Fresh lunar crater ejecta as revealed by the
Miniature Radio Frequency (Mini-RF)
instrument on the Lunar Reconnaissance Orbiter
Samuel W. Bell ‘11
Submitted to the Department of Astronomy of Amherst College in partial fulfillment of
the requirements for the degree of Bachelor of Arts with honors.
Advisor: Darby Dyar
Readers: George Greenstein and Peter Crowley
May 5, 2011
Abstract
On timescales of tens to hundreds of millions of years, micrometeorite, solar wind
ion, and cosmic ray bombardment gradually erode the ejecta blankets that form around
small lunar impact craters. Sensitive to surface roughness on the scale of its 12.6 cm
wavelength, the 30 m/pixel Miniature Radio Frequency (Mini-RF) instrument provides
detailed imagery of the ejecta blankets of small lunar craters with unprecedented
resolution and quality, allowing large numbers of ejecta blankets to be studied with a
higher degree of precision than previously possible (Thompson et al., 1981; Nozette et
al., 2010; Neish et al., 2011).
Using well-established crater-counting techniques
(Arvidson et al., 1979; Michael and Neukum, 2010), analysis of the lifetime of the
discontinuous portion of the ejecta blanket at varying crater diameters shows that the
discontinuous ejecta lifetime is proportional to the square of the crater diameter.
Absolute dates of individual craters can be estimated by combining the empirically
derived function for discontinuous halo lifetime with estimates of what fraction of its
lifetime each discontinuous ejecta blanket has lived through. Cosmic ray exposure ages
of craters visited by the Apollo missions provide confirmation of these results: The
resultant lifetime model predicts that the discontinuous ejecta blanket around the 25-30
Ma Cone Crater (Turner et al., 1971) will have vanished after 8.7(+1.5/-1.7) Ma, and the
discontinuous ejecta blanket is indeed absent. This method produces a radiometrically
determined age estimate of 54(+39/-29) Ma North Ray Crater, consistent with the known
age of 50.0±1.4 Ma (Arvidson et al., 1975).
i
Table of Contents
Abstract............................................................................................................................... i
1. Introduction ................................................................................................................... 1
I Dating individual craters ........................................................................................... 4
II Dynamics of ejecta degradation............................................................................... 4
2. Literature Review ......................................................................................................... 6
I.1 The Moon—history and general features ............................................................. 6
I.2 The Moon—surface water ...................................................................................... 7
I.3 The Moon—erosion processes ................................................................................ 9
II.1 The impact process—the basics .......................................................................... 11
II.2 The impact process—ejecta properties .............................................................. 14
II.3 The impact process—oblique impacts ............................................................... 14
III.1 Radar observation—the basics ......................................................................... 17
III.2 Radar observation—S1 imagery ....................................................................... 18
III.3 Radar observation—CPR imagery ................................................................... 21
III.4 Radar observation—topographic effects on position information ................ 23
IV.1 Optical crater dating—Trask (1971) method .................................................. 25
IV.2 Optical crater dating—erosion modeling method ........................................... 28
IV.3 Optical crater dating—space weathering......................................................... 30
V Radar-bright halos .................................................................................................. 31
3. Methods........................................................................................................................ 35
I Crater counting......................................................................................................... 35
I. Crater counting—R-plot analysis .......................................................................... 35
II.1 Data sets ................................................................................................................ 37
II.2 Datasets—initial search and highlands focus region ........................................ 39
II.3 Datasets—Mare Serenitatis and 2400s focus regions ....................................... 42
III Age quantification ................................................................................................. 42
IV Image processing ................................................................................................... 43
V Radial brightness profiles....................................................................................... 45
4. Results .......................................................................................................................... 47
ii
I Estimating Discontinuous Halo Lifetimes From Crater Counting ...................... 47
II Estimating Ages From Discontinuous Halo Lifetimes and Diameters............... 53
III Morphology Variation of Degrading Craters ..................................................... 53
IV.1 Comparison With Apollo Results—Cone Crater ............................................ 63
IV.2 Comparisons With Apollo Results—North Ray Crater. ................................ 67
V Thompson et al. (1981) comparison ...................................................................... 69
5. Discussion .................................................................................................................... 76
I.1 Secondary Cratering ............................................................................................. 76
I.2 Wells et al. (2010) Ejecta Morphologies—Diagnostic of Secondaries? ............ 77
II Problems With Halo Diameter Quantification .................................................... 80
III.1 The Discontinuous Ejecta Lifetime to Crater Diameter Relationship—
Extrapolation to Small Craters.................................................................................. 81
III.2 The Discontinuous Ejecta Lifetime to Crater Diameter Relationship—
Extrapolation to Large Craters ................................................................................. 83
IV Possible Effect of Lithology .................................................................................. 84
V.1 Variations in the Impact Rate ............................................................................. 85
V.2 Variations in the Micrometeorite Flux and Erosion Rate ................................ 87
6. Conclusion ................................................................................................................... 89
References ........................................................................................................................ 92
iii
Acknowledgements
I would like to thank Amherst College, the Applied Physics Laboratory intern program,
and NASA for sponsoring and funding this research. I would like to thank Josh Cahill,
G. Wesley Patterson, and Ben Bussey for general support and answering my questions
this summer; Mike Zanetti for help with LROC image processing; and Catherine Neish
for teaching me ISIS, C-shell, and the basics of radar observation. I would also like to
thank all of my friends for their help (especially with Word formatting) and support
throughout this process. And finally I would like to thank Brad Thomson and Darby
Dyar for all their help. I cannot say how much I appreciate everything they’ve done for
me.
iv
Introduction
The Moon may not have the cryovolcanic plumes of Enceladus and Triton, the
hydrocarbon seas of Titan, the subsurface ocean of Europa, the constant volcanic activity
of Io, or the sheer size of Ganymede, but it has two virtues that make it one of the most
scientifically important bodies in the solar system.
To begin with, it is close. Eleven years after NASA was founded, astronauts had
landed on the Moon; forty-one years later, no other extraterrestrial body in the solar
system has felt the bootprints of an astronaut. It can take more than half an hour for
robotic mission controllers to send a signal to a Mars and back but only a few seconds to
send one to the Moon. The Moon is, therefore, the second most easily accessible body in
the universe (after Earth).
Even more importantly, the Moon is a highly simplified system. It has only three
rock types (basalts, anorthosites, and impact breccias), exceptionally few water
molecules, no atmosphere, no active volcanism, no plate tectonics, and no evidence of
extraterrestrial life. The lunar surface is so quiet that the footprints the astronauts left
behind forty years ago remain pristine and virtually undisturbed today.
All the
complexities that plague terrestrial geology are dramatically reduced on the Moon. These
qualities make the Moon the perfect place to study impact processes.
Space debris periodically collides at high speeds with the Earth, the Moon, and all
other planetary bodies. When an impactor strikes the lunar surface, it usually makes a
roughly circular depression known as an impact crater. But it also kicks up a cloud of
debris, which spreads out on ballistic trajectories and deposits itself in a blanket of rubble
extending out to more than ten crater radii. Planetary geologists call the boulders,
1
pebbles, and powder that make up these debris “ejecta,” and they form one of the most
significant types of landform on the Moon. An incessant rain of microscopic impactors
obliterates the optical signature of the ejecta within a few tens of million years (rapidly,
geologically speaking) for craters with diameters in the range of a few kilometers (Swann
and Reed, 1974).
The visibility of ejecta depends strongly on the viewing and
illumination geometry, with high sun-angle photographs displaying the ejecta most
clearly (Schultz, 1976). Only the ejecta around the most recent craters, a tiny fraction of
the total, are evident in visible light images, and even then the appearance of the ejecta
varies heavily with the observation conditions. Fortunately, visible light is not our only
choice for imaging the Moon.
Earth-based radio observatories have long been observing the near side of the
Moon using radar wavelengths (3.8 to 70 cm) (e.g. Lincoln Laboratory, 1968; Thompson
et al., 1971; Ghent et al., 2005). Until recently, high-resolution coverage remained quite
limited, and the far side of the Moon lay hidden from even the best Earth-based radio
telescopes.
All that changed in June of 2009 when NASA launched the Lunar
Reconnaissance Orbiter, carrying with it a radio experiment known as Mini-RF, which is
short for “miniature radio frequency.” (A preliminary version of Mini-RF known as
Mini-SAR flew on Chandrayaan-1, an Indian spacecraft that launched in October of 2008
and failed in August of 2009). Because the orbiter passes over the entire Moon, it can see
a hemisphere impossible for Earth-based radar to image. Taking advantage of the orbital
motion of the spacecraft, Mini-RF produces images with 30 m resolution (Nozette et al.,
2010). At these wavelengths, numerous craters with ejecta preserved in bright “halos”
can be seen spreading out from crater rims, as seen in the example in Fig. 1.1. The
2
A
B
Figure 1.1: Two examples of fresh craters with ejecta displayed in Mini-RF total
backscatter. Both craters show the difference between the blocky inner continuous ejecta
and the fine outer discontinuous ejecta. Image A has a clear zone of avoidance in the
direction the indicator came from, indicating and oblique impact. Image B has an
asymmetry in the ejecta that may be due to a moderately oblique impact. Unlike most
other images in this thesis, these images have not been gamma-corrected, and they have
been contrast-enhanced to bring out subtle features in the ejecta blankets.
3
brightness in a radar image of a simple body like the Moon is largely due to the
roughness of the surface on the scale of the wavelength of the radar. This means that the
12.6 cm Mini-RF antenna is sensitive to the abundance of blocks on the order of 12.6 cm
across, so it will be able to detect small boulders in impact ejecta long after space
weathering has darkened their surfaces to the color of the rest of the Moon.
I Dating individual craters
There are few things more important to understanding any planetary body than
knowing the ages of its surface features. However, dating capabilities on bodies other
than the Earth are quite limited. By counting the number of impact craters superimposed
on a feature since it was formed, planetary geologists can roughly estimate its age
(Arvidson et al., 1979; Michael and Neukum, 2010). But dating individual impact craters
is harder because their small sizes make statistically significant crater counting difficult
(Guinness and Arvidson, 1977; Craddock and Howard, 2000).
Furthermore, crater
counts of small craters are less reliable because a significant fraction of these craters may
be secondary craters (craters formed by pieces of ejecta from much larger impacts), and
the crater counting methodology assumes only limited secondary cratering (Gunness and
Arvidson, 1977; Rodrigue, 2011). One of the most exciting possibilities offered by
studies of lingering radar signatures from crater ejecta is quantification of how much the
ejecta have faded since the crater first formed, thus constraining the crater’s age.
II Dynamics of ejecta degradation
Degraded impact ejecta dominate the lunar surface. Over the course of the 4.5
billion years since the lunar crust crystallized, nearly every part of the lunar surface has
4
been gardened and blanketed in countless layers of ejecta. As soon as the ejecta are
deposited, they begin to degrade from subsequent smaller impacts. Over the course of
millions of years, microscopic impactors and solar wind particles blast the rocks in the
ejecta to powder, ultimately leaving a sea of fine particles coating the entire Moon. The
only rocks remaining on the lunar surface are pieces of ejecta that have yet to completely
degrade. Most of the rock samples returned in the Apollo missions came from partially
degraded ejecta. In the 1970s, computer models predicted the erosion timescales of rocks
of different sizes on the lunar surface (McDonnell et al., 1977), but empirical
confirmation of those results is currently limited to cosmic ray exposure ages of Apollo
samples (e.g. Turner et al., 1971). Moreover, the evolving morphology of the ejecta
blanket as it degrades is poorly constrained. By studying ejecta from craters in various
habitats and states of degradation with radar imagery from the Mini-RF instrument, this
thesis seeks to address some of these issues.
5
Literature Review
I.1 The Moon—history and general features
The Moon is the only natural satellite of the Earth.
Although its mass
(73.4767±0.0033!1021kg, Wieczorek et al., 2006) is only 1.23% of the mass of the Earth,
it is the most massive moon in relation to the mass of its planet in our solar system
(although the Kuiper Belt object Charon is 12% of the mass of its companion, the dwarf
planet Pluto). This mass ratio makes the two normal scenarios for moon-formation
unlikely: For a planet to capture a moon, it must cause the orbit of the potential moon to
lose energy, usually by entering the atmosphere and losing energy through aerobraking
(Newsom and Taylor, 1989).
However, the abnormally high mass ratio makes it
exceedingly difficult for the Moon to have been captured by an Earth with an atmosphere
considerably thinner than the Moon is wide. Moreover, the high mass ratio means that
the angular momentum of the Earth-Moon system is unusually high given the total mass
of the system. If the Moon had formed by accretion around the Earth, it would be
difficult to explain how the Earth-Moon system could have acquired its extraordinarily
high angular momentum (Newsom and Taylor, 1989). Hartmann and Davis (1975)
proposed a possible solution to this conundrum, which was later modified by Hartmann
(1986): During accretion, a Mars-sized body slammed into the Earth in a giant impact.
This massive impact would have vaporized the outer layers of the Earth and created
enough angular momentum for the Moon to form from the debris (assuming the impactor
struck at a sufficiently low angle).
After its formation, the Moon was covered in a magma ocean, which formed a
crust when the lighter crystals floated to the surface (Warren, 1985). The outer crust was
6
composed wholly of a single rock type. Anorthosite, the rock that makes up the entirety
of the original outer crust of the Moon, is composed almost entirely of the mineral
plagioclase feldspar, (NaSi,CaAl)AlSi2O8. At around 4.0 Ga (billion years ago), Jupiter
and Saturn are thought to have entered into a 2:1 orbital resonance with each other, where
Jupiter completed two orbits around the Sun for every one orbit of Saturn (Gomes et al.,
2005). This resonance led to the destabilization of the disk of Pluto-like planetesimals
that once crowded the outer solar system, scattering the planetesimals around the solar
system, including across the orbit of the Earth. This dramatic increase in the number of
bodies crossing the orbit of the Earth caused a massive spike in the number of impacts on
both the terrestrial and lunar surface, forming vast impact basins 1000 km wide that still
dominate the surface geography of the Moon (erosion has removed most evidence of
these early impacts on the Earth). At the sites of the larger impacts, massive basaltic
volcanism often ensued, creating vast plains of basalt known as maria (singular mare).
Later impacts also created a third type of lunar rock by smashing and welding together
bits of preexisting rock into what is known as a breccia.
I.2 The Moon—surface water
The two dominant rock types on the Moon, basalt and anorthosite, both also occur
on the Earth, but lunar basalts and anorthosites differ from terrestrial examples in one
important aspect—their water content. All terrestrial rocks contain water, whether locked
into pore spaces or contained in hydrated minerals like amphiboles and micas. Only
recently (and controversially) have exceedingly small amounts of water (4-46 ppm) been
detected in Apollo samples (Saal et al., 2008).
Observations of the 3 µm water
absorption band in IR spectroscopy of the lunar surface have produced more widely
7
accepted evidence for water in the lunar regolith (Pieters et al., 2010). It is thought that
this water forms from solar wind implantation creating a monolayer of adsorbed water on
lunar regolith grains, but laboratory experiments have difficulty simulating this process
(Hibbitts et al., 2010).
Water ice may be lurking in permanently shadowed craters on the poles, and this
speculation was one impetus behind the Mini-RF instrument because radar can
distinguish between water ice and hydrogen in other forms (Nozette et al., 2010). While
it is generally believed that some form of enhanced hydrogen lies at the poles, there is
considerable debate about its nature and distribution. The LEND neutron spectrometer
on LRO, while confirming the presence of regions of concentrated hydrogen at the lunar
poles, did not find any statistically significant correspondence between the permanently
shadowed regions and the hydrogen concentrations (Mitrofanov et al., 2010). One
permanently shadowed region in Cabeus crater did correspond to the hydrogen
concentration, and it was here that the LCROSS impact took place (Schultz et al., 2010;
Colaprete et al., 2010). The LCROSS experiment crashed an impactor probe into the
lunar surface and produced a plume of ejecta, which was observed from another
spacecraft equipped with spectrometers covering from the near UV to the near IR
(Schultz et al., 2010; Colaprete et al., 2010). LCROSS did detect water and OH thought
to have formed from water, but the results are somewhat controversial because they also
show several unexpected species, such as organics and silver (Schultz et al., 2010;
Colaprete et al., 2010).
Even if relatively large water concentrations are confirmed at the poles, the Moon
will overall remain exceptionally dry.
Combined with the presence of only three
8
principal rock types, this lack of aqueous alteration helped create a Moon with
exceptional mineralogical simplicity. Because ice content has a very strong effect on
radar returns, this strongly simplifies the interpretation of Mini-RF data.
I.3 The Moon—erosion processes
Although the Moon is devoid of running water, glaciers, an atmosphere, life, and
all the forces that dominate erosion on Earth and Mars, it does still have erosion, albeit at
a very low rate. The predominant erosive process is micrometeorite impact. On Earth,
incoming interplanetary dust particles either burn up in the atmosphere or lose their
momentum and gradually drift to the surface. On an airless body like the Moon, the
interplanetary dust particles collide at the same speeds as the most massive impactors,
whose root mean square velocity is 19.2 km/s (Stuart and Binzel, 2004).
In the discrete problem of a rock on the lunar surface, there are three components
to micrometeorite erosion. When impacting particles are very small with respect to the
scale of the target rock, they create tiny craters like the one shown in Figure 2.1,
gradually removing material from the surface and wearing the rock down by abrasion
(Ashworth, 1978). When the impacting particles are large enough, the impact will be
powerful enough to shatter the rock into fragments in a process known as catastrophic
rupture (Ashworth, 1978). A third component to lunar erosion is sputtering, where
individual high-energy particles like cosmic rays and solar wind ions blast tiny numbers
of atoms from the surface of the rock (McKay et al., 1991). McDonnell et al. (1977)
developed a computer model to simulate the cumulative effects of these three erosion
processes on destruction of lunar rocks of varying sizes, although their results differed
9
Figure 2.1: A microscopic impact crater on a lunar regolith particle. From McKay et al.
(1991).
10
noticeably depending on whether their model of the flux of impacting particles was taken
from measurements of impact types on the lunar surface or from measurements of
particle fluxes taken on spacecraft (Figure 2.2). In their model, sputtering was the
dominant erosive process for microscopic particles, and catastrophic rupture was the
dominant erosive process for particles with diameters above 0.1 mm (Figure 2.2)
(McDonnell et al., 1977).
II.1 The impact process—the basics
As the most important geological process on the lunar surface, impact cratering
has received considerable study, and the basics of the process are now fairly well
understood. The impact process begins when a projectile impacts the lunar surface at a
supersonic velocity. The projectile has one of two possible sources: It may be a nearEarth asteroid or comet on a collision course with the Moon, or it may be a chunk of rock
ejected from the formation of another lunar crater. In the first case, the resulting crater is
known as a primary crater, and in the second case, the resulting crater is known as a
secondary crater. Primary impactors hit the lunar surface with a root mean square
velocity of 19.2 km/s (Stuart and Binzel, 2004), but secondary lunar impactors must
impact at below the Moon’s escape velocity of 2.4 km/s. A lower-velocity impactor will
form a smaller crater than a higher-velocity impactor of the same mass, but the diameter
of the resulting crater is also a function of impactor mass (Melosh, 1989). Diameter
alone cannot distinguish between a primary crater formed at higher velocity by a smaller
projectile and a secondary crater formed at lower velocity by a larger projectile. It has
been suggested that secondary craters have lower depth/diameter ratios (Pike and
Wilhelms, 1978) and less circular ejecta (Calef et al., 2009). In practice, however,
11
Figure 2.2: The lifetime of a rock on the lunar surface as a function of diameter according
to the McDonnell et al. (1977) computer model. The final curve depends on what
impactor flux model is used. The dotted solid line shows the curve obtained with an
impactor flux model taken from spacecraft data. The solid line shows the curve obtained
from an impactor flux model obtained from microcrater counting of the lunar surface and
returned
Apollo
samples.
From
McDonnell
et
al.
(1977).
12
secondary craters usually must be identified by the fact that they form in rays and in
association with other secondary craters (McEwen et al., 2005; Rodrigue, 2011).
The energy released by an impact excavates a bowl-shaped crater with a raised
rim and a depth/diameter ratio between roughly 1:3 and 1:4 (Melosh, 1989). This crater
is known as the “transient crater.” Below a crater diameter of ~10 km, the transient crater
closely resembles the final crater, with the steepest parts of the rim sliding into the crater
until the walls of the crater are beneath the angle of repose (Melosh, 1989). Typically, a
small pool of debris forms in the center of the crater (Melosh, 1989). Such craters are
known as “simple craters.” For some craters in the 10-20 km range and all craters above
~20 km, the transient crater collapses, forming a “complex crater” with a flat floor, a
slumped rim, and a central peak (Pike, 1977). This collapse is gravitationally driven.
Complex craters can form on the Earth (the terrestrial body with the highest gravity) at 2
km (Melosh, 1989), while on Jupiter’s low-gravity irregular satellite Amalthea, Pan
Crater maintains a bowl-shaped simple crater morphology despite a diameter of ~90 km
(Thomas, 1999).
The rim of a simple crater is typically elevated above the original ground surface
due to deformation of the surrounding rock, debris dikes thrust into the crater walls, and
the “overturned flap.” In the overturned flap, the near-surface layers from the region that
is now the crater have been flipped out of the crater and deposited upside-down on the
crater rim (Shoemaker, 1963).
13
II.2 The impact process—ejecta properties
While the majority of the depth of the crater is due to compaction, a significant
amount of material is nevertheless ejected from the crater in a plume (Melosh, 1989).
This material, known as the ejecta, is deposited in a blanket around the crater. There is a
clear dichotomy in the ejecta that forms 1-2 crater radii away from the rim. The inner
“continuous” ejecta are composed of large blocks deposited in concentric “dunes” whose
long axes lie more or less parallel to the crater rim. The outer “discontinuous” ejecta are
composed of a number of long rays that extend out radially from the crater (Schultz,
1972; Melosh, 1989) (Figure 1.1). Apollo astronauts reported that meter-sized blocks in
the ejecta of small craters were only present in the continuous ejecta (Thompson et al.,
1981). In both the continuous and discontinuous ejecta, the mean block size decreases
with distance from the crater (Melosh, 1989).
Although secondary crater ejecta in
general resemble primary crater ejecta, the largest blocks in the ejecta of a secondary
crater may be larger than they would be for a primary crater of equal diameter (Bart,
2007).
II.3 The impact process—oblique impacts
One variable does have major effects on the final crater not masked by a changing
diameter (like impact velocity is)—the angle at which the impactor strikes the surface.
Experimental studies of oblique impacts (impacts striking at low angles to the horizontal)
at the Vertical Gun Balistic Range at NASA’s Ames Research Laboratory have shown
that impacts at angles lower than ~5˚ will form elliptical craters (Gault and Wedekind,
1978). It has also been argued that elliptical craters will form at angles up to 12˚ (Bottke
et al., 2000). The major axis of the ellipse will be aligned with the impact direction,
14
although it is not always possible to determine which of the ends of the ellipse points in
the direction the impactor approached from.
Impacts oblique enough to form elliptical craters are rare (see Figure 2.4), but the
impact angle has a significant effect on the ejecta blanket at much higher angles. In
further experiments at the Vertical Gun Ballistic Range, Gault and Wedekind (1978)
characterized the behavior of the ejecta blanket at varying impact angles: At ~60˚, the
ejecta blanket becomes slightly asymmetric.
At ~45˚, a wedge-shaped “zone of
avoidance” without any ejecta begins to appear and continues to widen with decreasing
impact angle. At ~30˚, the zone of avoidance is fully developed; at ~20˚, a second zone
of avoidance begins to form. At 10˚, both zones of avoidance have widened to the point
where all the ejecta form a “butterfly pattern” with two “wings” perpendicular to the
impact direction.
It is generally believed that impacts strike the lunar surface at random angles, with a
differential probability1 of an impact occurring at a certain angle, dP(!), given by
dP(" ) = sin(2" ) ,
Equation 2.1
1
! represents the integrand used in the formula for determining
The differential probability
the probability, P, of an impactor striking in a particular angle range,
"2
P = #sin( 2" )d" ,
"1
where !1 and !2 represent the lower and upper bounds of the angle range. For example,
the probability of an impactor striking between 20˚ ("/9 radians) and 30˚ ("/6 radians) is
& 2# )
& 2# )
#
!
% cos( + % cos( +
6
' 6 *
' 9 *
P = $sin( 2" )d" =
%
, 0.133.
2
2
#
9
The probability of an impactor striking between 0˚ (0 radians) and 90˚ ("/2 radians) is
#
2
P = $sin( 2" )d" =
!
0
% cos(# ) % cos( 0)
%
= 1.
2
2
15
!
1.0
Differential probability of impact
0.8
0.6
0.4
0.2
20
40
60
80
Impact angle (degrees from horizontal)
Figure 2.3: Differential probability of an impact as a function of the impact angle in
degrees.
16
where the most common impact angle should be 45˚ (Figure 2.3) (Melosh, 1989; Gault
and Wedekind, 1978).
Departures from this model may, however, be possible. Schultz and Lutz-Garihan
(1982) support an abnormally high frequency of exceedingly oblique impacts on Mars
(<5˚ from horizontal) due to orbital decay of minor satellites or “moonlets,” but this
hypothesis has been vigorously disputed by Bottke et al. (2000). It is currently unknown
whether there are minor variations from the ideal impact angle distribution on the Moon.
III.1 Radar observation—the basics
Diffraction limits make it impossible for a satellite to carry a traditional singledish radar capable of high-resolution imaging because the aperture (dish) would be many
orders of magnitude larger than the spacecraft. To circumvent this problem, a technique
known as synthetic aperture radar (SAR) is used (Elachi, 1987). In a SAR system, the
instrument sends out a pulse of radar off to the side of the spacecraft and listens for
returning waves reflected off the target surface. The return is then broken into a line of
across-track pixels by time, and when the data are processed, the x-position of each pixel
is determined from how long it takes for the wave to return. After it receives the last
return from the first pulse, the instrument sends out another pulse and the process repeats.
Because the orbiter is in a polar mapping orbit, it determines the y-position of the pixels
from each pulse by the position of the spacecraft at the time. The Mini-RF instrument
used for radar imagery in this thesis is a synthetic aperture radar (SAR). Its primary
wavelength is in the S-band at 12.6 cm, its secondary wavelength is in the X-band at 4.2
17
cm, and it has a resolution of 30 m/pixel (Nozette et al., 2010; Raney, 2007; Bussey et al.,
2007).
One of the most important factors controlling the appearance of a radar image is
its “look direction,” the direction in which the radar beam is sent. The look direction of
any Mini-RF image can be easily identified by finding which wall of every crater in the
image is brightened and which wall is darkened. For example, if the western (left-hand)
walls of the craters in the image are brightened, the spacecraft will be situated to the east
of the image, and it will be looking off to the west, so the look direction will be “westlooking” or “left-looking.” Conversely, if the eastern (right-hand) walls of the craters are
brightened, the spacecraft will be situated to the west of the image, and it will be looking
off to the east, so the look direction will be “east-looking” or “right-looking.” In Figure
1.1a, the image is left-looking, and in Figure 1.1b, the image is right-looking.
III.2 Radar observation—S1 imagery
The normal way to display SAR images is as S1 images, where the pixel
brightness displays the intensity of the backscattered return. (S1 is the first Stokes
parameter, the sum of the horizontal and vertical linear polarization channels.) Several
factors contribute to backscatter intensity: The first and most important parameter is the
slope of the topography along the look direction. When the slope is angled towards the
spacecraft, more radar waves are reflected, and when the slope is angled away from the
spacecraft, fewer radar waves are reflected. The most extreme example of this effect is
the distinctive pattern that crater interiors take. The brightened wall is the one angled
towards the spacecraft, and the darkened wall is the one angled away from the spacecraft.
18
Another factor in determining the intensity of the backscatter is the roughness of
the surface on the scale of the wavelength of the radar. For instance, the S-band on MiniRF, which is used here in all the SAR imagery unless otherwise specified, has a
wavelength of 12.6 cm, so it scatters back to the receiver most strongly when the surface
it is observing has a large number of decimeter-sized blocks (Neish et al., 2011). The
backscattering properties of the lunar surface are actually quite sensitive to the
wavelength of the radar. For example, in Figure 2.4 the 4.2 cm X-band image of a crater
with a triangular region of bright ejecta appears quite different from the 12.6 cm S-band
image of the same crater. In the S-band, the ejecta appear considerably brighter even
though the backgrounds of both images have the same brightness value of 0.05. The
McDonnell et al. (1977) rock destruction model predicts that centimeter-scale blocks with
diameters on the order of ~4.2 cm will be destroyed several times faster than decimeterscale blocks with diameters on the order of ~12.6 cm. Due to the probable presence of
more decimeter-scale ~12.6 cm blocks than centimeter-scale ~4.2 cm blocks in the ejecta,
more 12.6 cm radar light will be scattered back to the spacecraft than 4.2 cm radar light.
The specific composition of the target surface is an important component in the
brightness of the SAR returns on the Earth, Venus, or Titan, but it is not a dominant
factor on the Moon. With the notable exception of the maria/highlands dichotomy, the
lunar surface (see above) is compositionally extremely homogenous at the relevant
scales, and the composition of the regolith varies little on the scale of Mini-RF images.
19
0.7
Radar Backscatter
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1
2
3
4
5
Distance from crater center �crater radii�
6
7
Figure 2.4: A Mini-RF total backscatter image of the same crater at 4.2 cm on the left and
at 12.6 cm on the right. Both of these images have the same stretch applied to them.
Below these images is a radially averaged brightness plot showing the difference between
the 12.6 cm image (the upper curve) and the 4.6 cm image (the lower curve)
20
III.3 Radar observation—CPR imagery
Another way to display SAR data is by the circular polarization2 ratio (CPR).
When the Mini-RF instrument sends out its radar beam, the beam is “circularly
polarized.” In a circularly polarized wave, the polarization of the wave rotates with time,
and the sense of the rotation depends on whether the wave rotates clockwise or
counterclockwise.3 Whenever a circularly polarized wave reflects off a surface, the sense
of its rotation reverses, so when the Mini-RF receiver measures a return with an opposite
sense of circular polarization from the sense of the original wave, the wave must have
reflected an odd number of times. When the receiver measures a return with the same
sense of circular polarization as the original wave, the wave must have reflected an even
number of times. By measuring the CPR (the ratio of same sense to opposite sense
returns) in a given pixel, the Mini-RF instrument can tease out additional information
about the lunar surface at that pixel.
Away from the polar regions, the main factor that affects CPR is the roughness of
the surface. On a Lambert (infinitely rough) surface, the radar wave will be reflected off
various surfaces a random number of times before being scattered back to the spacecraft.
This means that the probability of the beam being reflected an even number of times will
2
Polarization of an electromagnetic field is the orientation of the electric field wave in
the plane perpendicular to the direction of propagation.
3
A circularly polarized wave can be thought of as the addition of two perpendicular
linearly polarized waves "/2 radians out of phase with each other (so the electric field
vector in the horizontal wave is at zero when the electric field vector in the vertical wave
is at a crest or trough and vice versa). Because the waves are "/2 radians out of phase,
the horizontal wave can be seen as a cosine wave and the vertical wave can be seen as a
sine wave. Thus the addition of the two waves yields a circle because the parametrically
defined curve where the y-position is defined by the sine and the x-position is defined by
the cosine is, of course, a circle. Of course, because both waves are propagating forward,
the tip of the electric field vector actually traces out a helix, not a circle, but viewed headon it does trace out a circle.
21
be equal to the probability of it being reflected an odd number of times, so the CPR value
will be 1.0. In reality, surfaces are of varying roughness, and while roughness does
increase the CPR value, it is rarely enough to achieve CPR values as high as 1.0.
However, CPR values close to or even higher than 1.0 can be achieved in two situations:
The geometry of a crater is such that there are a number of waves that are scattered back
to the receiver by bouncing first off the floor of the crater and secondly off the wall.
These double-bounce returns yield CPR values so high that they can sometimes exceed
1.0. Because they travel a longer distance, the SAR image records their position as
further away from the spacecraft than they actually are, creating a half-halo of enhanced
CPR outside the crater rim.
The second way to achieve CPR values higher than 1.0 is with ice. The radar
scattering properties of ice are such that ice can reverse the direction of the wave through
refraction without ever reflecting the wave and reversing the sense of its circular
polarization. Adsorbed surface hydrogen or water present inside crystal structures does
not produce this effect, so by searching for CPR returns higher than 1.0, water in the form
of ice can be distinguished from other forms of hydrogen. Elevated CPR was observed in
permanently shadowed craters in Mercury’s polar regions (Slade et al., 1992). The MiniSAR experiment on India’s Chandrayaan-1 orbiter observed high values of CPR in small
polar craters (Spudis et al., 2010). However, when Mini-RF observed the LCROSS
impact site, it did not detect elevated CPR (Neish et al., 2011).
A useful feature of CPR imagery is that topography has the opposite effect on
CPR from the effect it has on S1. On slopes that face toward the spacecraft, it is more
likely for a single reflection to send the wave back to the receiver. On slopes that face
22
away from the spacecraft, it is more likely that the wave that returns to the receiver will
be the result of scattering between among several blocks, increasing the chance of an
even number of reflections (Neish et al., 2011).
The double-bounce effect also
contributes to brightening of the side of a ridge that faces away from the spacecraft,
although in some large ridges, the enhanced CPR from the double-bounce effect can be
seen at the top of the spacecraft-facing slope. Because both CPR and S1 images are
enhanced by surface roughness but affected oppositely by topography, combining the two
types of imagery can help distinguish the effects of surface roughness from the effects of
topography.
III.4 Radar observation—topographic effects on position information
Because the only way to determine the x-position of the pixels in a SAR image is
the time it takes for the radar pulse to return to the instrument, the topography of the
surface can distort the position information in the image, sometimes quite dramatically.
One effect, which can be seen most clearly in CPR imagery, is that waves that have taken
longer to return to the receiver because they have been bounced around several times are
mixed in the final image with returns from farther way from the spacecraft. Other effects
are best illustrated by the example in Figure 2.5, which shows North Ray Crater, a fresh
crater at the Apollo 16 landing site, in both Mini-RF total backscatter (S1) and visible
light. One effect is to lengthen slopes that face away from the orbiter and shorten those
that face it. This can be clearly seen in the distinctive pattern within the crater, where the
brightened westward-sloping eastern wall of the crater is shortened and the easternsloping western wall is lengthened. Were the look direction reversed, the pattern inside
the crater would also be reversed.
23
Figure 2.5: A Mini-RF total radar backscatter image of North Ray crater (PDS tag:
LSZ_02609_2S1_EKU_16S016_V1) and an optical image of the same region at low sunangle (9˚) (PDS tag: M102064759).
24
Another effect is for topographically higher features to appear arbitrarily close to
the spacecraft because the returns from those features arrive earlier than the returns from
level terrain. The crater lies on the lip of a valley, and the eastern half slopes downward
into the valley, on the far side of which rises the Smoky Mountains Massif, which towers
above the rest of the landscape. In the Mini-RF image, these effects cause the western
edge of the massif to appear arbitrarily close to the eastern edge of the crater because the
massif is higher than the eastern rim of the crater. Figure 2.5 also illustrates topographic
effects on pixel brightness. North Ray Crater has radar-bright ejecta, but the effects of
topography partially mask the radar-bright ejecta in the final image. Topography effects
have radically darkened the ejecta on the slope of the valley that faces away from the
spacecraft (to the west). While the brightened ejecta are still visible west of the valley
lip, the edge of the image cuts them off from the west, leaving a severely disrupted ejecta
pattern. Strongly brightened because it faces the spacecraft, the western face of the
Smoky Mountains massif illustrates the topographic brightening effect.
IV.1 Optical crater dating—Trask (1971) method
Attempts at optical determination of dates of individual lunar craters too small for
traditional crater counting have thus far met with only limited success. While certain
craters very clearly are more degraded in morphology than others, quantifying these
differences remains difficult (Trask, 1971; Swann and Reed, 1974).
Trask (1971) developed a system for obtaining relative ages of individual simple
craters. The method relied on a qualitative classification of crater morphology from
optical images to place craters into one of six age classes (Trask, 1971). Swann and Reed
(1974) add a seventh class representing extremely young craters to this dating paradigm.
25
The defining characteristics of a particular crater class vary with crater size, but Swann
and Reed (1974) developed a set of summary characteristics that do not depend on the
size variable and constitute seven classes as follows: Class 7 craters are so young that
they have clods of regolith formed by the impact that have not yet been broken up by
micrometeorite bombardment. Because the clods are below the limit of Apollo-era
cameras, class 7 craters could not be identified from orbital photography in 1974. They
are known solely from direct observation of very small craters by Apollo astronauts.
Class 6 consists of craters with very sharp rims and very clear rayed ejecta (rayed ejecta
have individual streaks or rays of ejecta that stand out from the background ejecta)
(Swann and Reed, 1974). Class 5 craters have a somewhat less sharp rim and clearly
present ejecta, but here the ejecta and crater rim are clearly somewhat subdued by erosion
(Swann and Reed, 1974). Class 4 craters have less crisp rims that are still clearly raised
above the background and may have some ejecta visible near the rims of the larger
craters (Swann and Reed, 1974). Class 3 craters do not have visible ejecta, but there is
still a clear break in slope on their rims (Swann and Reed, 1974). Class 2 craters have
smooth and rounded rims but still have an overall bowl-shaped morphology (Swann and
Reed, 1974). Class 1 craters, which are oldest, have been eroded to the point where they
have developed a pan-shaped crater morphology (Swann and Reed, 1974).
Prior to this study, the only methodology for estimating numerical ages of small
lunar craters was the process developed by Swann and Reed (1974), who calibrated the
Trask (1971) system with crater dates derived from cosmic ray exposure ages of samples
collected from the Apollo missions. They examined orbital photography of each crater
dated by Apollo samples and assigned each one an age classification number according to
26
the Trask (1971) scheme, which enabled them to estimate the age ranges associated with
the crater classes.
Unfortunately, the system developed by Swann and Reed (1974) does not
adequately address the question of crater size. By estimating the effect of size, Trask
(1971) did develop a set of comparison images for determining the crater number for
craters of varying sizes, and used this set of comparison images to produce a schematic of
how the characteristic properties vary with size. However, Swann and Reed (1974) did
not have a sufficient number of craters dated by Apollo samples to assess the validity of
the size comparison charts developed by Trask (1971).
A second problem with the Swann and Reed (1974) study is the effect of the
angle of illumination. A low sun angle sharpens the appearance of crater rims and mutes
the ejecta, while a high sun angle mutes the appearance of the crater rims and enhances
the ejecta (Swann and Reed, 1974). They address this by suggesting that the method be
applied using images with consistent sun angles of 15˚-25˚, but this still is a considerable
source of error.
A final issue with the method of Swann and Reed (1974) is that it was developed
using Lunar Orbiter images and may not be applicable to modern imagery. The ability to
identify features like ejecta and sharp rims is enhanced by the higher resolution delivered
by modern instruments, such as the narrow-angle camera (NAC) on the Lunar
Reconnaissance Orbiter. Human interpreters using NAC imagery may identify ejecta
blankets and sharp rims on craters where those same features would not have been
identifiable using Lunar Orbiter imagery.
27
IV.2 Optical crater dating—erosion modeling method
An additional approach to crater dating comes from the theory of diffusive
hillslope degradation. This models hillslope erosion where the erosion rate, or the rate of
change in surface elevation, is expressed by the equation:
dz
= k" 2 z ,
dt
Equation 2.2
where z is a three-dimensional function (of x and y) representing the surface of the
! known as diffusivity. The term dz/dt (the derivative of
hillslope, and k is a constant
surface elevation with respect to time) represents the erosion rate, and the term " 2 z (the
Laplacian of z as a function of x and y) expresses the curvature of the hillslope.
!
Craddock and Howard (2000) applied the diffusion model of hillslope
degradation
described above to generate a computer model to simulate the degradation of simple
lunar craters. The model used two-dimensional topographic profiles estimated from
Clementine optical imagery. Although Craddock and Howard (2000) were not explicit
about how they dealt with the three-dimensional reality of crater slopes, it can be
assumed that the necessary corrections were made. As the initial condition for their
model, Craddock and Howard (2000) created a general profile of very fresh simple
craters. From this initial condition, they subjected their crater to diffusive erosion, with
the eroded material transported downslope, where it filled in the bottom of the crater
(Figure 2.6). Craddock and Howard (2000) applied their model primarily to assess the
lunar erosion rate and its variability through time, but as they note, it has the potential to
help date individual craters. In order to apply this method, the diffusivity (k-value) of the
Moon would be estimated by applying the Craddock and Howard (2000) model to craters
with known dates, such as the Apollo-dated craters, and determining the diffusivity
28
Figure 2.6: The results from the Craddock and Howard (2000) erosion model showing
what a crater would look like now had it formed in a variety of time periods. The images
on the left show the degradation of a 3-km crater, and the images on the right show the
degradation of 10-km crater. The 3-km crater is shown in the first 10-km image for
comparison. The open squares represent the original crater, and the other symbols show
where the current crater would be.
29
necessary to produce the final craters when the model has been run for the known age of
the crater. Once the diffusivity had been estimated, individual lunar craters could be
dated from the time the Craddock and Howard (2000) model would take to produce their
topographic profiles from the initial condition profile.
There are, however, several difficulties with modeling lunar simple craters as
diffusive hillslopes. Trails from boulders rolling down into the crater are frequently
observed, and it is thought that mass wasting in the form of sliding occurs on the steepest
walls of the craters (Melosh, 1989). (The diffusive model assumes no mass wasting.)
Indeed, Soderblom and Lebofsky (1972), whom Craddock and Howard cite as saying that
lunar simple crater erosion can be modeled as pure diffusion, only state that diffusion is
the dominant process up to slopes of 20˚-25˚. The steepest slopes on a simple crater
typically lie at the ~30˚ angle of repose. Finally, when new craters with diameters a
significant fraction of the crater diameter are superimposed on the existing crater, they
and their ejecta seriously disrupt the diffusion process.
IV.3 Optical crater dating—space weathering
A possible second approach to optical crater dating is to use spectroscopy to
estimate exposure ages of material excavated or exposed by the impact from the degree
of space weathering. Using 750nm and 950nm Clementine data, Lucey et al. (2000) and
Grier et al. (2001) made progress towards this goal, developing an “optical maturity
parameter” (OMAT) that roughly correlated with surface freshness but also varied
noticeably as a function of lithology. Although Lucey et al. (2000) were not able to date
individual craters per se, this may be possible with data from the new visible-IR mapping
30
spectrometer M3 (Moon Mineralogy Mapper) on Chandrayaan-1 that are still being
processed.
V Radar-bright halos
Radar-bright halos around lunar craters were first observed in the 3.8 cm band at
the Haystack Observatory (Lincoln Laboratory, 1968), and Thompson et al. (1974) first
identified the halos as the radar representation of the ejecta of these craters. Using Earthbased radar (Zisk et al., 1974; Thompson et al., 1974), Thompson et al. (1981) conducted
a comprehensive 3.8 cm and 70 cm survey of the lunar nearside for the largest of these
craters. They identified 120 craters with 3.8 cm halos, but very few craters with 70 cm
signatures. Ghent et al. (2005) surveyed the Moon in the 70 cm band and observed dark
halos surrounding a subpopulation of craters, concluding that the initial ejecta deposits
for these particular craters were depleted in 70 cm blocks. It is probable that these 3.8
cm-bright, 70 cm-dark halos represent outer discontinuous ejecta, not inner continuous
ejecta. Ghent at al. (2010) did identify small bright 12.6 cm and 70cm halos within larger
dark halos surrounding a number of large lunar craters, and they attributed the bright
halos to the continuous ejecta and the dark halos to the discontinuous ejecta.
From their data, Thompson et al. (1981) determined that this crater population
represents the most recent lunar craters. These are craters whose ejecta were not yet
erased by micrometeorite bombardment, retaining their radar signature—thick with 3.8
cm-scale cobbles and not enhanced in 70 cm-scale boulders. Although Thompson et al.
(1981) did not develop a formal technique for dating these craters, they did characterize
the lifetimes of 3.8 cm bright halos as a function of crater diameter. To avoid a bias
against partially faded small craters that might have been missed, Thomspon et al. (1981)
31
only performed their size-frequency analysis on craters with diameters above 4 km. An
overabundance of large halo craters implied that halos around larger craters lasted longer,
it was necessary to take the diameter of the crater into account (Thompson et al., 1981).
So the Thompson et al. (1981) methodology for estimating the lifetimes relied on
presenting the data on an R plot, a standardized method of presenting crater sizefrequency established by the Crater Analysis Techniques Working Group (Arvidson et
al., 1979).
To make an R plot, the craters are binned by diameter into bins of
logarithmically increasing size. For each bin, the R parameter is calculated. R is defined
as:
D 3N
R=
,
A( Dmax " Dmin)
Equation 2.3
where D represents the geometric mean of the crater diameters in the bin, N the number
of craters in the bin, A !
the area of the focus region of the lunar surface, and Dmax and Dmin
!
the edges of the bin. After the R-values are calculated from Equation 2.3, they are plotted
against diameter on a log-log graph (using base 10 common logs). On the Thompson et
al. (1981) R plot, the halo crater data were plotted with data from Oceanus Procellarum
(Planetary Basaltic Volcanism Working Group, 1980) (Figure 2.7).
To estimate lifetimes for 3.8 cm-bright halos at various diameters, Thompson et
al. (1981) fit both the Oceanus Procellarum and the halo crater R-values to a linear fit
(linear on the log-log plot). The linear fit for the halo craters was
Log(R) = ("4.36 ± 0.19) + (0.64 ± 0.22)Log(D ) .
Equation 2.4
The linear fit for Oceanus Procellarum was
!
Log(R) = ("2.70 ± 0.28) + (0.20 ± 0.28)Log(D ) .
!
32
Equation 2.5
Figure 2.8: The Thompson et al. (1981) R plot showing crater size-frequency data for the
Thompson et al. (1981) halo crater database and the Planetary Basaltic Volcanism
Working Group (1980) database of visually identified craters in Oceanus Procellarum.
33
Assuming a constant rate of cratering over the past 3.3 Ga (as argued by Guinness and
Arvidson (1977)), Thompson et al. (1981) extrapolated out the curves to find the Rvalues on each one at the diameter in question. Then they calculated the ages by simply
finding the ratio of the R-values and multiplying it by the well-established 3.3 Ga age of
Oceanus Procellarum. For example, they calculated an estimated 3.8 cm halo lifetime of
0.13+0.05
"0.04 Ga for craters 4 km in diameter.
Thompson et al. (1981) were able to characterize the lifetimes of these halos, but
!
they did not extrapolate their analysis into a methodology for estimating the ages of
individual craters. Their study also suffered from the 2 km resolution of the Zisk et al.
(1974) dataset used in the analysis, which severely limited their ability to assess the
properties of halo craters, in particular the smaller craters. This lower resolution made it
difficult to detect fainter halos. Furthermore, the lack of an intermediate wavelength
between 3.8 cm and 70 cm restricted their ability to constrain the block size. Using 12.6
cm data from Mini-RF, this thesis hopes to address these issues.
34
Methods
I.1 Crater counting
The only features on the Moon with returned samples available for radioisotope
dating are those at the Apollo and Luna landing sites. Lunar features, however, can still
be dated using crater counting. By counting the number of impact craters superimposed
on a feature since it was formed, planetary geologists can roughly determine its age
(Arvidson et al., 1979; Michael and Neukum, 2010). In estimating the lifetimes of the
discontinuous ejecta blankets, the crater counting methodology can be applied by
counting the number of craters that still possess their discontinuous ejecta blankets. This
will effectively date the age of a surface one discontinuous ejecta lifetime old because all
craters that have formed after a date one lifetime in the past will have discontinuous
ejecta blankets. Discontinuous ejecta lifetime, however, varies with diameter. The
surface being dated in this study, therefore, is one that varies with crater diameter. Thus,
an R-plot, a modified version of the crater counting dating scheme (Arvidson et al., 1979;
Thompson et al., 1981; Michael and Neukum, 2010) was used to characterize the
relationship between crater diameter and discontinuous ejecta lifetime.
I.2 Crater counting—R-plot analysis
The crater counting analysis followed the R-plot methodology followed by
Thompson et al. (1981), laid out by the Crater Analysis Techniques Working Group
(Arvidson et al., 1979), and extended by Ivanov et al. (2001), Neukum et al. (2001), and
Michael and Neukum (2010). Craters were binned according to size, and for each bin,
35
the frequency of craters in the bin was estimated by calculating the R parameter
developed by Arvidson et al. (1979):
R=
D3 N
,
A ( Dmax ! Dmin )
Equation 3.1
where D represents the geometric mean of the crater diameters in the bin, N the number
of craters in the bin, A the area, and Dmax and Dmin the edges of the bin. The errors in the
!
R values were determined from the error function stated in Arvidson et al. (1979):
error =
R
.
N
Equation 3.2
In order to derive ages, calculated R values were compared against the lunar
production function, which describes how the frequency of cratering on the Moon varies
as a function of crater diameter. The production function gives the R values as a function
of crater diameter. Given a specific age of the surface, the production function will tell
you what R value is expected for a bin centered around a particular diameter. Michael and
Neukum (2010) derived a formula for a polynomial fit to the lunar production function:
n
"ai log(D)i
R[D] = !D 210 i=0
n
" ja
j
log(D) j!1 ,
Equation 3.3
j=1
where D is the diameter and the an numbers are coefficients given in Neukum et al.
(2001) based on crater counts by Ivanov et al. (2001). Using the Neukum, Ivanov, and
Hartmann (2001) values for an gives the 2 Ga production function. Assuming that the
cratering rate has remained constant over the past 2 Ga allows a set of R isochrons to be
produced. Given this assumption (see Discussion for a discussion on possible variations
in the cratering rate), R should scale linearly with time, so the production function for 1
36
Ga should be simply half of the 2 Ga production function, the 500 Ma production
function should be a quarter of the 2 Ga production function, etc.
Because halo lifetimes are thought to increase with crater diameter (Thompson et
al., 1981), determining the lifetime of 12.6 cm radar halos around fresh craters can be
thought of as dating a surface whose age varies with crater diameter. On a normal
surface, the R values for the various bins should all fall on or close to one isochron if the
age does not vary with diameter. However, if this assumption is violated, the R values
should be expected to fall on higher isochrons for bins with larger mean diameters. By
simply overlaying the R values (along with their error bars) on the isochrons in Figure
3.1, the lifetimes of craters of various diameters can be determined (Figure 4.1). For each
value of R, the lifetime from Rbin, the R value for the bin, and R2Ga, the R value along the
2 Ga isochron can be determined by:
lifetime = 2Ga !
Rbin
.
R2Ga
Equation 3.4
Similarly, Equation 3.4 was used to convert minimum and maximum R values to
minimum and maximum lifetimes. These lifetime values were fit to a linear fit in log-log
space to produce a function describing the discontinuous halo lifetime of a given
diameter (Figure 4.2). Minimum and maximum lifetime values were also produced from
the confidence bands of the fits to the minimum and maximum lifetime values.
II.1 Datasets
Three separate focus regions were investigated: a highlands focus region
including Mini-RF radar swaths from the farside in orbits 2250, 2251, 2252, 2253, 2254,
3124, and 3125; a mare focus region in Mare Serenitatis, where only the areas of the
37
Figure 3.1: Isochrons for surfaces of varying ages extrapolated from the Michael and
Neukum (2010) polynomial fit to the lunar production function and presented on a plot of
log(R) vs. log (diameter). All logs used are base 10 logs. Note how on the log-log scale
the vertical distance between the 100 Ma and the 50 Ma isochrons is the same as the
distance between the 2 Ga and 1 Ga isochrons. Crater counts to produce the Michael and
Neukum (2010) polynomial model were taken from Ivanov et al. (2001) and Neukum et
al. (2001).
38
mare portions of the strips were used; and a broad dominantly highlands focus region
selected based off orbit numbers, which ranged from 2400 to 2463, rather than specific
location (to eliminate any effect of location bias). Additionally, a number of strips
suspected to contain craters identified by Thompson et al. (1981) were examined in the
initial survey, and selected images with overlapping X-band and S-band coverage and
images of Apollo sites were investigated separately (without being included in the cratercounting analysis).
II.2 Datasets—initial search and highlands focus region
The initial search investigated the amount of time required for a crater halo to
fade below the point where it could no longer be readily identified. The set of images
included the highland focus region and a number of images targeting (but sometimes
missing) craters imaged by Thompson et al. (1981). Craters were counted using the
criterion that they contain a clearly identifiable halo, and no halo diameter or crater
diameter constraints were applied. The survey only recorded diameters with a precision
of 100 m because the search took place in a simple cylindrical projection, where the
diameters were harder to estimate. Overall, 177 craters with diameters ranging from 0.15
km to 3.5 km were observed. This search was performed using simple cylindrical MiniRF S1 total backscatter images, which had not been gamma-corrected, in the ArcGIS
software package. In order to highlight faint craters, a portion of each image was
observed at minimum-maximum stretches of 0-1.275, 0-0.75, 0-0.5, and 0-0.25, and a
custom minimum-maximum stretch was chosen to best fit the general background level
of the particular image being examined.
39
Because faint halos were more difficult for the human eye to identify around
small craters, there was a bias in the initial survey towards fresher, brighter craters with
more extensive halos for smaller craters. For craters with diameters below 0.45 km, halo
diameters (in units of crater diameters) increased with decreasing crater diameter (Figure
3.2). This effect was absent for craters with diameters above 0.45 km (Figure 3.2), so the
crater counting surveys used in the discontinuous halo lifetime analysis only counted
craters with diameters greater than 0.45 crater diameters.
Applying this constraint also resolved another problem posed by the results of the
initial survey. There was a significantly higher density of halo craters in the maria
(1.4!10-3 craters/km2) than in the highlands (5.2!10-4 craters/km2). However, when the
sample was limited to all the craters with diameters greater than 0.45 km, the clear
dichotomy in crater densities between the maria and the highlands disappeared. The
maria crater density became 5.2!10-4 craters/km2, and the highlands crater density
became 4.6!10-4 craters/km2.
Experience in the initial survey also demonstrated the difficulty of using a clearly
identifiable halo as a counting criterion. It was difficult to set a rigorous limit for clearly
identifiable halos. As a result, this study was refocused on the lifetimes of discontinuous
halos, defined as the time necessary for the halo diameter to shrink below four crater
diameters.
After identifying the crater counting criteria of a minimum diameter of 0.45 km
and a minimum halo diameter of four crater diameters, the criteria were applied to data
from the highlands focus region part of the initial search. The strips selected to be near
Thompson et al. (1981) craters were not included because they were near large radar-
40
Halo diameter (crater diameters)
12
10
8
6
4
2
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Crater diameter (km)
Figure 3.2: Distribution halo diameters of craters in the initial survey. Note the steadily
increasing halo diameters of craters with diameters below 0.45 km.
41
bright halo craters, which strongly increased the chance that a large radar-bright crater or
its secondaries could be imaged, potentially skewing the results. Results from the
highlands focus region were included in the crater counting analysis.
II.3 Datasets—Mare Serenitatis and 2400s focus regions
After the initial survey was completed, a focus region in Mare Serenitatis was
searched for halo craters using the inclusion criteria of a minimum crater diameter of 0.45
km and a minimum halo diameter of four crater diameters. To increase the N and
decrease the error in the R values for the larger diameter bins, a broader search was
conducted for craters based off orbit number instead of location, where the minimum
crater diameter for inclusion was 1.0 km. One advantage of this approach is that a set of
strips randomly distributed across the Moon would be less prone to bias from secondary
cratering than a focus region with a less broad spatial extent (see Discussion section).
These searches were performed with the qview viewer in the ISIS software package. The
images were examined in a global stretch calibrated to highlight differences based on the
brightness variations in the whole image. Each individual crater was examined in a
stretch of the region immediately surrounding it. Occasionally, portions of craters that
met the inclusion criteria were visible in our images, but only the craters whose centers
were present on the image being examined were included.
III Age quantification
Knowledge of the lifetime of a halo is not enough to determine the age of a halo
crater; it is necessary to quantify the lifetime fraction, the fraction of its discontinuous
halo lifetime the crater has undergone. Halo diameter (expressed in units of crater
42
diameter) was used to quantify a crater’s lifetime fraction. Assuming that craters with
larger halo diameters should be fresher and less advanced in their lifetimes, the fraction
of craters with larger halo diameters should be equal to the fraction of craters less
advanced in their lifetime. This in turn should be equal to the fraction of its lifetime that
the crater in question had undergone. These lifetime fractions for all the craters in our
dataset were plotted against halo diameter (4.4), and a linear interpolation was used to
produce a lifetime fraction function describing the lifetime fraction as a function of halo
diameter (Figure 4.4).
Once the lifetime fraction function has been empirically determined, a formula for
the age of the crater can be calculated:
!d $
fl # h &
" dc %
,
t=
lh ( dc )
Equation 3.5
where t represents the age, dh represents the halo diameter in km, dc represents the crater
diameter in km, fl(dh/ dc) represents the lifetime fraction as a function of dh and dc, and
lh(dc) represents the discontinuous halo lifetime in years as a function of dc. With this
analysis, the age of a particular halo crater can be estimated from just two parameters: the
crater diameter and the halo diameter.
IV Image processing
The raw S1 total images were imported into ISIS as 32-bit backscatter values,
where a backscatter of 1.0 represented all of the beamed energy returning to the receiver.
A c-shell script was then used to apply a gamma correction with a gamma factor of 4/9.
(A gamma correction scales the image by the range of pixel values and raises each scaled
43
pixel value to the power of the gamma factor.) Originally displayed in an equirectangular
projection similar to simple cylindrical, many of the images were reprojected into
Mercator to limit spatial distortions. Images with scale bars were produced in ArcGIS
from images reprojected into a custom transverse Mercator projection centered around a
line of longitude running through the Mini-RF image or focus region. In many cases, the
same transverse Mercator projection was used for an entire focus region. For example, in
the Mare Serenitatis focus region, each image used a transverse Mercator projection
centered around the 15˚E line of longitude with a scale factor of cos(5˚). Because MiniRF images are composed of long thin strips elongate north-south, a transverse Mercator
projection displays the entire image without significant distortion anywhere along the
strip.
In order to increase processing efficiency and view the images in ArcGIS, all
images were converted into byte-valued (8-bit) images by using ISIS to apply a simple
minimum-maximum stretch from 0 to 2.55. All pixels with a backscatter value at or
above 2.55 were converted to a byte value of 255, and all pixels with a floating-point
backscatter values of 0 were given a byte value of zero. All other pixels were scaled
linearly between these two bracketing values. The cutoff of 2.55 was chosen so that the
byte values would be precisely 100 times the original backscatter values. A cutoff of
1.275 was chosen for images that did not have the gamma correction applied to them,
such as those in Figure 1.1. During the crater counting searches, additional custom
stretches were applied to the images to highlight faint craters. Many images displayed in
this thesis have additional custom stretches applied to them to best highlight the relevant
44
features, but Figures 4.6-4.13 have been left in the original stretch for purposes of
comparison.
V Radial brightness profiles
For a number of images, it was useful to examine the radially averaged brightness
profile of the halo, so we an algorithm to construct these profiles from a cropped Mini-RF
image of a particular halo crater was created. Automated detection of craters from
images is a difficult problem only now beginning to be solved (Bandeira et al., 2010;
Salamuni!car and Lon!aric, 2010), so the area of the crater was manually determined by
blacking out the region with basic image software (Adobe Photoshop, Preview, or
Microsoft Paint). Using Mathematica’s MorphologicalComponents function, the pixels
representing the crater were identified by selecting the largest region of connected black
pixels in the central quarter of the image.
The crater center was then determined by averaging the positions of the pixels in
the crater.
In order to find the crater radius, the following algorithms were used
(depending on the map projection):
Simple cylindrical:
r=
A
nCos(l)
=
!
!
Equation 3.6
A
n
=
!
!
Equation 3.7
Mercator:
r=
In these equations, r is the radius, A is the area of the crater, n is the number of pixels
representing the crater, and l is the latitude. Because each pixel has an area of one square
45
pixel, the number of pixels is equal to the area of the crater in square pixels. However,
because the original images were in a simple cylindrical projection where the threedimensional latitude and longitude coordinates are fed unmodified into a rectangular
coordinate system, they were artificially distended in the horizontal dimension by a factor
of the secant of latitude. To correct for this, the area as determined from the number of
pixels was multiplied by the cosine of the latitude.
Once the crater center and radius were determined, the distance of each pixel from
the crater center was calculated, and the craters were binned by this distance into bins of
one pixel length in width. The value on the radial brightness curve at a given distance
was then calculated by taking the median of the brightness values of the pixels in the
appropriate distance bin. Finally, the distances were converted to crater radii to enable
better comparison between radial brightness curves.
In some cases, there were additional impacts that disturbed the ejecta of a
particular crater and potentially could affect the radial brightness curve. In order to
remove these features, they were identified manually using the same method used to
identify the crater itself. Because of look-direction effects, the ejecta on one side of the
image are artificially brighter than the ejecta on the opposite side. To correct for this
potential source of error, once a region was selected for removal, a symmetric region on
the opposite side of the crater was also selected for removal.
46
Results
In this chapter, the results of this study are presented. The relationship between
discontinuous halo lifetime and diameter is shown along with the crater counting data
used to empirically derive this relationship. The empirically derived lifetime fraction
function used to quantify what fraction of its lifetime a halo has undergone once it has
shrunk to a particular diameter is presented. Also discussed are morphological changes
in the ejecta blanket as it degrades, confirmations of results from analysis of craters
visited by the Apollo missions with known ages, and a reanalysis of the Thompson et al.
(1981) data using modern crater-counting techniques not available in 1981.
I Estimating Discontinuous Halo Lifetimes From Crater Counting
The R plot methodology detailed in the Methods section was used to assess how
discontinuous halo lifetime varies with crater diameter.
The craters that met the
bounding criteria of a diameter of 0.45 km and a halo diameter of at least 4 crater
diameters (large enough to have a discontinuous ejecta halo) were sorted into six bins and
calculated the predicted, minimum, and maximum R for each bin, excluding the two
larger bins because they contained too few craters (see Table 4.1). It is important to note
that there is probably some variation in the continuous halo diameter. A cutoff of 4 crater
diameters was chosen because it was estimated to be the maximum diameter of the
continuous halo in our initial survey.
There may be cases where elements of the
discontinuous halo are present in craters with halo diameters below 4 crater diameters,
but in these cases the discontinuous halo will have eroded to the point where its
47
morphology is indistinguishable from the continuous halo diameter. No craters were
observed with an identifiable discontinuous halo below 4 crater diameters.
bin (km)
0.45-0.75
0.75-1.15
1.15-1.65
1.65-2.35
2.35-3.55
3.55-5
number
of
craters
49
16
21
11
5
4
R value
log(R)
9.77E-5
1.06E-4
1.20E-4
1.47E-4
n/a
n/a
-4.010
-3.973
-3.920
-3.834
n/a
n/a
log(geometric
mean of
diameter)
-0.24
-0.03
0.14
0.30
0.46
0.62
Table 4.1: A table of radar-bright crater statistics, giving the number of craters, R, log(R),
and log(geometric mean diameter) for the six bins. The fifth and sixth bins were
excluded from the R plot analysis due to their small numbers of craters. All logs used are
base 10.
The R values from the four valid bins were then plotted against R parameter isochrons
extrapolated from polynomial fits (Neukum et al., 2001; Michael and Neukum, 2010) to a
crater size-frequency distribution by Ivanov et al. (2001) (see Methods for details and
Figure 4.1).
A constant cratering rate throughout the past 2 Ga was assumed;
implications of that choice will be discussed in the Discussion section.
To extrapolate the R values to other diameters, the predicted, minimum, and
maximum R values were converted to discontinuous halo lifetimes using Equation 3.4
(see Methods section). A linear regression to fit them to a straight line on log-log space
(Figure 4.2). A slope of ~2 is solidly within the error range of the slopes of the fit (Table
4.2), implying that the lifetime of the discontinuous ejecta is roughly proportional to the
square of the diameter of the crater, assuming that the lifetime of the 12.6 cm
discontinuous halo is comparable to the lifetime of the discontinuous ejecta blanket itself.
48
Figure 4.1: The log of R against the log of diameter (in km). The R parameter values for
the four valid bins are plotted over isochrons extrapolated from from polynomial fits
(Michael and Neukum, 2007; Neukum et al., 2001) to a crater size-frequency distribution
by Ivanov et al. (2001) (see Methods for details) and overlain with simple linear
interpolations of the logs of the R values and their minimum and maximum values.
49
log�lifetime�Ga��
�0.4
�0.2
0.2
0.4
0.6
log�diameter�km��
�0.5
�1.0
�1.5
�2.0
Figure 4.2: The log of the lifetime (in Ga) against the log of the crater diameter (in km)
with a linear fit to the lifetimes of the predicted, maximum, and minimum R values as
calculated using Equation 3.4. See Table 2 for the equations of the fits.
50
intercept with log(lifetime)-axis
slope
R2
log(predicted R value)
-1.12
2.00
0.99996
log(maximum R value)
-1.04
2.09
0.99996
log(minimum R value)
-1.23
1.85
0.998
Table 4.2: The slopes and log(R)-axis intercepts for the linear fits to the predicted,
maximum, and minimum R values shown in Figure 4.1.
The linear fit to the lifetime values was converted out of log-log space, yielding an
expression for discontinuous halo lifetime as a function of diameter:
lh ( dc ) = 10
+0.08
2.00+0.09
!0.15 log( dc )!1.12 !0.11
+0.08
+0.09
= 10 !1.12!0.11 dc2.00!0.15
,
Equation 4.1
where lh is the discontinuous halo lifetime in years and dc is the crater diameter in km.
The expression in Equation 4.1 is close to a parabola (Figure 4.3).
+0.08
+0.09
lh ( dc ) = 10 !1.12!0.11 dc2.00!0.15 " lh ( dc ) #~ dc2 .
51
Equation 4.2
Discontinuous halo lifetime (Ma)
1000
500
100
50
10
5
0.5
1.0
1.5
2.0
2.5
3.0
Crater diameter (km)
Figure 4.3: The discontinuous halo lifetime as a function of crater diameter, with the
discontinuous halo lifetime axis on a log scale. Due to the log scale, the true shape of the
curve, a concave-up parabola, is obscured.
52
II Estimating Ages From Discontinuous Halo Lifetimes and Diameters
The lifetime of a discontinuous halo alone is not sufficient to estimate the age of a
particular crater; it is also necessary to estimate how far along in its lifetime a particular
crater is. In order to quantify the crater’s “progress,” the fraction of craters with higher
(discontinuous) halo diameters (presumably younger craters) was calculated. These
“lifetime fractions” were plotted against halo diameter (Figure 4.4), and a linear
interpolation was used to produce a lifetime fraction function describing the lifetime
fraction as a function of halo diameter (Figure 4.4). Once the lifetime fraction function
was empirically determined, Equation 3.5 could be used to estimate the age of a crater
given the halo diameter and the crater diameter. In the lifetime fraction function shown
in Figure 4.4, the outer edges of the halo are seen to fade much more quickly than the
inner regions. After half its lifetime, the halo diameter will have shrunk to ~4.9 crater
diameters. It takes the rest of its lifetime to fade to 4 crater diameters.
III Morphology Variation of Degrading Craters
Analysis of large numbers of eroding ejecta blankets in varying states of
degradation provides a unique opportunity to characterize the gradual change in
morphology with time of eroding ejecta blankets.
By observing hundreds of ejecta
blankets at various stages in their lifetime, the paths they undergo in their time on the
Moon can be characterized. Figures 4.5-4.12 show eight different craters in varying
states of degradation, ranked by halo diameter (in units of crater diameters) from freshest
(largest halo diameter) to most degraded (smallest halo diameter). All of the craters are
from the Mare Serenitatis focus region, where the background topography causes fewer
53
1.0
0.8
Lifetime Fraction
0.6
0.4
0.2
4
6
8
10
12
Halo diameter (crater diameters)
Figure 4.4: The halo lifetime fraction plotted against halo diameter (given in units of
crater diameters) with linear interpolation. The halo lifetime fraction is the fraction of a
crater’s lifetime that it has thus far undergone. It is equal to the halo diameter fraction,
the fraction of craters with larger halo diameters (measured in units of crater diameters).
For example, for a crater with a halo with a diameter of ~6 crater diameters, ~20% of
craters have larger halo diameters, so ~20% of craters are less far along in their lifetimes,
so the halo is ~20% of the way through its lifetime. For a crater of ~5 crater diameters,
~50% of the craters have larger halo diameters (and are therefore less far along in their
lifetimes), so the halo is 50% of the way through its lifetime. Essentially, this plot shows
the cumulative distribution of halo diameters.
54
Figure 4.5: A Mini-RF S1 image of a very fresh ultra-bright halo crater with a diameter
of 0.45 km and a halo diameter of 5.4 km or 12 crater diameters. Its age is estimated at
0.3(+.2/-.3) Ma. It is located at (32.3427˚N, 18.6222˚E).
PDS tag:
LSZ_01385_2S1_EKU_33N018_V1
55
Figure 4.6: A Mini-RF S1 image of a very fresh crater with a diameter of 0.77 km and a
halo diameter of 6.5 km or 8.4 crater diameters. The presence of a smaller crater with a
more degraded halo (because it is smaller, and its lifetime is therefore shorter) implies
these two craters formed at the same time as part of a secondary field. Its estimated age
is 1.7(+1.7/-0.4) Ma.
It is located at (27.2762˚N, 17.6392˚E).
PDS tag:
LSZ_02608_2S1_EKU_22N017_V1
56
Figure 4.7: A Mini-RF S1 image of a fresh crater with a diameter of 0.52 km and a halo
diameter of 3.7 km or 7.1 crater diameters. Its estimated age is 1.6(+2.1/-0.6) Ma. It is
located at (35.4555˚N, 16.9565˚E). PDS tag: LSZ_02609_2S1_EKU_32N017_V1
57
Figure 4.8: A Mini-RF S1 image of a fresh crater with a diameter of 0.45 km and a halo
diameter of 2.9 km or 6.4 crater diameters. Its estimated age is 1.5(+3.8/-0.6) Ma. It is
located at (25.4016˚N, 15.4063˚E). PDS tag: LSZ_02610_2S1_EKU_32N016_V1
58
Figure 4.9: A Mini-RF S1 image of a fresh crater with a diameter of 0.50 km and a halo
diameter of 3.0 or 6.0 crater diameters. Its estimated age is 3.5(+6.7/-2.2) Ma. It is
located at (35.8426˚N, 15.8602˚E). PDS Tag: LSZ_02610_2S1_EKU_32N016_V1
59
Figure 4.10: A Mini-RF S1 image of a fresh crater with a diameter of 1.36 km and a halo
diameter of 8.1 km or 6.0 crater diameters. Its estimated age is 27(+15/-14) Ma. It is
located at (22.6431˚N, 17.3158˚E). PDS tag: LSZ_02608_2S1_EKU_22N017_V1
60
Figure 4.11: A Mini-RF S1 image of a moderately fresh crater with a diameter of 0.51 km
and a halo diameter of 2.5 km or 4.9 halo diameters. Its estimated age is 10.(+14/-6) Ma.
It is located at (28.8073˚N, 18.0082˚E). PDS tag: LSZ_02081_2S1_EKU_34N018_V1
61
Figure 4.12: A Mini-RF S1 image of a moderately fresh crater with a diameter of 0.85 km
and a halo diameter of 3.6 km or 4.2 crater diameters. It has faded to the point where the
discontinuous ejecta with their faint lineations are only barely visible around the fringes
of the halo. This crater is only barely fresh enough to have been counted in our sample.
Its estimated age is 47(+36/-26) Ma. It is located at (22.6209˚N, 11.3738˚E). PDS tag:
LSZ_01740_2S1_EKU_20N011_V1
62
distortions than in the highlands.
They have all been selected for the absence of
interfering factors like topography and overlapping ejecta blankets. Representing the
freshest of craters, the crater in Figure 4.5 has a halo diameter of 12 crater diameters, the
second-largest halo in Mare Serenitatis. It was selected as the archetype of a pristine halo
crater because it shows an extremely elevated radar backscatter. The inner regions of the
halo are brighter than the brightness of 0.255 used as the upper limit of the minimummaximum stretch that all of the images in this sequence are subjected to. These “ultrabright” halo craters are relatively rare. There are only a few examples in our formal
survey. However, a number of these craters were observed at diameters below our
diameter cutoff of 0.45 km. This was the only ultra-bright halo crater in the Mare
Serenitatis sample. The subsequent craters in the sequence show gradually decreasing
halo diameters, and as the halo diameter decreases, the radial lineations characteristic of
the discontinuous halo become more subdued. By the final crater in the sequence, only
the faintest hints of the discontinuous halo can be detected (Figure 4.12).
IV.1 Comparison With Apollo Results—Cone Crater
Crater counting is subject to numerous biases and sources of error, particularly for
small craters (see Discussion), so it is important to verify the crater counts by comparing
them with craters of known ages. Several of the Apollo landing sites were proximal to
craters from which samples were returned and dated using radiometric techniques and
cosmic ray exposure ages. Apollo 14 landed near Cone Crater, and Turner et al. (1971)
used its ejecta samples to estimate its age as 26-30 Ma. It was imaged by Mini-RF
(Figure 4.13).
63
Figure 4.13: Cone Crater, a 340 m crater at the Apollo 14 landing site dated at 26-30 Ma
from cosmic ray exposure ages of its ejecta samples (Turner et al., 1971). The image has
been contrast-enhanced to enhance the ejecta blanket.
64
With a diameter of 340 m, the projected lifetime of Cone Crater’s discontinuous
halo is 8.7(+1.5/-1.7) Ma, predicting that the discontinuous halo should be absent from
the 26-30 Ma crater. Based on the limited extent of the halo, it appears from Figure 4.13
that only the continuous ejecta blanket is present. However, Cone Crater is small enough
for the 30 m resolution of Mini-RF to be a major limitation, so it is not possible to
definitively state that the discontinuous halo is entirely absent. There are a number of
features of the ejecta blanket that are indicative of a discontinuous halo: a bulge in the
halo to the southeast, several bright patches around the crater, and a region of slightly
elevated background to the north. It is probable that none of these features accounts for a
full discontinuous halo, but the possibility that a discontinuous halo might become visible
at higher resolution cannot be ruled out from the Mini-RF imagery alone.
Mini-RF, however, is not the only instrument to cover Cone Crater. The Lunar
Reconnaissance Orbiter Camera Narrow Angle Camera (LROC NAC), an optical camera
flying with Mini-RF on LRO with a resolution of 0.5 m/pixel, captured an image of Cone
Crater at a moderate sun angle of 39˚ (Figure 4.14).
Figure 4.14 provides further
confirmation that the discontinuous ejecta blanket has disappeared. The continuous
ejecta blanket can be seen as an asymmetric region of mildly enhanced brightness
extending out to 2.5-4.0 crater radii from the crater center. Additionally, individual
continuous ejecta blocks several meters in diameter can be seen close to the rim.
However, no ejecta can be discerned beyond ~4 crater radii, and none of the radial
lineations typical of discontinuous ejecta can be seen.
65
Figure 4.14: A strongly contrast-enhanced LROC NAC image of Cone Crater at the
Apollo 14 landing site at moderate sun angle (39˚ above the horizon). In the lower lefthand corner, note the faintly visible footpath left by the Apollo astronauts collecting
samples of Cone Crater’s ejecta (indicated by the white arrows). PDS Tag:
M104634241LE.
66
There is a small possibility that the absence of the discontinuous ejecta in the
NAC image is due to illumination conditions. In optical images, ejecta from fresh impact
craters are brighter than the background, but this effect varies strongly with sun angle,
and a crater that shows clear ejecta with the sun directly overhead may not show any
visible signs of ejecta in an image with the sun low on the horizon (Schultz, 1971).
Figure 4.14 shows Cone Crater at a moderate sun angle of 39˚ above the horizon that
allows the ejecta to be discerned as a region of slightly elevated brightness surrounding
the crater, but the ejecta would most likely be considerably clearer at higher sun angles,
possibly showing a faint discontinuous blanket invisible at a sun angle of 39˚.
IV.2 Comparisons With Apollo Results—North Ray Crater.
Apollo 16 landed near North Ray Crater, a 1.0 km crater dated to 50.0±1.4 Ma
from cosmic ray exposure ages of ejecta samples collected by the astronauts (Arvidson et
al., 1975).
North Ray Crater was imaged by Mini-RF, but due to its underlying
topography, it is subject to significant distortions (Figure 4.15). The edge of the image
cuts off the west side of the ejecta, and the Smoky Mountains Massif interrupts the east
side. To the north, the ejecta are on the steep slope of a valley facing away from the
spacecraft, causing them to be darkened, but faint radial lineations can be seen on the
valley floor, indicating the presence of discontinuous ejecta. To the south, the ejecta are
undisturbed by topographic effects, and a halo can be seen, including a bright unlineated
continuous halo and a faint discontinuous halo with radial lineations. The limited nature
of the halo, coupled with the topographic distortions, makes quantifying the halo
diameter difficult and increases the error. A rough estimate is still possible, and the
67
Figure 4.15: A Mini-RF image of North Ray Crater showing both a continuous and
discontinuous halo despite major topographic distortions.
68
estimated halo diameter of 4.5±0.5 crater diameters yields an age estimate of 52(+42/-24)
Ma—consistent with the known age of 50.0±1.4 Ma. Verification that the small slice of
the halo visible in the Mini-RF image is representative of the image can be found in NAC
high sun-angle (82˚) imagery, where the discontinuous ejecta can be seen extending out
to 4-5 crater diameters (Figure 4.16).
V Thompson et al. (1981) comparison
Thompson et al. (1981) examined the entire nearside of the Moon using the Zisk
et al. (1974) 3.8 cm Earth-based (nearside) radar database, which had a spatial resolution
of 2 km. Counting the radar-bright craters with crater diameters greater that 4 km and
bright halo diameters of at least 20 km and at least 2 crater diameters, they built a
database of 59 craters. The 59 craters were divided into three bins, and R values were
calculated for all the bins. The Michael and Neukum (2010) R plot model did not yet
exist, so the data were plotted against a 3.3 Ga R value isochron derived from a linear fit
to R values from crater counts in Oceanus Procellarum by the Planetary Basaltic
Volcanism Study Project (1980) (Figure 2.8). The lifetimes were extracted by fitting the
three R values to a line in log-log space and multiplying by 3.3 Ga (the estimated age of
Oceanus Procellarum) the ratio of the R values from the fit to the R values from the fit of
the Oceanus Procellarum data. The errors were calculated using formal statistical errors
from the R plot counts, and the errors from the fits were ignored, a reasonable assumption
for relative dating but a poor assumption for absolute dating. The lifetime function from
the fit is plotted in Figure 4.17, with errors derived from the fit to the R value data,
excluding any error in the Oceanus Procellarum 3.3 Ga isochron.
69
Figure 4.16: An LROC NAC high sun-angle (82˚ above the horizon) image of North Ray
Crater showing discontinuous ejecta extending out to a diameter of 4-5 crater diameters.
Note how the ejecta can only be seen where the slope is very low or towards the west, the
direction of illumination. Image processing by Mike Zanetti. PDS Tag: M109134835R.
70
1000
700
3.8 cm halo lifetime
500
300
200
150
100
5
10
15
20
Crater diameter (km)
25
30
Figure 4.17: A plot of 3.8 cm halo lifetime (on a log-scale axis) against crater diameter
(in km) using data from Thompson et al. (1981). The criteria used for lifetime by
Thompson et al. (1981) (minimum halo diameter of 20 km or 2 crater diameters) differ
from those used in this thesis. The Thompson et al. (1981) lifetime curve excluding any
errors in the 3.3 Ga isochron derived from crater counts of Oceanus Procellarum by the
Planetary Basaltic Volcanism Study Project (1980).
71
Three decades of crater counting research lie between the 3.3 Ga Oceanus
Procellarum isochron and the modern isochrons (Michael and Neukum, 2010), which
differ considerably. To compare the Thompson et al. (1981) results to the data from the
present study, it is necessary to apply the Michael and Neukum (2010) isochrons to the
(Thompson et al. (1981) data (Figures 4.17-4.20).
In the diameter range used by the Thompson et al. (1981) study, a complication
arises with the Michael and Neukum (2010) isochrons. The polynomial curve that
Michael and Neukum (2010) display as an example is taken from crater counts in
Neukum (1983). However, there is a more recent paper, Ivanov et al. (2001), for which
Neukum is a co-author. The complication arises because Ivanov et al. (2001) include
updated crater counts and corresponding fit polynomial coefficients for the Moon.
Although the Ivanov et al. (2001) counts are more recent than the Neukum (1984) counts,
and they are included in the list of polynomial fit coefficients in Neukum et al. (2001),
Michael and Neukum (2010) do not include the Ivanov et al. (2001) data. There may,
however, be a valid unspecified reason for preferring the Neukum (1984) data. For
craters in the 0.5-3.0 km diameter range in our survey, the differences between the
isochrons derived from the two datasets are negligible, but for craters in the 4-32 km
diameter range in the Thompson et al. (1981) study, the isochrons do differ, and the
lifetimes have been calculated for both datasets (Figures 4.18-4.20).
72
Log(R)
Crater diameter (km)
Figure 4.18: A plot of log(R) against the crater diameter in km (shown on a log scale).
The Thomspon et al. (1981) R value fit (solid lines) and the fit to our lifetimes converted
back to R values (dotted lines) superimposed on the Michael and Neukum (2010)
isochrons as derived from the Ivanov et al. (2001) dataset. The errors for the Thompson
et al. (1981) fit are derived from the statistical errors for the fit given by Thompson et al.
(1981).
73
Log(R)
Crater diameter (km)
Figure 4.19: A plot of log(R) against the crater diameter in km (shown on a log scale).
The Thomspon et al. (1981) R value fit (solid lines) and the fit to our lifetimes converted
back to R values (dotted lines) superimposed on the Michael and Neukum (2010)
isochrons as derived from the Neukum (1983) dataset. The errors for the Thompson et al.
(1981) fit are derived from the statistical errors for the fit given by Thompson et al.
(1981).
74
2000
3.8 cm halo lifetime
1000
500
200
5
10
15
20
Crater diameter (km)
25
30
Figure 4.20: Halo lifetime (in Ma) as a function of crater diameter derived from the
Thompson et al. (1981) data using the Michael and Neukum (2010) isochrons. The
dashed lines show the lifetimes derived from isochrons derived using the Ivanov et al.
(2001) dataset, and the heavy lines show the lifetimes derived from isochrons derived
using the Neukum (1983) dataset. For each set of lines, the middle curve is the predicted
lifetime, the lower curve is the minimum lifetime, and the top curve is the maximum
lifetime.
75
Discussion
I.1 Secondary Cratering
Numerous studies have argued that primary craters dominate the population of
large (>10 km) craters, but secondary craters dominate the small (<1 km) crater
population, (e.g. Guiness and Arvidson, 1977; Melosh, 1989; Ivanov et al., 2001;
Neukum et al., 2001; Michael and Neukum, 2010; Rodrigue, 2011). Although secondary
craters elevate the crater counts for small craters, the negative slope of the Michael and
Neukum (2010) R plot isochrons compensates for this effect. Because secondaries do not
fall stochastically but in fields centered around their primaries, they do pose significant
problems for dating via the crater counting method. If a region falls within a secondary
field, its crater counts will be highly elevated. If it does not fall within one, its crater
counts will be strongly depressed. For this reason, Guinness and Arvidson (1977) argue
that crater counting cannot be used reliably for craters in a diameter range with
significant numbers of secondaries. As the diameter range studied here contains a large
number of secondaries, secondary cratering potentially represents a major source of error
in our results.
Guinness and Arvidson (1977), however, were examining small crater counting in
the context of dating small, constrained regions like individual craters and their ejecta
deposits. To some extent, selecting large focus regions that sample multiple locations on
the Moon can reduce the effect of secondaries. There are large gaps in Mini-RF coverage
between the images in the sample studied, so the spatial extent of the regions we sampled
was much larger than the sum of the areas of our images might suggest. Due to the
extent of the area covered in each focus region, the highlands region and the Mare
76
Serenitatis region, it is highly unlikely that a single secondary field would dominate the
entirety of either focus region, much less both. So the effect of secondary cratering on
the large and widely distributed sample used in this study is considerably less
problematic than it is for the small focus regions of Guinness and Arvidson (1977).
Distal secondaries can be found at considerable distances from their primaries (for
instance, Wells et al. (2010) identified Tycho (43.3°S, 11.2°W) secondaries in Newton A
Crater (79.7°S, 19.7°W)), so a number of the craters in this study may be secondaries of a
primary at a distance of 40˚ or more.
Because the non-stochastic distribution of
secondaries is the primary reason secondaries present a problem for crater age dating,
distal secondaries (distributed moderately randomly over significant fractions of the
Moon) are less likely to pose a significant problem. Secondary cratering, therefore, is
most likely a major source of error in dating, but because the sample covers a very large
region of the Moon, secondary cratering is less problematic than it would be in a study of
a smaller region.
I.2 Wells et al. (2010) Ejecta Morphologies—Diagnostic of Secondaries?
The Tycho secondaries investigated by Wells et al. (2010) had a distinctive ejecta
morphology that Wells et al. (2010) speculated might be diagnostic of secondary craters
(Figure 5.1). None of the craters examined had an ejecta morphology similar to the
Wells et al. (2010) craters, so either the sample contained no secondaries or not all
secondaries have the Wells et al. (2010) ejecta morphology. The second explanation is
strongly preferred.
Secondary craters are widely thought to dominate the relevant
diameter range because crater counts for small craters increase with decreasing diameter
77
E06008
WELLS ET AL.: SMALL TYCHO SECONDARIES
E06008
dary crater in the SC radar channel image. (b) The same secondary crater in the
blanket of the secondary
in comparison13
to cm
that radar
of the CPR
primary
crater,ofisa Tycho secondary with a tail of highFigure crater,
5.1: Earth-based
image
acing Tycho but elongated down trajectory. (c) A typical primary crater in the
CPR ejecta
primary
with
ejecta
blanket. Wells et al. (2010) propose that
e. (d) The same primary
crater inand
the aCPR
image.crater
Note that
theno
ejecta
blanket,
this ejecta morphology is diagnostic of secondaries, but we did not observe this
R, is highly symmetric.
morphology in our sample of fresh craters, which almost certainly contain distal
secondaries.
Fromcrater
Wells
et al. and
(2010).
wever, they stress that
this is that both
counting
primary/secondary classifica-
er production that does not tion were as systematic as possible. Crater diameters were
n or beyond rays evident in measured by fitting ellipses to crater rims. According to
Work on Mars [McEwen et convention, the minor axes of the fitted ellipses were used
Europa [Bierhaus et al., for the crater diameters, but the major axis size and thus
ations external to obvious crater eccentricity were also recorded. The regions in which
ary crater production of a craters with 400 m ≤ D ≤ 2 km were counted were an area of
nitude of more secondary 3644 km2 on the floors of Newton and Newton‐G craters
ayed Martian crater Zunil (henceforth: Newton region) and another of 996 km2 on the
n them, out to distances of floor of Newton‐A crater (henceforth: Newton‐A region).
Figure
2. (a) A
crater in the to
SCthe
radar
channel image.
(b) The same secondary crater in the
A major contribution
uncertainty
of secondary
[8] secondary
dary craters are still
beyond
CPR
image.
The
ejecta
blanket
of
the
secondary
crater,
in
comparison
700 km) [Preblich, 2005]. classification was the difficulty in establishing one‐to‐oneto that of the primary crater, is
direction facing between
Tycho but
elongated
trajectory. sec(c) A typical primary crater in the
small
craters down
and unresolved
ed in this workabsent
are in
notthe correspondence
radar channel
image.
The same
in thewas
CPRinimage.
identified
ondary
ejecta(d)blankets.
A primary
particularcrater
challenge
dis- Note that the ejecta blanket,
m2 of Tycho raysSC
in the CPR,which
is highly
symmetric.
and, therefore, while
probe visible
this tinguishing
of the
craters in the ejecta blankets were
econdary cratering for the responsible for the ejecta and which had merely been
superposed
by it.they
To stress
help break
theisdegeneracy,
simuldiameters greater than 63
m. However,
that this
that both the
crater
counting and primary/secondary classificataneous
age
of
the
Tycho
secondary
craters
was
employed.
a lower bound on secondary crater production that does not tion were as systematic as possible. Crater diameters were
Because
of the
shared age
Tycho in
and its
secondary
include secondary craters
between
or beyond
raysofevident
measured
bycraters
fitting ellipses to crater rims. According to
andmaps.
the assumed
homogeneity
of et
the lunar
terrain the
in minor
the
albedo
or
compositional
Work
on
Mars
[McEwen
convention,
axes of the fitted ellipses were used
ry Crater Classification
relatively
regions
of interest,
morphology
of
al., 2005; Preblich, 2005]
andsmall
Europa
[Bierhaus
et al.,the rim
for the
crater diameters,
but the major axis size and thus
of cratering
statistics
to that
the these
all Tycho
secondary
craters
the studycrater
should
be equallywere also recorded. The regions in which
2001]
suggests
populations
external
to inobvious
eccentricity
h care was
ensure the
degraded.
Tycho
crater
is an extremely
5 Myr
raystaken
may to
dominate
secondary
crater
production
of a young
craters (96
with±400
m ≤ D ≤ 2 km were counted were an area of
given event. An order of magnitude of more secondary 3644 km2 on the floors of Newton and Newton‐G craters
10
craters belonging 3toof the
small, rayed Martian crater Zunil (henceforth: Newton region) and another of 996 km2 on the
lies between obvious rays than in them, out to distances of floor of Newton‐A crater (henceforth: Newton‐A region).
[8] A major contribution to the uncertainty of secondary
700 km. Three times more secondary craters are still beyond
these rays entirely (distances > 700 km) [Preblich, 2005]. classification was the difficulty in establishing one‐to‐one
The secondary craters identified in this work are not correspondence between small craters and unresolved secencompassed by the 560,000 km2 of Tycho rays identified ondary ejecta blankets. A particular challenge was in disby Dundas and McEwen [2007] and, therefore, probe this tinguishing which of the craters in the ejecta blankets were
important parameter space for secondary cratering for the responsible for the ejecta and which had merely been
first time on the Moon.
superposed by it. To help break the degeneracy, the simultaneous age of the Tycho secondary craters was employed.
Because of the shared age of Tycho and its secondary craters
3. Method
and the assumed homogeneity of the lunar terrain in the
3.1. Primary Versus Secondary Crater Classification
relatively small regions of interest, the rim morphology of
[7] Because of the sensitivity of cratering statistics to the all Tycho secondary craters in the study should be equally
counting method employed, much care was taken to ensure degraded. Tycho crater is an extremely young (96 ± 5 Myr
3 of 1078
osaics of lunar craters Aristoteles (50.2!N, 17.4!E, d = 87 km) and (d) Aristarchus (23.7!N, 47.4!W, d = 40 km). In all frames, left: 70-cm
tion; right: 12.6-cm mosaic, Figure
80 m/pixel
spatial
resolution. (a)
OC mosaics;
(b) image
CPR mosaics
showing outlines
of bright
and dark the
haloes
as
5.2:
Earth-based
12.6
cm CPR
of Aristarchus
Crater,
showing
dark
rrows mark other craters with radar-dark haloes; (c) CPR as color overlay on OC radar image; outlines as in (b); and (c) CPR as color overlay
halos identified by Ghent et al. (2010). From Ghent et al. (2010).
rH, and r! are shown. Note that 12.6-cm bright halo extends beyond 70-cm bright halo, while 12.6- and 70-cm dark haloes are coincident.
eposits and concluded that different
ble for emplacing the inner versus outer
d that the outer layers are commonly
characterized by a distinct radial fabric that in places flows around
or over low-relief obstacles, indicating relatively slow motion
along the ground. In addition, they noted thin radial wisps
as: Ghent, R.R., et al. Generation and emplacement of fine-grained ejecta in planetary impacts. Icarus (2010), doi:10.1016/
79
(Guinness and Arvidson, 1977; Melosh, 1989; Ivanov et al., 2001; Neukum et al., 2001;
Michael and Neukum, 2010). A similar uptick in crater frequency at small craters was
found on the asteroid Gaspra, whose gravity is too low to allow secondary cratering
(Chapman et al., 1996). However, nearest-neighbor statistical analysis of Martian craters
for lineations diagnostic of secondary craters (which from in chains) found that the small
crater region is indeed dominated by secondaries (Rodrigue et al., 2011). Furthermore,
even if distal secondaries are not the dominant component of small craters, it is virtually
certain that at least one of the craters in this sample, none of which had the Wells et al.
(2010) ejecta morphology, would have been a secondary. The results of this study,
therefore, are inconsistent with the possibility that the Wells et al. (2010) ejecta
morphology is found in all secondary craters.
II Problems With Halo Diameter Quantification
A number of the features of the degradation process described above illuminate
complexities and difficulties with simply using the diameter of the halo to quantify how
far along in its lifetime a particular crater is. To begin with, it is not clear that the
original extent of the discontinuous ejecta is constant.
The fact that all of the
morphologically freshest craters have discontinuous ejecta diameters close to 12 crater
diameters (Figure 4.6) is evidence supporting this hypothesis. However, it is possible
that there are factors that effect the initial diameter of the discontinuous ejecta and, as a
result, skew the resultant estimates of the lifetime fraction.
Another major problem with this methodology is that it is often difficult to
quantify the diameter of the halo. The discontinuous ejecta consist of a number of
discrete rays; they do not form perfect circles with clear diameters. Furthermore, there is
80
asymmetry in the ejecta blanket from even moderately oblique impacts (Gault and
Wedekind, 1978), and in many cases different parts of the halo often have eroded more
than others. Finally, the boundary of a highly eroded halo is not crisp, and there is
unavoidable human error in measuring it. This represents an undeniable source of error.
III.1 The Discontinuous Ejecta Lifetime to Crater Diameter Relationship—
Extrapolation to Small Craters
While the Apollo comparisons show that the 12.6 cm discontinuous halo closely
tracks the discontinuous ejecta for craters in the 0.3-1.0 km range, it cannot be assumed
that this relationship will necessarily hold for significantly larger and significantly
smaller craters.
The observation of the relationship between crater diameter and
discontinuous halo diameter for craters in the 0.5-3 km range,
lh ( dc ) ! dc~2 ,
Equation 5.1
does demonstrate a relationship between crater diameter and discontinuous ejecta
lifetime. However, it is not necessarily the case that the 12.6 cm discontinuous halo
lifetime will continue to track the discontinuous ejecta at smaller and larger diameters.
Radar backscatter at 12.6 cm is primarily sensitive to decimeter-scale blocks
(Neish et al., 2011). While the relationship between crater diameter and discontinuous
ejecta block sizes is poorly constrained, the maximum block size (the largest blocks are
located in the continuous ejecta (Bart, 2007)) is known to vary with crater diameter by
~
2
d b ! dc 3 ,
Equation 5.2
where db is the block diameter and dc is the crater diameter (Housen, 1988). So, it is
unlikely that the radar backscatter properties of the discontinuous halo will remain
81
constant with varying diameter.
Indeed, below a certain crater diameter, the
discontinuous ejecta will be severely depleted of decimeter-scale blocks. Furthermore, it
is likely that the halo lifetime to crater diameter relationship may begin to break down at
crater diameters under 200 m. At this size, the regolith depth (~8-32 m, Wilcox et al.,
2005) becomes a significant fraction of the crater depth (0.25 to 0.33 of the diameter of
the crater), and the bedrock component that produces the decimeter-scale blocks
decreases in volume. The effect of regolith will vary significantly across the Moon
because the regolith depth varies by a factor of ~4 (Wilcox et al., 2005).
However, for a short time regolith-dominated craters may produce decimeterscale “blocks” capable of elevating radar backscatter. The Station 9 crater at the Apollo
15 landing site contained clods of regolith in its ejecta (Rancitelli et al., 1972). The age
of the Station 9 crater is uncertain. The 26Al age range is 0.75-1.0 Ma, although this may
be an underestimate caused by a very rapid erosion rate for regolith clods, and saturation
of
22
Na implies a higher age (Rancitelli et al., 1972). Given the presence of several
regolith clods at the Station 9 crater, regolith clods probably persist for several Ma after
crater formation. Although the lack of constraints on the formation of regolith clods
limits our ability to speculate, regolith clods in the small secondaries of very fresh
impacts may be the source of the extremely elevated radar backscatter in very fresh
craters like Figure 4.6.
Secondary craters are thought to dominate small crater populations (see above),
and they may have different ejecta block sizes. Bart (2007) showed that the largest
boulders in the continuous ejecta tend to be larger for secondaries than primaries, but it is
uncertain whether there is a similar effect in the discontinuous ejecta. If true, this would
82
imply that secondary crater discontinuous halo lifetimes may be significantly longer than
primary crater discontinuous halo lifetimes.
Although there are numerous potential problems with extrapolating out the
discontinuous halo lifetime to crater diameter curve to craters <<0.5 km, Cone Crater
does supply empirical confirmation that the curve is broadly correct at 0.34 km. It is
likely that the curve can be used, albeit with some caution, for craters where regolith does
not form a significant portion of the ejected material. However, there may be reasons
why the curve does not apply to particular classes of small craters, and it is probably
highly untrustworthy for craters whose ejecta are dominated by regolith.
III.2 The Discontinuous Ejecta Lifetime to Crater Diameter Relationship—
Extrapolation to Large Craters
The increase in discontinuous halo lifetime with increasing diameter is due partly
to the corresponding increase in block size, but there is an upper limit on the size of
blocks present at the surface. (The thickening of ejecta with increasing crater diameter
may also be a factor.) When blocks reach a certain size and ejection velocity, they form
secondary craters instead of being deposited on the surface (Melosh, 1989). For a
sufficiently large crater, the ejecta in the ejecta blanket will derive largely from secondary
craters rather than blocks ejected directly from the primaries. The blocks in the ejecta of
these secondaries will be considerably smaller than the blocks produced by direct ejection
from the primaries, so the 12.6 cm discontinuous halo lifetimes may be shortened as a
result.
Although limited by a resolution of 2 km/ pixel, results from the Thompson et al.
(1981) 3.8 cm radar survey imply that the halo lifetime reaches a plateau or decreases at
83
crater diameters larger than 10 km. With such low resolution, it is possible that this is
due to an observational effect. For example, the ejecta of larger craters may be more
likely to be disrupted by underlying topography.
Furthermore, Earth-based 12.6 cm CPR observations of large lunar craters by
Ghent et al. (2010) showed that the 12.6 cm bright halo was not necessarily present in
small bright halos that were interpreted as corresponding to the continuous ejecta. Most
of the discontinuous halos were represented by radar-dark halos instead of radar-bright
halos (Figure 5.2 shows the bright and dark halos around Aristarchus, a 41 km crater).
The outer portion of the Ghent et al. (2010) 12.6 cm bright halo in Figure 5.2 contains
radial lineations, indicating that it belongs to the inner portion of the discontinuous halo.
The results of Ghent et al. (2010) and Thompson et al. (1981) are inconsistent with the
results of our lifetime model extrapolated out to crater diameters greater than ~10 km.
IV Possible Effect of Lithology
While the similarity of the densities of craters with discontinuous halos in the
highlands and the maria suggests that basalt/anorthosite lithology dichotomy does not
invalidate the treatment of halo lifetime as lithology-independent, the possibility of a
small effect from the mare/highlands dichotomy cannot be ruled out.
Furthermore,
textural effects like grain size, vesicle density, and fracturing of the bedrock by nearby
impacts may alter the lifetime of a block in the discontinuous ejecta by reducing the
impact energy necessary to destroy the block by catastrophic rupture.
84
V.1 Variations in Impact Rate
The lifetime calculations in this study relied heavily on the assumption that the
cratering has remained constant with time.
However, justifying this assumption is
difficult. A number of studies have suggested that the impact rate over the past ~1 Ga is
elevated (e.g. Grieve, 1984; Baldwin, 1985; McEwen et al., 1997) or reduced (Hartmann
et al., 2007), although Guinness and Arvidson (1977) argue for a constant cratering rate
over the past 3.3 Ga.
Even if the lunar impacting rate is constant over long timescales, it most likely
varies significantly over short timescales as a result of collisions in the asteroid belt
(Zappalà et al., 1998). The main source of the near-Earth objects (NEOs) that dominate
the impactor population of the Earth-Moon system is the asteroid belt (Bottke et al.,
2006). Asteroids are ejected from the Main Belt when they cross a major resonance,
usually the #6 secular resonance with Saturn or 3:1 mean-motion resonance with Jupiter.
The number of asteroids near these resonances varies with time, spiking dramatically
when an impact destroys a large asteroid, leaving a profusion of fragments orbiting in
what is known as a collisional family (Bottke et al., 2006). The orbits of these asteroids
will then disperse, largely due to an phenomenon known as the Yarkovsky effect: Most
asteroids rotate with periods on the order of hours, and when a side faces the Sun, it heats
up, but it does not immediately radiate away all of its heat. Instead, after that face has
turned perpendicular to the Sun, it continues to emit infrared light off to the side (infrared
light is the primary means of radiating heat for asteroids). Because infrared light caries a
small amount of momentum, the infrared light emitted off the side exerts a thrust on the
asteroid. This is known as the Yarkovsky effect.
85
When an asteroid has prograde rotation (rotating in the same counter-clockwise
direction as its orbit around the Sun), the Yarkovsky effect exerts a thrust in the direction
the asteroid is orbiting (Bottke et al., 2006). This adds energy to the orbit and moves it
further away from the Sun. When an asteroid is in retrograde rotation (rotating clockwise while it orbits the Sun in a counter-clockwise direction), the Yarkovsky effect exerts
a thrust in the opposite direction from the direction the asteroid is orbiting, robbing the
orbit of energy and moving it closer to the Sun. The Yarkovsky effect continues to
disperse the asteroids in the Main Belt until they cross a resonance and are ejected into a
wildly different orbit—often one that crosses the Earth-Moon system. Because of the
Yarkovsky effect, asteroids formed in the creation of a collisional family near a major
resonance do not remain passively in the asteroid belt. Rather, they are delivered to the
inner solar system, causing a spike in the impact rate (Bottke et al., 2006). Furthermore,
because the Yarkovsky effect affects larger asteroids more weakly, larger impactors
resulting from a collisional family are delivered later, disrupting the ordinary sizefrequency distribution curve on short timescales. Over timescales of billions of years,
these short-wavelength fluctuations may well average out. However, on timescales of
tens or hundreds of millions of years, such as those employed in this study, the lunar
cratering rate is probably quite variable, possibly skewing many of the calculated ages by
as much as a factor of two.
Forming at 160(+30/-20) Ma, one of the collisional families most likely to skew
the results presented in this thesis is the Baptistina family. It has been interpreted as
causing a twofold increase in the impact rate of km-scale asteroids over the past ~100
million years, probably causing the 109 Ma Tycho impact on the Moon and the 65 Ma
86
Chicxulub K-T boundary impact on the Earth (Bottke et al., 2007). The lifetime of a 1.0
km discontinuous halo is only ~80 Ma, so the effect of the Baptistina shower for craters
1.0 km and smaller should be absent from our results. The spike from the Baptistina
family should be present in our data for craters larger than 1.0 km. This effect is
regrettable but unavoidable because the impactor rate is not yet known with sufficient
precision for its variations to be factored into the production of cratering size-frequency
isochrons. Compelled to assume a constant cratering rate, this study thus makes the
assumption that this is likely untrue and a source of considerable but unavoidable error in
lifetime calculations.
V.2 Variations in the Micrometeorite Flux and Erosion Rate
A further complication from asteroid collisions is variations in the micrometeorite
impact rate and, by extension, the lunar erosion rate. Due to the higher 3He abundances
in materials exposed to solar wind implantation, 3He records in ocean floor strata can be
used to trace the variations in interplanetary dust particle (IDP) flux at the Earth (Farley
et al., 1998; Farley et al., 2006). In the Eocene, a ~36 Ma spike in large terrestrial
impacts (producing the Chesapeake and Popigai events) was correlated with a spike in
the IDP flux from 3He (Farley et al., 1998). In the Miocene, a roughly fourfold ~1.5 Ma
spike in IDP flux beginning at 8.2±0.1 Ma was correlated with the 8.3±0.5 Ma formation
of the Veritas asteroid family (Farley et al., 2006). The asteroid family does not have to
be located near a resonance to cause a spike in IDP flux. The Veritas family is located in
a stable region of the asteroid belt unlikely to deliver large impactors to the inner solar
system.
However, the Poynting-Robertson drag (drag from the light the particle is
passing through) and the solar wind drag will deliver the dust produced in a stable
87
collision to the inner solar system, causing a spike in the micrometeorite impact rate
without affecting the cratering rate (Farley et al., 2006). Thus the assumption of a timeinvariant micrometeorite erosion rate is likely invalid on small timescales.
Because all asteroid collisions create dust showers, there are more spikes in the
micrometeorite flux than there are in the large impactor flux, so the effect averages out on
shorter timescales. The effect of dust showers probably only skews the results presented
in this thesis noticeably for craters younger than ~50 Ma. It is unclear whether the IDP
flux tracks the rate of the pebble-sized impactors responsible for catastrophic rupture, so
the effect may be limited to changes in the abrasion rate that do not radically affect the
lifetimes of decimeter-scale blocks.
88
Conclusion
Micrometeorite, solar wind ion, and cosmic ray bombardment gradually erode the
ejecta blankets that form around small lunar impact craters on timescales of tens to
hundreds of millions of years. Sensitive to surface roughness on the scale of its 12.6 cm
wavelength, the 30 m/pixel Mini-RF instrument (Nozette et al., 2010; Neish et al., 2011)
provides detailed imagery of the ejecta blankets of small lunar craters at an
unprecedented resolution and quality allowing us to examine large numbers of ejecta
blankets with a higher degree of precision than possible beforehand (Thompson et al.,
1981).
By observing hundreds of ejecta blankets at various stages in their lifetime, this
study has characterized the morphology variations in degrading ejecta: Pristine ejecta
blankets have a radar bright halo diameter of ~12 crater diameters and an ultra-bright
radar backscatter, most likely due to enhanced surface roughness from regolith clods like
those observed at the ~1 Ma Station 9 crater at the Apollo 15 landing site (Rancitelli et
al., 1972). Only present in the freshest of craters, the ultra-bright radar signature quickly
fades to a dimmer radar return whose brightness steadily decreases as the ejecta blanket
erodes.
As the discontinuous ejecta blanket (the outer portion) erodes, its radial
lineations gradually fade. Its diameter steadily decreases until the entire discontinuous
portion of the ejecta has vanished, leaving a faint signature representing the continuous
ejecta to linger until it too fades into the background. Derived from statistical analysis of
the distribution of different halo diameters, an empirically function can describe what
fraction of its lifetime a discontinuous ejecta blanket will have undergone once it has
shrunk to a particular halo diameter. The outer ejecta erode much more quickly than the
89
inner ejecta. It takes half of the lifetime of a discontinuous ejecta blanket to shrink from
~12 crater diameters to 4.9 crater diameters, and it takes the other half of its lifetime to
fade to 4 crater diameters, where it becomes indistinguishable from the continuous halo.
Using well-established crater-counting techniques, this study has characterized
the lifetime of the discontinuous portion of the ejecta blanket as a function of the crater
diameter. The discontinuous ejecta lifetime is proportional to the square of the crater
diameter. Combining the empirically derived function for discontinuous halo lifetime
with the empirically derived function quantifying what fraction of its lifetime a halo has
so far undergone allows estimation of absolute dates of individual craters.
Craters with absolute dates based on samples returned by the Apollo missions
provide an independent verification of these results: Cone Crater at the Apollo 14
landing site was dated to 25-30 Ma by cosmic ray exposure ages of its ejecta (Turner et
al., 1971) and imaged by Mini-RF. With a diameter of 340 m, the projected lifetime of
Cone Crater’s discontinuous halo is 8.7(+1.5/-1.7) Ma, predicting that the discontinuous
ejecta should be absent from the 26-30 Ma crater, and indeed they are. North Ray Crater
at the Apollo 16 landing site was dated to 50±1.4 Ma (Arvidson et al., 1975), and the age
estimate of 54(+39/-29) Ma is solidly in agreement with the known age.
However, it is unclear if these results can be extrapolate to craters with diameters
outside the range of ~0.3-5.0 km. Local lithology variations may affect the block size
distribution of the ejecta blanket. It must also be noted that crater counting studies of
small craters are prone to uneven contamination from secondary craters (Guinness and
Arvidson, 1977), an effect somewhat moderated by selecting images distributed over a
wide spatial extend of the Moon. These results cast serious doubt on one of the most
90
promising possibilities for resolving the secondary problem. The absence of any craters
with the distinctive ejecta morphology identified in select Tycho secondaries with Earthbased radar (Wells et al., 2010) renders unlikely the possibility that these distinctive
ejecta morphologies are diagnostic of secondaries and can therefore be used to remove
the secondaries from the crater counts. Furthermore, the impact rate has probably not
stayed constant with time, a reality that adds considerable error to our absolute age
estimates (Bottke et al., 2007).
Finally, this methodology is prone to human error
because the estimation of the ejecta diameters of patchy eroded ejecta blankets is not
entirely objective. However, previous methodologies for estimating absolute ages of
small lunar craters have even large sources of error (e.g. Swann and Reed, 1974), and
many of these sources of error could be addressed by expanding this study to a much
larger sample size.
91
References
Arvidson, B., Crozaz, G., Drozd, R., Hohenberg, C., Morgan, C., 1975, “Cosmic ray
exposure ages of features and events at the Apollo landing sites,” The Moon, 13,
259-276.
Arvidson, B., Chapman, C., Cintala, M., Fulchigoni, M., et al. (The Crater Analysis
Techniques Working Group), 1979, “Standard Techniques for Presentation and
Analysis of Crater Size-Frequency Data,” Icarus, 37, 467-474.
Ashworth, D. G., 1978, “Lunar and Planetary Impact Erosion,” in Cosmic Dust, J. A. M.
McDonnell, ed., 427-526.
Baldwin, R., B., 1985, “Relative and absolute ages of individual craters and the rate of
infalls on the moon in the post-Imbrium period,” 61, 63-91.
Bandeira, L., Ding, W., Stepinski, T., 2010, “Automatic detection of sub-km craters using
shape and texture information,” Lunar and Planetary Science Conference abstract.
Bart, G. D., 2007, Lunar Surface Geology from Analysis of Impact Craters and Their
Ejecta, Ph.D. Thesis, University of Arizona, Department of Planetary Sciences.
Bottke, W., Love, S., Tytell, D., and Glotch, T, 2000, “Interpreting the Elliptical Crater
Populations on Mars, Venus, and the Moon,” Icarus, 145, 108-121.
Bottke, W., Rubincam, D., Vokrouhlicky, D., Nesvorny, D., 2006, “The Yarkovsky and
YORP Effects: Implications for Asteroid Dynamics,” Annual Reviews of Earth
and Planetary Science, 34, 157-191.
Bottke, W., Vokrouhlicky, D., Nesvorny, D., 2007, “An asteroid breakup 160 Myr ago as
the probable source of the K/T impactor,” Nature, 449, 48-53.
Bussey, B. J. et al., 2007, “Mini-RF: Imaging radars for exploring the lunar poles,” LPSC
XXXVIII Abstract.
Calef, F., Herrick, R., and Sharpton, V., 2009, “Geomorphic analysis of small rayed
craters on Mars: Examining primary versus secondary impacts,” Journal of
Geophysical Research, 114.
Chapman, C., Veverka, J., Belton, M., Neukum, G., Morrison, D., 1996, Cratering on
Gaspra, Icarus, 120, 231-245.
Craddock, R., and Howard, A., 2000, “Simulated degradation of lunar craters and a new
method for age dating farside mare deposits,” Journal of Geophysical Research,
105, 20387-20401.
92
Colaprete, A., Schultz, P., Heldmann, J., Wooden, D., Shirley, M., et al., 2010,
“Detection of Water in the LCROSS Ejecta Plume,” Science, 330, 463-467.
Farley, K., Montanari, A., Shoemaker, E., Shoemaker, C., 1998, “Geochemical Evidence
for a Comet Shower in the Late Eocene,” Science, 280, 1250-1253.
Farley, K., Vokrouhlicky, D., Bottke, W., Nesvorny, D., 2006, “A late Miocene dust
shower from the break-up of an asteroid in the main belt,” Nature, 439, 295-297.
Gault, D., and Wedekind, J., 1978, “Experimental studies of oblique impact,”
Proceedings of the Ninth Lunar Science Conference, 3843-3875.
Ghent, R., Leverington, D., Campbell, B., Hawke, B., Campbell, D., 2005, “Earth-based
observation of radar-dark crater halos on the Moon: Implications for regolith
properties,” Journal of Geophysical Research, 110.
Ghent, R., Gupta, V., Campbell, B., Ferguson, S., Brown, J., et al., 2010, “Generation and
emplacement of fine-grained ejecta in planetary impacts,” Icarus, 209, 818-835.
Gomes, R., Levison, H., Tsiganis, K., Morbidelli, A., 2005, “Origin of the cataclysmic
Late Heavy Bombardment period of the terrestrial planets,” Nature, 435, 466-469.
Grier, J., McEwen, A., Lucey, P., Milazzo, M., and Strom, G., 2001, “Optical maturity of
ejecta from large rayed lunar craters,” Journal of Geophysical Research, 106,
32847-32862.
Grieve, R., 1984, “The impact cratering rate in recent time,” Journal of Geophysical
Research, 89, B403-B408.
Guinness, E., and Arvidson, R., 1977, “On the constancy of lunar cratering flux over the
past 3.3x109 yr,” Proceedings of the Eight Lunar Science Conferences, 34753494.
Hartmann, W., K., 1986, “Moon Origin: The Impact-Trigger Hypothesis,” Origin of the
Moon: Proceedings of the Conference: Kona, HI, 579-608.
Hartmann, W., Quantin, C., Mangold, N., 2007, “Possible long-term decline in impact
rates 2. Lunar impact-melt data regarding impact history,” Icarus, 186, 11-26.
Hibbitts, C., Dyar, M., Orlando, T., Grieves, G., Moriarty, D., et al., 2010, “Thermal
stability of water and hydroxyl on airless bodies,” Lunar and Planetary Science
Conference abstract.
Housen, K., 1988, “Scaling of Crater Ejecta Blocks,” Lunar and Planetary Science
Conference Abstract.
93
Ivanov, B., Neukum, G., and Wagner, R., 2001, “Size–Frequency Distributions of
Planetary Impact Craters and Asteroids,” in Rickman, H., and Marov, M (eds.),
Collisional Processes in the Solar System, Kluwer Academic Publishers,
Dordrecht.
Lincoln Laboratory, 1968, Radar Studies of the Moon, Final Report, 2, Massachusetts
Institute of Technology, Lexington, Massachusetts.
Lucey, P., Blewett, D., Taylor, G., Hawke, B., 2000, “Imaging of lunar surface maturity,”
Journal of Geophysical Research, 105, 20377-20386.
McDonnell, J., Ashworth, G., Flavill, R., Carey, W., Bateman, D., Jennison, R., 1977,
“The Characterization of Lunar Surface Impact Erosion and Solar Wind Sputter
Processes on the Lunar Surface,” Philosophical Transactions of the Royal Society
of London, Series A, Mathematical and Physical Sciences, 285, 303-308.
McEwen, A., Preblich, B., Turtle, E., Artemieva., N., Golombek, M., et al., 2005, “The
rayed crater Zunil and interpretations of small impact craters on Mars,” Icarus,
176, 351-381.
McEwen, A., Moore, J., Shoemaker, E. (1997), “The Phanerozoic impact cratering rate:
Evidence from the far side of the Moon,” Journal of Geophysical Research, 102,
9231-9242.
McKay, D., Heiken, G., Basu, A., Blanford, G., Simon, S., et al., 1991, “The Lunar
Regolith,” in Lunar Sourcebook: A User’s Guide to the Moon, Heiken, G.,
Vaniman, D., and French, B., eds., 285-356.
Melosh, J., 1989, Impact Cratering: A Geologic Process, Oxford University Press, New
York.
Michael, G., and Neukum, G., 2010, “Planetary surface dating from crater size–frequency
distribution measurements: Partial resurfacing events and statistical age
uncertainty,” Earth and Planetary Science Letters, 294, 223-229.
Mitrofanov, I., et al., 2010, “Hydrogen Mapping of the Lunar South Pole Using the LRO
Neutron Detector Experiment LEND,” Science, 330, 483-486.
Neish, C., Bussey, D., Spudis, P., Marshall, W., Thomson, B., et al., 2011, “The nature of
lunar volatiles as revealed by Mini!RF observations of the LCROSS impact site,”
Journal of Geophysical Research, 116.
Neukum, G., 1983, “Meteoritenbombardement and Datierung Planetarer Oberflächen,”
Habilitation Dissertation for Faculty Membership, University of Munich.
94
Neukum, G., Ivanov, B., and Hartmann, W., 2001, “Cratering Records in the Inner Solar
System in Relation to the Lunar Reference System,” Space Science Reviews, 96,
55-86.
Newsom, H., and Taylor, S., 1989, “Geochemical implications of the formation of the
Moon by a single impactor,” Nature, 338, 29-34.
Nozette, S. et al., 2010, “The Lunar Reconnaissance Orbiter Miniature Radio Frequency
(Mini-RF) Technology Demonstration,” Space Science Reviews, 150, 285-302.
Pieters, C., et al., 2009, “Character and Spatial Distribution of OH/H2O on the Surface of
the Moon Seen by M3 on Chandrayaan-1,” Science, 326, 568.
Pike, R., 1977, “Apparent depth/diameter relation for lunar craters,” Proceedings of the
Eight Lunar Science Conference, 3427-3436.
Pike, R., and Wilhelms, D., 1978, “Secondary-impact craters on the Moon: Topographic
form and geologic process,” Lunar and Planetary Science Conference Abstract.
Planetary Basaltic Volcanism Working Group, 1980, “Chronology of planetary
volcanism by comparative studies of planetary cratering,” Basaltic Volcanism
Study Project.
Rancitelli, L., Perkins, R., Felix, W., Wogman, N., 1972, “Cosmic ray flux and lunar
surface processes characterized from radionuclide measurements in Apollo 14 and
15 lunar samples, Lunar and Planetary Science Conference.
Raney, K. R., 2007, “Hybrid-Polarity SAR Architecture,” IEEE Transactions on
Geoscience and Remote Sensing, 45, 3397-3404.
Rodrigue, C. M., 2011, “Nearest neighbor analysis, regression, and secondary crater
prospecting on Mars,” Lunar and Planetary Science Conference abstract.
Saal, A., et al., 2008, “Volatile content of lunar volcanic glasses and the presence of
water in the Moon’s interior,” Nature, 454, 192.
Salamuni!car, G., and Lon!aric, S., 2010, “Basic principles and prototype of crater
detection algorithm for detection of craters from global mosaics of visual images
for the whole Mars,” Lunar and Planetary Science Conference abstract.
Schultz, P. H., 1976, Moon Morphology, University of Texas Press, Austin.
Schultz, P., Hermalyn, B., Colaprete, A., Ennico, K., Shirley, M., Marshall, W., 2010,
“The LCROSS Cratering Experiment,” Science, 330, 468-472.
95
Schultz, P., and Lutz-Garihan, A., 1972, “Grazing Impacts on Mars: A Record of Lost
Satellites,” Proceedings of the Thirteenth Lunar and Planetary Conference
(Journal of Geophysical Research, 87, A84-A96).
Shoemaker, E., 1963, “Impact Mechanics at Meteor Crater, Arizona,” in The Moon
Meteorites and Comets, eds. Kuiper, G., and Middlehurts, B., 301.
Slade, M., Butler, B., and Muhleman, D., 1992, “Mercury Radar Imaging: Evidence for
Polar Ice,” Science, 258, 635-640.
Soderblom, L., and Lebofsky, L., 1972, “Technique for Rapid Determination of Relative
Ages of Lunar Areas from Orbital Photography,” Journal of Geophysical
Research, 77, 279-296.
Spudis, P., Bussey, D., Butler, B., Carter, L., Chakraborty, J., et al., 2010, “Results of the
Mini-SAR imaging radar, Chandrayaan-1 mission to the Moon,” Lunar and
Planetary Science Conference abstract.
Stuart, J. S., and Binzel, R. P., 2004, “Bias-corrected population, size distribution, and
impact hazard for the near-Earth objects,” Icarus, 170, 295-311.
Swann, G. A., and Reed, V. S., 1974, “A method for estimating the ages of small
Copernican craters and its application to the determination of Copernican
meteorite flux,” Proceedings of the Fifth Lunar Conference (Supplement 5,
Geochimica et Cosmochimica Acta, 1, 151-158).
Thomas, P., 1999, “Large Craters on Small Objects: Occurrence, Morphology, and
Effects,” Icarus, 142, 89-96.
Thompson, T. W., Masurshy, H., Shorthill, R. W., Tyler, G. L., and Zisk, S. H., 1974, “A
comparison of infrared radar and geologic mapping of lunar craters,” Moon, 10,
87-117.
Thompson, T. W., Zisk, S. H., Shorthill, R. W., Schultz, P. H., Cutts, J. A., 1981, “Lunar
craters with radar bright ejecta,” Icarus, 46, 201-225.
Trask, N. J., 1971, “Geologic comparison of mare materials in the lunar equatorial belt,
including Apollo 11 and Apollo 12 landing sites,” U.S.G.S Professional Paper,
750D, 138-148.
Turner, G., Huneke, J., Posodek, F., and Wasserburg, G., 1971, “40Ar-39Ar ages and
cosmic ray exposure ages of Apollo 14 samples,” Earth and Planetary Science
Letters, 12, 19-35.
Warren, P., 1985, “The magma ocean concept and lunar evolution,” Annual Reviews of
Earth and Planetary Science, 13, 201-240.
96
Wells, K., Campbell, D., Campbell, B., Carter, L., 2010 “Detection of small lunar
secondary craters in circular polarization ratio radar images,” Journal of
Geophysical Research, 115.
Wieczorek, M., Jolliff, B., Khan, A., Pritchard, M., Weiss, B., et al., 2006, “The
Constitution and Structure of the Lunar Interior,” Reviews in Mineralogy and
Geochemistry, 60, 221-364.
Wilcox, B., Robinson, M., Thomas, P., Hawke, B., 2005, “Constraints on the depth and
variability of the lunar regolith,” Meteoritics and Planetary Science, 40, 695-710.
Zappalà, V., Cellino, A., Gladman, B., Manly, S., Migliorini, F., 1998, “Asteroid
Showers on Earth after Family Breakup Events,” Icarus, 134, 176-179.
Zisk, S., Pettengill, G., and Catuna, G., 1974, “High-resolution radar maps of the lunar
surface at 3.8-cm wavelength,” The Moon, 10, 17-50.
97