u of m taras gerya eth– zurich paul tackley david yuen ja-ren lin ntu taiwan eth– zurich
TRANSCRIPT
U of M
Taras Gerya
ETH– Zurich
PaulTackley
David Yuen
Ja-RenLin
NTUTaiwan ETH– Zurich
(Stevenson, 1981)
(Stevenson, 1981)
ppv
D“
concepts observationsmodels
??? ???
(Stevenson, 1981)
1.Visco-elasto-plastic rheology2. Large deformation3. Free surface4. Spherical geometry
?
1.Visco-elasto-plastic rheology2. Large deformation3. Free surface4. “Spherical Cartesian” geometry
BASIC EQUATIONS
Stockes equation of motion
∂σij /∂Xj = ∂P/∂xi- ρgi, (1)
where σij = 2ηε ij, ε ij =1/2(∂vi /∂xj+∂vj /∂xi),
continuity equation
div(v) = 0; (2)
heat transfer equation
∂T/∂ t - ΔT⋅k⋅ρ-1⋅Cp-1 = ∂H/∂ t⋅ρ-1⋅Cp-1 - v⋅grad(T), (3)
where x - coordinates, m; v - velocity, m⋅s-1; t - time, s; σ - viscous stress
tensor, Pa; ε - strain rate tensor, s-1; P - pressure, Pa; T - temperature, K; η -
viscosity, Pa⋅s; ρ - density, kg⋅m-3; g – acceleration within gravity field, m⋅s-2; k
- heat conductivity coefficient, w m-1 K-1; Cp – isobaric heat capacity, J kg-1 K-1;
∂H/∂t – heat generation, w⋅m-3.
momentum equation
continuity equation
temperature equation
heatflow
material
flow
ρCp[(T/t) + vi(T/xi)] = [k(T/xi)]/xi + (H/t)
400oC800oC
1200oC
200oC
400oC
600oC
800oC
1000oC
1200oC
400oC800oC
1200oC
200oC
400oC
600oC
800oC
1000oC
Numerical model : 1600 x 600 km
400oC800oC
1200oC
1400oC
Weak zone
Lithosphere
Asthenosphere
1600oC
Mantleplumeupwelling
Slab push
Slab pull
1400oC
Gerya & Yuen (2007)
Gravity vector amplitudeGravity potential
gz gx
Gerya & Yuen (2007)
Planet3300 kg/m3
1021 Pa s
Continents3000 kg/m3
1020 Pa s„Space“ 1 kg/m3
1018 Pa s
The End
pressure
MODEL 1
MODEL 1
MODEL 1
MODEL 1
MODEL 1
MODEL 1
MODEL 1
MODEL 1
MODEL 1
Transient deviation
from sphericity
MODEL 1
Transient deviation
from sphericity
MODEL 1
Transient deviation
from sphericity
MODEL 1
Transient deviation
from sphericity
MODEL 1
Transient deviation
from sphericity
MODEL 1
Transient deviation
from sphericity
MODEL 1
MODEL 1
MODEL 1
MODEL 1
MODEL 1
The End
MODEL 1
(This study)
(Stevenson, 1981)
(This study)
(Honda et al., 1993)
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
MODEL 4
The End
MODEL 4
(Stevenson, 1981)
(This study)
(This study)
(Honda et al., 1993)
MODEL 7silicate
metal
primordial
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
MODEL 7
The End
MODEL 7
Gerya & Yuen (2007)
(Stevenson, 1981)
(This study)
(This study)
(Honda et al., 1993)
Senshu et al. (2002)
silicate
metal
primordial
The End
(Stevenson, 1981)
(This study)
(Honda et al., 1993)
(This study)
The End (not really...)
Planetary reshaping is controlled by distinct type of tectonics that is SHELL TECTONICS:
1. Soft shell tectonics = viscous deformation
• 2. Hard shell tectonics = plastic deformation
3.To be continued
Ja-Ren LinPhD project: