15 October 2010

Friday fold: wavelength contrast

Posted by Callan Bentley

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 it apparently has 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)⅓

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 sandstone and 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 than the viscosity contrast between the quartz vein and the shale.

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, and 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… : )