Transcript Flexural Isostatic Analysis of Loading (western U.S. example)

GEO 5/6690 Geodynamics
24 Oct 2014
Last Time: Flexural Isostasy
Isostasy is a stress balance resulting in ~consistent pressure
at “asthenospheric” depth. Airy isostasy balances vertical
stress (in columns) only; flexural isostasy balances
vertical + horizontal & is governed by a 4th order PDE:
 2 D 2w P 2w  gw  q
ETe3
For a perfectly elastic plate, D 
121  2 
and for multiple layers: D  D1  D2  Tetot  3 Te31  Te32

For top-loading, the PDE has linear solution (in amplitudes of
sines/cosines) of theform:


WT k  
0
D
  k 4
g
Read for Fri 31 Oct: T&S 105-130

HT k
© A.R. Lowry 2014
Next Journal Article(s) Reading:
For Monday Nov 3: Audet & Bürgmann (2011) Dominant
role of tectonic inheritance in supercontinent cycles.
Nature Geosci. 4 184-187.
Important to think about:
What are the possible reasons for a directional
dependence of Te? Also, read the abstract and
conclusions (and look at the figures) of:
Kirby & Swain (2014) On the robustness of spectral
methods that measure anisotropy in the effective
elastic thickness. Geophys. J. Int. 199(1) 391-401.
Problem: What if loads are both surface and internal?
• Total isostatic balance includes
surface (topographic) mass
plus internal mass variations
plus lithospheric stress
• Surface loads are undercompensated by subsurface
mass because of flexural
strength of the lithosphere
• Internal loads are undercompensated by surface
topographic response
If rigidity D and mean profile density of the lithosphere are known,
can solve for two unknowns (surface and internal load mass)
from two observations (gravity and topography fields)
Separation of loads is useful for:
• Estimation of lithospheric strength and rheology
(parameterized by effective elastic thickness Te)
• Understanding processes of mass redistribution in/on the Earth
Surface loading processes:
Internal loading processes:
• Erosion/exhumation
• Deposition
• Normal faulting
(footwall uplift)
• Reverse faulting
(hanging-wall thrust)
• Volcanic construction
• Thermal mass variations
• Compositional mass
variations
• Crustal thickening or
thinning by lower crustal
flow
• Cooled igneous intrusions
Example Applications of
Isostatic Analysis:
• Monday’s paper used separation of surface and
internal loads for the western US
• More commonly, Te is used to model surface
processes (e.g., surface response to some
“known” load such as basin deposition or
erosional mass removal)
• And of course Te has implications for strength
& rheology
Implications For Mass Flux Processes:
Surface Loads
• Erosion
• Deposition
• Fault
Displacement
• Volcanic
Construction
Subsurface Loads
• Thermal
Variations
• Lithologic
Variations
• Crustal Thickness
(Lower Crustal
Flow)
Gravity & Topography reflect a complicated mix of all mass
flux processes… But if we can separate the loads from their
isostatic response, it narrows the field of candidate processes.
METHOD:
Using equations for observed
topography h and Bouguer
gravity anomaly b plus:
 the definition of surface load
 gravity due to internal mass variation
 flexure of a thin elastic plate
gives 2 eqns in 2 unknowns:
Then search for Te (& perhaps
other parameters) that minimize
the difference between observed
& predicted coherence
Or equivalently, that minimize
correlation of the load fields
Elevation of the
Western U.S.
Cordillera?
Elevation of the actively
extending Basin and Range
province in the western
United States is
anomalously high (average
~1650 m) given the
anomalously thin (30–35
km) crust.
Why?
Possible reasons include:
• Hot lithosphere due to
rifting (stretching)
• Hot asthenosphere
(e.g., introduced by the
Yellowstone hotspot).
Lowry et al. JGR 2000
Surface Load
Topography:
• Dominated by normal and
thrust fault uplift features,
stress-supported rift flank
uplift, volcanically
constructed topo
• Uncertainties reflect
uncertainties in the
estimate of Te,
uncertainties in reference
density structure,
measurement error in
the original topo and
gravity
But mostly instability of
the matrix solution for
loading!
Crustal Mass
Contribution:
• Used “old” seismic
refraction data and
estimated mass variations
for both crustal thickness
variations and internal
density variations
• Note we need to know
Te to turn mass variation
(loading) into elevation!
• Uncertainties reflect
interpolation error,
uncertainties in seismic
velocity structure, errors
in regression of seismic
velocities to density
Conductive Thermal
Contribution:
• Note error (neglected crust):
Really should be ~30-50%
larger.
• Thinning of the thermal
boundary layer does
contribute to high elevation
but only partly explains
total elevation
 Uncertainties: interpolation
error, heat flow
measurement error,
heat production model,
thermal conductivity,
coefficient of thermal
expansion
Take:
Minus:
Equals:
Minus:
Minus:
Possibility we considered at the time:
Example: Tharsis Rise, Mars:
Martian topography is dominated
by (1) a north-south hemispheric
“crustal dichotomy” and (2) the
Tharsis rise, average elevation
5000 m covering 20% of the planet
The geoid is the shape of the
gravity field. The 2000 m geoid
anomaly over Tharsis is the largest
in the solar system!
The Tharsis Rise Loading Controversy:
Surface topography
constructed by volcanism?
[e.g., Willemann & Turcotte, 1982;
Solomon & Head, 1982]
Thermal/chemical buoyancy
of a single mantle plume?
[e.g., Sleep & Phillips, 1979; Harder
& Christensen, 1996; Harder, 2000]
Probably some combination of both!