GG was recently dismayed by student “error analyses” in some reports that simply amounted to “well, we could have made a mistake”. As awful as these are, they are better than some of what is published in the professional literature these days.
We have so much data, so many big computers, so many clever coders that we can crunch and process huge datasets and then, in the end, the answer emerges. There it is, usually in blue and red, the world beneath our feet! Ta-da!
But wait. One big new model says the world at this point is red, but another says it is blue. Which is it? How are we to believe one or the other? All too often, a new model says nothing about why it is better or more believable than a previous model. In essence what you want is an error bar. Good luck finding that in a typical tomography paper, or a numerical modeling paper. Error bars are out of fashion.
This is worth a little investigation…
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.
OK, while pondering the bizarre motivations for evil alien monsters (must…destroy…schoolbus…which can dodge plasma blasts even as fighter jets cannot), GG wondered, why would any alien civilization want to conquer or destroy Earth?
Arguably the most likely reason would have something to do with our biosphere. Maybe there are cool new medicines to be found–the cure for some intergalactic plague. Or maybe they really are into zoos (hmm, didn’t Kurt Vonnegut go there?). Our biosphere is presumably highly unique and probably pretty rare (current enthusiasm for planets possibly harboring life not withstanding).
Not knowing anything about alien ecosystems or diseases or the like, can’t really go any further. Is there anything else special about Earth? In the past, movies and some science fiction have used the water on Earth as a main motivation (see Oblivion for a recent example). But water is simply hydrogen–which is widespread–and oxygen, which is also pretty common. If you have the muscle to move spaceships all over the place, making water is probably not that hard to do.
Oddly enough, one possibility is one that feels more like motivation for a spy movie and not for some extra-terrestrial invasion: gold.
Now gold on Earth isn’t the most common thing, but the funny part is that there is a lot more of it near the earth’s surface than you’d expect. If you make Earth by condensing all the material in the solar nebula at about this distance from the Sun, you kind of expect the gold to all end up in the core [woo-hoo! Another motivation for a movie about the core–travel there to get gold!]. Although this difference might be related to other elements present in early Earth and issues with experimental simulation of the partitioning of gold between core and mantle, if this is real, a decent proposal is that things like gold and iridium were emplaced on the earth’s surface in the Late Heavy Bombardment period just under 4 billion years ago (a review of much of this can be found here; a popular science story here and a 2011 Nature article providing observational support is here). What this might mean is that the earth might be uncommonly rich in metals like gold. And if our solar system were unusually rich in gold to start with (the production of gold in stars requires either supernovae or even more exotic events), we might be quite unusual. So maybe a good ET movie might combine sci-fi and a Ft. Knox heist….
Of course you’d have to have some big reason for wanting gold (hint: probably not to make coins with). But gold is exceptionally malleable and resistant to corrosion; it is also an exceptional conductor. Perhaps there is some kind of gold-based superconductor out there (so Earth could be Avatar’s Pandora for some other species).
GG will wait for that call from Hollywood….
No, this is not about being careful in what you say, or how quickly you jump if tapped on the shoulder. This is testing for how well an inversion can convince you of the presence of an anomaly.
Seismic tomography is one of those windows into the earth that is either a huge advance or a hall of mirrors. The single greatest challenge is to show that some high- or low-velocity blob is real. Sometimes you can do this by looking at raw travel time residuals, but most of the stuff we are looking at these days is lost in the noise in raw data–it takes the blending of tons of data to get to the anomalies in question. (Seismologists have been wading in big data for awhile now).
Probably the most convincing test is some kind of sensitivity test (or, if you do the full matrix inversion properly, an a posteriori covariance or resolution matrix–but with the numbers of degrees of freedom in most tomographic studies, these are few and far between). A simple form is a checkerboard, but let’s consider a better one, a hypothesis test. As we’ll see, there are unexpected pitfalls.
At times of late folks have decided to term volumes of the mantle (in particular) as being “red-ite” and “blue-ite” to avoid over interpreting such bodies as being hot or of some material. Even so, the general assumption in the upper mantle is that red-ite is hot and blue-ite cold. So what does this tell you about surface uplift rates?
And yet there is quite a literature where the presence of a red blob in tomography is taken to mean that overlying crust is rising, or a blue blob means it is sinking. This is nonsense for multiple reasons. (GG is here refraining from identifying some guilty parties, but it shouldn’t be hard to find some).
First, it would be the rate of change of buoyancy that would matter to start with. A present-day hot body (say, for instance, a pluton) would be in isostatic balance (as much as the flexural strength of the lithosphere would allow). If the pluton were simply sitting there, slowly cooling, little would happen until the thermal front from the pluton were to fade out enough that the whole volume of pluton and surrounding rock was losing heat. There would be no uplift; eventually there would even be subsidence, even as the pluton might remain somewhat hotter than its surroundings. For there to be uplift, the pluton either needs to get hotter or bigger. Seismic tomography has no temporal history; if you want to go there, you have to make a bunch of assumptions and then model processes.
Second, the assumption of buoyancy for a red blob, while defensible, is hardly certain.
Third, there are processes that can interfere with the expression of a mantle anomaly’s buoyancy at the surface. Several papers studying Rayleigh-Taylor instabilities have shown that the crust can flow in above a growing instability to produce uplift even as the anti-buoyant drip grows below.
Mistaking a rate for a level value is a blunder that earns rapid and widespread approbation in economics; perhaps similar blunders should be called out in earth science.
Hmmm, another paper has emerged with a big role for dynamic topography as a cause for deformation in the western U.S. (Becker et al., Nature, 2015), and if you read the press releases and resulting news coverage you’d think this was the Big Answer to earthquakes away from plate boundaries.
Sorry, don’t think so. But GG hasn’t had the time to really go through this paper in detail, and in any event feels kind of bad for picking on Thorsten earlier, who is a perfectly pleasant fellow. So let’s stand back and consider the root cause here, which is good old dynamic topography. A simple test a lot of us like to apply is to look for free-air gravity anomalies that should be associated with dynamic topography. While GG was involved with a paper that dealt with this is rather gory detail, let’s think of this really simply: what is a free-air anomaly, where and how can we use it, and what does it show where we can use it?