Tyranny of the Model

Ah, fall is in the air and so it is a perfect time to be grumpy.  Today it is about mistaking a model assumption for a model result, and our candidate for proving the point is the art of balancing cross sections.

Long ago, cross sections were drawn to, well, look like geologists thought they might look without too much worry about whether they made any sense.  That was of course silly, and over time some hardy souls wondered if you could take a cross section and treat it like a jigsaw puzzle, slicing it up on all the faults and unbending all the folds and then recovering something that looked reasonable for a starting model.  Formalizing such sections provided rules, such as the length of a bed had to stay constant as you undid deformation, or the area of a geologic unit had to be preserved.  While this allowed one to see if a section might be possible, it didn’t make for the easiest time in making a section that would work out.

In the late 1970s and early 1980s, John Suppe developed a geometrical approximation for deformation in fold-and-thrust belts he termed fault-bend folding, a methodology that allowed for the construction of balanced cross sections from primary geologic observations directly rather than through some trial-and-error process. Since then, the approach has had numerous adjustments and extensions made to it, but it still is the basis for most geologic cross sections made today. As such, it was a major step forward.

So what is the problem? As with many useful tools, it is in the approximations necessary to make the tool easily wielded.

Basically, for this to work you have to assume that beds behave in certain ways; in the original paper, Suppe noted that bed lengths and thicknesses had to be preserved and horizontal beds had no net distortion. In application, though, as sections grew to encompass whole thrust belts, you had to do something with the faults as they went down into the crust.  If you had on both ends of the section something that was at the same elevation both before and after deformation, then the faults had to become flat.  If they were not, if they had a dip as they exited the model, then one side of the model would rise up over the other side. So, in practice, areas adjacent to deformed zones were presumed to sit above flat-lying faults, or detachments.  Detachments exit these models on the sides.

The reason is simple: there is no mechanism for determining deformation below the stratified medium.  The area below could easily violate the rules of constructing the section, and it is trivial to show that many such decollements go away the moment you allow for laterally variable strain to exist in the lower crust. In some cases it becomes obvious this must be the case: a simple two-sided orogen produces kinematically impossible geometries unless there is deformation of the lower plate.  As an example, this section across the San Andreas Fault in central California:

namsondavis

Balanced sections across central California from Namson and Davis, GSA Bulletin, 1988.

Look at what has to happen under the Gabilan Range: if you are below the detachment, things collide, or above it and a big hole opens up to great depths.What must happen is that the material below the lowest detachment must deform.  But once it deforms, the necessity for the detachment actually goes away. The geometry of the folds above the detachment assumes that the detachment geometry does not change. This is an implicit assumption in all of these kinds of reconstructions. Once you relax it–say, allow the lower crust to be thickening under the Gabilan Range so that the detachment might be rising or tilting with time, then the model is broken. In this case, the certainty that the lower crust must be shortening, and the absence of that shortening from the kinematic model, means that the model is incomplete and likely wrong.

Let’s tear this apart a bit. Let’s hold the Pacific Ocean fixed on the left side of the above section.  Stretching back the material above the decollement pushes the San Andreas fault back to the right and the Sierra farther away.  As drawn (but to be clear, not as the authors would have interpreted it), the crust below the decollement on the right moves right while that on the left stays put, so a big hole then exists under the center of the model.  Now as there certainly was material there, what happened as the shortening occurred above the detachment?  Well, it certainly thickened and shortened. As this was crustal material, it seems likely that this would produce isostatic uplift that would bend the detachments upwards.  But that uplift was ignored in constructing the detachments. Also, that shortening would tend to change the offsets on the detachments: it is possible that there were places where there was no net motion between the upper and lower plates as drawn.

The basal detachments in these reconstructions are, fundamentally, necessary fictions to make the stuff higher up (where we actually have constraints) work. It is possible that they exist, but it is not necessary for them to have the specified geometry. [The ramps are a bit of a different story, as they create deformation above them that is presumably observed, but again, what happens if the ramps evolve over time?]

So here’s the mistake caused by the tyranny of the detachment: assuming that identifying the basal detachment is identifying a real fault is mistaking a useful fiction for an actual fact. And yes, GG is well aware of some workers making that interpretation. And to any of those who happen upon this page, before you start fuming and claiming GG does not understand all the cleverness of these techniques (which, you know, is quite possible), ask yourself these questions. (1) In your model, does the basal detachment change shape at any time in its history? (2) how likely is this if there is any deformation in the lower crust? and (3) how much evidence do you have that the lower crust is undeformed?

[Also, it seems unlikely that this has gone unnoticed, but GG isn’t aware of papers that take this on.  If you know of one, please point it out]

It seems to GG that if we want to use these models to get at orogen-scale structural evolution, we need some tools that can incorporate lower plate deformation as well.  Because, you know, those horizontal faults either have to go away as the lower plate catches up to the upper plate, or they bend down into the earth. GG is pretty certain they don’t simply circle the planet…

Tags: , ,

Trackbacks / Pingbacks

  1. Overthrowing the model | The Grumpy Geophysicist - October 14, 2016

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: