Tag Archives: Geochronology

This Year in Uranium Decay

Pumice from the Bishop Tuff (~767 ka).  Zircons in this pumice are rich (relatively) in uranium, with up to 0.5% U.[1,2]  Image credit: Bill Mitchell (CC-BY).
Pumice from the Bishop Tuff (~767 ka). Zircons in this pumice are rich (relatively) in uranium, with up to 0.5% U.[1,2] Image credit: Bill Mitchell (CC-BY).

With 2016 now upon us, I felt it would be appropriate to think about what a new year means for uranium geochronology. What can we expect from the year ahead? Without getting into any of the active research going on, I felt it would be useful to address simply what is physically happening.

On Earth, there is roughly 1×1017 kg of uranium.[3] The ratio of 238U:235U is about 137.8:1, and 238U has a mass of roughly 238 g/mol (=0.238 kg/mol). Looking only at 238U, that gives us
1x1017[kg]x(137.8/138.8)/0.238[kg/mol] = 4.17x1017 mol [238U]

Radioactive decay is exponential, with the surviving proportion given by e-λt where λ is the decay constant (in units of 1/time) and t is time, or alternatively, e-ln(2)/T1/2*t, where T1/2 is the half-life and t is time.

To find the proportion that decays, we subtract the surviving proportion from 1: (1-e-λt)

Multiplying this proportion by the number of moles of 238U will give us the moles of decay, and multiplying by the molar mass will give the mass lost to decay:

(1-e-λt)*molU

Plugging in numbers, with λ238 = 1.54*10-10 y-1, t = 1 y and the moles of 238U from above, we get:

(1-e-1.54*10-10)*4.17*1017 mol [238U] = 6.4*107 mol

That yields (with proper use of metric prefixes) roughly 64 Mmol U decay, or 15 Gg of U on Earth that will decay over the next year.

Although those numbers sound very large, they are much smaller than even the increase in US CO2 emissions from 2013 to 2014 (50 Tg, or 50,000 Gg); total US CO2 emissions in 2014 were estimated at 5.4 Pg (=5.4 million Gg).[US EIA]

As for what’s in store for geochronology as a field, I think there will be a lot of discussion and consideration regarding yet another analysis of the Bishop Tuff.[4] Dating samples which are <1 Ma (refresher on geologic time and conventions) using U/Pb can be tricky, and Ickert et al. get into some of the issues when trying to get extremely high-precision dates from zircons. The paper is not open access, but the authors can be contacted for a copy (@cwmagee and @srmulcahy are active on Twitter, too!).

***
[1] J. L. Crowley, B. Schoene, S. A. Bowring. “U-Pb dating of zircon in the Bishop Tuff at the millennial scale” Geology 2007, 35, p. 1123-1126. DOI: 10.1130/G24017A.1
[2] K. J. Chamberlain, C. J. N. Wilson, J. L. Wooden, B. L. A. Charlier, T. R. Ireland. “New Perspectives on the Bishop Tuff from Zircon Textures, Ages, and Trace Elements” Journal of Petrology 2014, 55, p. 395-426. DOI: 10.1093/petrology/egt072
[3] G. Fiorentini, M. Lissia, F. Mantovani, R. Vannucci. “Geo-Neutrinos: a short review” Arxiv 2004. arXiv:hep-ph/0409152 and final DOI: 10.1016/j.nuclphysbps.2005.01.087
[4] R. B. Ickert, R. Mundil, C. W. Magee, Jr., S. R. Mulcahy. “The U-Th-Pb systematics of zircon from the Bishop Tuff: A case study in challenges to high-precision Pb/U geochronology at the millennial scale” Geochimica et Cosmochimica Acta 2015, 168, p. 88-110. DOI: 10.1016/j.gca.2015.07.018

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Geoscientist’s Toolkit: Understanding Uncertainties

Tyrannosaurus rex skull, at the University of California Museum of Paleontology, University of California, Berkeley.  Image credit: EncycloPetey (CC-BY-SA).
Tyrannosaurus rex skull, at the University of California Museum of Paleontology, University of California, Berkeley. Image credit: EncycloPetey (CC-BY-SA).

Uncertainty, in the analytical or numeric sense, is a topic many people approach with trepidation. However, it is much more approachable and intuitive than it may seem.

Consider the following examples.

First, the local meteorologist has forecast a high temperature tomorrow of 45 °F (7 °C). Suppose I take my thermometer out tomorrow afternoon, let it sit in the shade for a while, and it reads 43 °F (6 °C). Was the forecast wrong?
What if it were 37 °F (3 °C)?

Perhaps a different example may be more familiar. You are on your way to meet a friend for lunch, and you tell them that you’ll be there in fifteen minutes. Seventeen minutes later, you arrive. Were you on time? Were you late?

Finally, here is yet another example, and one I struggle with: you are in a science museum, and the sign next to the T. rex says that it went extinct around 65 Ma. However, there was a paper published two years ago which determined that the Chixulub impact occurred at or slightly before 66.043 Ma (+/-22 ka, 2-sigma).[1] Is the sign on the exhibit wrong?

I hope that from these examples, you can see that uncertainty is something you encounter more often than you necessarily think about. You may also find you have some intuitive sense for what it means and where it might be important.

Here are my interpretations of the above scenarios.

The meteorologist’s forecast is correct. Although it is not usually mentioned, meteorologists in temperate climes expect their one-day forecasts to be accurate to about 2 °F. They have a fairly large area to cover, which may have some temperature differences within it, and there is some uncertainty in the reading given by the thermometer.

When meeting a friend for lunch, being off by two minutes in fifteen is probably fine. Most people understand that such an arrangement may be accurate only to within five minutes. For some people, even five minutes may be well within the understood uncertainty.

As for the museum, I would think it is a great opportunity to teach about uncertainty! On one hand, the casual use of 65 Ma (implying +/-2.5 Ma) is correct. On the other hand, that figure is quite imprecise compared to how well we know when the event happened. Even to the nearest million years, 66 Ma would be more appropriate. This brings up another point: our understanding of geochronology is based on the latest research. Advances in the field, analysis of different materials, or even different interpretations of previously existing data can lead to changes. Despite the great amount of effort put into compiling the best science and geochronology for the latest Geologic Time Scale (mostly not open access, sadly), parts became obsolete even as it went to press. Mostly, these changes are small, and primarily concern scientists who are studying events near these boundaries. If the Cretaceous-Paleogene boundary were to be moved from 66 Ma to 90 Ma, that radical change would need to be backed up with a lot of data, and would necessitate a new sign for T. rex or an acknowledgement that dinosaurs lasted well into the Paleogene (there is no widely accepted evidence that they did).

Hopefully these examples have illustrated that you already have an intuitive understanding of what analytical or numeric uncertainties are and why they are important. In science, where measurements are being made, and calculations based on those measurements are being computed, understanding the uncertainties becomes increasingly important. There are many resources available which outline the process for determining and reporting uncertainties, ranging from a ten-page worksheet to a [very handy and accessible] small book to a comprehensive tome (open access!).

***
[1] Renne, P. R., Deino, A. L., Hilgen, F. J., Kuiper, K. F., Mark, D. F., Mitchell, W. S., III, Morgan, L. E., Mundil, R., Smit, J. (2013) Time Scales of Critical Events Around the Cretaceous-Paleogene Boundary. Science 339: 684-687, doi: 10.1126/science.1230492.

Introduction to the Geologic Timescale and Geochronology

Geologic Time Scale. Image credit: GSA.

The Earth is pretty old.[1] Before we start talking about rocks, it is important to understand how to talk about time from scales of a human lifetime (50-100 years) to the age of the planet (~4.6 billion years). This is geochronology [Etymology: geo: Earth; chrono: time; logy: study].

Earth time is measured in units of a year, or annum (symbol: a). To this can be added metric prefixes, such as kilo (thousand), mega (million), and giga (billion). So something happening 100,000 years ago would be something which happened at 100 ka; an event 66 million years ago would be at 66 Ma, and something 2 billion years ago would be at 2 Ga. Durations of time use the same units, and it should be clear from context whether the time in question is a duration or a relative time before present.

At the top of this post is the most recently published geologic timescale. This timescale represents the best science available at the time of publication. However, as more evidence is gathered, these boundaries can be shifted around. To most people, the shift in the Cretaceous-Paleogene boundary (the break between the left-most major column and the second) from 65.5 Ma to 66.0 Ma in the newest revision of the timescale doesn’t mean much. However, if you are trying to understand causes and effects near that time period, it can make a big difference!

One major feature to notice about the geologic timescale is that it is depicted in a non-linear fashion. That is, the right-most column (Precambrian) represents 88% of Earth’s history. The Paleozoic represents 6%, and is longer than the Mesozoic and Cenozoic combined. The Cenozoic contains only the last 66.0 Ma, or 1.4% of Earth’s history.

Our ability to tell time for more recent events is better than for older ones: good geochronology has uncertainties between 1% and 0.1% of the age. For something 66 million years old, the uncertainty in age can be around 66 ka or less [2]; for something 2 billion years old, the uncertainty is likely to be closer to 2 million years. A lot can happen in 2 million years!

Getting back to the timescale chart, present-day is at the top left. As you go down the column, you are going back in time. The bottom of the column connects to the top of the column to the right of it. At the bottom of the right-most column is the earliest part of the rock record on Earth. Very little remains of this age which has not been recycled into new rock.

The divisions are made on the basis of major events in Earth history (or on big round numbers for the oldest parts). Many divisions represent shifts in the types of life (often plants or animals) found on Earth. For instance, the base of the Mesozoic is defined by the first appearance of Hindeodus parvus (a conodont, which is kind of like a modern eel) in the fossil record. The defining species tend to be marine, because marine records are usually more continuous, are more likely to be preserved, and have more species found across the globe (technical term: cosmopolitan).

Several different methods exist for determining the age of a rock: radio-isotopic dating, biostratigraphy, and paleomagnetism being the major methods employed. For sedimentary rocks younger than 50 Ma, astrochronology (or orbital tuning) can be used to match climate signals found in the rock to the Earth’s tilt, precession, and eccentricity.[3]

Radio-isotopic dating is the most reliable method.* By measuring how much radioactive decay has happened since a rock formed, and knowing the rate at which the decay occurs, the date of formation can be determined. For volcanic ash deposited in a sedimentary sequence, that formation is roughly equivalent to the eruption date.

Biostratigraphy is used when fossils are present but no suitable material for radio-isotopic dating is available. The appearance and disappearance of various species (again, usually marine species found world-wide) are used to mark time. This is relative, and subject to sampling and preservation biases, but can yield rough answers in places where otherwise there would be no answer at all. However, it is difficult to apply in the Precambrian, because there were fewer, less-complex lifeforms at that time. Most of the diversity of life on Earth post-dates the Cambrian explosion at ~541 Ma. For rocks newer than that, the fossils found within them can give a rough estimate of the age.

Paleomagnetism is used when there are recorded direction changes in the Earth’s magnetic field within a section of rock, and at least some of that rock is fairly precisely dated. By counting magnetic field reversals from a known-age point, the ages of the section in question can be determined by correlation to a well-dated section with the same reversals.

In summary, the Earth is old, and the ages of events are generally known to 0.1-1% precision. The geologic timescale is broken up into smaller parts, and the size of divisions generally decreases as modern time is approached. Units of Ma (mega-annum, million years) are appropriate for much of Earth’s history, with ka used for recent events and Ga used for the oldest parts. As we continue on our exploration of Heard Island and other topics, the geologic timescale will be a very useful tool for understanding how pieces fit together in time.

[1] Gradstein, F.M, Ogg, J.G., Schmitz, M.D., et al., 2012, The Geologic Time Scale 2012: Boston, USA, Elsevier, doi: 10.1016/B978-0-444-59425-9.00004-4.

[2] Renne, P. R., Deino, A. L., Hilgen, F. J., Kuiper, K. F., Mark, D. F., Mitchell, W. S., III, Morgan, L. E., Mundil, R., Smit, J. (2013) Time Scales of Critical Events Around the Cretaceous-Paleogene Boundary. Science 339: 684-687, doi: 10.1126/science.1230492.

[3] Kuiper, K.F., Deino, A., Hilgen, F.J., Krijgsman, W., Renne, P.R. and Wijbrans, J.R. (2008) Synchronizing the 40Ar/39Ar and astronomical clocks of Earth history. Science 320: 500-504, doi: 10.1126/science.1154339.

* Its theory and operation is more complicated than this blog post can contain. I may try to write one later which has much more of the nuance and technical details.