Friday fold: wavelength contrast

I scored this photo off the Internet more than five years ago, the first time I taught Structural Geology at George Mason University. I failed to note the website I got it from, and now that website has apparently disappeared, at least as far as the view from Google is concerned. If anyone knows the provenance of this image, please let me know so that I can properly attribute it.

I hesitate to post something like this without knowing who took it, but I did note to myself that it came from the Point Lake Greenstone Belt in the Northwestern Territories of Canada. This image and its implications follow so nicely on to our discussion last week about fold wavelength and the Ramberg-Biot equation that I can’t resist it. Ready? Brace yourself…


I think that this is one of the coolest structural geology photos ever taken. Here it is graced with some annotations:


Maximum compressive stress was in this case from the back to the front. The same vein, oriented ~parallel to σ1, is folded in two very different ways, depending on which rock type it is cutting across. As with a week ago, we can explain this behavior using the Ramberg-Biot equation:

L = 2 π t (η / 6ηo)

where L is the wavelength of the fold (in other words, the distance from one fold hinge to the next fold hinge); t is the thickness of the folded layer; η is the viscosity (resistance to flow) of the quartz vein (or, in general, the more competent of the two layers); and ηo is the viscosity of the rock unit (sandstone or shale) that the quartz vein cuts across.

If you keep t and η constant (for say, the rightmost of the two quartz veins), then the only thing left to vary would be ηo. So sandstone will have one ηo, while shale will have another ηo. The sandstone is more resistant to flowing than the shale is. The viscosity contrast between the quartz vein and the sandstone is less (they’re both made of quartz) than the viscosity contrast between the quartz vein and the shale (which have very different material properties).

The high viscosity contrast with the shale makes for a very big number, which raised to the ⅓ power (i.e., you take the cube root) makes for a very small number. This small number, multiplied by the constants of 2, π, and t, gives you L, which will also be a small number: hence the wavelength is small, and as a result, the folds are crunkled up next to one another like sardines in a can.

On the other hand, the low contrast between the viscosities of the quartz vein and the quartz sandstone means that you get a rather small number. Say η = 3. If ηo is also about 3, then you have: (3/(6*3)), or the fraction 1/6. Expressed as a decimal instead of a fraction, this is 0.167. Take the cube root of that, and you end up with a bigger number, in this case 0.55. Multiply that by 2, π, and t, and you get your new wavelength, L. Because you have a larger number in the (η / 6ηo) part of the equation, and everything else is the same, you end up with a larger wavelength. The result is only one fold antiform in the sandstone. In the neighboring shale, ~23 antiforms are packed into the same distance along strike of the vein.

Wild stuff, right? Happy Friday. Let’s hope your weekend is of sufficiently high contrast to the sludge of the week that you get all loose and wiggly, like the top part of the photo… : )

When the Sturtian happened

ResearchBlogging.orgLast Friday, I spent the evening riding up to New York on a bus. To pass the time, I had my iPod and a new paper by Francis Macdonald and colleagues in Science. The paper examines the timing of one of the episodes of “Snowball Earth” glaciation. There’s some important new data in this paper, and it helps constrain the “Sturtian” glaciation in time.

So here’s the deal with Precambrian glaciations: there have been several. Generally speaking, there was a big episode of glaciation around 2.5 Ga (“Ga” = billion years ago, for those new to geo-temporal argot, and “Ma” = million years ago). There were also a series of at least two, and maybe upwards of four episodes during the Neoproterozoic era (~700 Ma). These latter glaciations have been collectively dubbed the Snowball Earth glaciations for evidence which suggests that they were global in extent. The evidence was high-precision paleomagnetic signatures which suggest some of the glacial sediments were deposited within a few degrees of the equator. If the equator was frozen over, it follows that the rest of the planet was too, due to ice-albedo feedback. That’s kind of a big deal, and the Snowball Earth hypothesis has been a rich source of research inspiration over the past decade and a half.

Now, figuring out just when the Snowball Earth glaciers flowed is a bit tricky. You can’t directly date glacial sediments using radiogenic isotopes, as they will be composed of the pulverized remains of pre-existing rock bodies, and will yield older-than-actual ages. It would be cool to find volcanic layers within the sedimentary package, because we can date those, or to find igneous intrusives (like dikes) which cut across the glaciogenic sediments, because those too are worthy of dating. The younger of the two “main” Neoproterozoic glaciations is called the Marinoan glaciation, and it has been dated using methods like these in Namibia (635.5 ± 0.6 Ma) and China (between 636 ±4.9 Ma and 635.2 ± 0.2 Ma). Locations as farflung as China and Namibia and other Canada can be correlated with one another on the basis of stable isotope chemostratigraphy. Basically, the idea is that there are global fluctuations in the carbon (or sulfur, or oxygen, or whatever) isotope “signature” that gets locked in the sediments, due to whatever was happening in the world at that time (e.g., life gobbling up certain isotopes, or climatic shifts, or other “big picture” events). So the chemostratigraphy allows us to match up rock units of the same age, and the few places where we are lucky enough to get igneous units interacting with the sedimentary package allow us to pin the whole lot to a specific date.

Great… for the Marinoan.

But an earlier “Snowball” episode, the Sturtian glaciation, has not been as precisely dated. Enter the Macdonald, et al. (2010) study. They report four new high-precision U/Pb dates from igneous rocks in the Ogilvie Mountains of northwestern Canada. Three of these are part of the Sturtian stratigraphic package, following the paradigm I outlined above. One, from a tuff unit, yielded a date of 717.43 ± 0.14 Ma, and another yielded a date of 716.47 ± 0.24 Ma: both of these were essentially right at the bottom of the Upper Mount Harper Group, which includes strata that are interpreted as belonging to the Sturtian glaciation on the basis of dropstones (A) and striated clasts (C) like these (from the supporting figure S2 for the paper):

They also found evidence of “grounded ice”: soft-sediment folds that resulted when (they interpret) the nose of the glacier shoved its way forward. So this wasn’t just a floating glacier above: the glacier was in the muck, suggesting it was right there at sea level.

This is a lucky find: a datable volcanic ash layer right at the base of a big stack of glacial sediments. It’s a major advance for understanding the Sturtian in its own right.

They also report a date of 811.51 ± 0.25 Ma for strata deeper down in the stack, right before a global isotopic ‘excursion’ (a big, distinctive leftward squiggle on the carbon chemostratigraphy plot) called the Bitter Springs isotopic stage. Here’s a detail from the paper’s Figure 2, showing how this new date integrates absolute time with the relative time illustrated by the isotopic curve:

That’s δ13C data plotted from three Neoproterozoic sections (in Namibia, Svalbard, and the Yukon). The thick central vertical black line is 0‰, with the left bound being -8‰ and the right bound being +8‰. The horizontal green lines show the new dates from this paper.

So all that is good, and a significant new batch of data for helping pin down the timing of these ancient glacial episodes. We’ve been able to date some Sturtian glacial units and a pre-Sturtian isotopic excursion.

The paper presents a fourth date, too: this is from a diabase sill that is part of the Franklin Large Igneous Province (LIP) exposed on Victoria Island, over 1000 km to the northeast of the Ogilvie Mountains (where the other three dates come from). The Franklin diabase gives a U/Pb age just like those from the Sturtian glacial sediments: 716.33 ± 0.54 Ma. But is this relevant, considering how different the rocks are, and how very far apart they are? Check out this map to see their lack of proximity, from the paper’s supporting figure S1:

Why would the paper’s authors bother with a rock unit so far away from the Ogilivie section? Well, the Franklin LIP is integral to the Snowball story on at least three fronts that I can think of. It ties this story together quite nicely, and I think that it is just as important as the Ogilvie data.

First, on a tectonic note, it’s a mafic unit that is associated with the breakup of Rodinia, a Proterozoic supercontinent. (Rodinia’s position on the paleo-equator is supposed to have sped up weathering of the continental crust and resulting CO2 drawdown, cooling the planet.) Second, it has paleomagnetic orientations which suggest it was emplaced within 10° of the magnetic equator. (This is important because it demonstrates that grounded ice was present within 10° of the equator at the time the Franklin LIP erupted… and due to ice-albedo feedback, it implies higher latitudes were frozen-over at that time, too.) Third, the Franklin LIP has been fingered as a possible culprit in causing Snowball Earth. This is because mafic igneous rocks suck CO2 out of the atmosphere when they are chemically weathered, producing carbonate rocks. The Franklin LIP has the potential to be a major driving force for the CO2 drawdown which initiated the Sturtian Snowball via global cooling. A big package of mafic rock delivered raw right to the tropical weathering belt could be sufficient to trigger an ice age, some workers have suggested. The Franklin LIP was in the right place at the right time: was it the culprit, or only an accomplice? Witness the way that the authors (properly) hedge their bet in their conclusion’s penultimate sentence:

…the synchrony among continental extension, the Franklin LIP, and the Sturtian glaciation is consistent with the hypothesis that the drawdown of CO2 via rifting and weathering of the low-latitude Franklin basalts could have produced a climate state that was more susceptible to glaciation.


Macdonald, F., Schmitz, M., Crowley, J., Roots, C., Jones, D., Maloof, A., Strauss, J., Cohen, P., Johnston, D., & Schrag, D. (2010). Calibrating the Cryogenian Science, 327 (5970), 1241-1243 DOI: 10.1126/science.1183325