How Dynamic is Topography in the Western U.S.?
We have the unusual presence of two papers published in the same year essentially trying to do the same thing: determine how much topography is caused by isostasy in the crust and mantle and how much might be non-isostatic (or dynamic). And the two disagree strongly on the amount of dynamic topography. So let’s break this down and see where these papers really differ. The two are Levandowski et al. in JGR in early 2014 and Becker et al. in EPSL in late 2013 (well, the publication date is 2014; it came online back in October).
Advisory: GG is a coauthor on the Levandowski et al. paper. While this might be reflected in preferences expressed below, hopefully the analysis is still helpful to those with different preferences.
Outline: Basically both papers include the same routine: take a seismic model, convert it to density, subtract the effects of that density model and see what is left. The Becker et al. paper has a number of other analyses going on that make it harder to follow the most direct route. There are some wrinkles, but we’ll look at the seismic models first, then their conversion to density, and then how that is used. This is a bit more technical than many other posts here…
Crust and Moho Seismology: Becker et al. consider the depth of the Moho from a couple of different receiver function studies, which means that there is some conflation of crustal velocity and Moho depth. The Levander and Miller model uses CRUST2.0 velocities, which are based on interpolation and extrapolation of P-wave models across the west; the Lowry and Pérez-Gussinyé paper isn’t terribly clear about how (or even if) they determine absolute wave speeds in the crust (the paper is focused vp/vs ratios, which are kind of ignored in the Levander and Miller paper); they use the H-k stacking approach of Liu and Kanamori (2000), which relies on reverberations to remove ambiguity with uncertain in vp/vs (but still requires something to be assumed for a mean crustal vp; Liu & Kanamori basically argued that uncertainty in vp was not significant in the error on depth of Moho). Each of the models has a weakness when used for determining density as neither is fully self-consistent between crustal velocities and Moho depths; the Levander and Miller model relies on CRUST2.0, which is not always based on observation and which conflicts with receiver function Moho depths in several places; Lowry and Pérez-Gussinyé don’t have any obvious control on variations in mean wavespeed, which, while second order for Moho depth, is important in determining mean crustal density. Levandowski et al. relied on the SV-wave model of Shen et al. (JGR, 2013) constructed from ambient noise and ballistic surface waves combined with azimuthally filtered receiver functions. The crust includes a sediment layer, which can be a major contributor to Ps and Sp delay times for stations on basins. This is fully self-consistent but as it relies on SV, any variations in radial anisotropy will map into density unreliably. Moho depths are specifically at stations but the surface wave dispersion curves effectively cover a volume, so errors are to be expected in places where there are strong slopes on the Moho. The parameterization of the inversion allows for only a single Moho (this is true as well of the papers used by Becker et al.); areas that might have a “double Moho” will probably be aliased unpredictably.
Mantle Seismology: Becker et al. seem to rely on Ps (mainly) and Sp receiver function estimates of the lithosphere-asthenosphere boundary from Levander and Miller (2012): “Here, we will simply test if the LAB depths from Levander and Miller (2012) (P receiver function based as in Fig. 2) exert some control on the isostatic adjustment of a variable thickness, and constant density, lithosphere, assuming that a thermal boundary layer of variable thickness should approximately scale with the LAB.” GG thinks this means that some contribution to isostasy is considered to be proportional to mantle lithosphere thickness, though the constant of proportionality is either to be determined or is simply left unclear. There are many weaknesses here: first, there is considerable controversy as to the significance of the Ps and Sp “LAB” converters as they appear to be well within the lithosphere in the eastern U.S., which suggests they may be inappropriate markers in much of the western U.S. as well and are almost certainly inappropriate in the easternmost areas covered in the paper. Second, the Ps converters are frequently tangled with reverberations from the crust and are often unreliable; Sp is a difficult phase both because signal to noise is often weak but also because the converted phase travels at a high incidence angle through the lithosphere, so the LAB piercing point of the Sp wave is far from that of the direct S. They also derive the thickness of a constant-density lithosphere that would add to crustal models to produce observed topography. Later on, density variations in the mantle lithosphere are derived from the S-wave tomography of Schmandt and Humphreys and from a thermal estimate from Lowry and Perez-Gussinye (these are both found to have little impact as discussed further below). Levandowski et al. uses Shen et al’s model, which is primarily ballistic surface waves with some control from the amplitude of the Psconversion at the Moho to construct a velocity model to depths of 150 km. No attempt to identify the base of the lithosphere is made. This can mean that density variations in the asthenosphere will be improperly connected to the lithosphere and exaggerate their influence [in practice, though, the places with thinner lithosphere have such low wave speeds that there are negligible density variations at greater depth]. As before, radial anisotropy variations will map into variations improperly. Lithosphere thicker than 150 km will not be fully represented within the calculation [this should be relatively minor as the bottom of a thermal boundary layer will be close to asthenospheric temperatures and in general highly depleted mantle is generally above 150 km depth].
Density: Becker et al. hold crustal and mantle lithospheric densities constant in the initial analysis. They derive possible deviations of density from the difference between constant-density models and topography, mainly for illustration and not analysis. They apply a crustal density correction from Lowry and Perez-Gussinye. They consider a thermal density variation from S-wave tomography of Schmandt and Humphreys. When mixing and matching components of other models, there is always a risk of any covariance between model components really messing things up. For instance, the S-wave tomography depends on the crustal model used, especially at shallow depths in the mantle; if you pair this tomography with a different crustal model, you have a hybrid that might not satisfy the tomographic dataset. Levandowski et al. use a vs to density relation in the crust derived empirically by Brocher (2005) with a correction for thermal variations derived from surface heat flow, assuming a steady-state thermal profile. Disequilibrium thermal states will have a minor impact. A single-valued velocity-density relationship certainly has limitations that depend on the scale length of deviations from such a relationship; if large areas systematically lie off such a curve (e.g., crust largely made of quartzite), significant errors are possible. In the mantle a simple thermal relation for velocity to density is used, accounting for anelastic effects near the solidus and assuming no density variations below a threshold velocity assumed to represent the solidus. Variations in composition are ignored [but discussed when interpreted] and variations in solidus due to presence of water or variations in composition could produce deceptive density estimates.
Analysis: Becker et al. use a frequency-domain coherence between the two Moho maps (with and without the mantle lithospheric thickness) and topography. This has the advantage of relative insensitivity to the absolute density contrast across the Moho or between the mantle lithosphere and asthenosphere; however, it fails to account for varying density contrasts across the Moho or lateral variations in crustal or mantle lithospheric density, any of which would reduce the coherence of the compositional proxy (Moho depth, LAB depth) to topography and so appear to show a failure of isostasy. Spatially, the paper subtracts out the constant density crust and considers a few different flavors of lateral variations that could reconcile predicted to observed topography. Most relevant for comparison, they take the constant-density crust and constant thickness mantle lithosphere and add in density variations in the crust from one paper and in the mantle from another to obtain something in Fig. 6a that should be most like the residual topography (Fig. 4g) of Levandowski et al. Levandowski et al. works in the spatial domain, calculating topography from the crustal and mantle density structures. The initial calculation ignores crustal thermal variations, but these are then added in (based, as noted above, on heat flow). Areas where predicted topography are outside the uncertainty from observed topography are considered; areas where predicted topography is too high and heat flow is high are suggested to contain crustal melt; areas where predicted topography is too low are suggested to contain unusual amounts of quartz; areas where predicted topography is too high but cold are suggested to be affected by dynamic effects [basically, coupling to the slab, which exerts a greater downward force than is evident within the seismic model]. These effects are limited in extent and have a maximum contribution locally of 1 km of elevation. These posited possible effects are then reincorporated into the overall estimates of crustal and mantle contributions to topography. Obviously the assignments of dynamic effects, melt and quartz variations are arbitrary and not based on independent evidence [though the text argues that they are broadly consistent with other observations].
Comparison of some chief results. Both papers present topographic residuals:
(Sorry, cannot get on one line). Both show observed topography – predicted, but use opposite senses for the color bar. Both have an anomaly in the northern Nevada where elevations are higher than predicted, but otherwise the large residuals seen in the Becker et al. paper are absent in the Levandowski et al. paper. Why? It seems that the big difference is the mantle contribution. Consider below the contribution from the mantle in Levandowski et al.
What we see is that the Levandowski et el. formulation suggests that about 1.5 km of topography should be coming from variations within the upper mantle imaged by Shen et al. Although the Vs tomography of Schmandt and Humphreys differs some from Shen et al., in Becker et al., its effects on the residual topography are nearly negligible (basically, Fig. 5c and Fig. 6a look almost the same). It suggests that one of the main differences between these papers is buried in the way that mantle seismic velocities are mapped into density. It would seem that if the mantle contribution of Levandowski were added to the Becker et al. residual topography that the topographic residual would be pretty small. While there are additional terms in the Levandowski et al. formulation that are significant (e.g., a greater lateral variation in crustal buoyancy), this appears to be the big difference. Either Levandowski et al. overestimated the density change for a given change in vs, or Becker et al. underestimated it. Both papers assume (away from the solidus) that a 5% change in vs will produce a 1% change in density, so for a 70 km thick mantle lithosphere (about as used in Becker et al.), a 5% change should produce a topographic change of 70 km x 3250 kg/m^3 x 1% / 3250 kg/m^3 = 700m [changed 1/8/2015 as Moho moves up with crust if only difference in mantle–this was error T. Becker complained about in a comment]. Comparing figures 5c and 6a in Becker et al., it doesn’t seem that there is hundreds to over 1000 m of difference between the two, while the Hm plot from Levandowski et al. (above) has that order of signal.
So it appears that there was some kind of blunder in calculating the topographic effect of mantle density variations in Becker et al. With this corrected, it appears that most of the topographic anomaly will go away, much as was seen in Levandowski et al. This would mean that the need for the dynamic calculations (the remainder of the Becker et al. paper) would be irrelevant.
Is this right or did GG just add a new error in?