Lecture Notes for the Final
Third order of relief: Variations in crater density
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See Viewgraphs:
"Noachian regions, Part A"
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The third order of relief includes regions smaller in extent than most of the
second order features, though some are very large, as large or larger than
many second order features already described.
- As mentioned earlier, they do not "nest" within second order features
(though they do within the first order), as I reserved the second order as the
level of really conspicuous large features of the planet.
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Third order features are broad regions, but they are not visually conspicuous
in the way of, say, Syrtis Major or the seasonal polar ice caps.
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They typically range in diameter from ~1,000 km (e.g., Meridiani
Planum) to
5,500 km (e.g., Noachis Terra).
- They are all named as:
- Terra ("extensive land mass")
- Planum ("a plateau or high plain")
- Planitia ("a lowland or low-lying plain")
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It is at this order that we can clearly see the variations in crater density,
size, and condition, which are used to establish relative dating on the
martian surface. In discussing the third order of relief, then, I'll first
cover the crater-counting system of relative aging and then the epochs of
martian geology. Each epoch will be used to frame the third order landscape
features.
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Crater-counting
- The idea here is that the longer a planetary surface has been around,
the more "opportunity" it has to be the target of solar system debris.
- This debris consists of the small dust grains to planet-sized objects
that accreted, largely through gravitational attraction, out of the
planetary gas and dust nebula and disk that surrounded the proto-sun and sun.
- There is a magnitude-frequency relationship here, similar to what
we see
with many other hazards: The smaller impact events are vastly more common
than the larger ones.
- The ideal size-frequency distribution follows a power law
pattern, that
is something along the lines of Y = aX -b, or,
alternatively, log Y
= log a - b(log X), where Y = the number of craters in a given size range or
larger; X = crater diameters; a = the Y intercept (a calculated constant); and
b = the slope of the curve (the other calculated constant).
- Doing this as a log-log chart, the association, ideally, forms a
straight line, with slope b.
- The older the surface is, the higher a will be. The curve for an
older
surface will have the same slope as a younger surface, but its height on the
chart will be greater.
- Past a certain point, though, you reach saturation, a level of
bombardment so severe, a landscape so old, that there is literally no more
room for a new crater: Each new crater necessarily obliterates traces of
older craters.
- Once saturation is reached, it is no longer possible to say that one
saturated landscape is older or younger than another saturated landscape.
Once saturation is reached, all you can say is that surface is crazy-old, on
Mars, over 4.1 billion years old.
- To do a crater count study, you need to calculate the area of your study
area and normalize it (so that counts can be scaled to a common areal
base):
A common system (Hartmann and Neukum 2004) uses a square kilometer.
- Then, you identify every crater on your image, recording its diameter in
meters or kilometers.
- Then, you establish size bins to classify your crater diameters
by size categories: A common standard is an X axis with
each bin's upper boundary equal to the lower boundary times the square root of
2. So, starting at 1 km, the next bin boundary would be
1 *
√2, or 1.414. The next
one would be 1.414 *
√2, or 2. The next one
would be 2 *
√2, or 2.828, followed by
2.828 *
√2, or 4, and so on.
- After you have your size bins, you compare each of your crater diameter
measurements to your bins and count up the craters that fall within each of
the bins plus all the bins bigger than that one and then convert the counts so
that they are proportional to 1
km2, instead of the original size of your actual study area. So,
if your study area were 100 km2, you'd divide your counts by 100
(and, yes, it seems weird to count the number of 5 km wide craters in a 1
km2 standardized area).
- That done, you plot the adjusted number of craters in or above each bin
on the
Hartmann-Neukum "isochron" graph, available at http://www.psi.edu/research/mgs/template2008.JPG.
- You'll find that the pattern of dots you plot at the intersection of the
middle of the bins and the adjusted number of craters per square kilometer
will align
roughly with one of the dotted or solid lines on the isochron plot. This can
be very roughly: Typically, the rightmost dots, especially, can be more
widely
divergent from the isochrons. The counts in the larger bins are smaller and
smaller, so you may get statistical small-sample effects that sometimes allow
the dots to
range pretty far afield, even up above the saturation line.
- Paying attention to the dots on the left (smaller size bins), draw a line
through their directional trend, parallel to the isochrons, and then trace
that line out to the label identifying age. You're probably safest using the more abundant counts in the bins between 1 and 16 km in diameter.
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The
dotted lines are labelled with years ago (y = years; My = millions of years;
Gy = gigayears or billions of years).
- The long, straight solid line is saturation somewhere past 4.1 Gy. The
longer of the two short solid lines represents the boundary between the
Noachian Period and the Hesperian and the shorter, lower of the two short
lines
represents the boundary between the Hesperian and the Amazonian (about which,
later).
- By looking at the height of the line your craters align with, you can
estimate the relative age of your study area (Noachian, Hesperian, or
Amazonian) and put some constraints on the absolute age of that surface, based
on an elaborate adjustment of lunar cratering rates with corrections for Mars'
location in the solar system, its greater gravity, and its atmosphere.
- There are a few "plot complications" with the use of the crater magnitude
and frequency distribution for the estimation of absolute ages on Mars.
- If you look very closely at the dotted isochrons, you will see that they
do not form completely straight lines: They turn down somewhere around
64 km (producing a slope of -2.2, instead of -1.8).
This reflects the drop in the supply of humongous potential impactors after
about 3.7 billion years ago, at the end of the Late Heavy Bombardment. The
LHB is a point of some controversy:
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Did it simply mark the end of the era of
accretion and the removal of available big impactors by their making
themselves unavailable by, well, impacting into something
in the solar system?
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Was there a tumultuous and dramatic increase in the
number of big items stirred up in the solar system about 4.1 to 3.7 billion
years ago (perhaps by the movement outward of the outer two giant ice planets
at that time): The Late Heavy Bombardment?
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The exact meaning of the LHB is
controversial, but things really did quiet down in the inner solar system
after about 3.8 or
3.7 billion years ago.
- If you look at the other end of the X axis, you'll see a much steeper
turn upward at roughly (and variably) 1 km in crater diamter (slope is -3.82,
instead of -1.8). This has really
been controversial.
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Some argue that there really is a break in the size of potential impactors,
because there really is a qualitative break in the numbers
of smaller objects.
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Others suspect that the upward break in the curves
reflects secondary impacts: Ejecta that lands at various distances from the
primary crater, creating craters of their own.
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There's a whole cottage industry in trying to figure out ways of
differentiating secondary craters from primary ones just to get a handle on
how many of them there are and how their presence may distort estimated ages
of a surface.
- They may have different shapes or different depth to diameter relations
than primaries because they would be coming in at less than supersonic speeds
(but that is true mainly for the secondaries that fall close in; those that
get tossed out a far way may well attain very high velocities coming back to
ground).
- They seem to have a propensity for falling in distinct lines or rays.
Fresh craters generate rays of finer ejected materials interspersed with
bigger objects. The rays may erode away on Mars but the alignments of the
secondary craters may preserve that rayed appearance (this is the subject of
one of my own research projects on Mars, using statistical techniques to pick out potential
alignments of craters that might identify secondaries).
- If you look still farther to the left of the X axis, you'll notice yet
another inflection point in the isochrons around 10-25 m, where the lines
curve back down a bit. This probably reflects one or more of the following:
- the differential susceptibility of
smaller craters to obscuring by erosional and depositional processes
- the greater susceptibility of smaller objects to ablation
and shattering en route through the martian atmosphere
- resolution issues -- some craters are so small that they may not be
discernible, even on a high resolution image.
- So, power law mathematics are a great starting point, but Mars doesn't
completely coöperate with the simplicity of mathematics. The power law
seems to work with a slope of -1.8 or 2.0 for most martian surfaces for
craters with diameters in the ~1 km to ~64 km size range. Outside that range,
b would be larger and of different magnitudes at either end of the X scale
(about -3.82 for craters < ~1 km; about -2.2 for those larger than ~64
km).
- Hartmann was content to fit three separate power law curves, one for the
steep branch under 1 km, one for the shallow branch between 1 km and 64 km,
and one for the turned down branch above 64 km. Neukum tried to get around
the need for three separate models by using higher order polynomial
modelling, but he and Hartmann reconciled their different approaches to
develop that isochron chart linked above. So, there's now a more or less
standardized graphical approach to calculating relative ages and constraining
absolute
ages, but there remain all kinds of controversies over secondary cratering.
- So, through this set of constraints and a little jury-rigging, variations
in crater density and size distributions is converted into
a periodization scheme for Mars. Unfortunately, the scheme most commonly used
maddeningly departs from the system developed for geological time on Earth.
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Here's a quick overview of geological time and rock units on Earth:
- A distinction is made between geological time and geological rock units:
geochronology and chronostratigraphy.
- At the coarsest level is the eon time unit, which is associated
with eonothem rock units. On Earth, there are four of these: Hadean
(planet formation to ~4 Ga), Archean (~4 Ga to 2.5 Ga), Proterozoic (2.5 Ga to
~542 Ma), and Phanerozoic (~542 Ma to present).
- These eons/eonothems are broken down into eras and corresponding
erathems, such as the Palæozoic, Mesozoic, and Cenozoic within
the
Phanerozoic eon/eonothem.
- Eras/erathems are broken down into periods and the corresponding
systems. So, for example, we have the Palæogene and the Neogene
(the two used to be called the Tertiary) and the Quaternary
periods/systems within the Cenozoic era/erathem.
- Periods/systems are further
subdivided into epochs or the corresponding rock series (such as
our
own Holocene Epoch [from ~11,700 BP] and the Pleistocene Epoch from 2.58 Ma to
~11,700 BP), which fit within the Quaternary Period/System.
- Epochs (Series) within the Phanerozoic Eon (Eonothem) are subdivided even
further into ages or the
corresponding rock stages (e.g., the Pleistocene is subdivided into the
Gelasian, Calabrian, Middle, and Upper).
- There are some inconsistencies and arguments (stratigraphy is a rapidly
changing field, which you can keep up with at the International Commission on
Stratigraphy, but the general pattern of
eons, eras, periods, epochs, and ages is widely recognized. Here is a link to
a USGS geological time scale used for North American stratigraphy: https://pubs.usgs.gov/fs/2010/3059/.
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On Mars, given that we don't really have much detail yet, we have three main
subdivisions, each of which may be subdivided to one more level. The basic
levels you'll see referred to as periods, epochs, or eras, and I'll probably
use all three in what follows. Usage is converging on using "period"
for
these, even though it's pretty inconsistent with Earth geological time scale
customs. These divisions are based on
relative crater densities and superposition relationships. From oldest
to
youngest, these are the:
- Noachian (formation of the planet to the end of the Late Heavy
Bombardment, featuring the formation and collapse of the planetary magnetic
field and the initiation of intense volcanism in several locations and gradual
concentration largely in the Tharsis complex). Increasingly, the earliest
times older than crater saturation (~4.1 Ga) are being called "Pre-Noachian." If we use the term "Pre-Noachian," then the rest of the Noachian is subdivided into:
- Early Noachian Epoch (~4.10 Ga to ~3.95 Ga)
- Middle Noachian Epoch (~3.95 Ga to ~3.85 Ga
- Late Noachian Epoch (~3.85 Ga to ~3.70 Ga)
- Hesperian (progressive desiccation, sulfuric acid buildup in the
atmosphere and hydrosphere due to volcanism, great outwash events, and loss of
most of the atmosphere, starting about 3.7 or 3.8 Ga to, debatably, ~3.5 or
3.0 or 1.8 Ga). Most commonly, it ranges from ~3.7 Ga to ~3.0 or ~2.9 Ga. Subdivided into:
- Early Hesperian Epoch (~3.7 Ga to ~3.4 Ga)
- Late Hesperian Epoch (~3.4 Ga to ~3.0 Ga)
- Amazonian (desiccation and oxidation, from the Hesperian to the
present). Subdivided into (and there's a lot of variation in this period):
- Early Amazonian Epoch (~3.0 Ga to ~1.4 Ga)
- Middle Amazonian Epoch (~1.4 Ga to ~300 Ma)
- Late Amazonian Epoch (~300 Ma to present)
- Geochemical periodization. An alternative system has been proposed by
Jean-Pierre Bibring and a large team of colleagues in a Science journal
article in April 2006 (312, 5772: 400-404). It divided Mars' history, not in
terms of the traditional crater-counting derived Noachian, Hesperian, and
Amazonian periods but in terms of dominant geochemical processes. The result
was the following periodization (which they do call eras, which is more
consistent with Earth geological time at least!):
- Phyllocian Era: dominated by neutral or alkaline aqueous
chemistry,
resulting in the deposition of phyllosilicate clays. This would be the
geochemical régime most friendly to "life as we know it, Jim." Early to
middle Noachian time-frame.
- Theiikian Era: dominated by acidic water chemistry, as a result of
the
massive volcanism of the later Noachian and early to middle Hesperian.
Volcanic activity ejected massive amounts of sulfur dioxide into Mars'
atmosphere, which would interact with water to produce sulfuric acid,
drastically acidifying surface and subsurface waters.
- Siderikian Era: dominated by æolian processes and oxidative
geochemistry, resulting in the production of anhydrous iron oxides. This was
a time of progressive loss of surface waters and most of the atmosphere after
the collapse of the planetary magnetic field. Water photodissociated in the
atmosphere, freeing its hydrogen to scoot off into space in the exosphere and
drawing the heavier oxygen to bind with iron-bearing minerals ("rust") in dry
conditions. This would coïncide with the late Hesperian and the entire
Amazonian periods. In what follows, we'll use the traditional crater-counting
periodization but with attention paid to the geochemical issues at the heart
of the Bibring et al. system.
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