The death of isostasy?

One of the chestnuts of earth science for more than 100 years has been the concept of isostasy, which more or less holds that the outer part of the earth (the crust and mantle lithosphere) floats on the far less viscous asthenosphere.  Although the concept was floated in 1855 by Pratt and Airy in seeking to explain geodetic discrepancies in the great survey of India caused by the Himalaya, the term coined by USGS scientist Clarence Dutton in 1889, and the implications brilliantly described (along with the basics of plate flexure) by G. K. Gilbert in 1890, much of the geological (and especially the geophysical) community had no use for isostasy until 1914-5, when Joseph Barrell’s work advocating from multiple lines of evidence for an asthenosphere was published (in nine parts: quite the serial publication). So while we could be celebrating the centenary of physically-based isostasy, in some ways we appear to be ready to bury it.  Why?  Consider this plot from Moucha (2008):

ImageThis shows the predicted dynamic topography of the western U.S.; the scale is in kilometers, so about 2 km of variation of topography in the U.S. would seem to be from dynamic effects (the paper’s title cites ‘mantle convection’ as the cause). Given that average elevations in the west are only occasionally up around 3 km, this would seem to make isostasy moot; the mantle convection alluded to is shown to be extending to the outer core, far below the asthenosphere.  The paper’s abstract makes it clear that the authors are attributing much of the modern elevation of the Colorado Plateau (outlined above) to mantle convection and dynamic topography:

Herein we compute the viscous flow beneath North America that is driven by density anomalies inferred from joint seismic-geodynamic modeling. We find that the Colorado Plateau overlies a strong mantle upwelling that is coupled to the sinking Farallon slab, currently beneath the eastern United States. Consequently, the Colorado Plateau is currently a focused dynamic topography high within the western U.S. Cordillera.

So we’ve had a century of misdirection, right? Isostasy is dead, no?

Well, not so fast. In this paper (as in many similar papers), the definition of dynamic topography (which GG grumbled about before) is the topography produced by everything going on below the crust.  So variations in the mantle lithosphere count as dynamic topography (including variations entombed there for billions of years).  It turns out that much (most? all?) of this variation is because the mantle lithosphere has been removed from much of the western U.S. (which becomes somewhat clearer in a subsequent paper), a concept that, in terms of explaining the uplift of the Colorado Plateau, has been kicking around for quite awhile (e.g., here and here). As the mantle lithosphere lies above the asthenosphere, variations in thickness of mantle lithosphere are well within the purview of classic isostasy.  So while removal of mantle lithosphere (whether by convection, delamination, subduction erosion, or “deblobbing”) is a ‘dynamic’ process, relabeling it as a result of “dynamic topography” as a new insight seems, well, overblown and kind of misleading unless you separate the stuff from within and below the asthenosphere from those above.

So does isostasy get a stay of execution?  Well maybe, but we do know the mantle is convecting (let us not argue two-layer vs. one-layer today), that the convection is driven by density variations and that flow of a viscous medium will produce topography (an experiment you can try if you have a little pump: put an inlet and outlet in the bottom of a tub, connected by tubing and the pump.  Fill the tub with some nice viscous fluid: pancake syrup, molassas, etc (probably not too thick or the pump will fail) and then run the pump.  You will see the top of the fluid be low above the outlet and high above the inlet with the topography being more dramatic ths thinner the layer is). So just how much does that convection in the earth affect surface topography?

This turns out to be far more in dispute than you might think.  Consider this plot, from Flament et al., a group very much advocating the importance of mantle convection in surface topography:

Image

(GG thinks these maps are to be topography from sub-crustal effects with cooling oceanic plate effects removed, but isn’t positive). At first blush there is a lot of similarity: South America and SE Asia are depressed by the oceanic slabs descending under them, other areas are generally going up (since the plots sum to zero over the earth).  But look at the magnitudes: Ricard et al. have about a 1 km peak-to-peak variation, while several others vary by almost 4 km.  There are some pretty notable spatial variations, too: is Australia tilted down to the north, down to the east, or uniformly flat? And some of this rather demands from impressive crustal influence: would eastern South America truly sit more than a kilometer above sea level (many places more than 2 km above) if dynamic effects ended? Why the difference between these models?

There are two answers.  The most critical one for the question of the degree of influence of deep convection on surface topography is the viscosity structure of the earth.  Basically, for isostasy, the asthenosphere is approximated as an inviscid fluid: it should have no strength over geologic time. So in the little experiment above, if we pour water on the top of our sticky fluid with the pump moving it from one side to the other, we won’t see topography on the water’s surface while there will be topography on the viscous fluid’s top.  If there is a pretty inviscid layer under the lithosphere, you won’t tend to see much topography (except, probably, near subduction zones).  If it isn’t much less viscous than the mantle farther down, the effects of the deeper convection will be carried up.

So how well do we know the earth’s viscosity structure? Um, not as well as we need, and that is a big reason for some of the differences in the figure above.  Basically, a big knob that can be turned to adjust the amplitude of sublithospheric dynamic topography is the viscosity of the asthenosphere. Toss in other variations and you can amplify or tone down the contributions from specific depths.

The other main effect is what the density structure in the earth is like.  This is typically derived from seismic models, which have their own problems (something we’ll come back to at some point), but converting seismic wavespeeds to density is, um, as much art as science at the moment (e.g., consider what the density of the very large low-wavespeed body in the lower mantle under South Africa should be: seismic evidence for a sharp edge to this makes clear that it must differ chemically from surroundings and not just thermally, as is often the supposition behind conversions of seismic velocity to density) .  There are other large issues in play, too (such as the density changes across the transition zone from 400 to 700 km depth, where olivine changes to progressively denser minerals) that come into play.

Where does this leave us?  If global variations in sublithospheric dynamic topography are on the order of 4 km, one would expect that isostasy isn’t nearly as useful as we thought.  If variations are closer to 1 km and very long wavelength (especially away from subduction zones) then isostasy probably is a useful approximation. Are we ready to attribute major tectonic events to sublithospheric dynamic topography?  GG remains doubtful.

 

 

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