Download Postglacial Rebound & Mantle Flow

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Science searches for the true by tying to eliminate the untrue.
“It is a process of separating the demonstrably false from the probably true.”
[Lynton Caldwell]
Authentic science operates on the assumption that a concept can be shown to
be false. Falsification occurs when a concept either is shown to be logically
inconsistent or is demonstrated to run counter to direct observations.
Pressure, Isostasy, and Horizontal Forces
• Each column isostatic equilibrium has the same weight
of overburden at its base (equal pressure)
• If the mean densities and heights of each column are
different, there will be a net horizontal force on the
material (isostasy only reflects a vertical force balance)
h
Isostasy (same overburden at base)
leads to net horizontal force Ph/2

Ph
Flhs =
2
P
h/2
Frhs = Ph/4
2
P
How big?
• Continental crust is ~40km thick
• Continental shelves and their adjacent oceanic abyssal plains differ in
elevation by ~5-6km (5000m)
• Mean density of continental crust is 2800 kg/m3 (2.8Mg/m3)
• Pressure at base of continents (compensation depth) is 2800 kg/m3 x
10 m/s2 x 40,000m = 1.1GPa (1.1GN/m2)
• Net horizontal force F =1.1GPa x 5000m / 2 = 2.75TN
• Net horizontal stress associated with isostasy  = F/40000m = 0.07GPa
i.e. = ~2,500/40,000 (1/16) of the pressure at the depth of
compensation
• Implication: Lithosphere can elastically support stresses at least of
order 70 MPa (atmospheric pressure = 0.1 MPa, 700 times less). In
other words, crustal rocks do not typically creep under differential
stresses of order 700 atmospheres (and may be even stronger)
Earth’s Rheology: Visco-elastic
• Rock becomes viscous at depth (below lithosphere)
• Rock is elastic/brittle when cold (lithosphere)
F/A
u
D
Analogy to rock deformation:
Bragg’s bubble model
~1011
Pa (100GPa)
~1021 Pa-s (1ZPa-s)
Elastic
 ue  F
z A
ue = elastic displacement =
uv 
Viscous
 u&v  F t
z
A
DF  1 
A   
uv
DF  1 
 rate of viscous disp lacement =
t
A   
Earth’s Rheology: Visco-elastic
F/A
u
D
Analogy to rock deformation:
Bragg’s bubble model
Elastic
Viscous
 u&v  F t
 ue  F
z A
z
DF  1 
ue = elastic displacement =
A   
u
DF  1 
uv  v  rate of viscous disp lacement =
t
A   
A
u = ue +uv
u
DF  1 t 
 ,

A   
Main mechanisms for creep: Movement of
imperfections in crystal lattice (dislocations &
vacancies)
How do we know Earth’s mantle is viscous?
• Isostasy exists (implies underlying mantle must
flow to balance changes in crustal thickness/load)
— but no direct inference for how viscous
• Post-glacial rebound (Areas covered by icesheets
~12,000 years ago are still rising ~m/100yr. Also
see rebound from removal of large lakes and
mountain glaciers)
• Uniform plate motions measured by GPS (no
‘jerks’ in motion of plate interiors, implies ‘fluid’
movement with underlying mantle)
• At ~1200°C+ temperatures, rocks exhibit viscous
creep (flow) in laboratory experiments
Modern ice sheets (Antarctica)
Modern ice sheets
(Greenland)
Pleistocene ice sheets (North)
Evidence for Pleistocene ice
sheets (N.A.)
Pleistocene lakes (western
US)
Evidence for Pleistocene
lakes (western US)
Shoreline of Lake Bonneville
Postglacial Rebound
Shoreline of Lake Bonneville
PGR

Finland and Sweden are rising today

Holmström, 1869, pointed out that Sweden is rising with respect to the
Baltic (comparison of historic water levels in harbors).
In the 1800s it was noticed that
 Lakes and Canels in Finland rose (and rose faster near the W. Coast
than inland).
 Raised beaches were also remarked upon (e.g. Gotland)
Gotland
Finnland (1)
Sweden (1)
Sweden (2)
Isostasy - PGR
•
•
•
•
Nansen, 1928 - quantified the uplift rates of beachfronts in Gotland
(100 m in 10.000 years)
Daly, 1934 - suggested that postglacial rebound was the cause of this
Haskell, 1937 - quantified the uplift over an infinite halfspace mantle Van
Bemmelen & Berlage (1935) (Vening-Munesz, 1937)
used uplift history to suggest a weak asthenosphere layer above a more viscous
lower mantle
300m of uplift have already occurred in Fennoscandia, ~20m remains to be
uplifted to reach isostatic equilibrium.
Angermann Uplift
Ice vs. Time
Sealevel Rise
Daly
Postglacial Rebound (uplift
rates)
Shoreline of Lake Bonneville
Postglacial Rebound
Shoreline of Lake Bonneville
Why we know Earth can be viscous
(postglacial rebound)
postglacial rebound (cont.)
w
d
Velocity Gradient: W/d
W   h



Stress:
d d t
Upward ‘buoyancy’:   gh
  h  gh or  h  gd h  h


t
d t




  t  
h  h0e
 
gd
Flow Solutions
Horizontal
Velocity
Component
(at kx=Pi/2)
Depth
Depthkz
Vertical
Velocity
Component
(at kx=0)
Depth kz
Flow due to sinusoidal loading (view 1)
50%
kz
80%
90%
kx
Flow due to sinusoidal loading (view 2)
50%
kz
80%
90%
Depth of Flow
Flow Depth Depends on wavelength  of load (k = 2/):
50% of flow above kz = 1.68, i.e. z < 0.27
80% of flow above kz = 3,
i.e. z < 0.48
Depth
Depthkz
Vertical
Velocity
Component
(at kx=0)
Depth kz
What happens
to hot rising
blobs in mantle
convection?
asthenosphere
Once formed, what removes
an asthenosphere layer?
• plate accretion&subduction
• Slab dragdown
asthenosphere flow & entrainment
Pressure, Isostasy, and Horizontal Forces
• Each column isostatic equilibrium has the same weight
of overburden at its base (equal pressure)
• If the mean densities and heights of each column are
different, there will be a net horizontal force on the
material (isostasy only reflects a vertical force balance)
h
Isostasy (same overburden at base)
leads to net horizontal force Ph/2

Ph
Flhs =
2
P
h/2
Frhs = Ph/4
2
P
Dynamic Isostasy — Compensation of
Pressure effects of lateral flow

h w
a
d m

 P   -   g h


a
w
P
 P    -   g d
 m
a
Good depth vs. age fit of seafloor relief means that
dynamic topography must have a relatively small
effect on seafloor depth
(J. Sclater & coworkers, 1980s)
All oceans
depth vs. age
Ravine et al., in prep.
Effects of buoyant
asthenosphere
Lab Models
Numerical/Lab Comparison