Subduction
modeling
From 2D to 3D…
Subduction modeling
About the plate tectonics
 2D subduction model
 3D subduction model
 Future works

Subduction modeling
About the plate tectonics
 2D subduction model
 3D subduction model
 Future works

Plate tectonics
Plate
tectonics
Transform
boundaries
PlateDivergent
tectonics
boundaries
Plate tectonics
Convergent
boundaries
Plate tectonics
Convergent
boundaries
Collision
Subduction
Subduction modeling
About the plate tectonics
 2D subduction model
 3D subduction model
 Future works

First subduction model : 2D

Rectangle domain
Plate
Upper mantle
First subduction model : 2D

Lengths of the domain
Plate
660 km
100 km
Upper mantle
Lower mantle
3120 km
First subduction model : 2D

Boundary conditions
Plate
Upper mantle
Lower mantle
No slip
First subduction model : 2D

Boundary conditions
Plate
Free slip
Upper mantle
Lower mantle
No slip
First subduction model : 2D

Boundary conditions
Plate
Free slip
Upper mantle
Free slip
Lower mantle
No slip
Free slip
First subduction model : 2D

Boundary conditions
Plate
Free slip
No slip
Upper mantle
Free slip
Lower mantle
No slip
Free slip
Governing equations

Rayleigh-Taylor Instability: dense slab
sinks into a less dense mantle

v  0

    p  g
… conservation of mass, incompressible medium
… conservation of momentum
 vi v j
with    ij   

 x
 j xi
no energy equation




… deviatoric stress tensor
Rheology

Viscous mantle

Viscoplastic plate
mantle  const.
 creep

 yield
Viscous
 creep  2 creep e II


creep
creep
  yield 
  yield 
Plastic
 yield 
 yield
2e II
The software
Escript
Finley
Model setup : escript
 PDE solver : Finley

Tracking of the plate : level set method
 Visualization : Pyvisi, Gnuplot

The hardware

Altix @ UQ
2D subduction results
Velocity field : vortex
Lifecycle : initiation
Lifecycle : flow reorganization
Limits of the 2D model
Necessity of the third dimension
Importance of the mantle flow
 Real subductions have a limited lateral
extent
 Interactions on the lateral edges of
subduction zones

Subduction modeling
About the plate tectonics
 2D subduction model
 3D subduction model
 Future works

3D subduction model
Same governing equations
 Same tools used
 … only a different setup

3D subduction model
no upper plate
plate with subduction zone
upper
mantle
Box size: big enough,
for side walls to have little effect on subducting slab
The level set field
use level set to define and track
the subducting plate
subducting slab
only subducting part of the plate is included in the FE domain
Symmetry hypothesis
free slip
side boundary
assume symmetry: model only half of the domain
Bottom boundary condition
fixed bottom
boundary
higher viscosity in LM and phase boundary hinder convection
Slab boundary conditions
free slip
top boundary
fixed
end
plate fixed, to isolate effects of tearing and rollback
Edge of the slab
extreme case:
free slip
tear zone
Top boundary condition
plate bottom
fixed
Sides boundary conditions
Freeslip on
the sides
3D subduction results
Velocity field : toroidal flow
Lifecycle of the subduction
Initiation
Reorganization of the flow
Hinge position
Hinge
position
(km)
Time
(M years)
Hinge position
Hinge
position
(km)
Time
(M years)
Hinge rollback velocity
Hinge
rollback
velocity
(mm/year)
Time
(M years)
Hinge rollback velocity
Hinge
rollback
velocity
Initiation
(mm/year)
Time
(M years)
Hinge rollback velocity
Hinge
rollback
velocity
(mm/year)
Reorganization
of the mantle
flow
Time
(M years)
Hinge rollback velocity
Hinge
rollback
velocity
(mm/year)
2.5 mm/year
Steady subduction
Time
(M years)
Hinge from the top
20 My
40 My
60 My
80 My
Why arcs ?

Ping pong ball hypothesis
Why arcs ?

Toroidal flow
Inhomogeneities in the subducting plate
 Tear resistance on the edges

Subduction modeling
About the plate tectonics
 2D subduction model
 3D subduction model
 Future works

To be continued …
weak zone,
part of the
FE domain
fixed
normal case: tearing follows a pre-existing weak zone
subduction possible if slab strength > strength of the weak zone
First results
Thank you ! 
Hans Mülhaus
 Laurent Bourgouin
 Klaus Gottschaldt


… you for coming