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Keywords:

  • Mars;
  • impact crater;
  • Lyot crater;
  • age-dating

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Identification of Craters and Secondary Clusters
  5. 3. Size-Frequency Distributions of Secondary Clusters
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[1] The population of secondary craters - craters formed by the ejecta from an initial impact event - is important to understand when deriving the age of a solid body's surface. Only one crater on Mars, Zunil, has been studied in-depth to examine the distribution, sizes, and number of these features. Here, we present results from a much larger and older Martian crater, Lyot, and we find secondary crater clusters at least 5200 km from the primary impact. Individual craters with diameters >800 m number on the order of 104. Unlike the previous results from Zunil, these craters are not contained in obvious rays, but they are linked back to Lyot due to the clusters' alignment along great circles that converge to a common origin. These widespread and abundant craters from a single impact limit the accuracy of crater age-dating on the Martian surface and beyond.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Identification of Craters and Secondary Clusters
  5. 3. Size-Frequency Distributions of Secondary Clusters
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[2] Crater counting is the only way to estimate absolute ages on solid surfaces without returned samples, akin to the Apollo missions. This practice has been refined and utilized for decades [e.g., Arvidson et al., 1979; Hartmann, 2005]. A fundamental assumption of crater age-dating is that crater formation is a stochastic process. Nearly half a century ago, Shoemaker [1965] identified the issue of secondary craters (craters that form from the ejecta of a larger primary impact event and are necessarily smaller). The subject of secondary craters was controversial but generally ignored in the literature until Bierhaus et al. [2005] identified >104 secondary craters that contaminate crater statistics on Jupiter's moon Europa, and McEwen et al. [2005] identified >106 around the fresh crater Zunil on Mars.

[3] Understanding the role secondary craters have on local and global crater statistics is important, especially because the crater population with diameters D < 1 km on Mars may be significantly contaminated by secondary craters [McEwen and Bierhaus, 2006]. Secondary fields are typically manifest as a visible and tight annulus around the primary, though recent work has shown that secondary fields can be several thousand kilometers from the primary [Preblich et al., 2007]. With current and forthcoming high-resolution imagery of Mars, the Moon, and Mercury, case studies of fields of secondaries from large primary craters are necessary to assess their effects on the overall crater population.

[4] Here, we discuss the identification of thousands of secondary craters originating from one of the largest fresh craters on Mars: Lyot crater is a 222-km-diameter peak-ring crater centered at 50.5°N, 29.3°E (Figure 1), with a Middle Amazonian age of ∼1.6–3.3 Ga [Tanaka et al., 2005; Dickson et al., 2009]. The secondaries are up to 25% of the way across the planet, and there could be countless more not clearly linked to Lyot due to degradation, resurfacing, resolution limitations, or lack of easily identifiable tight clusters. Besides the basic identification of Lyot secondaries in the near- and far-field (Section 2), we detail their size-frequency distribution relative to primary craters (Section 3), and discuss implications (Section 4).

image

Figure 1. THEMIS Daytime IR mosaic [Christensen et al., 2004] showing the region around Lyot crater in a local sinusoidal projection. The continuous ejecta blanket of Lyot is outlined in black and the identified near-field secondaries are shown as white circles. Black regions correspond to gaps in the THEMIS data.

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2. Identification of Craters and Secondary Clusters

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Identification of Craters and Secondary Clusters
  5. 3. Size-Frequency Distributions of Secondary Clusters
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[5] Over 500,000 craters ≳1-km-diameter have been identified on Mars in a nearly completed global Mars crater database [Robbins and Hynek, 2010]. Craters were visually identified in ArcGIS software using 100 m/pix global THEMIS Daytime IR mosaics [Christensen et al., 2004], and rims were mapped using ArcGIS's edit tools. Polygons representing crater rims were imported into Igor Pro where a non-linear least-squares (NLLS) circle-fit algorithm was used to calculate each crater's diameter and center latitude and longitude. The NLLS algorithm corrects for map projection by converting the polygon's geographic coordinates into meters from the polygon's centroid, accounting for the first-order spherical surface of Mars.

[6] The global database's small crater distribution contains numerous clusters that appear to trend radially from Lyot crater at distances up to ∼5200 km. Over 90% are in the quadrant southeast of Lyot (Figure 2). Determining if these clusters likely originated from Lyot was not aided by observable rays nor a nearly crater-free landscape as is the case with Zunil [McEwen et al., 2005]. Great circles were traced between the potential clusters and Lyot to determine if the cluster was aligned with it (i.e., a circle described by the intersection of the surface of a sphere with a plane passing through the center).

image

Figure 2. Distribution of identified secondary crater clusters from Lyot. Arcs are representative examples of great circles between Lyot and distal secondary craters. Dark outlines show each cluster.

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[7] The formula prescribed by Vincenty [1975] was used to construct great circle arcs via an iterative approach: An initial bearing along the great circle connecting the starting position (the cluster) and ending position (Lyot) was calculated. Then, the point 1 km from the starting point along the bearing was calculated (∼1/60° at the equator; resolution tests at 10 km and 100 m showed differences <0.0005°, or <30 m). At this point, a new bearing was calculated and the process was repeated until Lyot was reached.

[8] Potential Lyot secondary clusters were initially identified by visual inspection from the database, but a more robust clustering algorithm was run to isolate potential groups: Every crater D ≤ 5 km was analyzed for its distance to all other craters within 2°. If the fifth-nearest crater was within 10 crater diameters, it was considered to be in a potential cluster; otherwise it was removed. The fifth-nearest was chosen to eliminate random over-densities; in the clusters observed initially, several dozen craters are often closely packed with rims touching. Candidate clusters were visually inspected in THEMIS mosaics to validate the cluster and determine, based upon morphology, if the cluster was composed of secondaries. Great circle arcs were drawn between the secondary clusters and Lyot to test orientation (e.g., Figure 2). This only identifies clusters of craters and frequently fields of smaller craters were observed that were also likely from Lyot but not included in this study. In this case, “fields” define regions of craters that show an over-density from the background that are probably secondaries, and “clusters” are craters that are packed closely with rims often touching.

[9] The search identified 143 distinct clusters of 10–300 craters each, where craters have diameters D > ∼800 m. A total of 5341 craters from the global database were extracted as members of these distant secondaries, similar in magnitude to the number identified on Europa [Bierhaus et al., 2005]. The closest cluster is ∼700 km away (∼6 crater radii) and the farthest is ∼5200 km (∼46 crater radii). Close secondaries occur in an annulus around Lyot with generally distinct morphologies [Shoemaker, 1962, 1965; Oberbeck and Morrison, 1974] (Figure 1), while “distant” or “far” clusters are not as clearly linked to Lyot. These two populations are examined separately in Section 3.

3. Size-Frequency Distributions of Secondary Clusters

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Identification of Craters and Secondary Clusters
  5. 3. Size-Frequency Distributions of Secondary Clusters
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[10] Crater size-frequency distributions (SFDs) were calculated following Arvidson et al. [1979] with some modifications: Craters were binned in multiplicative 21/8D intervals for purposes of slope-fitting. Finer binning than the more standard 21/2D was used to bring out detail in the SFDs that would otherwise be obscured. Craters were binned such that Dbin−1 < DcraterDbin, putting all craters in a diameter bin that is the largest crater size in that bin. Since the distribution of craters is not even across all diameter bins, nor does it have a single typical power-law distribution with a slope of −2, the local slope between each bin and the next-smallest was used in order to shift the diameter to a more robust weighted mean:

  • equation image

where N(Da) is the number of craters at diameter bin Da. This has a side-effect of having bins that are unevenly spaced in log(D).

[11] Three additional features in our SFD algorithm were run on the incremental SFDs. The first removes the largest bins with too few craters – this cut-off was set at <3 craters in a cumulative bin to eliminate some issues with small-number statistics. The second removes incremental bins (and hence cumulative bins) that had no craters within them. The final feature removes bins below the estimated statistical completeness; we defined this as the incremental bin with the greatest number of craters. Error bars were calculated by ±equation image Poisson statistics [Arvidson et al., 1979]. Once these operations were performed, the incremental SFDs were integrated (discretely summed) to yield a cumulative SFD (Figures 3 and 4). Comparative R-plots (Figure 4) were calculated with similar adjustments. All slopes quoted in this paper are fits to the incremental SFDs with −1 added to yield a statistically accurate slope on a cumulative SFD [Chapman and Haefner, 1967].

image

Figure 3. Lyot's nearby secondary crater size-frequency distribution (SFD) and the overall SFD of far-field secondaries. The slope for the nearby secondaries is significantly different from the typical SFD slope of −2 [McEwen and Bierhaus, 2006].

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image

Figure 4. Two case-study SFDs of distant secondary crater clusters analyzed both from the THEMIS-based crater database [Robbins and Hynek, 2010] and re-analyzed in CTX imagery: (a and b) cumulative SFD, (c and d) same data in an R-plot. The two clusters analyzed are located at 31.5°N, 89.2°E (Figures 4a and 4c), and −8.3°N, −13.4°E (Figures 4b and 4d). Cluster A/C's decameter inflection can be explained by crater saturation [Melosh, 1989], but B/D's cannot because for D < 300 m the slope is constant and below empirical saturation. For illustration purposes, the cumulative SFDs are binned in 21/32D intervals and the R-plots in 21/4D intervals.

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3.1. Close Secondary Craters

[12] Secondary craters are easier to identify close to their primary crater because they are usually entrained in its ejecta and show an over-density as an annulus around the primary. Lyot is a good example and has a large secondary field nearby (Figure 1). Most secondary craters identified are found in long troughs emanating radially from Lyot in its continuous ejecta (Figure 1). The largest crater with secondary-type morphology is a D = 28 km crater just outside the northwest rim, though this is abnormally large at 13% the primary's diameter. The largest alternative is an 11-km crater to the northwest which fits the canonical 5% of primary size relation [Melosh, 1989]. 1719 of these nearby secondary craters were extracted and their SFD is displayed in Figure 3. The diameter range 3.2 < D < 7.0 km has a power-law slope of −5.6 ± 0.3. This is significantly steeper than a normal crater population with slopes between −2 and −3, but it is typical for secondary crater populations [McEwen and Bierhaus, 2006].

3.2. Distant Secondary Craters

[13] All 5341 craters in Lyot's far-field clusters were combined into one SFD (Figure 3); based on SFD slopes, D > 2.5 km craters are likely mostly primaries, but the overall contamination by primaries is minimal since D > 2.5 km craters comprise 0.3% of the total. The power-law slope is −3.9 ± 0.1 for 1.0 < D < 2.5 km. To determine if this was representative, SFDs of all 26 individual clusters with N ≥ 50 craters were created and slopes were fit over approximately the same diameter range; the power-law exponent ranged between −3.4 and −11 with μ = −5.2 (σ = 1.6) and median −4.7. The five largest clusters (N > 120) averaged −5.1 with a range of −3.9 to −6.9. Given the somewhat small numbers involved, we consider these to be consistent with secondary populations but emphasize there is a spread in slope.

3.3. CTX-Based Case Studies of Distant Secondary Crater Clusters

[14] Complementary to the THEMIS-based identification, six clusters were re-analyzed with CTX imagery (ConTeXt Camera from Mars Reconnaissance Orbiter [Malin et al., 2007]). The clusters were selected at random from those with complete CTX coverage. Ranging 5.5–7.5 m/pix scale, crater cluster members down to D ≈ 25 m were identified. The extended SFDs for two clusters are shown in Figure 4, illustrating that higher resolution data yields the same quantitative results as THEMIS for the larger D > ∼800 m. However, the SFD slope abruptly changes at D ≈ 500 m, and the power-law slope ranges between −1.4 and −2.0. This pattern was noted in all test cases and likely extends to the other clusters, the significance of which is discussed below.

4. Discussion and Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Identification of Craters and Secondary Clusters
  5. 3. Size-Frequency Distributions of Secondary Clusters
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[15] Previous identification of Zunil crater secondaries found on the order of 108 craters with D ≥ 15 m up to 3600 km from the primary [Preblich et al., 2007]. Lyot crater is significantly larger (D = 222 km vs. 10.1 km) and significantly older (∼1.6–3.3 Ga vs. ∼200–550 ka) [Kreslavsky, 2008]. Identification and analysis of Lyot secondaries provides another important constraint for the overall study of secondary craters' effects on crater statistics and, by extension, their use in dating planetary surfaces.

[16] We have identified ∼150 secondary crater clusters up to 1500 km farther from their primary than Zunil. They are mainly located southeast of Lyot; six clusters were found southwest and four east and northeast. The continuous ejecta blanket has a preferential east-northeast direction (Figure 1). The ejecta distribution would seem to conflict with the secondary clusters, but it can be explained by modification and burial towards the south, an interpretation supported by Mars geologic mapping [Tanaka et al., 2005]. Due to the ambiguity, we infer the impactor hit Mars obliquely from the west, but determining compass quadrant is more open to interpretation. The impact produced deep radial troughs filled with secondary craters within ∼1–2 crater radii from the rim - different from Zunil which produced very few secondaries within 16 crater radii [Preblich et al., 2007].

[17] Lyot also produced on the order of 104 identifiable far-field secondary craters D > ∼800 m in clusters, although there are likely many more. The overall SFD matches previous work on Martian secondaries [McEwen and Bierhaus, 2006], but we found a different pattern at D < ∼500 m from our CTX-based studies. Since CTX resolution is more than sufficient to identify all decameter-size craters, we interpret this to be a real feature in these secondary crater clusters. In two of the six cases, this can be attributed to crater saturation [Melosh, 1989] (see Figure 4). Three additional non-mutually exclusive hypotheses may explain this feature: First, steep SFD slopes cannot continue to indefinitely small sizes due to a cut-off in the production function; with large craters, this is thought to be ∼2 orders of magnitude before the volume of material needed would exceed the volume of material excavated [McEwen et al., 2005]. Although volume estimates suggest these secondaries are insufficient in number to reach this limit, it remains a likely contributor. A second explanation could be infilling: over 3.3 Ga, to fill a D = 500 m secondary crater (∼50-m deep) would require a rate of 15 nm/yr, but this is at least 10 × faster than observed [e.g., Golombek et al., 2006]. A third hypothesis is that only blocks of a sufficient size can be coherently launched from a large primary, travel several thousand kilometers, and form a secondary cluster; the requisite cut-off would be ∼10–20 m in this case [Melosh, 1989]. Calculations [Melosh, 1989] show that stony projectiles D < ∼1 m would be filtered traveling through Mars' present-day atmosphere. However, the clusters traveled 700–5000 km, ≫10 × the current scale height of Mars' atmosphere, which could plausibly filter blocks of the requisite size. If the CTX SFDs are treated as a model for all identified clusters, Lyot may have produced a minimum of 106 craters D > 50 m and 107 craters D > 15 m, similar to Zunil. This is very likely a lower limit due to erasure processes, inability to locate all clusters, and exclusion of possible crater fields from Lyot.

[18] The implications for using craters to age-date surfaces are significant: First, in agreement with previous work, secondary crater contamination needs to be considered and can significantly affect crater size-frequency distributions (Figures 34). Near large craters, it is an important factor at multi-kilometer scales (Figures 1 and 3). Isolated secondary clusters have steep SFDs and if one were to include these craters when age-dating a sizeable surface, it will result in an erroneously older surface age. While the issue of a large number of secondary craters contaminating kilometer-sized crater statistics has been known for years [e.g., Wilhelms et al., 1978], it has been generally ignored. Second, this study shows that one cannot rely upon a nearby primary crater to use as a criterion for determining if a cluster is secondary in nature - something that is still a point of contention in the community. Third, the inflection to shallower slopes at D < ∼500 m (Figure 4) illustrates a phenomenon that should be studied further: Forthcoming studies from lunar and mercurian high-resolution imagery may elucidate this anomaly, providing discriminating tests of the proposed hypotheses. Further case studies of secondary craters on Mars and other bodies are needed since Lyot and Zunil show significant differences. A more robust model and understanding of secondary cratering is needed to better constrain planetary surface ages and their implications for the history of the solar system.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Identification of Craters and Secondary Clusters
  5. 3. Size-Frequency Distributions of Secondary Clusters
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[19] This paper benefited from useful discussions with J. Skinner and R.A. Nava and from reviews by C. Chapman and an anonymous individual. This work was supported through NASA award NNX10AL65G.

[20] M.E. Wysession thanks Alfred McEwen and Clark Chapman.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Identification of Craters and Secondary Clusters
  5. 3. Size-Frequency Distributions of Secondary Clusters
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References