The South Pole Aitken (SPA) basin is the stratigraphically oldest identifiable lunar basin and is therefore one of the most important targets for absolute age-dating to help understand whether ancient lunar bombardment history smoothly declined or was punctuated by a cataclysm. A feasible near-term approach to this problem is to robotically collect a sample from near the center of the basin, where vertical and lateral mixing provided by post-basin impacts ensures that such a sample will be composed of small rock fragments from SPA itself, from local impact craters, and from faraway giant basins. The range of ages, intermediate spikes in the age distribution, and the oldest ages are all part of the definition of the absolute age and impact history recorded within the SPA basin

Cohen, Barbara A.

Coker, Robert F.

NASA Technical Reports Server

PULLING MARBLES FROM A BAG: DEDUCING THE REGIONAL IMPACT HISTORY OF THE SPA 
BASIN FROM IMPACT-MELT ROCKS.  B. A. Cohen and R. F. Coker, NASA Marshall Space Flight Center, 
Huntsville AL 35806 (Barbara.A.Cohen@nasa.gov). 
 
Introduction: The South Pole–Aitken (SPA) basin 
is the stratigraphically oldest identifiable lunar basin 
and is therefore one of the most important targets for 
absolute age-dating to help understand whether ancient 
lunar bombardment history smoothly declined or was 
punctuated by a cataclysm. A feasible near-term 
approach to this problem is to robotically collect a 
sample from near the center of the basin, where 
vertical and lateral mixing provided by post-basin 
impacts ensures that such a sample will be composed 
of small rock fragments from SPA itself, from local 
impact craters, and from faraway giant basins. The 
range of ages, intermediate spikes in the age 
distribution, and the oldest ages are all part of the 
definition of the absolute age and impact history 
recorded within the SPA basin. 
Impact melt in a scoop sample: SPA near-surface 
materials are a mixture of original SPA rocks, 
reworked SPA material from interior basins, and 
exogeneous material. Because ejecta deposition is a 
ballistic process, successive ejecta deposits excavate 
and mix the target substrate with the ejected material. 
Within the SPA basin, about 20% of the regolith at the 
site is foreign [1, 2], but much of the foreign material 
will not be impact melt, but cold ejecta. We calculated 
the fraction of contributed material that is likely to be 
impact melt using scaling laws in the literature related 
to the transient crater diameter (Dtc). These scaling 
laws are not proven to be valid in the largest basin-
sized impacts such as Imbrium, but are used here as a 
starting point. The fraction of melt in each ejecta 
deposit (Fmelt) can be expressed as the volume of 
impact melt created by the basin (Vmelt) [3] × the 
fraction of melt ejected from the basin (Efficiency) [4] 
/ the total amount of ejecta (Vej) [5]. Fmelt can then be 
applied to the contribution by each basin at any site to 
estimate the relative fraction of impact melt rocks 
derived from each basin (Table 1). 
In a sieved sample, 1 kg of rock fragments greater 
than 2 mm would yield some 10,000 2-4 mm particles, 
over 3000 4-10 mm fragments, and a significant 
number of rocklets >1 cm. Table 1 shows Pmelt, the 
number of particles expected to be impact melt from 
each event in a sample of 15,000 fragments. This 
number is probably only good to an order of 
magnitude, but illustrates that SPA melt is by far the 
dominant impact-melt rock likely to be present. 
Sampling statistics: On the lunar near side, mixing 
of ejecta and local bedrock has led to some ambiguity 
in the origin of specific impact-melt rock groups, 
because we do not have definitive information on the 
composition of the basin floors. In contrast, the unique 
geochemical signature of SPA materials links impact 
melt rocks to the SPA basin and subsequent interior 
basins and craters. It is likely that melt fragments will 
be grouped based on their petrography, geochemistry, 
mineralogy, and spectroscopy, and that perhaps only a 
few fragments from each group will need to be dated 
to recover the age of an event. However, we 
constructed a simple statistical model to understand 
how many randomly-selected impact-melt fragments 
would need to be dated, and with what accuracy, to 
confidently reproduce the impact history of a site, 
using the site and impact events chosen by Haskin [6].  
Each basin event was assigned an age (A) and an 
uncertainty (σA) that represents the actual spread of 
ages a rock created in that event might have. The ages 
of Serenitatis, Imbrium, and Orientale are relatively 
precisely known [7]; the others are straw ages for 
illustration. A melt sheet the size of SPA might be 
expected to yield rocks with a relatively wide spread in 
ages as the sheet cooled, thus its higher σA. 
A sample set of 2000 “marbles” was apportioned 
according to the melt fraction at the model site and 
assigned an age using a random number generator with 
a normal distribution corresponding to A±σA. Each 
marble was also assigned an uncertainty from a 
distribution U±σU, corresponding to a laboratory 
Table 1: Calculated impact melt abundance and provenance at model site 
Basin D (km) Dtc (km) Vej (km3) Vmelt (km3) 
Efficiency  
(%)  Fmelt (%) 
Contribution 
(%) 
Pejecta 
(15000) Pmelt 
SPA 2500 1035       50 82.0 12300 6150 
Australe 880 426 1.01E+07 1.89E+06 41 7.6 1.7 255 19 
M-R 630 321 4.32E+06 6.33E+05 42 6.2 1.5 225 14 
Serenitatis 920 443 1.13E+07 2.18E+06 40 7.8 4.0 600 47 
Bhaba 64 46 1.27E+04 3.56E+02 52 1.5 0.5 75 1 
Imbrium 1160 539 2.05E+07 4.66E+06 39 9.0 6.5 975 87 
Orientale 930 447 1.17E+07 2.26E+06 40 7.8 4.0 600 47 
 
https://ntrs.nasa.gov/search.jsp?R=20100017287 2019-08-30T09:21:51+00:00Z
measurement uncertainty. A reference data set 
consisting of 2000 particles, each having the exact ages 
A±σA represented the “true” impact history. Marbles 
were randomly selected from the set and plotted on 
ideograms (Fig. 1). Subsets of 100, 1000, and 2000 
marbles were selected and added together to compare 
the model datasets with the “true” distribution.  
Scenario 1, with a large σA but small U, was run 
multiple times, because the discreteness of each 
sample curve sometimes flattened the ideogram peak, 
or even produced false subpeaks. Scenario 2 appears 
less discretized, aiding in determining A but masking 
differences in events that have a small ∆A. In Scenario 
3, the reference set is rapidly reproduced with only a 
few hundred marbles. However, younger basins are 
still hard to recognize because only a few marbles 
represent them. If the reference set has half the SPA 
marbles removed, and the rest renormalized, the 
younger basins become more apparent, but the data 
still do not resolve the difference between them. It will 
be crucial to have more information (e.g. 
compositional, mineralogical, remote sensing) to 
cluster fragments with the same age as each other. 
 
 
 
We plan to extend this simple model to any 
location by generalizing the to all large lunar basins as 
well as young, local events that dominate material 
derived from the upper surface [8]. A robotic sample 
should dig past this top layer, but will certainly contain 
many fragments from hundreds of successive nearby 
events. Also necessary is application of statistical tests 
by which individual impact event ages can be assigned 
to groups of samples, such as fitting to a normal 
distribution function [9]. However, these exercises 
show that SPA melt has a high probability of being 
present in a robotic scoop sample and that even if it 
weren’t recognizable by geochemical or petrologic 
means, dating of a few thousand impact-melt 
fragments will still yield the age of the SPA basin from 
such a sample. 
References: [1] Haskin, L.A., et al. (2003) MAPS 38, 13. [2] 
Petro, N.E. and C.M. Pieters (2004) JGR-Planets 109, doi 
10.1029/2003JE002182. [3] Cintala, M.J. and R.A.F. Grieve (1998) 
MAPS 33, 889. [4] Warren, P.H. (1996) LPSC 27, 1381. [5] Collins, 
G.S., et al. (2005) MAPS 40, 817. [6] Haskin, L.A., et al. (2003) 
LPSC abstract #1434. [7] Stöffler, D. and G. Ryder (2001) Space 
Science Reviews 96, 9. [8] Cohen, B.A., et al. (2005) MAPS 40, 755. 
[9] Muller, R.A. et al. (2000) in Accretion of Extraterrestrial Matter 
Throughout Earth's History, ed B. Peucker-Ehrenbrink and B. 
Schmitz, Kluwer Publishers. Table 2. Model run parameters 
Basin A ± σA (Ma) U ± σU (Ma) # 
Scenario 1     
SPA 4400 ± 100 10 ± 10 1800 
Australe 4200 ± 40 5 ± 10 19 
M-R 3920 ± 30 5 ± 10 16 
Serenitatis 3890 ± 10 5 ± 10 44 
Bhaba 3870 ± 10 5 ± 10 5 
Imbrium 3850 ± 20 5 ± 10 71 
Orientale 3750 ± 20 5 ± 10 44 
Scenario 2     
SPA 4400 ± 100 70 ± 30 1800 
Australe 4200 ± 40 30 ± 15 19 
M-R 3920 ± 30 10 ± 10 16 
Serenitatis 3890 ± 10 10 ± 10 44 
Bhaba 3870 ± 10 10 ± 10 5 
Imbrium 3850 ± 20 10 ± 10 71 
Orientale 3750 ± 20 10 ± 10 44 
Scenario 3     
SPA 4400 ± 30 10 ± 10 1800 
Australe 4200 ± 20 5 ± 10 19 
M-R 3920 ± 20 5 ± 10 16 
Serenitatis 3890 ± 10 5 ± 10 44 
Bhaba 3870 ± 10 5 ± 10 5 
Imbrium 3850 ± 20 5 ± 10 71 
Orientale 3750 ± 20 5 ± 10 44 
Scenario 3     
SPA 4400 ± 100 10 ± 10 948 
Australe 4200 ± 40 5 ± 10 98 
M-R 3920 ± 30 5 ± 10 87 
Serenitatis 3890 ± 10 5 ± 10 231 
Bhaba 3870 ± 10 5 ± 10 29 
Imbrium 3850 ± 20 5 ± 10 376 
Orientale 3750 ± 20 5 ± 10 231 
 
Figure 1. Model results. 
 
Pulling marbles from a bag: Deducing the regional 
impact history of the SPA basin from impact-melt rocks 
Barbara Cohen and Robert Coker, NASA Marshall Space Flight Center, Huntsville AL 35806 
Introduction 
• South Pole-Aitken (SPA) basin is an important target for absolute 
age-dating to constrain ancient lunar bombardment history 
Contribution (%) 
• After formation, SPA surface materials became a mixture of original 
SPA floor rocks, reworked SPA material from interior basins, and 
exogeneous material SPA 
Australe 
M-R 
Serenitatis 
Bhaba 
Imbrium 
Orientale 
• This is a different starting point from Apollo sites - SPA floor is the 
substrate; remote sensing sees a unique SPA geochemical signature 
• The range of ages, intermediate spikes in the age distribution, and 
the oldest ages are all part of the definition of the absolute age and 
impact history recorded within the SPA basin 
Provenance of melt rocks 
• Because ejecta deposition is a ballistic 
process, successive ejecta deposits 
excavate and mix the target substrate 
with the ejected material 
• Ejecta and mixing models (Haskin et al. 
2003, Petro & Pieters 2004) show -20% 
of SPA regolith is foreign - but much of 
the foreign material will be cold ejecta, 
not impact melt rocks 
• Fraction of material that is likely to be 
non-SPA impact melt using scaling laws: 
F me lt = (V me lt / Veiecta ) X E 
Volume of 
impact melt 
(Cintala & 
Grieve 1998) 
Volume of 
ejecta 
(Collins 
2005) 
Efficiency, or 
Fraction of melt 
ejected (Warren 
1996) 
• One can use these relationships to 
calculate the volumetric amount of 
impact-melt rocks at any site 
• Combine with mixing models to 
calculate the proportion at the site 
• Calculations shown here are for the SPA 
site in Haskin et al. 2003 
Basin 
SPA 
Australe 
M-R 
Serenitatis 
Bhaba 
Imbrium 
Diameter 
(km) 
2500 
880 
630 
920 
64 
1160 
Volume of 
material ejected 
km 3 
1.01E+07 
4.32E+06 
1.13E+07 
1.27E+04 
2.05E+07 
Volume of 
material 
melted km3 
1.89E+06 
6.33E+05 
2.18E+06 
3.56E+02 
4.66E+06 
Age history of melt rocks 
• If you randomly dated 2000 impact melt-rocks from this site, what would the age 
distribution look like? 
• Reference dataset: Age (A) of 7 basins 
± aA represents the range in real ages for a single event (e.g . slow cooling) 
• Model dataset: 2000 impact-melt rocks apportioned according to the calculated melt 
fraction at the model site 
Assigned a sample age (A ± aA) from within the normal distribution aA 
Assigned an uncertainty (U ± aU) associated with laboratory measurement 
Conclusions 
• SPA-floor impact melt exists at interior landing sites and will be the dominant impact-
melt rock type in any sample 
• Corroborating information (petrology, elemental composition, regional context, RS) are 
important to correct interpretation 
• Even if it weren 't recognizable by geochemical or petrologic means, dating of a few 
thousand impact-melt fragments is still likely to statistically yield the age of the SPA 
basin ••
Future Work: 
I 
• A fuller regolith model to track the f 
distribution of impact melt rocks from distant 
basins and young , local events 
• A statistical test by which individual impact 
event ages can be assigned to groups of 
samples, such as a simple signal-to-noise 
threshold or fit to a normal distribution 
Efficiency 
(%) 
41 
42 
40 
52 
39 
Fraction of impact-melt 
material ejected from 
each basin % 
50 
7.6 
6.2 
7.8 
1.5 
9.0 
Contribution of basin 
ejecta to the study 
site % 
82.0 
1.7 
1.5 
4.0 
0.5 
6.5 
, , , 
Future work includes a full three-dimensional Monte Cario model of impact-melt 
redistribution, proposed with Amy Barr and Clal1l Chapman at SwRI. The proposed 
3D megaregolith model will run on the same numerical "backbone" as the core 
formation model applied to Saturn's moon Titan (after Barr and Canup, 2010). Shown 
here is the density (colors) of Titan's surface as a function of latitude and longitude 
after its bombardment by 3xl021 9 of comets during an outer solar system late heavy 
bombardment. Dark blue indicates mixed ice and rock; light blue indicates ice-rich 
i . " 
For 15000 random 
fragments, # derived from 
each basin 
12300 
255 
225 
600 
75 
975 
For 15000 random 
fragments, # impact melt 
derived from each basin 
6150 
19 
14 
47 
1 
87 
Model results (so far) 
3.77,-,------~ --c-
3.30 
2.83 
~ j,> 2.36 
o 
~ 
• 
'5 1.89 
.~ 
~ o 1.41 
" 
• 
0.94 
0.47 
0.00 --::::-:-' 
3600 
7." 
660 
5.65 
i 
<l> 4.71 
0. j 
'5 3.77 
~ 
" ~ 2.83 
" 
• 
1.88 
0.94 
3800 4000 4200 4400 
Apparent Age (Mal 
4600 4800 
0.00 --::::-:--
3600 3800 4000 4200 4400 4600 4800 
25.13 
21.99 
18.85 
i 
<l> 15.71 
0. j 
'5 12.57 
~ 
" ~ 9.42 
• 
6.28 
3.14 
Apparent Age (Mal 
0.00 --:::,,-' 
3600 3800 4000 4200 4400 4600 4800 
13.24 
11.58 
9.93 
i ~ 8.27 
j 
'5 6.62 
~ 
" ~ 4.96 
• 
3.31 
1.65 
Apparent Age (Mal 
0.00 --::::-:-" ~I" 
3600 3800 4000 4200 4400 4600 4800 
Apparent Age (Mal 
5000 
5000 
Scenario 1 
Basin A:t oA (Mal U :I: aU (Mal # 
SPA 4400:1: 100 10:1: 10 
Australe 4200 :I: 40 
f-::-.:::M",-R 3920 :I: 30 
Serenitatis 3890:1: 10 
Bhaba 3870:1: 10 
Imbrium 3850 :I: 20 
Orientale 3750 :I: 20 
Large aA small U 
5:1: 10 
5:1: 10 
5:1: 10 
5:1: 10 
5:1: 10 
5:1: 10 
1800 
19 
16 
44 
S 
71 
44 
Small U discretizes the curve, 
sometimes flattening the 
ideogram peak, or even 
producing false subpeaks . 
Scenario 2 
SPA 4400:1: 100 70:1: 30 1800 
Australe 4200:1: 40 30:1: 15 19 
M-R 3920:1:30 10:1:10 16 
Serenitatis 3890:1: 10 10:1: 10 44 
Bhaba 3870:1: 10 10:1: 10 5 
Imbrium 3850:1: 20 10:1: 10 71 
Orientale 3750:1: 20 10:1: 10 44 
Large aA, large U 
Large U smooths the curve, 
more faithfully reproduces A but 
can mask events with small M 
Scenario 3 
SPA 4400:1: 30 10:1: 10 1800 
Australe 4200:1: 20 5:1: 10 19 
M-R 3920:1: 20 5:1: 10 16 
Serenitatis 3890:1: 10 5:1: 10 44 
Bhaba 3870:1: 10 5:1: 10 5 
Imbrium 3850:1:20 5:1:10 71 
Orientale 3750:1: 20 5:1: 10 44 
Small aA, small U 
Reference set reproduced with 
only a few hundred marbles, but 
younger basins are hard to 
recognize because only a few 
5000 marbles represent them 
Scenario 4 
Basin A:t oA (Mal U :I: aU (Mal # 
SPA 4400:1: 100 10:1: 10 948 
Australe 4200:1: 40 5:1: 10 98 
f-::-.:::M",-R 3920:1: 30 5:1: 10 -::87':--1 
Serenitatis 3890:1: 10 5:1: 10 231 
Bhaba 3870:1: 10 5:1: 10 29 ---I 
Imbrium 3850:1: 20 5:1: 10 376 
Orientale 3750 :I: 20 5:1: 10 231 
Small aA, small U, fewer SPA 
Same as Scenario 3 but 
reference set removes half the 
SPA samples and renormalizes 
the rest so the younger basins 
5000 become more apparent 


Pulling Marbles from a Bag: Deducing the Regional Impact History of the SPA Basin from Impact-Melt Rocks

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