Sierran Escarpment: Uplift Driver or Sideshow?

Perhaps the most impressive aspect of the Sierra Nevada is its eastern front.  A bold wall of rock challenges any who would cross the range; the southern part in particular is so daunting that Americans weren’t inclined to try to cross it until well after the Gold Rush was underway. No road crosses the range crest between Devil’s Postpile and Nine Mile Canyon Road to Kennedy Meadows (on the South Fork of the Kern).  That eastern front is controlled by a system of normal faults, and as such they define the eastern edge of the Sierra.

For many years in talking about the uplift of the Sierra Nevada, GG has been asked from time to time about whether the Sierran uplift is a response to normal faulting on the east side.  And the answer has been essentially no; this adds some height near the fault but isn’t the main player.  Now a couple of papers have shown up in the last few years on this, and they proceed from some occasionally complex assumptions to investigate this.  Frankly this was more work than was warranted; you can show pretty directly with little work that there is a firm upper bound on how much that faulting could create.  What is more, what little is predicted also carries a prediction about the gravity field, one that is very much at odds with observation.

The zeroth order observation is simple: all games envisioning normal faulting as a player are zero sum or even negative sum for elevation (normal faulting thins the crust, which will produce subsidence).  For one area to go up (like the Sierran crest), something else has to go down.  Since the region east of the Sierra is no lower than 1 km above sea level (and that only locally near Owens Lake at the south end), you are reduced to talking about the uplift of the Sierra relative to the mean–and the mean is about 2 km elevation near Owens Valley.  So now we’re reduced to considering the last kilometer or so of mean elevation of the High Sierra as possibly being caused by faulting.

Let’s examine this in more detail (which means make a few calculations).  First consider isostasy, the idea that the lithosphere is floating on the mantle.  Like an iceberg, if you remove a big chunk from the top, the rest rises up but falls a bit short of the top. If we assume that the asthenosphere under the lithosphere is a fluid, then we know that the pressure at a given depth below sea level within the asthenosphere is laterally constant, so when you remove a big weight, the asthenosphere below suddenly has a lower pressure and rises up until the weight of everything above is back to the value at the start.  We can quantify the restoring force as a buoyancy force; in this case, it is simply the weight of the material that is missing.  So, for instance, in a 2-D case like across Owens Valley, we might imagine that a 15 km wide chunk of crust nearly 3 km thick has been removed.  If it has a density of 2700 kg/m³, we have a total force per unit length along the Sierra of 15,000 x 3,000 x 2700 x g (we’ll use 10 m/s² for easy computation) to get 1.2 x 1012 N/m. To counter that force, things rise up and it is that excess weight that will balance things out. So if we limited the region of uplift to where we removed the rock (the 15 km wide valley), we need to raise up Owens Valley’s crust and upper mantle some height D such that the weight of the new stuff equals that buoyancy force. If we are just moving stuff up, then the crust has the same weight and it is the new thickness of asthenosphere that balances things out. So that weight is 15,000m x D x 3200 kg/m³ x 10 m/s² = 1.2 x 1012 N/m, or D = 2530 m. So we end up with a hole nearly 500m deep in this case from removing (by faulting) the 3 km thick slab of rock. Put another way, removing a 15 km wide and 3 km thick slab of upper crust allows for an uplift of a cross sectional area of 2.53 x 15 km² = 38 km². You could balance this by having a 5 km wide area rise up 7.5 km while leaving the rest of the area low, or having a 38 km wide area rise 1 km.

This hints at the way to get something other that Owens Valley to rise up: we have about 38 km² of area it can raise.  If we somehow got all of this applied to the Sierra, which is a bit over 100 km wide, we’d get an average elevation increase of 380m.  Since the Sierra is more or less a tilted block and so a triangle in cross section, this will get us 760m of uplift at the crest and less and less as we go west to zero at the foothills–basically no more than one quarter of the elevation of the range today. This is an absolute upper bound to the effect of removing a load from the top; we will get no more than that total.  In fact, we should get a lot less: the Inyo and White Mountains on the east should also see this effect, which would suggest this number drops in half, and then some part of the uplift will occur within the Owens Valley, too.  So something under 1/8th of the modern elevation of the Sierra could be attributed to the creation of a big hole on the east side–and this is probably being generous as the hole is less than 3 km deep along most of the eastern Sierra.

If you know your geophysics, you know that the classic formulation has another side to this.  If the faults dropping Owens Valley down extend into the mantle, then pushing the valley down 3 km also pushes the Moho down 3 km; in fact, the maximum throw on these faults is probably closer to 5 km (we filled up the hole a fair bit with sediment).  Pushing the Moho down is a lot like pushing an ice cube down–there is now a force pushing it back up and it is once again a buoyancy force.  Here it would be the density contrast between the crust and mantle (which, with our sample numbers above, is 500 kg/m³) times the width times the thickness times gravity, or 500 kg/m³ x 15,000m x 5,000m x 10 m/s² = 3.75 x 1011 N/m, which is perhaps a third of the value from making the hole in the first place. Adding this to what we had above, we could maybe get 1/6th of the Sierran uplift from this effect.  However, there is no indication that the Moho under the valleys east of the Sierra is deeper than under the Sierra itself from either refraction work or teleseismic receiver functions. And as the faults are accommodating extension, there would be a component working in the other direction as thinning the crust will cause subsidence, not uplift. So this is an unlikely contribution to Sierran elevation.

So at most about 12% of the modern elevation of the Sierra as a whole could be caused by faulting on the east, but in fact how that uplift gets distributed depends on a bunch of other assumptions. So the papers by Martel and others and Thompson and Parsons are really just shuffling chairs on the deck of the Titanic: you can play with this to get more uplift near the faults but then you have less farther away; you can adjust for the fill in the valleys on the east side of the Sierra, etc..  And if that matters to you, then some of the parameters they have to play with (geometry of the faults, flexural rigidity, etc.) become significant.  But this is not buying you much in terms of understanding why the Sierra is there; it is maybe telling you something of why Mt. Whitney is higher than Black Kaweah or Mt. Goddard.

There is a final objection that is overlooked by papers appealing to this process.  For this process to work, the Moho gets pushed up; this means there is a mass excess at depth that is being supported by a mass deficit somewhere else. This produces a positive gravity anomaly.  Now this isn’t a big positive anomaly but the Sierra is fact sits on a huge negative gravity anomaly, which means that the Sierra itself sits on a big mass deficit which supports the high elevations. This further reinforces the case against the faulting being a large player in creating the elevations in the Sierra: there is observational evidence that there is plenty of buoyant material there to push the mountains up.  The big question, the one worth pursuing, is what is that buoyant material, how did it come to be and how did it evolve.

A final grump.  Martel et al., at the end of their paper, say “much of the present elevation of the Sierra Nevada predates formation of the eastern escarpment ca. 10 Ma.” This may prove to be true (and of course “much” is vague), but their analysis has nothing to say about this; it is a gratuitous grasp for relevance because most of the slip on the Sierran front is post 3 Ma, and even if slip started at 10 Ma (which is mainly a contention from within a volcanic center in the northern Sierra), nothing in their analysis would require that slip to have started with the Sierra at its modern elevation.  The irony is that they spent a huge amount of time and effort to reach the same conclusion (and essentially for the same reasons) as this simple analysis: “Uplift of the Sierra Nevada in response to slip along the range-front faults was probably no more than a few hundred meters to as much as 1 km at the crest.”

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