5.1.1. Evidence for Widespread Erosion on Early Mars
 One of the first observations made from early Mariner data was the Martian craters did not look like those seen on the Moon [Leighton et al., 1965]. To explain the unique morphology of the Martian craters, many subsequent investigators proposed burial by air fall deposits [Hartmann, 1971; Wilhelms and Baldwin, 1989; Grizzaffi and Schultz, 1989; Grant and Schultz, 1990; Moore, 1990]. This interpretation may have been influenced by the prevalence of ongoing eolian processes on Mars, but also by the presence of large air fall deposits in the regions where many of these studies took place (e.g., Arabia [Christensen, 1982, 1986]). The problem with a uniform blanket of material, such as an air fall deposit, lava flow, and even many sedimentary deposits, is that such materials do not explain the size range of modified craters. Typically, these deposits obtain a fairly uniform thickness, and would thus obliterate craters with depths less than the deposit, obscure all but the rims of craters similar in-depth to the deposit, and would only modestly affect deeper, larger craters. This would result in a narrow range of crater diameters with the characteristic flat floor, rimless morphology. Erosional processes, on the other hand, would affect a wider range of crater diameters similarly. A small diameter crater would be eroded to the same general morphology as a larger diameter crater only faster. This scale dependency means that smaller diameter craters may be completely eradicated, which has been argued by Jones  and Chapman and Jones  to explain the deficit in the number of smaller craters observed in size-frequency distribution curves of highland crater populations.
 The emplacement of a contiguous, uniform deposit is also inconsistent with the timing of highland erosion as well as the temporal relation between valley networks and modified impact craters. Although Wilhelms and Baldwin  suggested that valley incision took place after a volatile-rich air fall deposit was emplaced, crater modification was a long-lived process that continued to erode impact craters as they were forming [Craddock and Maxwell, 1993; Craddock et al., 1997]. An air fall deposit emplaced quickly does not explain the stages in crater modification. If it were emplaced slowly over time, then the deposit would quickly bury the smaller valley networks before affecting the larger impact craters; however, both valley networks were clearly forming simultaneously while craters were being modified (Figure 6). Alternatively, Clifford  proposed that highlands craters were modified by liquefaction induced by the seismicity following large impact events. However, such an erosional mechanism would simultaneously destroy the smaller valley networks, and this is clearly not the case. More recently, Malin and Edgett  proposed that erosion, deposition, and impact cratering occurred simultaneously, resulting in a complex interbedding of craters and previously exposed surfaces. However, they do not identify the erosion mechanisms or the scale that the resulting “heavily cratered volume” would become important. Their model appears to explain large layered deposits in the highlands that are fairly isolated [Malin and Edgett, 2000a] as well as exhumed craters tens of meters in diameter, but not the modified morphology of larger diameter craters that are prevalent throughout the highlands. From the analysis of crater populations in the Martian highlands, we proposed that only an erosional process, most likely fluvial, could explain the morphology and the size-range of affected craters (2 km to basin size impacts) [Craddock and Maxwell, 1990, 1993; Craddock et al., 1997].
5.1.2. Timing and Stages of Crater Degradation
 Detailed analyses of crater modification in the Martian highlands have been presented for the cratered (Npl1) and dissected (Npld) highland geologic units defined at the 1:15M-scale [Scott and Tanaka, 1986; Greeley and Guest, 1987] and located between ±30° latitude [Craddock and Maxwell, 1990, 1993; Craddock et al., 1997]. Fresh craters in these materials were identified by their well-defined raised rims, hummocky floors with central peaks or pits, and obvious ejecta deposits (Figure 7a). Because fresh impact crater populations can be useful in estimating the time at which crater modification ceased and the highland surface became stable, these data were binned by geologic unit, latitude, and the elevation data available at the time and, by convention, normalized to 1 million km2 so that N[X] = number of craters > [X] km diameter per 106 km2. Although there was no relation between cessation and latitude, fresh crater populations suggest that highland crater modification operated from the end of heavy bombardment (N(5) = 359 ± 26) through the early Amazonian (N(5) = 35 ± 8), which correlates well with the timing of valley network formation [Dohm and Scott, 1993].
Figure 7. Stages in crater modification can be seen in these images. (A) Fresh craters have sharp central peaks with hummocky ejecta and rim deposits. (MOC image M0900776.) (B) During the initial stages of modification, the central peak is quickly eroded and buried. Often the ejecta becomes incised by valley networks and the interior walls of the crater develop gullies. (MOC image M0901754.) (C) Although the central peaks and ejecta have been removed, some craters appear to have been “smoothed” or “softened.” Viking-based analyses suggest that such craters represent a style of modification that occurred later in Martian history. (MOC image M1700974.) (D) During advanced stages of degradation, the rim of the crater is nearly completely removed and the craters become progressively infilled. This leads to the classic flat-floored, rimless morphology (arrows). (MOC image M0807597.) (MOC image M0900776.) (E) Frequently flat-floored, rimless craters become breached by valley networks. (F) Eventually the craters become heavily eroded and buried, producing a “ghost” crater (arrows). (MOC image M0700832.) Analyses of such modified impact craters indicate that rainfall occurred early in Martian history.
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 Many modified highland craters lack obvious ejecta deposits, suggesting that such materials were easily eroded. The remaining crater ejecta appears etched or hummocky and is frequently dissected by valley networks (Figure 7b) [Masursky et al., 1977; Gurnis, 1981; Craddock and Maxwell, 1993]. Valley networks occur frequently on the continuous ejecta of larger impact craters (>∼40 km) and often form extensive radial drainage patterns. However, not all modified craters have incised ejecta (Figure 7c). As explained below, such craters may represent a temporal difference in the degradational process. The smooth floors also associated with most craters in the early stage of degradation indicate that central peaks were eroded and/or buried quickly. Crater interiors are often dissected by numerous parallel valleys that terminate at the crater floor. These features closely resemble the debris chutes associated with terrestrial impact structures in the early stages of dissection (e.g., Meteor Crater [Grant and Schultz, 1991c]). Crater rims also became lower and generally more rounded.
 As degradation progressed the crater rims were removed by both continued downward erosion and interior backwasting. This results in the characteristic flat-floored, rimless crater morphology (Figure 7d). By balancing the mass loss from backwasting and infilling at a variety of crater diameters and stages of degradation, crater diameters were estimated to have been enlarged by ∼10% initially and by as much as ∼30% during the terminal stage of degradation [Craddock et al., 1997]. Similar amounts of enlargement have been estimated from analyses of terrestrial craters with similar degraded morphology [Grant and Schultz, 1993]. Only craters <∼60 km in diameter seem to have been modified extensively by such extreme erosion and backwasting [Arvidson, 1974; Craddock and Maxwell, 1993]. Infilling dominated in the late stages, perhaps depositing as much as ∼60 m of sedimentary material in the interior of rimless craters in the Sinus Sabaeus and Margaritifer Sinus area [Craddock et al., 1997]. Extreme deposition in other areas produced very shallow “ghost” craters which appear to be almost completely buried (Figure 7e). Crater walls that remain are steep-sided and contain interior gullies. In particular, smaller diameter craters (<20 km) appear to have been completely modified or eradicated [McGill and Wise, 1972; Craddock and Maxwell, 1990, 1993].
5.1.3. Crater Infilling
 The recent availability of detailed topographic information from the Mars Orbiter Laser Altimeter (MOLA) permits precise measurements of crater morphology and a reexamination of modification processes. Determining the types of processes responsible for crater infilling is of particular interest because of the geomorphic evidence suggesting that many contained paleolakes [Cabrol and Grin, 1999] and morphometric analyses suggesting they acted as sediment sinks [Craddock et al., 1997]. Typically, the processes responsible for crater degradation caused a significant decrease in overall crater depth simply by eroding the crater rim, predominately through backwasting [Craddock et al., 1997]. Once the crater rim has been completely eroded, there is no longer a topographic obstruction preventing material eroded from the surrounding landscape from being transported into the crater. Thus, contrary to suggestions by Malin and Edgett , we have remained conscious of the possibility that material within modified impact craters may have resulted from erosion of neighboring terrain [Craddock and Maxwell, 1993; Craddock et al., 1997]. As an example, Figures 8a and 8b compare a modified crater with one at a similar diameter but at the terminal stage of degradation. MOLA data reveal that the degree of infilling during the terminal stages of degradation is often dramatic.
Figure 8. Massive erosion and infilling are evidenced by this group of craters on the border of the Sinus Sabaeus quadrangle centered at −21°, 317°. (A) The two largest craters are both ∼55 km in diameter and have undergone appreciable modification. (B) However, MOLA data show that the western crater has been infilled by perhaps as much as ∼1 km of material. Either it has experience extensive backwasting or sediments were transported from the surrounding terrain. It is unlikely volcanic infilling has take place since such deposits should fill surrounding craters to the same level [Howard, 1999; Howard and Craddock, 2000].
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 Using MOLA data, we quantified the amount of infilling by measuring the depths of both fresh and degraded craters >10 km in diameter in the parts of the Iapygia and Margaritifer Sinus regions of Mars (Figure 9a). Only MOLA tracks crossing close to the center of craters were utilized. Fresh craters were defined as those exhibiting primary texture on the ejecta blankets and little or no presence of smooth interior crater deposits. Degraded craters were conversely defined to have no obvious primary ejecta morphology and to have smooth interior deposits. To better evaluate the processes infilling degraded craters, we did not include any craters that were breached by channels. Calculation of crater depth utilized the average of the highest points on the two crossings of the MOLA track. For comparison, Figure 9a also shows summary relationships for fresh crater depth previously derived using photoclinometry [Craddock et al., 1997] and global analysis of MOLA Digital Elevation Maps [Garvin et al., 2000], as well as the relationship for craters in increasingly advanced stages of degradation [Craddock et al., 1997]. The greater average depth of fresh craters in the present study may be influenced by the fact that most MOLA profiles do not precisely pass along the crater center, and thus underestimate the crater diameter. Degraded craters are generally at least 500 m to as much as 3000 m shallower than fresh craters at equivalent diameters (Figure 9a). A small amount of shallowing can be attributed to erosional lowering of the crater rim. In addition, extensive backwasting often makes it difficult to determine the diameter of the crater prior to modification (i.e., its initial, fresh diameter). A smaller diameter crater is inherently shallower prior to backwasting. Nevertheless, much of the change in-depth must be the result of crater infilling [Craddock and Chuang, 1996; Craddock et al., 1997].
Figure 9. Geometric properties of Martian craters and terrestrial fan and basin deposits. (A) Plot of crater depth (from rim to crater floor) versus crater diameter for fresh and degraded craters. Measurements made from MOLA data in the Margaritifer Sinus and Iapygia regions of Mars. Summary depth/diameter relationships for relatively unmodified craters are from Craddock et al.  “Craddock Fresh,” based upon photoclinometric techniques and from MOLA DEM data “Garvin Fresh” from Garvin et al. . Also shown are summary relationships for moderately degraded craters of class B and C “[b/c]” and for highly degraded craters “[e]” from Craddock et al. . A plot of the temporal change of crater depth and crater diameter is shown for simulated dissection of a 50-km crater (see Figure 11). (B) Plot showing the relationship between the average gradient of the inward-sloping surfaces of degraded crater floors (e.g., Figure 10) and the average gradient of the corresponding interior crater rim, from measurements made from MOLA profiles. Also shown are the gradients of alluvial fans in the Southwestern United States plotted against the average gradient of the source mountains (from mountain crest to fan head), as well as a similar relationship for lower-gradient alluvial basins in the United States. The terrestrial data is from topographic maps and 1:250,000 DEM data. (C) The relationship between the concavity of Martian degraded crater floors and the gradient of the crater floor, as well as corresponding data from terrestrial fans and basins. (D) The total relief of Martian degraded crater floors (from the base of the interior crater wall to the center of the crater) is plotted versus crater diameter.
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 Appreciable amounts (hundreds of meters) of post-Noachian eolian infilling are unlikely. MOC images show that eolian deposition and scour in craters occurs in spatial patches considerably smaller than the size of large basin floors [Edgett and Malin, 2000]. Air fall deposition during the Noachian may have included planet-wide deposition of ejecta and volcanic ash, as well as eolian deposition [Grant and Schultz, 1990, 1991a, 1991b]. However, the preservation of channels and persistence of crater rims and unburied intercrater uplands indicates that if extensive air fall deposition occurred, such deposits would have had to be subsequently eroded and transported by other processes to contribute appreciably to crater infilling. Also, Edgett and Malin  noticed that dark regions (e.g., Syrtis Major) do not appear to be capable of “cleaning themselves” of bright dust following a global dust storm as suggested by Christensen , which may indicate that there is no homogenous, planet-wide fall-out of eolian material today.
 MOLA data indicate that a number of craters and basins with diameters of ∼100 km or greater have flat floors (e.g., Dawes at −9° lat., 322° long, Figure 10). Occasionally these basins also contain wrinkle ridges (e.g., Flaugergues at −17° lat., 341° long.). Lava infilling is a plausible explanation, either from eruptions from within the crater or from flows breaching the crater rim from elsewhere. However, because sources for lava flows are generally isolated, lava infilling is unlikely to account for the nearly symmetrical profiles of the majority of degraded craters <60 km in diameter (Figures 9b and 11b–11e). It is also important to note that wrinkle ridge formation can occur in sedimentary deposits [Watters, 1988], so such features are not diagnostic of lithology. Also, the highly dissected interior crater rims indicate that at least some of the interior crater deposits are of fluvial origin. Lava flows may have contributed to large basin infilling, but the final stages of infilling appear to be fluvial, as discussed below. Because of the discrete number of lava sources, volcanic infilling would be a plausible candidate if future work indicates that depths of infilling do not vary systematically with crater size.
Figure 10. The 180-km-diameter crater Dawes. (A) A portion of MDIM quadrangle MI10S322 showing the track of MOLA orbit 10922. (B) The MOLA topographic data showing the flat-floored crater floor with less than 100 m of relief. Vertical exaggeration is about 44X.
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Figure 11. The results of a 50-km-diameter crater that has been eroded using the computer model of Howard [1994b]. In these simulations the erosion rate is limited by a finite rate of weathering of the host rock. (A) A simulated 50-km fresh crater. (B) Degraded crater corresponding to modification stage in Figure 7b. (C–D) Advanced stages of degradation. Note the increase in crater diameter due to backwasting. (E) Topographic profiles through the center of the crater showing advanced stages of degradation. Vertical exaggeration is about 18.3X. Compare with Figure 12.
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 Besides a common flat floor, most degraded craters have nearly symmetrical, inward-sloping floors with gradients of 0.005 to 0.02 (Figures 9b and 11b–11e). Fluvial erosion and sedimentation appear to be the most likely processes to have produced these fan-like deposits. The channeling of inner crater walls (e.g., Figure 10a) also requires an advective process, such as fluvial incision or rapid, presumably wet, debris avalanches [Howard, 1994a, 1994b]. In addition, the sediment eroded from crater walls had to be carried several tens of kilometers to produce the smoothly graded crater floors, and again fluvial transport is the most likely mechanism. MOLA data allow this fluvial interpretation to be evaluated both by comparing basin slopes and profile shapes with terrestrial basin deposits and through simulation modeling of fluvial crater degradation.
 Two properties of the crater floor morphometry can be compared with terrestrial basin deposits (pediments, fans, bajadas, and playas). These are the gradient and the profile concavity. The average basin gradient is measured from the base of the crater wall, which is usually an abrupt break in slope at the inner edge of the lower gradient crater floor, to the center of the crater. On terrestrial fans and basins gradients were measured from the basin fill-mountain contact to the basin center, the inner edge of playas, or through-flowing streams, whichever was closest to the mountain. These data were derived from topographic maps (at scale ranging from 1:24,000 to 1:250,000) and ∼90 m DEMs at 1:250,000-scale. Locations were selected where the mountain front was nearly linear and flow into the basins was neither strongly convergent nor divergent. For Mars craters, the basin source area was defined as extending from rim crest to the bottom of the crater wall. For terrestrial basins the source area was defined from the drainage divide to the head of fluvial fans/basin fills.
 Average gradients of Martian degraded crater floors are lower than alluvial fans in the Basin and Range and Mojave Desert region (“Earth Fan”, Figure 9b), but are equivalent to low gradient fans and basin fills in humid environments (“Earth Basin”, e.g., the Rocky Mountain-Great Plains transition, fans in the Shenandoah Valley), and alluvial fans in low relief basins in Arizona. Low gradient terrestrial basin fills can result from high water to sediment ratios (e.g., humid climate or low sediment delivery rates) or fine-textured sediment (sand and finer sediment rather than gravel). In addition, the lower Martian gravity can result in a 0 to 40% decrease in gradient for equivalent water and sediment supply, depending upon whether threshold, bed load, or suspended load conditions apply (A. D. Howard, in preparation). Furthermore, water flow into the interior of craters is strongly convergent, which may result in greater discharges and lower gradients as compared to nonconvergent flow. The average gradient of both terrestrial fans/basins and Martian crater floors exhibits a moderate positive correlation with the average gradient of the source region (interior crater wall for craters, the source mountains for terrestrial fans/basins) (Figure 9b).
 The long profile concavity of fans and crater floors was measured by fitting an exponential downstream decrease in gradient
where S is gradient, x is the distance from the crater rim (or mountain crest), K is an estimated constant, and b is the estimated concavity. Both terrestrial basin deposits and Martian degraded crater floors exhibit similar concavity (Figure 9c), again suggesting a similarity in emplacement mechanisms. Crater floor concavity could also be the result of differential compaction or dissolution of interior fill deposits, however. The average relief from crater floor edge to crater center for 28 measured craters (15–90 km in diameter) is 140 m. Based upon estimated crater fill depths (Figure 9a), >10% decrease in volume would be required to result in the observed concavity, which does not seem reasonable. Concentric fractures commonly occur at the margins of basin fills which have undergone appreciable downwarping (e.g., in the lunar mare [Maxwell, 1978]). None are apparent in Martian crater fills. With the notable exception of the occasional basin containing wrinkle ridges, there is little evidence for interior compression that should also occur with appreciable downwarping [e.g., Muehlberger, 1974].
 The inward sloping fan-like surfaces forming the floor of degraded craters <60 km in diameter seldom exhibit flat central regions that might correspond to the playa lake beds in interior-drained desert basins of the southwestern United States. This could indicate that the sediment eroded from crater walls had little material in the silt and clay size range that would have been carried in suspension to be deposited in temporary lakes. Another possibility is that precipitation levels were sufficiently high that lakes of appreciable (but variable) depth occupied crater interiors during the epoch of crater degradation. Channels debouching into such lakes would extend a variety of distances into the crater interior depending upon existing lake levels. The effect that lakes varying in-depth would have upon the morphology of crater floors is uncertain. Shorelines and deltas might not survive subsequent eolian reworking and small impact gardening if lake levels were highly variable; Pleistocene lake basins in the Basin and Range Province of the United States that lack an outflow sill controlling lake level have numerous poorly developed shorelines over a wide range of lake depths. A few Martian highland craters exhibit symmetrical interior terraces, and a lacustrine origin for such terraces has been suggested [Forsythe and Zimbelman, 1995; Cabrol and Grin, 1999]. Lacustrine processes may be an alternative to lava inundation as an explanation for large flat-floored craters, such as Dawes (Figure 10). Because of the great initial depth of large crater basins, they would have preferred sites for intermittent or perennial lakes.
 To evaluate the affects of infilling on crater morphology and morphometry, a spatially explicit computer model has been developed to simulate landform evolution on the ancient cratered terrain of Mars [Howard, 1994a, 1994b; Craddock et al., 1997; A. D. Howard, in preparation]. The model includes the processes of cratering, weathering, mass wasting, fluvial erosion and deposition, and eolian erosion and deposition. For the present discussion, only weathering, mass-wasting, and fluvial erosion and deposition are utilized to simulate modification of a 50 km fresh crater (Figure 11). For this simulation rainfall and surface runoff are assumed to be areally uniform, and the crater is assumed to be composed of bedrock that weathers at a finite rate into regolith that is 10 times more erodible. Fluvial erosion concentrated at the base of the crater wall causes backwasting of the crater walls and deposition of a crater basin fill with concave profile. Additional simulations with other process assumptions are presented by A. D. Howard (in preparation), but the general pattern of strong interior crater wall erosion and radial infilling by deposited sediment is characteristic of all simulations, and the simulated morphology bears a striking similarity to degraded Martian craters.
 Figure 9a shows the path of change of crater diameter and depth for the simulation shown in Figure 11. The curve is jagged because measured crater diameters are quantized by the 0.4 km grid spacing used in the simulation. Because of the bowl-like shape of fresh crater interiors, crater depth diminishes more rapidly in early stages of degradation than during later stages (Figure 9a). For a 50 km crater the modest B/C stage of degradation corresponds to about 0.9 km reduction in-depth and about a 10% expansion of diameter. The highly degraded E stage corresponds to about 1.3 km reduction in-depth and a 20% increase in diameter. These figures are close to the estimates reported by Craddock et al. . The simulations indicate that crater diameter increases nearly linearly with time, assuming temporally constant intensity of fluvial erosion, so that a crater near the terminal stage of degradation (stage E) has undergone about twice the duration of modification as a crater with modest amounts of degradation (stage B/C). The scattering of very shallow degraded craters lying well below the line denoting terminal degradation (stage E) have extreme amounts of sediment infilling, possibly from channels debouching into the crater interior, or extensive, local accumulations of eolian or volcanic materials.