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Decline of crater obliteration rates during early martian history
Icarus 317 (2019) 427–433
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Decline of crater obliteration rates during early Martian history a,⁎
b
a
a
C. Quantin-Nataf , R.A. Craddock , F. Dubuffet , L. Lozac'h , M. Martinot
T
a
a Laboratoire de Géologie de Lyon, Terre, Planètes, Environnement (Université de Lyon- Université Claude Bernard lyon1-CNRS-ENS Lyon), ERC eMars Team, 2 rue Raphaël Dubois 69622 Villeurbanne Cedex, France b Center for Earth and Planetary Studies, National Air and Space Museum, Smithsonian Institution, Washington, District of Columbia, USA
A B S T R A C T
A change in the global climate on early Mars is suspected from the geologic evidence of warmer wetter conditions that prevailed during the Noachian but stands in contrast to the dry and cold conditions observed currently. However, the timing and evolution of this climatic change represents a gap in our understanding of the history of Mars. Here, we document the time-dependence of the crater obliteration rates on Mars that decreased continuously between 3.8 Ga and 3 Ga. Our results indicate that the erosion responsible for crater modification and obliteration declined gradually through the Noachian and into the Hesperian periods. These results suggest that the climatic conditions also changed gradually and the amount of water available on the surface of Mars slowly decreased over time.
1. Introduction Understanding the nature and types of surface processes on Mars over time is essential for constraining the climatic evolution of the planet. Long-term crater degradation analyses have revealed that erosion rates in the Amazonian are about 0.01 m/My (Golombek et al., 2006), which is at least two orders of magnitude lower than the erosion rates estimated in the Noachian (about 1 m/My) (Craddock and Maxwell, 1993). The differences in erosion rates between the Noachian and Amazonian may be that liquid water was the main erosional agent during the Noachian, and this was followed by a drier Amazonian climate where aeolian processes are dominant (Mangold et al., 2012; Golombek et al., 2014; Kreslavsky and Head, 2018; ). However, the evolution from erosion-intensive wet conditions to the current dry and cold Martian climate where erosion is limited is not well understood. In particular, it is not clear whether Noachian conditions suddenly collapsed or if erosion rates waned gradually over time. Impact craters are ubiquitous features that have formed continually throughout the entire history of Mars, so by analyzing their size frequency distributions it is possible to assess the integrated history of impacting objects as well as the processes that have modified the surface. Assuming that the theoretical crater size distributions are the natural result of meteoritic bombardment are correct, any variations from these theoretical crater size distributions would indicate resurfacing by other geologic processes (e.g., Werner, 2009; Kite et al., 2013; Platz et al., 2013). One-time events, such as lava emplacement, would have a much different effect on the crater size distribution than a longlived process like erosion or aggradation. One-time events led to a distribution that is stepped as opposed to the theoretical straight-line
⁎
function, while long-lived processes lead to broader, flatter distributions (e.g., Hartmann, 1971). Since spacecraft observations began with the Mariner missions, it has been known that large Martian impact craters have been modified, and that many craters smaller than 60 km have been deleted from the cratering record (Hartmann, 1971; Chapman and Jones, 1977). The fact that craters are preserved at different stages of modification at different diameters indicates that the modification processes continued as new craters were forming (Chapman and Jones, 1977; Craddock and Howard, 2002; Mangold et al., 2012). Now, thanks to decades of orbital missions and higher resolution imagery, we have a complete inventory of Martian craters down to ∼1 km (Robbins et al., 2012), and coupled with global Martian geological map (Tanaka et al., 2014) it is possible to derive the crater size distribution of each era of Mars’ history or each geological unit (Irwin et al., 2013). If we do so for all Noachian terrains, craters larger than 60 km follow the Martian >4 Ga isochron, which is defined as the theoretical crater size distribution of an undisturbed surface 4 Ga; Intermediate crater size-frequency distributions for diameters from 4 km to 64 km have a clear flatter slope than isochrons well highlighted in incremental diagrams; And small craters connect to a younger isochron, typically Hesperian in age (Fig. 1). The fact that crater distributions over several size bins is flatter than the isochrons and below the saturation line implies that there was a continuous process of crater degradation over time that ceased or changed in magnitude at an age reflected by the smallest craters located at the bend (Hartmann, 1971; Chapman and Jones, 1977). Fig. 1 is based on the Hartmann (2005) crater production distribution, but a similar deviation is observed when compared to others crater production functions (see Supplementary material).
Corresponding author. E-mail address: [email protected] (C. Quantin-Nataf).
https://doi.org/10.1016/j.icarus.2018.08.005 Received 24 January 2018; Received in revised form 30 July 2018; Accepted 2 August 2018 Available online 15 August 2018 0019-1035/ © 2018 Elsevier Inc. All rights reserved.
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Fig. 1. (A) Three different crater obliteration evolution models over the last 4 Gy. Blue shows no obliteration. Red represents a first period of intense crater obliteration followed by a period with no obliteration. Green represents moderate but constant crater obliteration during 4 Gy. Martian eras (Werner and Tanaka, 2011) are plotted respectively in green for Noachian periods (MN for Mid Noachian and LN for Late Noachian), purple for Hesperian periods (EH and LH for Early and Late Hesperian), blue for Amazonian periods (EA, MA, LA for Early, Middle and Late Amazonian). (B) The synthetic crater size distribution produced by the models presented in A in a Hartmann incremental diagram (Hartmann, 2005; Hartmann and Neukum, 2001); The model in blue with no crater obliteration reproduces the 4 Ga isochron as expected. The model in green with moderate crater obliteration but that is held constant over the last 4 Gy produces a drop in the population of craters smaller than 43 km. The red model produces an distribution similar to the one observed in C for the entire Noachian terrains on Mars. Note that scaling law linking the crater diameter to its depth used in the model is plotted in Fig. 2B. (C) Crater size distribution of the entire Noachian terrains. We used the craters from Robbins and Hynek (2012) that lie within Noachian units defined by Tanaka et al. (2014) to obtain this distribution. The crater size distribution of the Noachian terrains shows a S-shape typical of individual Noachian units. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
(Hartmann, 2005; Hartmann and Neukum, 2001). Thus n is a function of two separated variables n(D,T) = f(D)N(T). N(T) is the accumulated number of craters larger than 1 km per unit area and is defined as follow (Neukum et al. 2001):
Here, we present a simple numerical model used as a tool for determining how the rate of crater modification may have changed over time. We use this model to explain the observed deviations in crater size distributions to crater production for the entire population of Noachian craters, as a test case. The method was then applied to 33 individual areas on Mars. Because these 33 areas are of different ages, the results we obtained can provide constraints on the time-dependence of the crater obliteration rate over time on Mars. The results have implications for the climatic evolution of Mars.
ND > 1 km (T ) = 5.44*10−14 (e6.93T − 1) + 8.38*10−14T
(1)
N′, the derivative of N, is the impact rate:
N ′D > 1 km (T ) =
dND > 1 km (T ) = 3.77*10−13e6.93T + 8.38*10−14 dT
(2)
The time evolution of the crater density is modeled according to the following equation:
2. Method
∂T n (D , T ) = f (D) N ′ (T )
To assess the crater obliteration rates, we simplified the erosion/or infilling of craters to a 1D process. The evolution of the crater depth (d) with time (t) can be described as following: Δd/Δt. Our goal was not to assess the amount of crater erosion or the amount of infilling; accurately describing such processes would require much more than a simple 1D decrease in crater depth. Rather, our goal was to retrieve the time dependence of crater obliteration processes.
(3)
The crater size distribution f(D) is calculated by dividing a Martian isochron at time T from (Table 2 in Hartmann, 2005) by N(T). The initial condition is n(D, T = 0) = 0. This equation is then integrated between T and T + ΔΤ:
N (D , T + ΔT ) = n (D , T ) + f (D)[N (T + ΔT ) − N (T )]
(4)
where f(D)[N(T + ΔT) − N(T)] is the number of craters added during the time step ΔT. To model the obliteration history of craters within our study areas, we used the concept of lifetime of an impact crater (Jones, 1974). Basically, because depth increases as a function of crater diameter, larger diameter craters will take longer to eradicate completely. In our model, at each time step ΔT craters were added only if they had a depth large enough to survive through the total amount of erosion that would occur during the remaining obliteration history. We convert the remaining time of obliteration to a maximum depth of obliteration z (in km) using a time-dependence of obliteration υ (in km/Gy):
2.1. The model We constructed a simple numerical model that generates synthetic crater size distributions simulating impact crater production and crater obliteration. The design for the model is described below. Our model for the impact rate evolution begins by assuming that the crater density of a planetary surface n(D,T) is the number of craters per unit area (in km2), where D (in km) is the crater diameter and T (in Gy) is the age of the surface. This crater production function is generally assumed to have the same time dependence for all diameters 428
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Fig. 2. Inversion of the crater size distribution of Noachian terrains. (A) presents the crater obliteration rate evolution that produces the synthetic crater size distribution with the best goodness of fit plotted in blue in the incremental diagram C. Martian eras (Werner and Tanaka, 2011) are plotted respectively in green for Noachian periods (MN for Mid Noachian and LN for Late Noachian), purple for Hesperian periods (EH and LH for Early and Late Hesperian), blue for Amazonian periods (EA, MA, LA for Early, Middle and Late Amazonian). (B) presents the depth vs. diameter dependence used in the model. We used the scaling law published by Garvin et al. (2003) for simple (purple points) and complex craters (green points). For the crater diameter bin at the transition between simple and complex crater (yellow), we used the average between the lower and the largest size bin. The red point in C represents the crater size distribution of the Noachian terrains obtained by extraction from the crater database from Robbins and Hynek (2012) contained in the terrains mapped by Tanaka et al. (2014) as Noachian. The best fit model is plotted in blue and implies a first period with a crater obliteration rate of 3.5 m/My from 3.99 Ga to 3.46 Ga. We note that this best fit reproduces the shape of the Noachian crater size distribution. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
z (T ) =
∫0
T
υ (t ) dt
(Ivanov, 2001) because the Neukum production function curve shape is different from Hartmann's, particularly for crater diameters of 4–60 km, the range where we observe a deviation to the theoretical crater production. Whatever the production function used in our model, the same results are observed (see Supplementary material). Additionally, Forsberg-Taylor et al. (2004) have shown that crater infilling rates from fluvial processes decreases as erosional modification advances because the crater wall height decreases and the depositional area increases due to backwasting, slope relaxation, and crater enlargement. Simply stated, the rate of infilling changes as the crater continues to be eroded, but our model does not take this into account. To do this accurately would require us to vary the infilling rate according the degradation state of each individual crater. Our goal is to simply explain how impact craters may go missing when compared to a theoretical distribution. This assumption may lead us to underestimate the rate of crater obliteration in case of fluvial erosion. Finally, our model is only 1D in that it includes only one space dimension: crater depth. We infill craters until their entire depth has disappear at which point they are considered “obliterated.” Small craters will be obliterated faster than larger ones because they are shallower. Other dimensional effects from crater modification (e.g., crater enlargement due to backwasting; Craddock et al., 1997) were also not considered.
(5)
where z is the crater depth that can disappear during a time T. Thus, the crater density n varies during ΔT (Eq. (4)) only if the depth of the crater to be added is greater that z(T). To scale crater depth to diameter, we used the following scaling relationships for simple and complex craters (Garvin et al., 2003): when D < 4 km, we use d = 0.21 × D0.81 which is the relationship for simple craters. When D > 5.66 km, we use the formula for complex craters, d = 0.36 × D0.49. In both equations, D and d are in kilometers. For the transitional diameter bin between 4 and 5.66 km, as the crater population is a mixture between simple and complex craters (Robbins and Hynek, 2012), we use an average between the depth of the diameter bin between 2.83 and 4 km and the depth of the diameter bin between 5.66 and 8 km. Fig. 2B displays the depth to diameter relationships we used in our simulations. Both equations (cratering rate and obliteration rate) were integrated from 0 to T with a time step of 1 My. 2.2. Assumptions behind the model The use of the model requires making several assumptions. First, we assume that the shape of the production function curve does not change through time; however, the total rate of crater production does decrease. This has been validated by several studies of the lunar surface (Neukum et al., 2001). This assumption has also been made by other studies using crater chronology techniques to assess Martian ages. It is important to note, however, that several production function curve shapes have been published (Neukum et al., 2001; Michael and Neukum, 2010). Here we use the Hartmann (2005) production function, but we also did tests with the Neukum production function
2.3. Tests of the model The qualitative explanation for the observed Noachian deviation of crater size distribution between craters larger than 64 km which align with the 4 Ga isochron and the crater smaller than 4 km which align with 3.5 Ga (Fig. 1) is that there was a continuous process of crater 429
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sizes of these areas range from 105 to 106 km2, which is large enough to contain statistically viable impact crater populations ≥60 km in diameter while still being located in contiguous geologic units (Tanaka et al., 2014). We applied the same approach in applying our model to these additional areas as we did previously for the whole Noachian crater size frequency distribution. Only 34 areas returned a satisfying and unique Goodness of Fit (Fig. 3). The Goodness of fits of these 34 area range from 0.42 to 6.91. But most importantly, they all correspond to clear minimum Goodness of Fit (see Extended Fig. 2C). Most of the extracted distributions display a complex crater size distribution with stepped parts indicative of short-lived or one-time resurfacing events (e.g., volcanic resurfacing) which may be common for much of the surface of Mars (e.g., Platz et al., 2013). These stepped distributions suggest more complex geological histories where the use of our simple obliteration model cannot be applied adequately, as demonstrated by our inability to return a satisfying and unique Goodness of Fit. The excluded areas are located mainly around the large volcanic provinces (e.g., Northern plains, Tharsis region, Tyrrhena Paterra, and Syrtis Major) where the volcanic resurfacing is expected (see Supplementary material). The 34 areas with a clear returned minimum GF have a wide range of age from 4.17 Ga to 3.34 Ga (From Early Noachian to late Hesperian). But most of them are located in Noachian terrains (Fig. 3). This is explained by the fact that most of Hesperian and Amazonian large units are volcanic units and thus have very complex crater distributions where our model would not be appropriate. The time at which the change in the magnitude of the crater obliteration rate occurred varies from 3.63 Ga to 960 Ma. Fig. 3B plots the results of the best-fit evolution of the crater obliteration rate for the 34 areas in dark lines. Red points correspond to the crater obliteration rates of each first period vs. the average age of each first period. Interestingly, both dark lines and red points display a steady decrease of the crater obliteration rate over one order of magnitude from 3.8 to 3.0 Ga corresponding to the middle/Late Noachian to the end of Hesperian based on ages from Hartmann, (2005) and timescale from Werner and Tanaka (2011). Spikes or sudden decreases in the crater obliteration rates are not observed over this time period. The values of obliteration rates decrease from 6 m/My at 3.8 Ga to 0.6 m/My at 3.16 Ga, recalling that these values are for 1D crater obliteration rates. Given that the crater modifications processes are often complex and the assumptions involved in our model, these values do not directly correspond to actual erosion rates. However, we could expect that they could be similar. Our results show that 1D crater obliteration rate is a powerful tool in revealing the time dependence of erosional and resurfacing processes. The time-dependence presented in Fig. 3B is well constrained from 3.8 Ga to 3 Ga where many inversions have been done and these inversions have about the same duration of the initial phase of high crater obliteration rates. However, after 3 Ga, only 2 crater size distribution inversions support the results and require longer initial periods of erosion (>2 Ga) where underestimating the returned obliteration rate may be influenced by the Sadler effect. The Sadler effect states that measured sedimentary rates systematically decrease with measurement duration, which is explained by the intermittent nature of sedimentary processes that leads to gaps in the stratigraphic record (Sadler, 1981). So only obliteration rates integrated over the same range of time can be compared. But this effect should not be important as even in the younger areas we analyze the duration of the obliteration event is the same order of magnitude. The Sadler effect becomes a larger issue when comparing processes that occurred over time periods that different by several orders of magnitude. This effect is also referred as the timescale bias. Efforts to quantify this effect have been done for Martian erosion rate analyses (Golombek et al., 2014). There is a clear effect on the deduced erosion rate according to the spam time over which the erosion rate is calculated. It can be noted that the obliteration rate at 3.16 Ga is still one order of magnitude larger than the current erosion rate estimated from lander
obliteration between 4 Ga and 3.5 Ga that ceased or changed in intensity at 3.5 Ga (e.g., Hartmann, 1971; Chapman and Jones, 1977). We tested various rates of crater obliteration in order to reproduce the shape of the observed deviation at the 4 Ga isochron observed in Noachian craters. The tests we conducted included: (1) no crater obliteration, (2) a constant rate obliteration over 4 Gy, (3) a linear decrease of crater obliteration with time and (4) an old period with large crater obliteration rate followed by a second period with reduced crater obliteration rates (Fig. 1A and B). Fig. 2C shows that only the 4th model with 2 distinct periods of crater obliteration can explain, to first order, the observed shape of the Noachian crater size frequency distribution and the deviation observed at 4–64 km diameter craters. These results imply that there was an abrupt change in the obliteration rate at the end of the Noachian, so we decided to use this two-phase model of crater obliteration to analyze the other crater size distributions. 2.4. Inverse approach We applied an inverse method to determine the two-phase evolution model of crater obliteration v(t) that best fit the observed crater size frequency distributions. The two-phase model of obliteration rates requires four parameters: the age of the surface, the age of the obliteration rate change, and the obliteration rates for both periods. For a given deviated crater size distribution, the age of the surface is deduced from the populations of the large impact craters that follow the isochron slope with a precision of 0.01 Gy using the age system of Hartmann (2005). The age at which the sharp change in obliteration rate occurred is deduced from the populations of the smallest impact craters that follow a younger isochron also with a precision of 0.01 Gy. For each inversion, we fixed the rate of obliteration of the latter stage at 0.01 m/ My, which is the Amazonian erosion rate as estimated in situ by rover data (Golombek et al., 2006). The only free parameter is the rate of obliteration of the oldest period of crater obliteration. We varied this free parameter by increments of 10−1 m/My while returning a goodness-of-fit (GF) defined as the following sum of differences between the model and the observed data:
GF =
∑
(Nmodel − Ndata)2 (σdata)2
for σdata < Ndata
where Ndata is the number of measured craters in each diameter bin, Nmodel is the number of craters predicted by the model for each diameter bin and σdata is the Poissonian error bar, calculated as the square root of the total number of measured craters. Once a minimum GF was found the corresponding value of obliteration rate of the first period was recorded. For each best two-phase obliteration model presented in Figs. 2 and 3, a minimum GF is clearly found as a unique solution, returning the obliteration rate of the old period with a precision of 0.1 m/My. 3. Results Fig. 2 illustrates the best-fit models that reproduce the shapes of the crater size frequency distributions for all terrains Noachian in age. The average age of the surface deduced from the crater size distribution is 3.99 Ga (Early Noachian times; Werner and Tanaka, 2011), and the age deduced by craters smaller than 4 km is 3.46 Ga (Early Hesperian times, Werner and Tanaka, 2011). By applying the obliteration rate at 0.01 m/ My after 3.46 Ga, the results of the best-fit model return an obliteration rate of 3.5 m/My between 3.99 and 3.46 Ga. This indicates that the rate of crater obliteration during early Mars was more than two orders of magnitude greater than it is today. This result presents the average rate of crater obliteration during the Noachian and can be used as a proxy for the average surface erosion rate during this time. To determine if the crater obliteration rate changed over time, we extracted crater size frequency distributions for more than hundred large areas on Mars from various places located all over the planet. The 430
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Fig. 3. (A) Map of 34 areas where crater size distributions larger than 1 km were analyzed with the light of our model. (B) Evolution of the retrieved crater obliteration rate with time for the 34 areas. The dark lines correspond to the 34 best fit models returned from the inversions, and the red points correspond to the crater obliteration rates of each first period attributed to the average age of the first period. The range of erosion rate measured today by in situ analyses from rover's data is also displayed. The lowest modern erosion rates have been estimated at 0.01 m/My at Meridiani Planum landing site from the analyses of local crater degradation (Golombek et al., 2006). Martian eras (Werner and Tanaka, 2011) are displayed respectively in green for Noachian periods (MN for Mid Noachian and LN for Late Noachian), purple for Hesperian periods (EH and LH for Early and Late Hesperian), blue for Amazonian periods (EA, MA, LA for Early, Middle and Late Amazonian). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
lead to a slight shift in the age or even a slight stretch in the age range of the results, but the decrease in crater obliteration over time is still observed. Our 1D model simplifies an impact crater to its depth. So the scaling relationship between the crater diameter and the crater depth is a crucial parameter. Several scaling relationships exist and we had to choose one. Would using other scaling relations affect the results? As the depth of the crater contributes to the returned crater obliteration rate, changing the scaling law would slightly affect the returned values rates of crater obliteration. But if the absolute values of crater obliteration rate may vary depending on the crater/depth scaling law used, it cannot explain the relative decrease of the obliteration rate with time. Our numerical model including crater obliteration reproduces successfully the shape of the Noachian crater population in an incremental diagram. Many authors had already suspected that the distribution of ancient Martian craters > 1 km was due to long lived resurfacing processes (Chapman and Jones, 1977; Craddock and Howard, 2002; Mangold et al., 2012). The alternative hypothesis would be that the broad shape of the Noachian crater population is primary and reflects the distribution of impacting objects (e.g., Strom et al., 2005). However, the difference between Martian crater and lunar craters distribution at corresponding impact or size (Neukum et al., 2001) suggests that
data (Golombek et al., 2006). This suggests that the documented decrease in the crater obliteration rates during late Noachian and Hesperian probably continued through the Amazonian. However, because we only analyzed crater size frequencies distributions for craters >1 km in diameter, we are unable to test this hypothesis here. Resolving the crater obliteration history of the Amazonian would require analyses of smaller craters populations. 4. Discussion Any interpretations of our results must be placed into context with the limitations of our approach. First, the surface ages and duration of obliteration events are based on Hartmann's (2005) theoretical crater size frequency distribution and impact rate. However, other distributions or Martian impact rates have also been published (e.g., Werner and Tanaka, 2011). We did tests with other theoretical crater size distribution and they lead to same general results (see Supplementary material). Essentially, using these other models does not affect our general conclusions. The most important factor is not the choice of the impact rate or the theoretical crater size distribution, it is applying a coherent crater production system through the entire procedure. The age estimation as well as the model used with the inverse approach applied the same Martian age model. Applying another model would 431
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Acknowledgments
Mars underwent crater obliteration processes (Chapman and Jones, 1977). Our results document a decrease in crater obliteration rate from middle/Late Noachian to the end of Hesperian. Although our results do not provide direct information about the processes responsible for crater obliteration, there are many possible processes, including obliteration by impact cratering, aeolian erosion, or water (liquid or ice) related erosion. As the theoretical crater size distribution is based from lunar surface analyses where impact cratering is the major process that has modified the surface until an equilibrium of size distribution (Neukum et al., 2001), we may assume that any impact-related crater obliteration process is already included in the theoretical crater distribution we are using. Aeolian erosion is restricted in magnitude at ∼10−5 m/My (Armstrong and Leovy, 2005) and cannot explain the range of crater obliteration rate we are observing. So, an intense sedimentary erosion process is the best candidate to explain the ancient crater obliteration rates on Mars. Even if our 1D crater obliteration rate cannot be directly compared to erosion rate, at least the order of magnitude of terrestrial erosion rates may help us to enlighten our results. On Earth estimated erosion rates are the complex interplay between the relief and climate (primarily temperature and precipitation) and average ∼10 m/My over the last 500 My (Willenbring and Von Blanckenburg, 2010). Water plays a key role in surface erosion (Portenga and Bierman, 2011). The highest rates of erosion are found in both cold and temperate climate zones, indicating that both liquid water and ice are efficient erosion agents. However, the high erosion rates in the glacial or periglacial areas are probably controlled by freeze/thaw cycles (Portenga and Bierman, 2011). Evidence for processes that may be responsible of the crater degradation rate during Early Mars come from analyses of the morphology of modified Noachian craters (Craddock and Maxwell, 1993; Howard, 2007). All these studies argue that crater modification was controlled by rainfall or snowmelt (e.g., Craddock and Howard, 2002; Howard, 2007). The Martian obliteration rate are similar to those on earth that are dominated by the action of liquid water and so liquid water is likely for Mars as is observed in the eroded craters. The rates in the Amazonian on Mars are far too slow to have had liquid water involved (Golombek et al., 2006, 2014). The similarity of Noachian rates of erosion on Mars to erosion rates on Earth where liquid water dominates requires that liquid water was involved on early Mars. Our results may suggest that there was a decrease in the efficiency of water-related resurfacing processes (liquid or warm based ice cover) over time from at least the middle of Noachian until the end of Hesperian where the crater obliteration rate are still one order in magnitude larger than the ones estimated over the last 1 Gy. Instead of an abrupt climate change, our results may be more in agreement with a long-driven dry out of the red Planet.
The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Program (FP7/2007-2013)/ERC Grant agreement no. 280168. R. Craddock acknowledges support from NASA's Mars Data Analysis Program, Grant 80NSSC17K0454. The manuscript benefited greatly from constructive reviews by Matt Golombek and Mikhail Kreslavsky. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.icarus.2018.08.005. References Armstrong, J., Leovy, C., 2005. Long term wind erosion on Mars. Icarus 176, 57–74. Chapman, C.R., Jones, K.L., 1977. Cratering and obliteration history of Mars. Ann. Rev. Earth Planet. Sci. 5, 515–540. Craddock, R.A., Maxwell, T.A., 1993. Geomorphic evolution of Martian Highlands through ancient fluvial processes. JGR-Planet 98, 3453–3468. Craddock, R.A., Maxwell, T.A., Howard, A.D., 1997. Crater morphometry and modification in the Sinus Sabaeus and Margaritifer Sinus regions of Mars. J. Geophys. Res. 102 13,321–13,340. Craddock, R.A., Howard, A.D., 2002. The case for rainfall on a warm, wet early Mars. JGR-Planet 107, 21–36. Forsberg-Taylor, N.K., Howard, A.D., Craddock, R.A., 2004. Crater degradation in the Martian highlands: morphometric analysis of the Sinus Sabaeus region and simulation modeling suggest fluvial processes. J. Geophys. Res. 109, E05002. https://doi. org/10.1029/2004JE002242. Garvin, J.B., Sakimoto, S.E.H., Frawley, J.J., 2003. Craters on Mars: geometric properties from gridded MOLA topography, Abstract 3277. In: Proceedings of the Sixth International Conference on Mars. Pasadena, California. California Institute of Technology 20–25 July. Golombek, M.P., Grant, J.A., Crumpler, L.S., Greeley, R., Arvidson, R.E., et al., 2006. Erosion rates at the Mars exploration rover landing sites and long-term climate change on Mars. JGR-Planet 111, E12S10. Golombek, M.P., Warner, N.H., Ganti, V., Lamb, M.P., Parker, T.J., Fergason, R.L., Sullivan, R., 2014. Small crater modification on Meridiani Planum and implications for erosion rates and climate change on Mars. J. Geophys. Res. Planets 119, 2522–2547. https://doi.org/10.1002/2014JE004658. Hartmann, W.K., 1971. Martian cratering III: theory of crater obliteration. Icarus 15, 410–428. Hartmann, W.K., Neukum, G., 2001. Cratering chronology and the evolution of Mars. Space Sci. Rev. 96, 165–194. Hartmann, W.K., 2005. Martian cratering 8: isochron refinement and the chronology of Mars. Icarus 174, 294–320. Howard, A.D., 2007. Simulating the development of martian highland landscapes through the interaction of impact cratering, fluvial erosion and variable hydrological forcing. Geomorphology 91, 332–363. Irwin, R.P., Tanaka, K.L., Robbins, S.J., 2013. Distribution of Early, Middle, and Late Noachian cratered surfaces in the Martian highlands: implications for resurfacing events and processes. JGR-Planet 118, 278–291. Ivanov, B.A., 2001. Mars/Moon cratering rate ratio estimates. Space Sci. Rev. 96, 87–104. Jones, K.L., 1974. Evidence for an episode of crater obliteration intermediate in Martian history. JGR-Planet 79 (26), 3917–3931. Kreslavsky, M.A., Head, J.W., 2018. Mars climate history: insights from impact crater wall slope statistics. Geophys. Res. Lett. 45, 1751–1758. https://doi.org/10.1002/ 2017GL075663. Kite, E.S., Lucas, A., Fassett, C.I., 2013. Pacing early Mars river activity: embedded craters in the Aeolis Dorsa region imply river activity spanned ≳1–20 Mar. Icarus 225, 850–855. ISSN 0019-1035. http://dx.doi.org/10.1016/j.icarus.2013.03.029. Mangold, N., Adeli, S., Conway, S., et al., 2012. A chronology of early Mars climatic evolution from impact crater degradation. JGR-Planet 117, E04003. Neukum, G., Ivanov, B.A., Hartmann, W.K., 2001. Cratering records in the inner solar system in relation to the lunar reference system. Space Sci. Rev. 96, 55. Michael, G.G., Neukum, G., 2010. Planetary surface dating from crater size-frequency distribution measurements: Partial resurfacing events and statistical age uncertainty. Earth Planet. Sci. Lett. 294 (3–4), 223–229. Platz, T., Michael, G.G., Tanaka, K.L., Skinner Jr., J.A., Fortezzo, C.M., 2013. Crater-based dating of geological units on Mars: methods and application for the new global geological map. Icarus 225, 806–827. https://doi.org/10.1016/j.icarus.2013.04.021. Portenga, E.W., Bierman, P.R., 2011. Understanding Earth's eroding surface with 10Be. GSA Today 21, 4–10. Robbins, S.J., Hynek, B.M., 2012. A new global database of mars impact craters ≥1 km: 1. Database creation, properties, and parameter. JGR-Planet 117, E05004. Sadler, P.M., 1981. Sediment accumulation rates and the completeness of stratigraphic sections. J. Geol. 89, 569–584. Strom, R.G., Malhotra, R., Ito, T., Yoshida, F., Kring, D.A., 2005. The origin of planetary
5. Conclusion We used a 1D crater degradation model to extract for the first time key information looked up in the crater size distributions of large Martian impact craters. Thanks to about 30 areas on Mars, we document the time-dependence of the crater obliteration rates on Mars that continuously decreased between 3.8 Ga and 3 Ga (Hartmann, 2005 timescale). The ancient Martian crater obliteration rates would be at least one order in magnitude larger than current values. Given the previous geomorphologic analysis of ancient Martian crater degradation and the order of magnitude of the returned Noachian crater obliteration rates, our results appear to document the efficiency of waterrelated resurfacing processes over time and their associated sedimentary cycle. Our results suggest that the planet would have never experienced a dramatic climatic shift, but rather Mars initial warmer wetter conditions gradually deteriorated over time.
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Werner, S.C., 2009. The global Martian volcanic evolutionary history. Icarus 201 (1), 44–48. https://doi.org/10.1016/j.icarus.2008 12.019. Werner, S.C., Tanaka, K.L., 2011. Redefinition of the crater-density and absolute-age boundaries for the chronostratigraphic system of Mars. Icarus 215 (2), 603–607. Willenbring, J.K., Von Blanckenburg, F., 2010. Long-term stability of global erosion rates and weathering during late-Cenozoic cooling. Nature 465, 211–214.
impactors in the inner solar system. Science 309, 1847–1850. https://doi.org/10. 1126/science.1113544. Tanaka, K.L., Skinner, J.A., Jr., Dohm, J.M., Irwin, R.P., III, Kolb, E.J., Fortezzo, C.M., Platz, T., Michael, G.G., and Hare, T.M., (2014), Geologic map of Mars: U.S. Geological Survey Scientific Investigations Map 3292, Scale 1:20,000,000, Pamphlet 43 p.,http://dx.doi.org/10.3133/sim3292.
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Decline of crater obliteration rates during early Martian history a,⁎
b
a
a
C. Quantin-Nataf , R.A. Craddock , F. Dubuffet , L. Lozac'h , M. Martinot
T
a
a Laboratoire de Géologie de Lyon, Terre, Planètes, Environnement (Université de Lyon- Université Claude Bernard lyon1-CNRS-ENS Lyon), ERC eMars Team, 2 rue Raphaël Dubois 69622 Villeurbanne Cedex, France b Center for Earth and Planetary Studies, National Air and Space Museum, Smithsonian Institution, Washington, District of Columbia, USA
A B S T R A C T
A change in the global climate on early Mars is suspected from the geologic evidence of warmer wetter conditions that prevailed during the Noachian but stands in contrast to the dry and cold conditions observed currently. However, the timing and evolution of this climatic change represents a gap in our understanding of the history of Mars. Here, we document the time-dependence of the crater obliteration rates on Mars that decreased continuously between 3.8 Ga and 3 Ga. Our results indicate that the erosion responsible for crater modification and obliteration declined gradually through the Noachian and into the Hesperian periods. These results suggest that the climatic conditions also changed gradually and the amount of water available on the surface of Mars slowly decreased over time.
1. Introduction Understanding the nature and types of surface processes on Mars over time is essential for constraining the climatic evolution of the planet. Long-term crater degradation analyses have revealed that erosion rates in the Amazonian are about 0.01 m/My (Golombek et al., 2006), which is at least two orders of magnitude lower than the erosion rates estimated in the Noachian (about 1 m/My) (Craddock and Maxwell, 1993). The differences in erosion rates between the Noachian and Amazonian may be that liquid water was the main erosional agent during the Noachian, and this was followed by a drier Amazonian climate where aeolian processes are dominant (Mangold et al., 2012; Golombek et al., 2014; Kreslavsky and Head, 2018; ). However, the evolution from erosion-intensive wet conditions to the current dry and cold Martian climate where erosion is limited is not well understood. In particular, it is not clear whether Noachian conditions suddenly collapsed or if erosion rates waned gradually over time. Impact craters are ubiquitous features that have formed continually throughout the entire history of Mars, so by analyzing their size frequency distributions it is possible to assess the integrated history of impacting objects as well as the processes that have modified the surface. Assuming that the theoretical crater size distributions are the natural result of meteoritic bombardment are correct, any variations from these theoretical crater size distributions would indicate resurfacing by other geologic processes (e.g., Werner, 2009; Kite et al., 2013; Platz et al., 2013). One-time events, such as lava emplacement, would have a much different effect on the crater size distribution than a longlived process like erosion or aggradation. One-time events led to a distribution that is stepped as opposed to the theoretical straight-line
⁎
function, while long-lived processes lead to broader, flatter distributions (e.g., Hartmann, 1971). Since spacecraft observations began with the Mariner missions, it has been known that large Martian impact craters have been modified, and that many craters smaller than 60 km have been deleted from the cratering record (Hartmann, 1971; Chapman and Jones, 1977). The fact that craters are preserved at different stages of modification at different diameters indicates that the modification processes continued as new craters were forming (Chapman and Jones, 1977; Craddock and Howard, 2002; Mangold et al., 2012). Now, thanks to decades of orbital missions and higher resolution imagery, we have a complete inventory of Martian craters down to ∼1 km (Robbins et al., 2012), and coupled with global Martian geological map (Tanaka et al., 2014) it is possible to derive the crater size distribution of each era of Mars’ history or each geological unit (Irwin et al., 2013). If we do so for all Noachian terrains, craters larger than 60 km follow the Martian >4 Ga isochron, which is defined as the theoretical crater size distribution of an undisturbed surface 4 Ga; Intermediate crater size-frequency distributions for diameters from 4 km to 64 km have a clear flatter slope than isochrons well highlighted in incremental diagrams; And small craters connect to a younger isochron, typically Hesperian in age (Fig. 1). The fact that crater distributions over several size bins is flatter than the isochrons and below the saturation line implies that there was a continuous process of crater degradation over time that ceased or changed in magnitude at an age reflected by the smallest craters located at the bend (Hartmann, 1971; Chapman and Jones, 1977). Fig. 1 is based on the Hartmann (2005) crater production distribution, but a similar deviation is observed when compared to others crater production functions (see Supplementary material).
Corresponding author. E-mail address: [email protected] (C. Quantin-Nataf).
https://doi.org/10.1016/j.icarus.2018.08.005 Received 24 January 2018; Received in revised form 30 July 2018; Accepted 2 August 2018 Available online 15 August 2018 0019-1035/ © 2018 Elsevier Inc. All rights reserved.
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Fig. 1. (A) Three different crater obliteration evolution models over the last 4 Gy. Blue shows no obliteration. Red represents a first period of intense crater obliteration followed by a period with no obliteration. Green represents moderate but constant crater obliteration during 4 Gy. Martian eras (Werner and Tanaka, 2011) are plotted respectively in green for Noachian periods (MN for Mid Noachian and LN for Late Noachian), purple for Hesperian periods (EH and LH for Early and Late Hesperian), blue for Amazonian periods (EA, MA, LA for Early, Middle and Late Amazonian). (B) The synthetic crater size distribution produced by the models presented in A in a Hartmann incremental diagram (Hartmann, 2005; Hartmann and Neukum, 2001); The model in blue with no crater obliteration reproduces the 4 Ga isochron as expected. The model in green with moderate crater obliteration but that is held constant over the last 4 Gy produces a drop in the population of craters smaller than 43 km. The red model produces an distribution similar to the one observed in C for the entire Noachian terrains on Mars. Note that scaling law linking the crater diameter to its depth used in the model is plotted in Fig. 2B. (C) Crater size distribution of the entire Noachian terrains. We used the craters from Robbins and Hynek (2012) that lie within Noachian units defined by Tanaka et al. (2014) to obtain this distribution. The crater size distribution of the Noachian terrains shows a S-shape typical of individual Noachian units. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
(Hartmann, 2005; Hartmann and Neukum, 2001). Thus n is a function of two separated variables n(D,T) = f(D)N(T). N(T) is the accumulated number of craters larger than 1 km per unit area and is defined as follow (Neukum et al. 2001):
Here, we present a simple numerical model used as a tool for determining how the rate of crater modification may have changed over time. We use this model to explain the observed deviations in crater size distributions to crater production for the entire population of Noachian craters, as a test case. The method was then applied to 33 individual areas on Mars. Because these 33 areas are of different ages, the results we obtained can provide constraints on the time-dependence of the crater obliteration rate over time on Mars. The results have implications for the climatic evolution of Mars.
ND > 1 km (T ) = 5.44*10−14 (e6.93T − 1) + 8.38*10−14T
(1)
N′, the derivative of N, is the impact rate:
N ′D > 1 km (T ) =
dND > 1 km (T ) = 3.77*10−13e6.93T + 8.38*10−14 dT
(2)
The time evolution of the crater density is modeled according to the following equation:
2. Method
∂T n (D , T ) = f (D) N ′ (T )
To assess the crater obliteration rates, we simplified the erosion/or infilling of craters to a 1D process. The evolution of the crater depth (d) with time (t) can be described as following: Δd/Δt. Our goal was not to assess the amount of crater erosion or the amount of infilling; accurately describing such processes would require much more than a simple 1D decrease in crater depth. Rather, our goal was to retrieve the time dependence of crater obliteration processes.
(3)
The crater size distribution f(D) is calculated by dividing a Martian isochron at time T from (Table 2 in Hartmann, 2005) by N(T). The initial condition is n(D, T = 0) = 0. This equation is then integrated between T and T + ΔΤ:
N (D , T + ΔT ) = n (D , T ) + f (D)[N (T + ΔT ) − N (T )]
(4)
where f(D)[N(T + ΔT) − N(T)] is the number of craters added during the time step ΔT. To model the obliteration history of craters within our study areas, we used the concept of lifetime of an impact crater (Jones, 1974). Basically, because depth increases as a function of crater diameter, larger diameter craters will take longer to eradicate completely. In our model, at each time step ΔT craters were added only if they had a depth large enough to survive through the total amount of erosion that would occur during the remaining obliteration history. We convert the remaining time of obliteration to a maximum depth of obliteration z (in km) using a time-dependence of obliteration υ (in km/Gy):
2.1. The model We constructed a simple numerical model that generates synthetic crater size distributions simulating impact crater production and crater obliteration. The design for the model is described below. Our model for the impact rate evolution begins by assuming that the crater density of a planetary surface n(D,T) is the number of craters per unit area (in km2), where D (in km) is the crater diameter and T (in Gy) is the age of the surface. This crater production function is generally assumed to have the same time dependence for all diameters 428
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Fig. 2. Inversion of the crater size distribution of Noachian terrains. (A) presents the crater obliteration rate evolution that produces the synthetic crater size distribution with the best goodness of fit plotted in blue in the incremental diagram C. Martian eras (Werner and Tanaka, 2011) are plotted respectively in green for Noachian periods (MN for Mid Noachian and LN for Late Noachian), purple for Hesperian periods (EH and LH for Early and Late Hesperian), blue for Amazonian periods (EA, MA, LA for Early, Middle and Late Amazonian). (B) presents the depth vs. diameter dependence used in the model. We used the scaling law published by Garvin et al. (2003) for simple (purple points) and complex craters (green points). For the crater diameter bin at the transition between simple and complex crater (yellow), we used the average between the lower and the largest size bin. The red point in C represents the crater size distribution of the Noachian terrains obtained by extraction from the crater database from Robbins and Hynek (2012) contained in the terrains mapped by Tanaka et al. (2014) as Noachian. The best fit model is plotted in blue and implies a first period with a crater obliteration rate of 3.5 m/My from 3.99 Ga to 3.46 Ga. We note that this best fit reproduces the shape of the Noachian crater size distribution. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
z (T ) =
∫0
T
υ (t ) dt
(Ivanov, 2001) because the Neukum production function curve shape is different from Hartmann's, particularly for crater diameters of 4–60 km, the range where we observe a deviation to the theoretical crater production. Whatever the production function used in our model, the same results are observed (see Supplementary material). Additionally, Forsberg-Taylor et al. (2004) have shown that crater infilling rates from fluvial processes decreases as erosional modification advances because the crater wall height decreases and the depositional area increases due to backwasting, slope relaxation, and crater enlargement. Simply stated, the rate of infilling changes as the crater continues to be eroded, but our model does not take this into account. To do this accurately would require us to vary the infilling rate according the degradation state of each individual crater. Our goal is to simply explain how impact craters may go missing when compared to a theoretical distribution. This assumption may lead us to underestimate the rate of crater obliteration in case of fluvial erosion. Finally, our model is only 1D in that it includes only one space dimension: crater depth. We infill craters until their entire depth has disappear at which point they are considered “obliterated.” Small craters will be obliterated faster than larger ones because they are shallower. Other dimensional effects from crater modification (e.g., crater enlargement due to backwasting; Craddock et al., 1997) were also not considered.
(5)
where z is the crater depth that can disappear during a time T. Thus, the crater density n varies during ΔT (Eq. (4)) only if the depth of the crater to be added is greater that z(T). To scale crater depth to diameter, we used the following scaling relationships for simple and complex craters (Garvin et al., 2003): when D < 4 km, we use d = 0.21 × D0.81 which is the relationship for simple craters. When D > 5.66 km, we use the formula for complex craters, d = 0.36 × D0.49. In both equations, D and d are in kilometers. For the transitional diameter bin between 4 and 5.66 km, as the crater population is a mixture between simple and complex craters (Robbins and Hynek, 2012), we use an average between the depth of the diameter bin between 2.83 and 4 km and the depth of the diameter bin between 5.66 and 8 km. Fig. 2B displays the depth to diameter relationships we used in our simulations. Both equations (cratering rate and obliteration rate) were integrated from 0 to T with a time step of 1 My. 2.2. Assumptions behind the model The use of the model requires making several assumptions. First, we assume that the shape of the production function curve does not change through time; however, the total rate of crater production does decrease. This has been validated by several studies of the lunar surface (Neukum et al., 2001). This assumption has also been made by other studies using crater chronology techniques to assess Martian ages. It is important to note, however, that several production function curve shapes have been published (Neukum et al., 2001; Michael and Neukum, 2010). Here we use the Hartmann (2005) production function, but we also did tests with the Neukum production function
2.3. Tests of the model The qualitative explanation for the observed Noachian deviation of crater size distribution between craters larger than 64 km which align with the 4 Ga isochron and the crater smaller than 4 km which align with 3.5 Ga (Fig. 1) is that there was a continuous process of crater 429
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sizes of these areas range from 105 to 106 km2, which is large enough to contain statistically viable impact crater populations ≥60 km in diameter while still being located in contiguous geologic units (Tanaka et al., 2014). We applied the same approach in applying our model to these additional areas as we did previously for the whole Noachian crater size frequency distribution. Only 34 areas returned a satisfying and unique Goodness of Fit (Fig. 3). The Goodness of fits of these 34 area range from 0.42 to 6.91. But most importantly, they all correspond to clear minimum Goodness of Fit (see Extended Fig. 2C). Most of the extracted distributions display a complex crater size distribution with stepped parts indicative of short-lived or one-time resurfacing events (e.g., volcanic resurfacing) which may be common for much of the surface of Mars (e.g., Platz et al., 2013). These stepped distributions suggest more complex geological histories where the use of our simple obliteration model cannot be applied adequately, as demonstrated by our inability to return a satisfying and unique Goodness of Fit. The excluded areas are located mainly around the large volcanic provinces (e.g., Northern plains, Tharsis region, Tyrrhena Paterra, and Syrtis Major) where the volcanic resurfacing is expected (see Supplementary material). The 34 areas with a clear returned minimum GF have a wide range of age from 4.17 Ga to 3.34 Ga (From Early Noachian to late Hesperian). But most of them are located in Noachian terrains (Fig. 3). This is explained by the fact that most of Hesperian and Amazonian large units are volcanic units and thus have very complex crater distributions where our model would not be appropriate. The time at which the change in the magnitude of the crater obliteration rate occurred varies from 3.63 Ga to 960 Ma. Fig. 3B plots the results of the best-fit evolution of the crater obliteration rate for the 34 areas in dark lines. Red points correspond to the crater obliteration rates of each first period vs. the average age of each first period. Interestingly, both dark lines and red points display a steady decrease of the crater obliteration rate over one order of magnitude from 3.8 to 3.0 Ga corresponding to the middle/Late Noachian to the end of Hesperian based on ages from Hartmann, (2005) and timescale from Werner and Tanaka (2011). Spikes or sudden decreases in the crater obliteration rates are not observed over this time period. The values of obliteration rates decrease from 6 m/My at 3.8 Ga to 0.6 m/My at 3.16 Ga, recalling that these values are for 1D crater obliteration rates. Given that the crater modifications processes are often complex and the assumptions involved in our model, these values do not directly correspond to actual erosion rates. However, we could expect that they could be similar. Our results show that 1D crater obliteration rate is a powerful tool in revealing the time dependence of erosional and resurfacing processes. The time-dependence presented in Fig. 3B is well constrained from 3.8 Ga to 3 Ga where many inversions have been done and these inversions have about the same duration of the initial phase of high crater obliteration rates. However, after 3 Ga, only 2 crater size distribution inversions support the results and require longer initial periods of erosion (>2 Ga) where underestimating the returned obliteration rate may be influenced by the Sadler effect. The Sadler effect states that measured sedimentary rates systematically decrease with measurement duration, which is explained by the intermittent nature of sedimentary processes that leads to gaps in the stratigraphic record (Sadler, 1981). So only obliteration rates integrated over the same range of time can be compared. But this effect should not be important as even in the younger areas we analyze the duration of the obliteration event is the same order of magnitude. The Sadler effect becomes a larger issue when comparing processes that occurred over time periods that different by several orders of magnitude. This effect is also referred as the timescale bias. Efforts to quantify this effect have been done for Martian erosion rate analyses (Golombek et al., 2014). There is a clear effect on the deduced erosion rate according to the spam time over which the erosion rate is calculated. It can be noted that the obliteration rate at 3.16 Ga is still one order of magnitude larger than the current erosion rate estimated from lander
obliteration between 4 Ga and 3.5 Ga that ceased or changed in intensity at 3.5 Ga (e.g., Hartmann, 1971; Chapman and Jones, 1977). We tested various rates of crater obliteration in order to reproduce the shape of the observed deviation at the 4 Ga isochron observed in Noachian craters. The tests we conducted included: (1) no crater obliteration, (2) a constant rate obliteration over 4 Gy, (3) a linear decrease of crater obliteration with time and (4) an old period with large crater obliteration rate followed by a second period with reduced crater obliteration rates (Fig. 1A and B). Fig. 2C shows that only the 4th model with 2 distinct periods of crater obliteration can explain, to first order, the observed shape of the Noachian crater size frequency distribution and the deviation observed at 4–64 km diameter craters. These results imply that there was an abrupt change in the obliteration rate at the end of the Noachian, so we decided to use this two-phase model of crater obliteration to analyze the other crater size distributions. 2.4. Inverse approach We applied an inverse method to determine the two-phase evolution model of crater obliteration v(t) that best fit the observed crater size frequency distributions. The two-phase model of obliteration rates requires four parameters: the age of the surface, the age of the obliteration rate change, and the obliteration rates for both periods. For a given deviated crater size distribution, the age of the surface is deduced from the populations of the large impact craters that follow the isochron slope with a precision of 0.01 Gy using the age system of Hartmann (2005). The age at which the sharp change in obliteration rate occurred is deduced from the populations of the smallest impact craters that follow a younger isochron also with a precision of 0.01 Gy. For each inversion, we fixed the rate of obliteration of the latter stage at 0.01 m/ My, which is the Amazonian erosion rate as estimated in situ by rover data (Golombek et al., 2006). The only free parameter is the rate of obliteration of the oldest period of crater obliteration. We varied this free parameter by increments of 10−1 m/My while returning a goodness-of-fit (GF) defined as the following sum of differences between the model and the observed data:
GF =
∑
(Nmodel − Ndata)2 (σdata)2
for σdata < Ndata
where Ndata is the number of measured craters in each diameter bin, Nmodel is the number of craters predicted by the model for each diameter bin and σdata is the Poissonian error bar, calculated as the square root of the total number of measured craters. Once a minimum GF was found the corresponding value of obliteration rate of the first period was recorded. For each best two-phase obliteration model presented in Figs. 2 and 3, a minimum GF is clearly found as a unique solution, returning the obliteration rate of the old period with a precision of 0.1 m/My. 3. Results Fig. 2 illustrates the best-fit models that reproduce the shapes of the crater size frequency distributions for all terrains Noachian in age. The average age of the surface deduced from the crater size distribution is 3.99 Ga (Early Noachian times; Werner and Tanaka, 2011), and the age deduced by craters smaller than 4 km is 3.46 Ga (Early Hesperian times, Werner and Tanaka, 2011). By applying the obliteration rate at 0.01 m/ My after 3.46 Ga, the results of the best-fit model return an obliteration rate of 3.5 m/My between 3.99 and 3.46 Ga. This indicates that the rate of crater obliteration during early Mars was more than two orders of magnitude greater than it is today. This result presents the average rate of crater obliteration during the Noachian and can be used as a proxy for the average surface erosion rate during this time. To determine if the crater obliteration rate changed over time, we extracted crater size frequency distributions for more than hundred large areas on Mars from various places located all over the planet. The 430
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Fig. 3. (A) Map of 34 areas where crater size distributions larger than 1 km were analyzed with the light of our model. (B) Evolution of the retrieved crater obliteration rate with time for the 34 areas. The dark lines correspond to the 34 best fit models returned from the inversions, and the red points correspond to the crater obliteration rates of each first period attributed to the average age of the first period. The range of erosion rate measured today by in situ analyses from rover's data is also displayed. The lowest modern erosion rates have been estimated at 0.01 m/My at Meridiani Planum landing site from the analyses of local crater degradation (Golombek et al., 2006). Martian eras (Werner and Tanaka, 2011) are displayed respectively in green for Noachian periods (MN for Mid Noachian and LN for Late Noachian), purple for Hesperian periods (EH and LH for Early and Late Hesperian), blue for Amazonian periods (EA, MA, LA for Early, Middle and Late Amazonian). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
lead to a slight shift in the age or even a slight stretch in the age range of the results, but the decrease in crater obliteration over time is still observed. Our 1D model simplifies an impact crater to its depth. So the scaling relationship between the crater diameter and the crater depth is a crucial parameter. Several scaling relationships exist and we had to choose one. Would using other scaling relations affect the results? As the depth of the crater contributes to the returned crater obliteration rate, changing the scaling law would slightly affect the returned values rates of crater obliteration. But if the absolute values of crater obliteration rate may vary depending on the crater/depth scaling law used, it cannot explain the relative decrease of the obliteration rate with time. Our numerical model including crater obliteration reproduces successfully the shape of the Noachian crater population in an incremental diagram. Many authors had already suspected that the distribution of ancient Martian craters > 1 km was due to long lived resurfacing processes (Chapman and Jones, 1977; Craddock and Howard, 2002; Mangold et al., 2012). The alternative hypothesis would be that the broad shape of the Noachian crater population is primary and reflects the distribution of impacting objects (e.g., Strom et al., 2005). However, the difference between Martian crater and lunar craters distribution at corresponding impact or size (Neukum et al., 2001) suggests that
data (Golombek et al., 2006). This suggests that the documented decrease in the crater obliteration rates during late Noachian and Hesperian probably continued through the Amazonian. However, because we only analyzed crater size frequencies distributions for craters >1 km in diameter, we are unable to test this hypothesis here. Resolving the crater obliteration history of the Amazonian would require analyses of smaller craters populations. 4. Discussion Any interpretations of our results must be placed into context with the limitations of our approach. First, the surface ages and duration of obliteration events are based on Hartmann's (2005) theoretical crater size frequency distribution and impact rate. However, other distributions or Martian impact rates have also been published (e.g., Werner and Tanaka, 2011). We did tests with other theoretical crater size distribution and they lead to same general results (see Supplementary material). Essentially, using these other models does not affect our general conclusions. The most important factor is not the choice of the impact rate or the theoretical crater size distribution, it is applying a coherent crater production system through the entire procedure. The age estimation as well as the model used with the inverse approach applied the same Martian age model. Applying another model would 431
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Acknowledgments
Mars underwent crater obliteration processes (Chapman and Jones, 1977). Our results document a decrease in crater obliteration rate from middle/Late Noachian to the end of Hesperian. Although our results do not provide direct information about the processes responsible for crater obliteration, there are many possible processes, including obliteration by impact cratering, aeolian erosion, or water (liquid or ice) related erosion. As the theoretical crater size distribution is based from lunar surface analyses where impact cratering is the major process that has modified the surface until an equilibrium of size distribution (Neukum et al., 2001), we may assume that any impact-related crater obliteration process is already included in the theoretical crater distribution we are using. Aeolian erosion is restricted in magnitude at ∼10−5 m/My (Armstrong and Leovy, 2005) and cannot explain the range of crater obliteration rate we are observing. So, an intense sedimentary erosion process is the best candidate to explain the ancient crater obliteration rates on Mars. Even if our 1D crater obliteration rate cannot be directly compared to erosion rate, at least the order of magnitude of terrestrial erosion rates may help us to enlighten our results. On Earth estimated erosion rates are the complex interplay between the relief and climate (primarily temperature and precipitation) and average ∼10 m/My over the last 500 My (Willenbring and Von Blanckenburg, 2010). Water plays a key role in surface erosion (Portenga and Bierman, 2011). The highest rates of erosion are found in both cold and temperate climate zones, indicating that both liquid water and ice are efficient erosion agents. However, the high erosion rates in the glacial or periglacial areas are probably controlled by freeze/thaw cycles (Portenga and Bierman, 2011). Evidence for processes that may be responsible of the crater degradation rate during Early Mars come from analyses of the morphology of modified Noachian craters (Craddock and Maxwell, 1993; Howard, 2007). All these studies argue that crater modification was controlled by rainfall or snowmelt (e.g., Craddock and Howard, 2002; Howard, 2007). The Martian obliteration rate are similar to those on earth that are dominated by the action of liquid water and so liquid water is likely for Mars as is observed in the eroded craters. The rates in the Amazonian on Mars are far too slow to have had liquid water involved (Golombek et al., 2006, 2014). The similarity of Noachian rates of erosion on Mars to erosion rates on Earth where liquid water dominates requires that liquid water was involved on early Mars. Our results may suggest that there was a decrease in the efficiency of water-related resurfacing processes (liquid or warm based ice cover) over time from at least the middle of Noachian until the end of Hesperian where the crater obliteration rate are still one order in magnitude larger than the ones estimated over the last 1 Gy. Instead of an abrupt climate change, our results may be more in agreement with a long-driven dry out of the red Planet.
The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Program (FP7/2007-2013)/ERC Grant agreement no. 280168. R. Craddock acknowledges support from NASA's Mars Data Analysis Program, Grant 80NSSC17K0454. The manuscript benefited greatly from constructive reviews by Matt Golombek and Mikhail Kreslavsky. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.icarus.2018.08.005. References Armstrong, J., Leovy, C., 2005. Long term wind erosion on Mars. Icarus 176, 57–74. Chapman, C.R., Jones, K.L., 1977. Cratering and obliteration history of Mars. Ann. Rev. Earth Planet. Sci. 5, 515–540. Craddock, R.A., Maxwell, T.A., 1993. Geomorphic evolution of Martian Highlands through ancient fluvial processes. JGR-Planet 98, 3453–3468. Craddock, R.A., Maxwell, T.A., Howard, A.D., 1997. Crater morphometry and modification in the Sinus Sabaeus and Margaritifer Sinus regions of Mars. J. Geophys. Res. 102 13,321–13,340. Craddock, R.A., Howard, A.D., 2002. The case for rainfall on a warm, wet early Mars. JGR-Planet 107, 21–36. Forsberg-Taylor, N.K., Howard, A.D., Craddock, R.A., 2004. Crater degradation in the Martian highlands: morphometric analysis of the Sinus Sabaeus region and simulation modeling suggest fluvial processes. J. Geophys. Res. 109, E05002. https://doi. org/10.1029/2004JE002242. Garvin, J.B., Sakimoto, S.E.H., Frawley, J.J., 2003. Craters on Mars: geometric properties from gridded MOLA topography, Abstract 3277. In: Proceedings of the Sixth International Conference on Mars. Pasadena, California. California Institute of Technology 20–25 July. Golombek, M.P., Grant, J.A., Crumpler, L.S., Greeley, R., Arvidson, R.E., et al., 2006. Erosion rates at the Mars exploration rover landing sites and long-term climate change on Mars. JGR-Planet 111, E12S10. Golombek, M.P., Warner, N.H., Ganti, V., Lamb, M.P., Parker, T.J., Fergason, R.L., Sullivan, R., 2014. Small crater modification on Meridiani Planum and implications for erosion rates and climate change on Mars. J. Geophys. Res. Planets 119, 2522–2547. https://doi.org/10.1002/2014JE004658. Hartmann, W.K., 1971. Martian cratering III: theory of crater obliteration. Icarus 15, 410–428. Hartmann, W.K., Neukum, G., 2001. Cratering chronology and the evolution of Mars. Space Sci. Rev. 96, 165–194. Hartmann, W.K., 2005. Martian cratering 8: isochron refinement and the chronology of Mars. Icarus 174, 294–320. Howard, A.D., 2007. Simulating the development of martian highland landscapes through the interaction of impact cratering, fluvial erosion and variable hydrological forcing. Geomorphology 91, 332–363. Irwin, R.P., Tanaka, K.L., Robbins, S.J., 2013. Distribution of Early, Middle, and Late Noachian cratered surfaces in the Martian highlands: implications for resurfacing events and processes. JGR-Planet 118, 278–291. Ivanov, B.A., 2001. Mars/Moon cratering rate ratio estimates. Space Sci. Rev. 96, 87–104. Jones, K.L., 1974. Evidence for an episode of crater obliteration intermediate in Martian history. JGR-Planet 79 (26), 3917–3931. Kreslavsky, M.A., Head, J.W., 2018. Mars climate history: insights from impact crater wall slope statistics. Geophys. Res. Lett. 45, 1751–1758. https://doi.org/10.1002/ 2017GL075663. Kite, E.S., Lucas, A., Fassett, C.I., 2013. Pacing early Mars river activity: embedded craters in the Aeolis Dorsa region imply river activity spanned ≳1–20 Mar. Icarus 225, 850–855. ISSN 0019-1035. http://dx.doi.org/10.1016/j.icarus.2013.03.029. Mangold, N., Adeli, S., Conway, S., et al., 2012. A chronology of early Mars climatic evolution from impact crater degradation. JGR-Planet 117, E04003. Neukum, G., Ivanov, B.A., Hartmann, W.K., 2001. Cratering records in the inner solar system in relation to the lunar reference system. Space Sci. Rev. 96, 55. Michael, G.G., Neukum, G., 2010. Planetary surface dating from crater size-frequency distribution measurements: Partial resurfacing events and statistical age uncertainty. Earth Planet. Sci. Lett. 294 (3–4), 223–229. Platz, T., Michael, G.G., Tanaka, K.L., Skinner Jr., J.A., Fortezzo, C.M., 2013. Crater-based dating of geological units on Mars: methods and application for the new global geological map. Icarus 225, 806–827. https://doi.org/10.1016/j.icarus.2013.04.021. Portenga, E.W., Bierman, P.R., 2011. Understanding Earth's eroding surface with 10Be. GSA Today 21, 4–10. Robbins, S.J., Hynek, B.M., 2012. A new global database of mars impact craters ≥1 km: 1. Database creation, properties, and parameter. JGR-Planet 117, E05004. Sadler, P.M., 1981. Sediment accumulation rates and the completeness of stratigraphic sections. J. Geol. 89, 569–584. Strom, R.G., Malhotra, R., Ito, T., Yoshida, F., Kring, D.A., 2005. The origin of planetary
5. Conclusion We used a 1D crater degradation model to extract for the first time key information looked up in the crater size distributions of large Martian impact craters. Thanks to about 30 areas on Mars, we document the time-dependence of the crater obliteration rates on Mars that continuously decreased between 3.8 Ga and 3 Ga (Hartmann, 2005 timescale). The ancient Martian crater obliteration rates would be at least one order in magnitude larger than current values. Given the previous geomorphologic analysis of ancient Martian crater degradation and the order of magnitude of the returned Noachian crater obliteration rates, our results appear to document the efficiency of waterrelated resurfacing processes over time and their associated sedimentary cycle. Our results suggest that the planet would have never experienced a dramatic climatic shift, but rather Mars initial warmer wetter conditions gradually deteriorated over time.
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