Refinement of the Lunar Production Function - The CSFD-Slope of Small Crater Diameters on Ejecta Blankets
Authors: Oetting Astrid , Hiesinger Harald , van der Bogert Carolyn 
Published: September 2022

&lt;p&gt;&lt;strong&gt;Introduction:&lt;/strong&gt; The dating of geological surfaces on the Moon is crucial for understanding its geological history and evolution. The measurement of Crater Size-Frequency Distributions (CSFDs) can be used for determining relative and absolute ages of surfaces. Older surfaces reflect more and larger craters than younger geological units [1-4]. To determine the relative surface ages, a production function (PF) is constructed to which the CSFD is fitted. One frequently used PF was empirically-derived by measuring craters on reference surfaces using Apollo era data (Neukum, 1983 [1]), which was revised in 2001 [5], and is valid for crater diameters of 10 m - 300 km and 10 m - 100 km, respectively. With increased image resolution of more recent missions [e.g., 6], it has been possible to measure CSFDs for crater diameters down to a few meters. Therefore, it would be beneficial to be able to extend the PF to smaller crater diameters, which would allow the determination of relative and absolute ages for young/small geological units.&lt;/p&gt;
&lt;p&gt;A crucial influence on small craters formed in the strength regime are target properties, which has been investigated in several studies [e.g., 7, 8, 9]. Therefore, we aim to perform the crater counts exclusively on continuous ejecta blankets. Secondary craters [e.g., 10-12] influence the CSFD as well and can contaminate the count area, causing a steeper CSFD-slope [e.g., 10, 13, 14]. To avoid this effect and obtain the cleanest PF possible, we selected ejecta areas derived from young Copernican-aged craters. This minimizes the number of field secondary craters on the ejecta and also avoides major degradation of the small craters [15, 16]. However, the identification of self-secondary craters remains problematic, since they occur irregularly distributed on the ejecta blankets and often have morphologies similar to primary craters [e.g., 12, 13].&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Method:&lt;/strong&gt; We used Lunar Reconnaissance Orbiter Narrow Angle Camera (NAC) images [6] including M180509194LE, M1122929850LE and M103831840LE/RE at Giordano Bruno (GB), M1107052575RE and M1112971104RE at Moore F, M129187331LE/RE &amp;#160;at North Ray (NR), M119754107RE at South Ray (SR) and M114064206LE at Cone. The resolutions vary between 1.6 m/px and 0.5 m/px, the incidence angles are from 54&amp;#176; to 78&amp;#176;. The CSFDs were measured in ArcGIS with the CraterTools add-in of [18] and displayed in CraterStats with pseudo-log binning [19].&lt;/p&gt;
&lt;p&gt;Two areas were investigated at Cone, three at GB, Moore F and SR, respectively. Four areas were investigated by [17] at NR. The selected counting areas are all on the ejecta blakets of the named craters.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Results:&lt;/strong&gt; Similar to [17] we combined the statistics from the separate count areas into one file and display these CSFDs in a cumulative plot in Figure 1.&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; width=&quot;367&quot; height=&quot;510&quot; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;em&gt;Figure &lt;/em&gt;&lt;em&gt;1&lt;/em&gt;&lt;em&gt;: Display of the combined CSFDs at GB (green), Moore F (blue), NR (violet), SR (red) and Cone (orange), respectively. The vertical lines of individual data points represent the error bars.&lt;/em&gt;&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;The comparison between the individual CSFD-slopes at GB, Moore F, NR, SR and Cone generally show slightly steeper slopes than the nominal -3 slope of [1] for crater diameters between 10 m and 23 m (in our case 20 m, see Table 1).&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; width=&quot;433&quot; height=&quot;91&quot; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;em&gt;Table 1: Display of the considered crater diameter range and the respective CSFD-slopes.&lt;/em&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Discussion:&lt;/strong&gt; We found that the CSFD-slopes on the ejecta blakets of the investigated craters show a tendency regarding the crater diameter. Considering only diameters &amp;#8804;10 m the slope is marginally shallower than Neukum&amp;#8217;s [1] -3 slope, except at GB, which might be explained through secondary cratering. This trend was also observed by [15] (and references therein) and [20] who investigated NR, Cone, Copernicus and Tycho. This might suggest that CSFDs of young Copernican craters have actually a slightly shallower slope at smaller crater diameters. Another possible explanation is the faster degradation of smaller craters [e.g., 21]. Further effects might be the coverage of ejecta material of nearby craters; NR (52.3 Ma [20]), might be influenced by the ejecta of SR (2 Ma [22]), SR by Baby Ray. Moreover, larger craters in two areas at NR and Cone probably penetrated through the ejecta blanket, which can lead to mixed target propertie effects.&lt;/p&gt;
&lt;p&gt;Further investigations are required to quantify the effects of secondary cratering, target properties, crater degradation or impactor flux on the determination of our CSFDs. Additional investigation is necessary to determine at which crater diameter the slope becomes shallower or if a transition zone is present.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Acknowledgments:&lt;/strong&gt; This Project is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) &amp;#8211; Project-ID 263649064 &amp;#8211; TRR 170.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;References:&lt;/strong&gt; [1] Neukum (1983), NASA TM-77558. [2] &amp;#214;pik (1960), RAS 120(5), 404-41. [3] Shoemaker et al. (1970), Science, 167 (3918), 452-455. [4] Baldwin (1971), Icarus, 14, 36-52. [5] Neukum et al. (2001), Space Sci. Rev., 96, 55. [6] Robinson et al. (2010), Space Sci. Rev. 150, 81-124. [7] van der Bogert et al. (2010), LPSC 41, #2165. [8] W&amp;#252;nnemann et al. (2011), Proceedings of the 11th hypervelocity impact symposium., Vol. 20. [9] van der Bogert et al. (2017), Icarus, 298, 49-63. [10] McEwen and Bierhaus (2006), Annu. Rev. Earth Planet. Sci. 34, 535-567. [11] Xiao and Strom (2012), Icarus 220, 254. [12] Zanetti et al. (2017), Icarus 298, 64-77. [13] Plescia et al. (2010), LPSC 41, #2038. [14] Plescia and Robinson (2011), LPSC 42, #1839. [15] Moore et al. (1980), Moon and Planets, 23, 231-252. [16] Fassett and Thomson. Journal of Geophysical Research: Planets 119.10, 2255-2271. [17] Hiesinger et al. (2012), JGR 117, E00H10. [18] Kneissl et al. (2011), PSS 59, 1243-1254. [19] Michael et al. (2016), Icarus 277, 279-285. [20] Williams et al. (2014), Icarus 235, 23-36. [21] Mahanti et al. (2018), Icarus, 299, 475-501. [22] St&amp;#246;ffler and Ryder (2001), Space Sci. Rev., 96, 9-54.&lt;/p&gt;
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