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… : )

Rumeli Hisarı

Right after I got to Istanbul on this most recent trip, I took a taxi from my hotel down to the Bosphorus, to check out the Rumeli Hisarı, a fort complex built in 1452 by Sultan Mehmet the II in anticipation of the following year’s siege of Constantinople. It’s constructed at the narrowest point on the Bosphorus (660 m wide), with the aim of controlling boat traffic coming from the Black Sea. This narrow spot is today where they have the second of two bridges spanning the Bosphorus. It looks like this:


It’s in Europe; that’s Asia on the far right of the photo. A few more shots of the fortress’s pattern of towers and interconnecting walls:




Inside, I was pleased to note the variety of building stones. Here’s a nice porphyritic andesite which was a common constituent of the walls:

And a folded limestone:


Here are some yellowish blocks that are weathering away faster than the mortar which holds them in place. There is a Turkish 1-lira coin in front of the dark block near the center, to provide a sense of scale:


Here’s a similar phenomenon playing out with some bricks used to make an archway, except here the mortar is the more rapidly weathering component:


Check out this slab of brick… it’s got a curious adornment:


Zoomed in to show this detail:


Dog prints! Sometime a long time ago, maybe more than 500 years ago, a brick maker put out slabs of clay to dry, and some long-dead dog walked across it. The dog’s footprints are a kind of “historical trace fossil” that was then incorporated into this ancient structure.

Visiting the Rumeli Hisarı was a pleasant experience. I walked down along the Bosphorus next, peering into its surprisingly clear waters and counting jellyfish, then got a pide at a cafe. I caught another cab back to the hotel, and eventually fell asleep, a victim of jet lag…


Lola, the cartoonist’s companion

It’s been a while since I’ve posted any photos of my supremely helpful cat Lola on the blog, so here you go:


Lola loves to sit on paper, so when I break out the sketchbook to start working on my monthly cartoon for EARTH magazine, she sidles right up and stakes a claim. Fortunately, I was able to continue working in this case, as she wasn’t perched on the “active area” of the paper.


As you may be able to discern, the cartoon is about the newly-fraught relationship between geologists and the law… watch for it in December’s issue of EARTH.

The word is out…

Others have started announcing our move to a new blog consortium hosted by the American Geophysical Union, so I suppose I will go ahead and reveal that I, too, am part of this scientific cabal…

Sometime before the end of the month, Mountain Beltway and six other top-notch earth and space science blogs will relocate to AGU servers and a new URL. I’ll leave directions here for folks to follow…

Photos from Virginia Geological Field Conference

For the second year in a row, more exotic travel plans meant that I wasn’t able to attend the superb Virginia Geological Field Conference. I see that they have now posted some photos on the group’s Facebook page, so go check them out to see what we both missed last weekend. Here’s a taste:

Sheared meta-conglomerate:

Metamorphosed mantle (?) xenoliths:

Güvem geoheritage site, Turkey

Looks like I’m late to the party…

While I was away, apparently the geoblogosphere went on a rampage of cooling columns. Everyone was posting images of their favorite columnar joints, and I was left out in the cold. Let me remedy that now. As it turns out, I was visiting some columns while everyone else was writing about them. Here are some images from the Güvem area of Turkey, north of Ankara, where there are a mix of late Miocene lake sediments and intercalated volcanic rocks, including these basalt flows. We stopped to visit them last Wednesday on our way to the North Anatolian Fault:


The dark entablature looms above:guvem_columns01

A nice central panel with a good cross-section of the flow: guvem_columns03

Around the corner, some more:

I ran across the street (and a stream) to check out a similar exposure there:guvem_columns05

Zooming in:guvem_columns06

Close-up of a few columns (with my hand for scale):guvem_columns08

Looking up along the columns:guvem_columns09

And a few more shots of the scene:guvem_columns10


A full list of Turkish geoheritage sites may be found at the end of this document. Lockwood maintained a list of the other blog posts in this meme here, which I’ll quote below since it’s so nicely laid out already:

Geotripper, here, here and here,
Sam at Geology Blues
Phillip, also at Geology Blues
Silver Fox, and another columnar post here.
Glacial Till and another!
Life in Plane Light: Squashed columns!
Aaron at Got The Time
Geology Rocks
Dana at En Tequila Es Verdad
Cujo 359 (see comment on Dana’s post for description)
Wayne at Earthly Musings has a gorgeous photo of columns below the rapids at Lava Falls in Grand Canyon.
MB Griggs at The Rocks Know has photos of what may well be the most perfect columns in the world.
Jessica, AKA Tuff Cookie, showcases a variety in different rock types.
Hypocentre finds columns in a very unlikely place, as well as a spectacular photo of radiating columns.
Dave Tucker at Northwest Geology Field Trips displays precisely one slew of columnar displays in Washington State.
Dave Bressan at History of Geology shares the first printed image of columnar basalts, from 1565.
A couple more variations from Dana’s and my driving about W. Oregon.
Dr. Jerque has some spectacular examples from the bottom of the Grand Canyon.
Silver Fox Has another (better than mine) photo of horizontal columns in a set of dikes, and points out a couple more links to columny goodness (not to be confused with calumny, which is not good)
Dan McShane offers some more Washington State columns.
Garry Hayes, who deserves credit for starting this meme (see first links in the list, above), adds yet another set of photos from the opening of the Atlantic Ocean, and a lovely guest photo by Ivan Ivanyvienen, of columnar jointing in rhyolite at the San Juan Precordillera.
Update, October 4: Eric Klemetti- who did his doctoral work just down the street from where I’m sitting- has joined the fray. (Also, check out the links readers have left in the comments)
Helena Heliotrope at Liberty, Equality and Geology shows off some more Washington columns.
Chris and Anne at Highly Allochthonous each toss in a photo- Tokatee Falls looks awesome!
Some more Cape Perpetua jointed dike photos from Cujo359, and Devil’s Churn- again, numerous dikes with horizontal columns.

Remains of a mud puddle

Last Wednesday, I took a field trip to the North Anatolian Fault in Turkey, but I got distracted by this fine looking display of sedimentary structures in  a dried-up mud puddle in an old quarry.


The coin, a Turkish lira, is about the same size as a U.S. quarter. What you’re seeing here are dessication cracks (“mud cracks”), and accompanying them are exquisite little raindrop impressions, the minute craters excavated by a light sprinkle of rain after the mud has already started to dry out and “gel.” (If the water which deposited the mud were still there when the rain fell, the standing water would have dissipated the energy of the drops’ impacts, and no craters would have been excavated.)



Here’s a slightly more oblique perspective, to give a sense of how the individual mud flakes are internally laminated, and curl along the edges, producing a concave-up shape.


Note too that the cracks bisect some of the rain drop impressions, and therefore the raindrops fell first, and then the dessication cracks propagated on through them, a nice example of cross-cutting relationships. In some cases, the propagating crack used the “crater rim” of the drops as a mechanical zone of weakness, fracturing there preferentially. Here, let’s zoom in on a couple of nice examples (one from photo #1, a second from photo #2):



If anyone wants a full-sized copy of any of these images for teaching purposes, let me know via e-mail, and I’ll send you one.


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