Jones, C. H. ,L. J. Sonder, and J. R. Unruh, Implications of Topography for Tectonics of the SW U.S., Geol. Soc. Am. Abstr. Prog., 28 (7), A-513, 1996.

The age and origin of the high elevations of the southwestern U.S. (SWUS) have been longstanding geotectonic problems, as highlighted by recent paleobotanical estimates of SWUS paleoelevations that challenge the long-held belief that the uplift is late Cenozoic. Our recent analysis of the modern-day budget of lithospheric gravitational potential energy (GPE) for the SWUS (Jones et al., 1996) yields estimates ranging from -0.7 x 10¹² N/m to 2.6 x 10¹² N/m, sufficient to produce lithospheric stresses capable of driving strain rates of ~10^-15 s^-1. We can make inferences about uplift and paleotectonics using this technique. A 45 km thick crust's GPE increases by 10 ¹³ N/m (3x the modern range of GPE values in the SWUS) if its mean elevation increases from sea level to 3 km due to density changes in the mantle. In contrast, thickening a 35-km thick crust to produce the same change in surface elevation increases the GPE by only 2.5 x 10¹² N/m. In both cases, the change in GPE changes the stress state of the lithosphere. For comparable values of average lithospheric strength, however, the resulting strain rates differ significantly. By constructing simple structures of paleolithosphere, applying these principals, and comparing the results with the observed tectonics, we can test different tectonic hypotheses for consistency with isostasy, the tectonic history, plausible lithospheric structures, and plausible lithospheric forces with a minimal number of free parameters. We will illustrate this potential with some simple examples.

This document was prepared primarily as an aid to us in putting together this talk; it seemed ashame to simply destroy it once the talk was given, so it is here to provide a virtual talk for those who didn't get to bask in the glow of the slide projectors on Halloween 1996.

The bullets following each pair of slides are summaries of points made (hopefully) in the talk; they can be somewhat cryptic as this is not a replacement for an eventual paper.

Slide 1

Left slide: Topo map SW USA (Fig. 1a from Jones et al., 1996) Shaded topographic map with physiographic provinces	Right slide: Delta-PE map SW USA (Fig. 1c from Jones et al., 1996) Gravitational potential energy (GPE) derived from seismic profiles (at points). Points are scaled by quality. Colored field between points obtained by kriging; overlaid on shaded relief. Zero contour represents GPE equal to that of a column of asthenosphere (our reference structure)

• SW USA contains quite diverse deformation:
  • Plate margin strike-slip (San Andreas, Eastern California Shear Zone)
  • Margin-normal compression (Calif. Coast Ranges)
  • Margin-normal extension (eastern Basin and Range, Rio Grande Rift)
  • Low-strain rate regions (e.g., Colorado Plateau)
• The gravitational potential energy (GPE) (defined below) measures forces derived from body forces that act to deform lithosphere; we have derived these from seismic profiles (velocity -> density -> mantle buoyancy -> GPE).
• GPE variations match sense of deformation and when combined with plausible rheologies yield realistic deformation rates at the scale of physiographic provinces despite the very simple assumptions we use here (Jones et al., 1996)
• Thus, GPE is very important in understanding continental tectonics (a point underscored by the role of these forces in driving plates).
• Can this help in the past?--Yes; outline talk.
• This technique operating on modern situation allows topo to provide info on tectonics; could we reverse this for past situations? (use tectonics to bound elevation and/or structure?)

Slide 2

Left slide: GPE definition and relation to strain rate	Right slide: GPE derivation summary

• Note formal def'n of PE and how it reduces with assumption of isostasy
• Describe calculation method:
  • Estimate mean crustal thickness and density (from geologic constraints)
  • Use trial elevations, can calculate mantle lid consistent with crust
  • From this info, use equations presented to get PE
  • Contrast sense of deformation with that known; inconsistencies require either external forces or indicate error in assumed structure/elevation
  • If possible, can estimate thermal structure and then derive strain rate.
• Note that 1-D relation of strain to PE more complicated in real life, but this is a good starting place

Slide 3

Left slide: simple orogen cartoon: thickening crust	Right slide: PE and Lm vs. elevation for uniformly thickening lithosphere

Consider a simple "classic" orogen. First step is to thicken lithosphere uniformly.

• Thickening lithosphere uniformly: what happens?
• As elevation increases and crust and mantle thicken, PE decreases
• Since negative PE inconsistent with extension, uniformly thickening orogen will not collapse (in fact, could become self-perpetuating)
• Fine print: started with 30 km, 2800 kg/m³ crust; lid density on average 50 kg/m³ greater than 3200 kg/m³ asthenosphere. Density decreases linearlly with depth in mantle lid. These assumptions generally apply to the following figures when not explicitly restated

Slide 4

Left slide: Cartoon: Simple orogen thickened, now Lm (lid thickness) decreasing	Right slide: Lm and PE vs. elevation with addition of decreasing Lm curves

Step two of our simple orogen: post-orogenic thinning of mantle lid.

• Now have lid mechanically or thermally thin (Bird, Houseman et al. suggestion)
• Elevation continues to increase, but PE now increases
• PE eventually goes positive, allowing extension
• Note: steps one and two can overlap in time--done this way for simplicity.

Slide 5

Left slide: Cartoon: Orogen now extending	Right slide: Lm and PE vs. elevation with crossover to potential extension (delta-PE > 0) highlighted

• Continued thinning of lid increases delta-PE to exceed 0 (GPE exceeds reference structure), implying that internally-generated stresses are now deviatoric tensional.
• Note that crossover to extension occurs before lid returns to preorogenic thickness
• Note lithosphere weaker in extension than in compression, so relatively small positive PEs can drive deformation
• This is not new, but is a very simple analysis yielding clear picture of orogenic evolution.
• Can we consider more involved situations? YES. In particular, we can query this framework in specific ways.

Slide 6

Left slide: Cartoon of B&R over time: passive margin, thickening, early T, extension. Blue are passive margin sediments (Pz); green are allocthonous terrains, brown is pC basement (shading indicates greater thinning to left), yellows are T sediments. Oranges on left are the Sierran volcanic arc/ batholith.	Right slide: PE and Lm vs. elevation for three different crustal thicknesses. Assumptions as noted earlier on densities, etc.

• Review evolution of Great Basin:
  • Passive margin
  • Mz contraction
  • K - early T minor (?) extension at unknown elevation
  • Neogene extension; by late Pliocene at modern elevations
• From both the observed Mz thickening, Pz isopachs, and reconstructing Cz extension, crust was thick in early T
• Often said that elevation was low (< about 1 km)--what would this predict?
• Note from plot that 50-70 km thick crust at low (< 1 km) elevations has negative (often extremely negative! delta-PE)
• Such negative PEs are inconsistent with early T extension and seem unlikely to be corrected through edge force application.
• In fact, PEs are so negative that lithosphere could fail in compression.

Slide 7

Left slide: Strain rates for paleo-Great Basin setup Curves represent strain rate from PE for a specified rheology (discussed in more detail in Jones et al., 1996). Warmer colors = weaker lithosphere. PE estimated for scenarios in right slide by thick vertical lines above red arrows. PE line to left of a curve indicates that strain rate below range shown (note logarithmic axes). PE to right of a curve implies extremely rapid strain (probably would not reach this PE but would have started straining prior to this). Top panel is compressional stress, bottom is tensional stress (positive delta-PE, corresponding to the thin low elevation crust at right).

Right slide: PE and Lm vs. elevation with points in left slide marked

• What sort of strain rates might be expected?
• Low elevation, thick Great Basin (preextension) likely to contract
• Medium elevation (2-3 km) Great Basin probably will not deform
• Require higher elevation Great Basin to extend--depends on geotherm
• Note that this is similar to more sophisticated analysis of Sonder et al. (1987, I think) (but maybe more clearly illustrates importance of high elevation in this).

Slide 8

Left slide: Cartoon of geologic history of southern Rocky Mtns. Blue is Pz sediments, green is Mz (including K subsidence occuring between first two panels), yellow is T (mostly Laramide) basin fill.	Right slide: PE and Lm vs. crustal thickness for several fixed elevations

Consider Southern Rocky Mountains: (and a final Great Basin point)

• Look at things differently--what thickness of crust is consistent with a given elevation? (right slide)
• For Great Basin to be low (< 1 km) and extensional, crust has to be < 36 km thick (noting assumptions).
• Similar questions for Rockies, which had late Oligocene extension--were they high, too?
• Rockies had to have crust no thicker than about 40 km for them to be low (< 1 km) (giving a few km for denser crust)
• Thinner crust if any compressional stresses still being applied to edge.

Slide 9

Left slide: Strain rate plots for paleo-Rockies. Top is for thick crust at 500m (compressional), bottom for thinner (pre-Laramide) paleo-Rockies PEs (marginal compression?)	Right slide: PE and Lm vs. crustal thickness with points on left slide marked

• Modern strain rates for Rockies less than Great Basin
• What was required for Oligocene Rockies to have extension?
• Note that current crust at low elevation would have marginal contractional strain rates.
• Thin (pre-Laramide?) crust at sea level has no strain (even farther to left of curves than low modern crust).
• An interesting Laramide point: lowering elevation, especially if caused within mantle, lowers PE-> pushes lithosphere towards contractional failure--which might be the start of the Laramide. Recall too that without removal of lid thickening, localization of contraction will start a positive feedback loop (see Slide 3).

Slide 10

Left slide: Colorado Plateau cartoon; colors as in Slide 8 left.	Right slide: PE and rhom - rhoa plot vs. Moho depth, Lm fixed at 100 km, for 5 elevations

• How does absence of strong deformation fit in?
• Colorado Plateau:
  • 'cratonic' crust and sedimentation (with limited exceptions) to Cenozoic
  • contraction in Laramide, much less severe than to the east
  • uplift post-K, enigmatic timing
  • mid-T volcanism (cryptic crustal thickening?)
  • T hydration of mantle??
  • late Cz incision
• First, what is present stress state of lithosphere here?
• Note that our earlier work points to mantle as source of some support, but numerous studies of xenoliths suggest anomalous upper mantle
• So consider different mantle densities and see how that changes PE
• Use plot here to show how PE increases more for change in lid (here, decrease in lid density) than increase in crustal thickness, holding change in elevation fixed.
• Effects of altering lid density somewhat less than changing lid thickness.
• Thus if CP was elevated by lid density decrease (hydration), PE prior to uplift was probably negative.

Slide 11

Left slide: CP strain rates today	Right slide: PE/Lm against crustal thickness for elev=1800m, vary rho-c

• little modern deformation, but extensional except for local deviation
• tension is not coaxial with B&R
• discuss role of crustal density--could have changed with time...
• (Set up what mid-T might have looked like)

Slide 12

Left slide: CP strain rates for lower plateau, same crust	Right slide: PE/Lm against crustal thickness for elev=500m, vary rho-c

• Plateau at 500m elevation: now mildly compressional
• absence of significant strain rate implies that CP could transmit stresses before deforming; these additional stresses might bring strain rate up to Laramide rates.
• could only get extensional strain at these elevations with much thinner crust (crustal density won't do the job alone).
• Thus one possible route of investigation is to date oldest possible extensional features in CP--would date uplift.

Slide 13

Left slide: Points made	Right slide: Things to do

• This simple construct permits gross constraints from structure, tectonics, and elevation to interact and limit most unconstrained variables
• Simple calculations can rule out large classes of possible scenarios:
  • Low early Cz Great Basin with thick crust and tensional deviatoric stress
  • Low early T Rockies with modern crust and tension sufficient to drive small Late Oligocene basins
• Assumptions are not too restrictive: isostasy and ability to crudely bound density distribution in the mantle. Assumption of absence of external forces actually useful, for can determine sense of external forces needed to bring stresses in line with paleotectonics. Assumption of 1-D more troublesome, but for large areas probably ok.
• When considering impacts of elevation change on delta-PE, note that changes decrease in this order (i.e., d(delta-PE)/d(factor) for fixed elevation change decreases from top to bottom of the list):
  1. Change to lid thickness
  2. Change to lid density
  3. Change to crustal thickness
  4. Change to crustal density
• Also note that numbers on slide depend on lid structure (thinner lid decreases its importance).
• Future work:
  • internal consistency: properly relate thermal structure to both PE and strain rates so as to clearly isolate compositional variations from thermal effects.
  • 2-D: understand how PE forces turn into boundary forces on adjacent areas (initially modern day)
  • 2-D: understand role of vertically varying rheology (initially modern day)
  • self consistency: investigate further constraints from physically possible variations in thermal structure with time.
  • boundary forces: understand and include likely forces (edge and bottom loads) and find their limits soas to make constraints on past tectonics as tight as possible.

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