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Episode 40: Crater Age Dating Explained, Part 1

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Recap: An overview discussion of craters and how they are used to date surfaces in the solar system as well as some of the caveats, complications, and limitations that go with the method.

Puzzler: If a 1-km-diameter comet hits the moon, and a 1-km-diameter asteroid hits the moon, is the crater created by the asteroid likely to be larger, the same size, or smaller than the one created by the comet. Why or why not?

Solution to Episode 39's Puzzler: The answer is pretty much a "Yes." There are a few areas on Earth where we have some very complete geologic columns, going from present time back to the precambrian or older. This is contrary to what many creationists claim, such as the quote from Morris and Parker (1987), "Now, the geologic column is an idea, not an actual series of rock layers. Nowhere do we find the complete sequence."

Q&A: This episode's question is a bit of a spoiler, so if you haven't seen the movie "Prometheus" and you don't want to know anything about it, even though this is covered in the trailer, skip forward about two minutes. The question comes from Coffee who asked me to weigh in on some discussion he had read about some of the astronomy in the movie "Prometheus." Among the points raised was: "Can you really tell where a unique star system is based on five dots in a cave painting?"

The answer is a resounding "NO," even though this was a main premise of the film, that people were able to figure out where the planet was that they should visit based on the same drawing of five stars in ancient cultures around the world.

There are two main problems with this that I want to mention. The first is that you can designate any random pattern of five points and then find innumerable matches in stars in the sky, especially if you go to stars not visible to the unaided eye. So uniquely specifying a system based on this is wrong.

Another problem is that you're talking about a 2D projection of a 3D distribution. Paintings, drawings, etc. are flat. You can't get any depth information out of it which makes the number of matches go up even more.

To those steeped in UFO lore, you may remember the Betty and Barney Hill "star map" issue, which has the same problem: Betty drew in 2D a 3D star map she allegedly saw, and then a school teacher somehow converted that back into 3D and claimed she found where the aliens were from that allegedly abducted the Hills. But that's another episode.

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Transcript

Absolute versus Relative Ages

The first necessary part of this discussion is about the concept of relative versus absolute ages.

An absolute age is when you have a number that is evidenced by some physical argument. It may or may not be an exact number. For example, when I say that the United States of America, as a formal country, is 236 years old, that is an absolute age. If I say that Earth is approximately 4.54 billion years old, even though I put that "approximately" in there, that's an absolute age.

A relative age is when we don't have a number assigned, but we know that something is older or younger than something else. For example, my brother was born after I, so I'm older than he is. My parents were born before I was, so they're older than I. Relatively speaking, the chronology would be my parents are oldest, then me, then my brother. Or, to use countries again, Britain is older than the USA, which is older than Germany, which is older than India.

You may remember this discussion a little bit from when Rachael and I were talking about radiometric dating and the geologic column in episode 38: The geologic column was a column of RELATIVE ages of rock layers and fossils, and when radiometric dating was discovered, geologists could put ABSOLUTE ages to those rock layers.

We're going to take the same concept today and expand it to craters and dating the surfaces of other planets.

Importance of Crater Age-Dating

You might be wondering now why I'm devoting two full episodes to crater age dating. The reason is that craters are important. EXCEPT for Earth and the moon, absolutely ANY age or relative age you hear or read about on ANY other surface is ENTIRELY based on craters.

Literally, they are the only method we have of dating surfaces in the solar system that we haven't been to and collected samples from and returned to Earth for absolute dating.

Basic Idea of Crater Age-Dating

I should note before we get into the mechanics and concepts behind this that craters is my field of research, and crater age-dating is about half of what I do. I'll be submitting a paper on Monday to a journal that's 34 pages of crater age-dating. So, there may be a few times during this episode that I get into some niggling details that aren't critical, but are thrown in there because this is what I've been studying for the past six years.

I should also note that when I say "crater" during this discussion, I mean an "impact crater," not a volcanic crater. And when I say "planet," I may also mean "moon" -- basically I mean an object that has a solid surface.

With all that said, the two very basic assumptions of crater age dating are that first, craters occur randomly across the surface of a planet, and second, they occur at some potentially knowable rate that may or may not change with time. Therefore, the basic concept of crater age dating is that if a surface has more craters per unit area than another surface, it's going to be older. More craters means it's older because it must have been around longer in order to accumulate more craters.

And before I go any further, I should point out that there are lots of statistics that go into this kind of work and the calculation of formal uncertainties. For the sake of simplifying this discussion, insert in your head the word "statistically" before any time that I say "older," "younger," "more," or "less" throughout this discussion. So the line before should have sounded to you like: "Statistically more craters means it's statistically older because it must have been around longer in order to accumulate statistically more craters." Now you can see why I didn't actually say it that way. Moving on ...

From that basic concept, we really only need two pieces of information in order to start to assign RELATIVE ages to a surface: The area of that surface, and a census of the craters on it down to an agreed-upon diameter. If you count the craters down to, say, 1 km across on Surface A and you do the same on Surface B and both have the same area, then Surface A is older if it has more craters.

But, I've now slid in a new complication: Crater diameter. Crater diameter is important because, technically, craters can be any diameter, from micrometers to thousands of kilometers. Due to the population of impactors - the things that actually form these impact craters - there are many more small craters that form in the same time window that a single large crater will be formed. For example, on Mars, there are around 10 craters that are 1000 km across or larger. But, there are around 500 craters that are 100 km across or larger. And around 15,000 that are 10 km across, but almost 400,000 that are 1 km across. This is an exponential increase. And I know these numbers because my doctoral work was creating a global crater database of Mars that has every crater down to 1 km in diameter and another quarter-million smaller craters.

From this, you can see that it wouldn't be a fair comparison if I said, "There are 10 craters on Surface A that are larger than 20 km across, but there are 50 craters on Surface B that are larger than 2 km across." It may seem at first glance - again with A and B having the same surface area - that B is older than A 'cause it has more craters. But, because I counted craters to different diameters, it's comparing apples and meatloaf, not apples to apples.

Using N(≥D) Relative Ages

So to back to the basic idea, one of the ways that real crater folks will determine a relative age is what we call an "N-density." The "N" refers to the number of craters larger than or equal to a certain diameter, and the density is how many of those craters there are when you divide it into a certain standard surface area -- normally either per square kilometer or per million square kilometers.

And so, in this paper that I mentioned that I'll be submitting shortly, I actually quote these N-densities for 78 different surfaces in order to assign relative ages. I counted down to 10-km-diameter craters, 16, 25, and 50. So in the paper, I quote for every surface that I dated the number of craters larger than 50 km across per million square kilometers, the number of craters larger than 25 km across per million square kilometers, the number of craters larger than 16 km across per million square kilometers, and the number of craters larger than 10 km across per million square kilometers.

From each of these, I can then rank the relative ages of these surfaces from the one with the most craters being oldest down to the one with the fewest craters being youngest. The reason that I used N(10, 16, 25, and 50) densities is something I'll talk about in the "complications of the method" part of this episode in about 10 minutes.

Assigning Geologic Epochs

The next part of this discussion is how we divide up geologic time. Geologists like to classify things and figure out stratigraphic relationships. That means that we like to know when something happened relative to something else because it helps us to unravel the history of a region or planet.

We also like to classify things into epochs of time. On Earth, that's done with fossils. The Permian, Quaternary, Triassic, Archaen -- all those geologic ages are based on what fossils are or are not found in those layers of rock. And to an Earth geologist, if I say that something happened in the Cretaceous, then they know what time I'm talking about and other stuff that happened during that time for context.

We would like to do that on other planets, but we obviously can't use fossils. Instead, we use craters, and now I need to introduce another concept: Geologic mapping.

For a definition, geologic mapping is when you map out different types of features across a surface. For example, if I were to make a VERY coarse geologic map of the United States of America, I would have different units for large lakes, large rivers, mountains, plains, wetlands, and other things. Although they're not "geologic maps," the same basic concept is given by a map you'd get when you go to an amusement or theme park, a zoo, or museum. It lays out the shape of the area, and then has different colored regions for different kinds of attractions that you can see. For a zoo, all of the places with mammals might be yellow, and reptiles might be green, and fish might be blue.

We do the same thing on other planets, though it's much harder. We use visual data, topographic data, spectroscopic data, and other pieces of information to try to figure out what is the same kind of surface and geologic unit, and what's different.

For example, again if we wanted to make a VERY coarse geologic map of the moon, then you would have two units: The bright white highlands and the darker maria. That's your geologic map, and a young child would be able to do something like that. If you want to get a little more detailed, then you would mark some of the largest craters as another type of unit.

It obviously gets MUCH more complicated than that once you get pretty detailed and creating geologic maps takes months or even years -- in fact, I'm involved with a group of people from around the world who are working on redoing the Mars global geologic maps, and we're near the end of the roughly 6-year process. So hopefully by this point you have the basic idea behind geologic mapping.

The point of this is that once you have geologic maps, then you have distinct, clear kinds of surfaces, much like different rock strata on Earth. You can use the same geologic principles we use on Earth, like superposition - what's on top of what - to figure out some of the relative ages.

And, you can use crater counts on these different surfaces to fine-tune those relative ages.

But I also need to emphasize that it's ONLY AFTER doing this kind of mapping that crater counting and relative ages have any meaning. I started out this episode by comparing two "surfaces:" "Surface A" and "Surface B." If you hadn't mapped these out, then you'd have "Surface AB" and you'd get some sort of average age, but that wouldn't make any sense -- it would be like saying that the age of MomMe is 45, the average age of myself and my mother. It's a fairly meaningless number.

Once you have this information, then you can figure out when different things happened on other planets, and lump them together into major geologic epochs. For example, on Mars, the most ancient time period is something that we call the Noachian. This is characterized by very heavy cratering and evidence for lots of water on the surface. Geologic units in the time after that are called Hesperian when we see lots of volcanic terrain and valley networks, and fewer craters. The time we're in now is called the Amazonian and it's characterized by the fewest craters and latest flood volcanism.

So that now means to someone who studies Mars that I could say, "This feature happened during the Hesperian," and they would have a general idea of what that means relative to when other stuff happened on the planet.

In other words, this stuff works exactly the same was as the geologic column on Earth: First you map out the regions, then determine the corresponding crater density to a certain crater diameter in those regions. Once you have that, you can go elsewhere on the planet, determine the crater density down to that size, and from that figure out what time period it fits into. And, just like creationists argue that "The rocks date the fossils and the fossils date the rocks" is a circular argument that I disabused you of last time, they have a similar argument with craters that I'll probably talk about in the next episode.

But, once we have these crater densities, and we have these epochs, and we can use these craters to figure out where in the timeline of a planet a certain surface fits, the next logical question that's often more important for a press release than the science, is, "What's the number? How old is this thing REALLY?"

Determining Absolute Ages on the Moon

To figure that out, we need to go from relative ages to absolute ages. Instead of saying that any Noachian surface on Mars is older than any given Amazonian surface, I want to be able to say that it's at least 600 million years older than any Amazonian surface.

To do that, we go back to the Moon. And Apollo.

Besides proving to the world and the Soviets that we had a bigger space phallus, one of the absolute top science priorities of the Apollo missions was to calibrate the crater chronology of the Moon.

That means that we needed to bring back rocks that were FROM DIFFERENT GEOLOGIC UNITS on the Moon that corresponded to different crater densities, get those to Earth, and use radiometric dating techniques on Earth to get absolute ages of those rocks.

Once we have ages of rocks that formed when that surface formed - such as pools of melted rock from the impact of a very large crater, or lava from one of the mare - then we can say that if another surface has the same crater density, then it should also be that absolute age.

It's really as simple as that and as complicated as that. The basic idea is simple; putting it into practice is more complicated, but I'm already running long and we're only half-way through what's supposed to be an overview episode.

Moving to Other Planets with Absolute Ages

So at this point in the episode, I've talked about how a surface with more craters of a given size is older, that you have to compare craters of the same size across different surfaces, how we can use these in the context of geology to get epochs of time on other planets, and the basic idea of how to convert a crater relative age to an absolute age on the moon.

Now we're going to go to other planets. Whenever you hear an absolute age for a surface on another planet or moon in the solar system, it is ALL based on what we learned from Apollo and Luna sample return missions from our moon.

To take this information to other planets, there are several factors to consider.

The first is where it is in the solar system. If it's between the sun and asteroid belt, then we think we have a reasonable idea of what crater densities correspond to what ages. If it's inside the asteroid belt or beyond, like moons of Jupiter, then we have a worse idea because the rate of impacts will be different, and the role of comets is different.

That said, we're now going to ignore everything beyond Mars for this discussion.

To transfer the cratering rate at the Moon to other planets in the inner solar system, one of the primary factors is where it is. Because of Kepler's laws - which I discussed in practically every-other episode for the first ten episodes - objects travel faster when they're closer to the sun. So if you have an impactor coming from the asteroid belt and it hits Mars, statistically it's going to hit more slowly than if it were hitting Mercury. The faster it hits, the more energy it hits with, and the larger the crater will be for any given size impactor.

But, if it's closer to the asteroid belt, such as Mars versus Mercury, it has a much closer population of potential impactors, so it's more likely to get hit.

And you have to factor in surface gravity; this affects how large the final crater will be.

For something with an atmosphere, like Mars and Venus, you also have to figure out at what diameter impactor the atmosphere is going to start to affect. For example, Venus has no craters smaller than about 3 km across due to its tremendously thick atmosphere. Mars has millions of craters just 10s of meters across, but not as many as it would have if it didn't have any atmosphere.

All of those things have been worked out by people much smarter than I, and so we do have what we think is a reasonable idea of how to convert the lunar rate to other objects. Current estimates generally quote an uncertainty of a factor of 2 when doing this. That may seem like a lot, but just like geologists are usually more interested in the relative ages, so are extraplanetary geologists -- an uncertainty of a factor of 2 is fine for many things.

Isochrons

One final topic before I get into the complications and caveats of the method is isochrons. These should not be confused with isochrons from radiometric dating, so pretend for this discussion as though we didn't briefly touch on them without explaining them in Episode 38.

The term "isochron" can be broken up into two parts and from that, you can get an idea of what it means: "iso" means "same," and "chron" means "time." And "isochron" is a line of same-time or same-age.

I talked before about "N-densities" of craters, where you can choose what diameter you want to count craters to so long as you do it to the same diameter for all surfaces you're dating.

An expansion of this is instead of assigning an age based on one diameter, you do it for all diameters larger than a certain size. A histogram that shows bins of crater diameter on the x-axis and the number of craters in each bin on the y-axis is called an "incremental size-frequency diagram." "Size-frequency" because you're looking at crater size (diameter) versus frequency (number of craters at each size).

What researchers have done is created standardized size-frequency diagrams based on areas of the moon that haven't been affected by any kind of erosion or resurfacing, or have been affected the least. These surfaces were calibrated with Apollo and Luna sample returns. In this manner, we have a model for what a size-frequency diagram should be for surfaces of a certain age. That's an isochron.

We can then scale these isochrons - again, based on the crater densities versus absolute ages from the Moon from Apollo and Luna sample returns - to figure out the age of any surface using any single crater diameter or any range of crater diameters.

So we actually have two methods of assigning an absolute or relative age with craters: One is looking at the sum of all craters larger than a certain diameter, and the other is fitting a range of diameters to a known curve called an isochron.

Complications and Caveats: Have to Have Craters

With all that said, there are complications of this technique.

Hopefully one of the most obvious is that you have to have craters present to use them to date something. The only solid surface in the solar system that we know of that has no craters on it is Jupiter's incredibly volcanic moon, Io, and so we can only get a statistical maximum age for that surface of somewhere around 50 years.

All other objects that we've imaged have craters, but there are regions of them that don't. Earth is an obvious example. The highly active southern pole of Saturn's moon Enceladus is another.

But beyond just having craters, you also need enough at the diameter you want for a good statistical sample. One crater present is just as unuseful as having zero from a statistics point.

This also is expandable to having enough at the diameter you want. If you're trying to use craters to age-date a very small lava flow on Mars, then you're not going to be able to use 50-km-diameter craters. You're probably only going to be able to use craters that are 10s of meters across.

Complications and Caveats: Resurfacing

The second complication that I want to talk about is resurfacing. Earth has around 200 known impact craters larger than about half a kilometer or so. The Moon has between 500,000 and a million craters of the same size. Given everything I've discussed so far, that should mean Earth is much, much younger than the Moon.

What it actually means is that Earth was LAST RESURFACED at a much, much more recent time than the Moon. Craters can only give you an age of last resurfacing because resurfacing is going to wipe away older craters. Sometimes the really big old craters will poke through, and we call those "ghost craters," but I'll talk more about those in the next episode.

Ongoing resurfacing can be a real pain to deal with, but it's mostly just a problem on anything with an atmosphere, like Venus or Mars or Earth. To deal with the problem, we often try to just use large craters because those are harder to erase. But it is a complication.

Complications and Caveats: N(≥D) Don't Always Agree

Another complication is that the N-density ages don't always agree. Around 15 minutes ago, I said that I'm submitting a paper where I calculated N(10, 16, 25, 50) densities each for 78 different surfaces on Mars. I also used the techniques I just discussed to assign absolute ages to those crater densities, too.

The complication is that these don't often agree with each other. I had one example where there was an N(10) age that was about 3.3 billion years old, and an N(50) age for the same surface that corresponded to 3.9 billion years old. No, I didn't make a mistake, that's what the math shows.

So how do you get ages that differ by 15%? Well, first, I think it's important to again mention that our absolute age chronology is estimated to be accurate to around a factor of 2. 15% is smaller than a factor of 2.

But beyond that, the reason is that the crater population on a given surface doesn't always follow the established functions that it quote-unquote "should." There could be other processes going on that act to modify the crater population, and usually those are the resurfacing ones I just talked about.

The way this manifests is that as you use smaller craters, you tend to get younger ages. So in that example, my N(10) age was 3.3 billion and my N(50) age was 3.9 billion -- the smaller craters gave a younger age because, what likely happened, is that something acted to erase the smaller craters so there weren't as many as should be on a surface that's 3.9 billion years old. The bigger ones still survived, so they gave the age that the surface more likely is.

And that's how we deal with this issue: When assigning an age - be it a relative crater age or an absolute model crater age - we try to use the largest craters possible to avoid these resurfacing issues.

Complications and Caveats: Changing Size-Frequency Distribution of Impactors

But, what also or instead might be going on is that the actual population of impactors that struck the surface may have changed with time and be different from the standard isochrons.

There is evidence that the size-frequency distribution of impactors (remember: that's the number of craters of certain sizes) has changed with time, most notably being somewhat different before around 4 billion years ago. This means that if those isochrons were developed based on a surface that's 3 billion years old, they aren't accurate for one that's 4.2 billion years old, so you can't just scale it to a higher crater density to give it an older age.

This is a known complication with crater age dating, but again, it ONLY affects ABSOLUTE ages, not relative ages. For relative ages, we're still talking about the basic idea that if you have more craters of a certain size, your surface is older.

Complications and Caveats: Secondary Craters

A final complication that I'm only going to describe in this episode but go into much more detail in the next one is secondary craters.

I started this episode off by stating that one of the assumptions of crater age dating is that craters form randomly over a surface and at a statistical rate. Secondary craters are neither of these.

A primary impact happens when something extraplanetary strikes the surface and makes a crater. From this, stuff gets shot out that we call "ejecta." If you have a large enough block of ejecta that's cohesive - as in, it doesn't shatter as it flies out - then when it lands on the planet, it can form its own crater. We call that a "secondary crater."

So, secondary craters happen at the same effective instant in time as a primary crater does. And, secondary craters are near to that primary impactor. This neither happens randomly with time nor randomly across the planet.

That poses a complication for crater age dating, and it's one that young-Earth creationists like to bring up and as such, I'll talk about it in Episode 41, due out next Sunday.

Summary: So, to recap and bring it all back together, the fundamental idea behind crater age dating is that a surface with more craters is older. You can expand this to using different diameters, to calibrating your relative scale of basic crater densities to an absolute timescale if you have radiometrically dated when some of your key mapped craters formed, and as with any tool, there are complications. Its within those complications that, just like with radiometric dating, young-Earth creationists will stake their claims that the whole technique is flawed and the entire solar system is 6000 years old. But that's a topic for another episode ... the next one, in fact.

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