Dynamics and Composition of the
Mantle: From the Atomic to the
Global Scale
Day Lecturer
Lectures
2  CLB
Mantle Flow- Deformation; Fluid Mantle
2 CLB
Mantle Flow- Governing Equations; Theory and applications
Tutorial 2: Modelling the geoid and dynamic topography
3 CLB
Geoid and Dynamic Topography
3 CLB
Dynamics of Plate Motions
Tutorial 2: Modelling the geoid and dynamic topography (continued)
Gravity from Grace
Geoid from Goce
Review of Basic Principles
Gravitational Potential
point mass
Earth’s Geoid
Geoid Anomaly
Earth
R
ΔN (θ,ϕ ) ~
∫ Δρ(r,θ,φ )rdr
0
Self-gravitation
€
Deflection of upper surface represents a mass deficit
that opposes mass excess of sphere. Amount of
deflection depends on viscosity structure.
Downward deflection of core-mantle boundary also a
mass deficit
Geoid Anomaly
δρ( r,θ, φ ) = ∑ Dlm ( r)Ylm (θ, φ )
l,m
R
δN lm (θ, φ ) =
∫ G(r,l)D (r)dr
lm
0
Earth
Formally separate structure (Dlm) and dynamics (G)
€
Green s function or Kernel G(r,l) is the geoid
anomaly due to a unit density anomaly of
wavelength l at depth r
G depends on viscosity structure. Compute
separately.
Geoid Anomaly
δρ( r,θ, φ ) = ∑ Dlm ( r)Ylm (θ, φ )
l,m
R
δN lm (θ, φ ) =
∫ G(r,l)D (r)dr
lm
Earth
0
Dynamic topography
Geoid Kernel
€
Standard η structure
LM~50xUM
Panasyuk et al. (2000)
Geoid from Goce
So now what?
Seismic Tomography- Convert velocity to density---- BUT HOW?!
[ Masters and Bolton, 1998]
Mantle Density Heterogeneity Model
Based on Geologic Information-Plate Motion History"
Depth = 1000 Km
[ Lithgow-Bertelloni and Richards, 1998]
Velocity-Density Scaling
Birch s law
δv=aδρ
Factors=0.1-0.5 g s/km cm3
[Stixrude and Lithgow-Bertelloni, 2005]
Velocity-Density Scaling
Rρ / S
$ δ ln ρ '
=&
)
% δ lnVS ( Depth
If due to lateral T variations:
Rρ / S
$ ∂ ln ρ ' $ ∂ lnVS '−1
=&
) &
)
% ∂T ( P % ∂T ( P
Attenuation (anelasticity)
decreases value significantly
Claim: Cannot be negative
Not so! (phase transformations)
$ ∂ ln ρ ' $ ∂ ln ρ '
$ ∂ ln ρ ' $ ∂n '
&
) =&
) +&
) & )
% ∂T ( P % ∂T ( P,n % ∂n ( P,T % ∂T ( P
[ Karato and Karki, 2001]
n¼
!
R¼
!
A
met
the three prominent sets of peaks in αme near 410,
520, and 660 km depth. Assuming typical values ⟨ρ⟩ =
Velocity-Density Scaling
[Stixrude
and Lithgow-Bertelloni,
2007] velocity ξ (red)
Fig. 8. Relative variations
of density
and shear wave
and the isomorphic contribution to ξ (blue) compared with the results
A
A
where t
include
the isom
able va
transfo
contrib
consiste
region
negativ
to garn
variatio
Estimating the Locations and
Densities of Mantle Slabs
!Drop plates into the mantle at
! regions of convergence
After Lithgow-Bertelloni and Richards [1998]
Direct Comparisons: Using Past Tectonics
[Replumaz et al., 2004]
[Voo et al., 1999]
Predicted Geoid
from Slabs
Best fitting viscosity structure
Lithosphere-10 * UM
Lower Mantle-50 * UM
Predicted Geoid
from Tomography
Viscosity Structure: Robust?
[Forte and Mitrovica, 2001]
100000
10000
1000
100
10
1
0.1
0.01
0.001
0.0001
Preferred Viscosity Structures
P & S differences
Weak vs Strong TZ
KWH98b
KH01
Slab
TXBW
P20RTS
S16U6L8
J362D28p
li
SB10L18b
MNDMEH04
GHW97s
WE1997s
SPRD6p
S20RTS
J362D28s
tr
BDP98
SB10L18p
KWH98s
MK12WM13b
SPRD6r
SAW24B16
S362C1
BSE98
WE1997p
SB10L18s
MK12WM13p
MK12WM13s
SKS12WM13
KWH98b
lo
GHW97p
WEPP2
SB4L18
P16B30
S16B30
SPRD6s
Lateral Viscosity
Variations
Çadek and Fleitout (2003)
Flow layering and boundary conditions
[Cadek and Fleitout, 1999]
Dynamic Topography
h=- τr/δρg
h
τr
Mantle Flow
ρ1
ρ2
Topography
Global Dynamic Topography
26
Continents"
[Lithgow-Bertelloni and Silver, 1998]
Thursday, December 4, 2008"
Edinburgh-2008"
Oceans"
CIDER-KITP
July 13, 2004
[Conrad, Lithgow-Bertelloni and Louden, 2004]
Basin Subsidence
Caribbean Plate
Cocos
Plate
(a)
12 Ma
0º
onas
NAB
Amaz
Shira Mountains
Fitzcarrald
30 Ma
Nazca Plate
SAB
60 Ma
Sierras
Pampeanas
32º S Fernandez R.
Juan
35 Ma
R.
12 Ma
Antarctic Plate
2 cm/yr
Fig. 3b
Atlantic
Patag
onia
Ch
ile
Pampas
Na
zc
a
R.
/yr
7-9 cm
80º W 24 Ma
Depth (km)
(b)
Scotia Plate
50º W
Peruvian
flat slab
Argentine
flat slab
0
-500
-1000
-40 -35
-30 -25
-20 -15
-10
-5 -0
5
Longitu
de
-60
50
-64
-68
40
-72
30
-76
-80
de
titu
La
20
10
3
0 kg/m
Effect of density and morphology
10°
0°
13º SL
20º SL
32º SL
40º SL
- 10°
- 20°
- 30°
- 40°
Dynamic topography (m)
Subduction with 30º (Cenozoic model)
(a)
400
0
800
1200
1600
2000
400
800
1200
1600
- 50°
Distance from trench (Km)
400
40º SL
32º SL
13º SL
20º SL
- 60°
- 90° - 80° - 70° - 60° - 50° - 40° - 30°
Flat slabs
Normal slabs
0°
- 10°
Flat slabs
- 20°
- 30°
- 40°
Dynamic topography (m)
Present day model with flat slabs
10°
400
Distance from trench (Km)
400
0
400
800
800
1200
1600
2000
32º SL
13º SL
40º SL
1200
1600
20º SL
- 50°
- 60°
- 90° - 80° - 70° - 60° - 50° - 40° - 30°
- 1750 - 1500 - 1250 - 1000 - 750 - 500 - 250
0
250
500
Dynamic topography (m)
Dynamic topography (m)
- 90° - 80° - 70° - 60° - 50° - 40° - 30°
Flat slabs cause uplift!
2800
SM
FA
Flat slabs
SP
Change of dynamic topogrpahy (m)
(b)
High
Andes
2400
Sierras
Pampeanas
2000
1600
1200
Residual
topography
at 32º S
13º S
800
32º S
SLAB FLATTENING
400
0
20º S
40º S
Pampas
-400
-800
Flat slab
segment
400
800
Residual
topography
Change of dynamic topography (m)
Data band
1200 1600 2000
Distance from trench (Km)
Flat slabs
Normal slabs
FA: Fiztcarrald Arch SM: Shira Mountains
SP: Sierras Pampeanas
Plate Driving Forces
Slab pull and Ridge Push
Primary driving forces
What is a plate?
ª Lithospheric Fragment Strong non-­‐deforming interior Diffuse plate boundaries? Narrow, weak, rapidly deforming boundaries Ridges-­‐passive SubducBon zones-­‐asymmetric Transforms? MoBon described by rotaBon ª Plate moBons Non-­‐acceleraBng Piecewise conBnuous velocity field in space and Bme Hard for fluid dynamics Significant toroidal moBon (I.e transform-­‐like) ª Part of convecBng system (top thermal boundary layer…) ConBnental plates Fluid Dynamics and Plate Tectonics
Piecewise Continuity in Space and Time
25-43 Ma
EU
AF
FA
IN
NA
PA
NZ
SA
AU
CR
PH
AN
43-48 Ma
GR
EU
AF
NA
FA
PA
IN
NZ
AU
CR
AN
PH
SA
Toroidal Motions
-Homogeneous convecting
fluid-No toroidal power
-Lateral viscosity variations
i.e. PLATES!
-But why? Dissipates no heat
-Ratio: Plate characteristic
m
∇ H •V = ∑∑ De yem
l
(
)
Horizontal divergence
(poloidal)
m
m
∇ × v • r = ∑∑Ve yem
l
m
Radial vorticity
(toroidal)
[Dumoulin et al., 1998]
Observed P/T Ratios
ª P/T power not equipartitioned
ª Reference Frames!
ª Toroidal power
ª Pacific basin (largely)
ª Oblique subduction
[Lithgow-Bertelloni et al., 1993]
How to treat plates?
ª Generating plates self-­‐consistently “Exotic” Rheologies with a physical basis ª Imposing Plate Motions Investigate scales of =low Construct mantle circulation models compare to seismology ª History of plate motions Past plate motions (driving forces) Plate Rearrangements Imposing plate velocities
[Zhong et al., 1998]
ª Study scales of flow in the mantle Do plates organize flow Suppress smaller scales (capture plumes?) ª Influence heat flow at the CMB? [Bunge and Grand, 2000]
Making plates: theory
ª Shear-­‐localizing feedback mechanisms required Broad, strong plate-­‐like regions Weak, narrow plate boundaries Toroidal moBon (almost transforms) Ridge localizaBon ª Physical basis? ª Many characterisBcs not reproduced SubducBon initaBon Asymmetry Temporal evoluBon and plate rearrangement [Bercovici, 2003]
Making plates: Advances
ª Melt viscosity reducBon key to Asthenosphere generaBon Localizing ridges BeTer plate-­‐like behavior Stability and no fragmentaBon ª Long-­‐wavelength heterogeneity [Tackley, 2000]
Subduction and Slabs
ª How do they start? ª Asymmetric Downwelling ª Seismically acBve to ~700 km (phase transiBons? ReacBvaBon of faults?) ª Cold-­‐-­‐-­‐-­‐-­‐-­‐> STRONG? ª Long-­‐lived ª VolaBle fluxing [Zhao et al., 1997]
How do slabs drive plate motions?
[Conrad and Lithgow-Bertelloni, 2004]
Estimating the Locations and
Densities of Mantle Slabs
!Drop plates into the mantle at
! regions of convergence
After Lithgow-Bertelloni and Richards [1998]
Computing Mantle Flow
CIDER-KITP
July 13, 2004
Mantle Tractions
[Lithgow-Bertelloni & Guynn, 2004]
Strength of Slabs
Half of viscous dissipation in bending and unbending?
[Conrad and Hager,1999]
If Slabs are Directly Attached to Subducting
Plates
Calculate Slab Pull Force:
As excess weight of upper mantle
slabs
Combined Model
Slab Pull from Upper Mantle Slabs
Slab Suction from Lower Mantle Slabs
Prediction of
Cenozoic Plate
Motions
• Estimate slab
locations through
Cenozoic.
• Predict Cenozoic
speedup of Pacific
basin.
Cenozoic Plate-Driving Forces
So far...
Plate velocities are best explained by:
Pull from Upper Mantle Slabs (~60%)
Suction from Lower Mantle Slabs (~40%)
Upper Mantle Slabs:
1. Are physically attached to
plates
2. Are supported by guiding
stresses within the slab
Lower Mantle Slabs
1. Are unattached to surface
plates
2. Are supported by viscous
stresses from the surrounding
mantle
Problems
• Pacific motion is too northerly
• South America is too stationary
• Nazca motion is too rotational
Does the pull force vary between subduction zones?
Some slabs may not be fully attached to plates
Slab Detachment
Which slabs must be
detached to produce
the best fit to plate
motions?
Best-Fit Slab Pull Model
Invert for the fraction of slab pull that
provides the best fit to plate motions
Comparison of Pull Models
Best-Fit Pull Model
!!
Observed Plate Motions
Equal Pull from all UM Slabs
Including other effects
[van Summeren, Conrad and Lithgow-Bertelloni, 2012]