Mass input from beyond crater Kinematic processes to be Diffusion Backwasting Infilling tested for Topographic signature Steep slopes removed; Steep slopes retained; Crater shallowed out-of- crater wall shallows rim retreats; floor proportion to rim retreat shallows. Physical processes Seismic shaking Detachment-limited Lava flooding corresponding Slope creep Airfall infilling (including to these shape changes Active-layer creep abrasion/plucking2 distal ejecta) (bold: most likely) processes1 Debris-flow erosion Saltation infilling Micrometeorite Pyroclastic flows (these tend to gardening hug crater floors, but will also Transport-limited mantle and smooth crater rims, fluvial processes so map to a combination of Any local process that diffusion and infilling) has an efficiency proportional to slope. Notes: 1. Perron et al. 2003. 2. Howard et al. 1994.

Table 1. Crater-modification processes, assuming a closed-basin crater.

Because different surface processes leave a distinct topographic signature, constraining the contribution of these topographic signatures to modern crater form can constrain the contribution of different processes. We use a simple axisymmetric volume-balance model (Fig. 8). Through volume-balance modeling of a large ensemble of craters, we will constrain dynamical models of the dominant crater-modification processes. Our work will thus complement detailed studies of dynamical processes in individual craters (Fig. 3).

11 Unscrambling Noachian crater degradation on Mars.

Figure 8. Workflow for best fit for isolated crater radial profiles (setting diffusion = 0; adding diffusion slightly improves the fit). RMS error marginalizes over other parameters.

Our workflow is as follows (Fig. 8). We first average the radial profiles of isolated craters. For each crater, we then carry out a systematic grid search with four free parameters: amount of diffusion (m2), amount of backwasting (m horizontal), amount of infilling (m vertical), and initial crater diameter (m). We do not use steepest-descent techniques because we found abundant local minima, and we do not use Markov Chain Monte Carlo because the computational burden of a systematic grid search is not high enough to motivate this more complex procedure. A systematic grid search also allows straightforward quantification of degeneracies (e.g., the partial degeneracy between infilling and backwasting in Fig. 8). Marginalizing over initial crater size, we find the best-fit and the error for each crater. Results are shown in terms of the fraction of sediment volume moved. Computation requirements are modest (the fit for isolated craters from 1 quad runs overnight on one PC).

Our volume-balance assumes that material can only enter the crater by backwasting, from above, or from below. Therefore, we exclude craters with visible entrance or exit valleys, and craters with any evidence for ice infill (e.g. Shean et al. 2010).

The uncertainty in this procedure is dominated by uncertainty in the initial shape of the crater. Initial shape is constrained by surveys of craters showing multiple morphologic markers for relative youth (low crater-retention age, pitted terrain, bright radial features in nighttime IR, secondary crater chains) (Tornabene et al. 2012). These allow construction of scaling relations for “pristine” Martian craters, including the variability between complex craters (Tornabene et al. 2013a). We fit rim height by fitting a power law to observed young-crater rim heights spanning a range from 10.2 to ~150 km diameter. In detail, pristine-crater depth/diameter variations show systematic regional variability, although this is unimportantly small for our purposes, strong regions are rare, and the Noachian highlands are probably “weak” (Boyce & Garbeil 2007, Bandfield et al. 2013). We fit cavity shape using a power-law fit from Northern Plains data (Stewart & Valiant 2006). Initial crater depths for Noachian craters are uncertain by ±20% (Grant 2015), and we will mitigate this uncertainty by testing the sensitivity of our results to initial conditions obtained using the shallowest and the deepest craters in each size class of the entire Tornabene et al. (2012) catalog (n ~ 100). Currently we do not treat crater central peaks (because their volume is minor), but we will add central peaks in the proposed work.

We assume no change in density following erosion and deposition (§2.4.4). With this assumption, our quantification of backwasting (rim retreat normalized to initial crater radius) is

12 Unscrambling Noachian crater degradation on Mars. not affected by uncertain pediment slope (Collaborator Howard, 1994). Under fluvial transport, we assume a crater inner-wall slope of 25%, which is an average over small-scale ridges and valleys.

2.4.3. Synthesis: Link crater modification to crater obliteration. The final task has two elements. In the first element, we will compare the duration of crater modification inferred from crosscutting-craters is the same as the duration of crater modification independently inferred from crater statistics (Lillis et al. 2013, Quantin et al. 2014), and analyze any differences. In the second element, we test the hypothesis that the paucity of craters in the 4- 32 km diameter size range results from spatially patchy crater-obliteration that did not obliterate larger craters. This test relies on the fact that crater-obliteration processes are rarely spatially uniform (a possible exception is the catastrophic resurfacing of Venus). For example, flood tend to fill local lows, fluvial erosion preferentially infills low regions, and aeolian mantling preferentially blankets areas where wind stress is low (Kreslavsky & Head 2002, Mangold et al. 2009, Irwin et al. 2013). On the other hand, crater production is a spatially uniform process (when crater density is not close to saturation, and filtering out self-occlusion, averaging over many orbits, and for that are not in spin:orbit resonance). Therefore, if incomplete resurfacing is the cause of the “S-curve,” then craters between 4 km and 32 km in diameter (test set) will be less randomly distributed (more clustered) than craters <4 km or >32 km in diameter (control sets). Fig. 5 shows a proof-of-concept. On Noachian terrains, little crater-obliteration has occurred for >8 km diameter craters since the Early Hesperian (for example, shallow <0.5 km diameter Holden secondaries are preserved; Mangold et al. 2012b). Therefore, we can also use the less-degraded mode of craters (Fig. 2) as a control case. If regions of low and high 4-32 km density relative to >4 km and <32 km density can be identified, then these regions can be inspected for geologic coherence. Regional variations between crater size- frequency distributions can be used as a further check of the incomplete-erosion hypothesis (Robbins et al. 2013).1 This geologically-agnostic procedure is complementary to the approach of Irwin et al. (2013), who used a new global geologic map (Tanaka et al. 2014) to confirm that subdivisions of the Noachian mapped partly on the basis of crater density (Tanaka et al. 2014) do have different crater densities.

We will also use this spatial-statistics framework to test if absolute depth of floors is spatially correlated (suggesting volcanism), and if absolute thickness of infill is spatially correlated (suggesting airfall mantling). It will also be straightforward to test the earlier suggestion that crater modification is a function of elevation (Craddock & Maxwell 1989, 1990; see also Irwin et al. 2013), which were based on Viking data, photoclinometry, and a smaller study area.

2.4.4. Assumptions and caveats It is worth emphasizing the assumptions driving the design of our analysis. First, all crater modification studies must assume an initial shape (e.g. Grant et al. 2015) in order to reconstruct modification from present-day topography. Similar to previous work (e.g. Grant et al. 2015), we

1 If Mars were incompletely eroded with different intensities in different regions (destruction), then the turnoff in the S-curve will move to higher or lower diameters (Jones & Chapman, 1977, Quantin 2014). Alternatively, if different regions of Mars were completely resurfaced at different times followed by accumulation of a crater population (production), then the turnoff at the “S” curve will be at the same position, but the amplitude of the “S”-curve will differ between regions.

13 Unscrambling Noachian crater degradation on Mars. assume that just after formation, ancient impact craters on Mars had rim heights and depth- diameter ratios similar to craters seen just after formation on Mars today. This assumption is supported by the continuous (although bimodal) gradation in degradation states from Noachian Mars to pristine Mars craters. Although Early Mars’ may have had more volatiles, Hale and formed in volatile-rich targets, and these post-Noachian craters still have steep rims and deep floors. Steep rims and deep floors are also seen in fresh craters on icy objects (Ganymede, Callisto and Ceres). Second, using radially-averaged profiles as representative of an ‘equivalent circular’ crater is, in principle, dangerous! This is because a key morphologic signature of backwasting – a steep inner wall – can be ‘smeared out’ by averaging, and the crater will then incorrectly be assigned to diffusion+infilling. In practice, we found in preliminary work that the ‘smearing’ of crater-wall slope due to averaging over slightly-elliptical craters was minor. If ‘smearing’ nevertheless proves to be a problem, we will mitigate this using rim-anchored radial averaging (defining the rim as the locus of maximum negative curvature adjacent to the crater’s nominal diameter). Any remaining ‘smearing’ will tend to undercount fluvial erosion, which is conservative in terms of our hypothesis test. Third, our isolated-craters work introduces a bias towards low-crater-density areas (i.e., Middle Noachian as opposed to Early Noachian). We will mitigate this possible source of bias by testing the sensitivity of our results to Early vs. Middle Noachian subsets (Tanaka et al., 2014). Fourth, shallow-floored craters with subdued rims emerge from simulations of moderate-sized impacts into icy crusts (Senft & Stewart 2008, Weiss & Head 2015), suggesting that shallow floors and subdued rims can result from slurry inflow during the impact process and do not necessarily imply a climate that supported surface liquid water (Hartmann & Esquerdo 1999). Finally, change is not included – we assume volume balance is proportional to mass balance. The density difference between dense bedrock and less-dense is unlikely to be >15% because the Noachian crust probably had pre- erosion impact-generated porosity (Weiczorek et al. 2013), and because of post-erosion mechanical compaction of sediments.

2.5. Perceived Impact of the Proposed Work. Constraints on the extent and timing of Early and Middle Noachian crater modification are valuable, because the Early and Middle Noachian is a poorly understood, yet important interval, in the history of Mars surface habitability. The Late Noachian / Early Hesperian valley network incision defines a relatively short-lived climatic optimum (Irwin et al. 2002, Irwin et al. 2005, Grotzinger et al. 2014). Was this a “blip” on a long-term trend of climate deterioration, or an oasis preceded by and succeeded by a global desert? The Late Noachian / Early Hesperian can only be put in context by quantifying the relative importance and duration of fluvial erosion (§2.4.1, §2.4.2). If Noachian crater modification lasted >100 Myr as suggested by preliminary work (Fig. 7), this would be much greater than previous lower-bound constraints (Irwin et al. 2015, Hoke et al. 2011).

Determining the duration of crater modification (§2.4.1) would place a valuable constraint on the surface regime corresponding to erosion. For example, if erosion occurred throughout the Late Heavy Bombardment, then maybe impact processes directly or indirectly triggered the erosion (Segura et al. 2013, Urata & Toon 2013), or a clement (habitable), though arid climate was sustained (Craddock & Howard 2002). However, if erosion occurred in a brief window close to the Hesperian/Noachian boundary, then perhaps crater degradation was associated with that runoff optimum.

14 Unscrambling Noachian crater degradation on Mars.

By providing better topographic constraints on Earlier Noachian surface aqueous activity, our work will aid the interpretation of the contested aqueous-alteration record of the Early Noachian crust (e.g., Ehlmann et al. 2011, Tornabene et al. 2013b, Carter et al. 2015). For example, output from reaction-transport alteration codes constraining the timescale for surface Al-phyllosilicate formation via leaching may be compared to our crater-modification timescale results.

2.6. Relevance of the Proposed Work. Our proposed work is within the scope of the Mars Data Analysis Program call, because we will analyze, synthesize and summarize data from the MRO, ODY, and MGS missions and convert it to a form than can be used to constrain physical models of Early Mars processes. The proposed work will thus enhance the return from those missions. Our work directly addresses an open science question, defined by the MEPAG Goals (MEPAG 2015) - “Determine the role of water and other processes in the sediment cycle” (Investigation III.A1.1). It is also relevant to Investigations III.A3.2 (“Characterize surface-atmosphere interactions as recorded by aeolian, […] fluvial, […] mechanical erosion, cratering […]”) and III.A2.2 (“assess the characteristics of Martian craters and document their distribution”).

2.7. Work Plan. Activities/milestones Deliverables • Implement crosscutting-craters chronology ✓ LPSC presentation on: Statistics and analysis of work for quads MC-20, MC-21, MC-22. crater crosscuts.

• Train graduate student on modeling approach ✓ Short GRL-length manuscript on: The duration of for isolated-crater analysis. crater modification on Noachian Mars.

Year 1 Year • Filter isolated craters for process modeling. • Extend duration workflow to quad MC-16. ✓ LPSC presentation on: Variation in rim height /

• Determine how rim-height/floor-fill correlation floor fill relations between quads. relates to distance from volcanic centers. ✓ Detailed manuscript on: The processes of crater

Year 2 Year • Carry out isolated-crater modeling. modification on Noachian Mars. • Determine spatial statistics of craters. ✓ LPSC presentation on: Spatial statistics of crater obliteration versus crater modification. • Analyze modeling results. ✓ Short manuscript on: Synthesis of crater modification and implications for surface processes;

Year 3 Year comparison to Valley Network .

2.8. Personnel and Qualifications. (For FTE information, see §6, Budget Justification). PI Edwin Kite is an assistant professor at the University of Chicago (UChicago). As PI, he will participate to some degree in all aspects of the proposed work and oversee its implementation. Collaborator Alan Howard is a professor at the University of Virginia; Howard will assist with the geomorphic interpretation. A graduate student at UChicago (to be identified) will carry out a substantial portion of the geologic analysis. As a member of PI Kite’s group at UChicago, Planetary GIS/Data Specialist Mayer will produce the crater profiles, determine crosscutting relationships, filter out open-basin craters, and map the output of the modeling onto GIS. All personnel will participate in interpretation of results.

15 Unscrambling Noachian crater degradation on Mars.

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