Rheology of Earth

1
Rheology of Earth

• Evidences for an elastic lithosphere and fluid
  mantle

2
Evidence for elastic Earth

• Mountains! Lithosphere must be elastic
• Seismic waves propagation (mantle and
  lithosphere)
• Stress and strain on plate tectonics
• Flexure of plates

3
Hydrostatic compensation
For the parameters given in class
4
Gravity anomalies
From model EIGEN_GL04C (Forste et al, J.
Geod.,2007)
Long -wavelength (Lmax 10)
mgal
5
Gravity anomalies
From model EIGEN_GL04C (Forste et al, J.
Geod.,2007)
Lmax 200
mgal
6
Sea floor age
7
Plate velocities
From sea floor age, earthquake data, land
surveys, etc.
8
Plate velocities
Comparison with geodetic techniques (GPS, SLR,
VLBI)
9
World seismicity
10
Fault geometry
11
World stress map
12
World strain-rate map
red high, blue low
13
Strain accumulation
14
Strain release Earthquake
15
Strain rate San Andreas fault
16
Elastic flexure of lithosphere
Bending of the elastic lithosphere at ocean
trenches Turcotte et al., 1978, Tectonophysics,
vol 47, p193-205
17
Bathymetry vs elastic theory
Bending of lithosphere at ocean trenches
Mariana trench
Kuril trench
Turcotte et al, 1978
18
Bending of lithosphere at ocean trenches
Bathymetry vs elastic theory
Tonga trench
elastic
elastic-perfectly plastic
Aleutian trench
Turcotte et al, 1978
19
Bending of elastic lithosphere under the load of
island chainsfrom Watts Daly, 1981, Ann.
Rev. Earth Planet. Sci.
Elastic behavior of the lithosphere
20
Fluid mantle

• Required for driving plate tectonics
• Non-hydrostatic geoid anomalies
• Evidence from glacial isostatic adjustment (GIA)
  or post-glacial rebound

21
Gravity anomalies
From model EIGEN_GL04C (Forste et al, J.
Geod.,2007)
Long -wavelength (Lmax 10)
mgal
22
Post-glacial rebound
21 000 years ago
today
Image credit Seth Stein
23
Post-glacial rebound
Past history of continental uplift is constrained
by raised beaches and history of sea level
change
From Peltier, Ann Rev Earth Planet Sci, 1981
24
Post-glacial rebound
Todays rate of uplift can be measured be
geodetic techniques
25
Gravity signal from post glacial rebound
Static gravity field measured by GRACE
Time-dependent gravity field measured by GRACE
Tamisiea et al., Science , 2007
26
Idea

• Use post-glacial rebound observations to
  constrain past history of ice-sheets (important
  for climate models) and mantle viscosity profile
  (important for mantle convection models)
• Find a model of paleo ice-sheet and mantle
  viscosity that are able to reproduce past uplift
  history as well as current uplift, gravity and
  time-dependent gravity.
• Models take into account feedback between
  ice-sheet and sea-level changes, as well as
  feedback from changes in Earth rotation.

Goal
27
Change in Earth rotation from post-glacial rebound
By conservation of angular Momentum, rotation
rate should speed up
Non-axially symmetric rebound history change in
the location of rotation axis with respect to
fixed point at surface (true polar wander)
28
Secular change Tidal friction
Earths rotation is indeed slowing down at a
present rate of 0.0018 seconds per century
29
Lunar and solar eclipses recorded by ancient
civilizations
Babylon, solar eclipse of April 15 136 BC
China, lunar eclipse Sept 4/5 434 AD
Images from Stephenson, Astron. Geophys., 2003
30
Lunar and solar eclipses recorded by ancient
civilizations
Offset between predicted and observed
eclipse path when Earths rotation rate is
constant
from Stephenson, Astron. Geophys., 2003
31
Lunar and solar eclipses recorded by ancient
civilizations
Reconstruction of past Earths rotation rate
from Stephenson, Astron. Geophys., 2003
32
Lunar and solar eclipses recorded by ancient
civilizations
Reconstruction of past Earths rotation rate
From LLR difference with mean observed change is
from GIA
from Stephenson, Astron. Geophys., 2003
33
Change in Earths ellipticity
Observed changes in J2 (Cox and Chao, Science,
2002)
Decrease of Earths ellipticity due to GIA
34
True Polar wander
3.5 mas/yr in the direction of Greenland
35
Sea-level change
Peltier, Ann. Rev. Earth Planet. Sci., 2004
36
Inferred mantle viscosity
Tamisiea et al., Science, 2007
From Peltier, Rev. Geophys., 1998
37
Gravity signal from mantle convection
Static gravity minus GIA contribution mantle
convection
Static gravity
Tamisiea et al., Science , 2007