Download Mechanisms of Shear Zone Localization on Modern Earth, Early

www.sci.monash.edu
Challenges in Earth Modelling
(Plate tectonics, Subduction … )
www.moresi.info
L!" Mor#i et al
Moresi
1
Plate Tectonics
The grand challenge of understanding plate tectonics — “The grand unifying theory of
everything in Geology” — the great systematising framework for global data.
But it’s not a global theory
Continental deformation is not plate like
Mantle motion is tangential
Early Earth ?
And it has insubstantial dynamic underpinnings
How does the Earth’s heat engine produce plate tectonics ?
How did it begin ?
Why do we see no other examples & what should we look for anyway ?
Computational modelling and simulation as a key tool
What constitutes plate tectonics / subduction ?
Integrating observations
What does success in modelling look like ?
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Modelling or Simulation ?
What is the difference ?
Models are about developing an understanding of basic processes and exploring how these play
out in potentially complicated interactions.
Simplification
Interacting processes
Weighting effects / identifying principle components
Looking for what can be ignored
Simulations are about reproducing what happened and predicting what might happen in given
scenario
Fidelity to observations
Assimilating data constraints
“Prediction” or Forecasting
Understanding uncertainty
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Ingredients for global models with plates
Combine understanding gained from
kinematics and reconstruction with dynamic
modeling
Kinematics
Pattern evolution (“rules of plate tectonics”)
Far-field surface velocities
Dynamics
Mantle evolution
“Rigid” plate interiors (near-surface constraint)
Appropriate failure models for distinct
boundary types (different small-scale physics in
each case)
Constitutive models for distinct plate boundary
types (different small-scale physics in each
case)
Continental rheology distinct from oceanic
Cratonic lithosphere preservation !
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Multiple coupled phenomena
Rheology / constitutive laws
Non-linearities (including plasticity)
Elasticity
Damage
Anisotropy!
Magmatism
Heat transport
Compositional Evolution (crust / continents / deep anti-continents)
Rheology
Atmosphere / Hydrosphere / Cryosphere
Physical / Chemical interchanges
Interactions across surfaces / entrainment
Geomorphology & Landscapes
Formation
Contingencies of accretion
Heat / Element budgets
Core dynamics
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Integrated Earth modelling
Seismic sections and
interpretation
Evolution of basin
structure
Basin subsidence &
stretching models
Surface erosion and
sediment transport
3D tomography
and seismicity
mantle instabilities
reconstructed plate
margins
subduction zone
thermal and
mechanical evolution
simulation & data
grid infrastructure
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Plate tectonics — a multi-scale / multi-physics* problem
*In the sense of Earnest Rutherford
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Ingredients #1 — non-linear softening !
Figure 1: Stress v. Strain-rate relation of equation (7) for ye
viscosity of equation (6) with various values of the power-law
index.
Softening —!Bercovici, 1993
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Velocity
Vrms
Viscosity
Ingredients # 2 — History / material tracking
Width
Nusselt Number
Lenardic et Kaula, 1994 - Self Lubricated Mantel Convection: models in two dimensiones
History dependence —!Lenardic & Kaula, various papers 1993-4
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Plate boundaries
Compare transform boundaries with spreading centres:
Macroscopic element
deformation not parallel to
micro-scale deformation
Micro-scale deformation
deformation approximately
represented by macroscopic
element deformation
Constitutive law at plate boundary scale is going to be different for each
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Boundary evolution is not isotropic at macro scale
E
Kinematic / reconstruction model provide very strong!
geometrical “constraints” at the large scale which
require that stress and strain-rate are, at the least, not
coaxial — i.e. there is a change in constitutive-law
symmetry from one scale to the next
A
D
Dynamic model
ij,j
ij
B
= g⇢0 ↵T
= ⌧ij
p
⌧ij = ✓ij
(I)
✓ij
= 2⌘
C
ij
⇧ijkl ✓kl
e↵,(I)
T,t = T,ii
i3
t
ij,j
e↵,(I)
Dij
E
τ
Viscoelastic
stress prediction
Plastic correction
to yield surface
ui T,i + Q
|D|
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Strain-dependence of lithospheric deformation
This is a simulation of continental crust being !
stretched in response to far field stresses !
imposed by plate motions.
At modest strain, the deformation will often localise onto faults which can be very long-lasting
structures; very fine scale in width, but with large lateral dimension and relatively weak.
time
The history dependence of shear deformation is tractable if we use a Lagrangian frame.
active
"fault"
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Fixed mesh with moving “particles”
Regular Eulerian mesh for !
momentum equation (efficient solvers)
Lagrangian reference frame for:
Stress
Underworld Material point method
! y (!0 )
! y (")
Viscoelastic
B
A
C
Material not destined to be in
shear band
D
Shear band material
Compositional tracking
Stress-history tensor
Strain
Plastic strain history (scalar / tensor)
Finite element formulation
robust, versatile
very simple to go back and forth between!
particle and mesh representation
KE =
!
KE =
∑ w p BTp (x p )C p (x p )B p (x p )
ΩE
B T (x)C(x)B(x)dΩ
p
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Lagrangian History & Efficient Fluid solvers
In the material point method we can keep a mesh which is computationally efficient for diffusion-dominated
problems (including Stokes flow) and material points — a.k.a. particles — for tracking history variables.
!
!
!
!
This is the technique implemented in Underworld (and other similar codes) and leads to a very natural approach to
many “difficult” issues in geological thermal / mechanical models (www.underworldproject.org)
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Lagrangian History & Efficient Fluid solvers
In the material point method we can keep a mesh which is computationally efficient for diffusion-dominated
problems (including Stokes flow) and material points — a.k.a. particles — for tracking history variables.
!
!
!
!
This is the technique implemented in Underworld (and other similar codes) and leads to a very natural approach to
many “difficult” issues in geological thermal / mechanical models (www.underworldproject.org)
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Is subduction always “classical”, “textbook” ?
The Australian accretion of the VanDieland
microcontinent resulted in the terrane being deeply
embedded in the over-riding plate and left largely
undisturbed since then.
Evidence of rotations in present day structural grain (from
potential fields, paleomagnetism and other indicators).
Moresi, L., Betts, P. G., Miller, M. S., & Cayley, R. A. (2014). Dynamics of
continental accretion. Nature. doi:10.1038/nature13033
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Congested subduction zones
Importance of continental crust
Mason et al, 2008, Betts et al, 2012, Moresi et al, 2014
showed how trench motion and!
slab configuration are influenced by!
buoyant material colliding!
with a subduction zone.
raised question: how does!
subduction continue after!
accretion of one terrane ?
How does a microcontinent / !
plateau switch to the !
over-riding plate ?
This is important at many !
different scales.
!
Can we understand!
this process better and can !
we apply this to understand places!
where accretion is complete ?
17
Subduction — plate scale models with material history
What can we learn about subduction from simple models ?
Underworld — finite element models with tracking of small-scale physics
Highly parallel code for modern petascale machines
Open source / based on open libraries (StGermain and PETSc)
Checkpointed and so forth
Adopted child of CITCOM
Moresi, Betts, Miller, Cayley,
Dynamics of continental accretion.
Nature, 2014, doi: 10.1038/nature13033
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Model setup using UNDERWORLD
Layer 1 density accounts for ~7km oceanic crust (but not phases changes during subduction)
Layer 1 yield strength is (very) low to account for (unresolved) near-surface faulting, entrainment
of sediments into the plate boundary &c
Viscosity is truncated after averaging (to 105 x asthenosphere)
Layer 3 has significant strength for 80 Myr old lithosophere. In some models this layer yields too.
Continental Ribbon material replaces layer 1 and layer 2.
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2D thinking is misleading !
35 Myr
In 3D a small buoyant block is easily accreted or
eaten by the subduction zone. How about a large one ?
45 Myr
55 Myr
65 Myr
70 Myr
80 Myr
How does the slab recover from accretion with break-off / windowing ?
What should we look for in the superficial geological record ?
What happens for a large terrane / microcontinent ?
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Building a mountain belt
21
Like a swan, the motion is driven from below
Older & Stronger
Moresi, Betts, Miller, Cayley,
Dynamics of continental
accretion.
Nature, 2014, doi: 10.1038/
nature13033
Younger & Weaker
22
Deep embedding — and the mechanics of oroclines
A’
Over-riding Plate
A
Oceanic Plate
Margin!
shortens
and bends
The slab rolls back in two different directions (doesn’t need
to stretch / tear to do this)
There is no plate boundary along A-A’ so any convergence not
accommodated by rollback results in indentation
Pinning at the end of the indenter supplies the lateral loads that
result in lateral transport of material along the margin and bending.
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Where is the arc ?
Trajectories during lateral
subduction — almost pure rollback
creates dangling slab
A
A’
A
0
A'
19 Myr
100
22 Myr
23 Myr
200
26 Myr
0
Plan View
300
500
1000
400
A
Trench parallel
location
Depth (km)
15 Myr
500
600
2500
3000
3500
A'
2000
2500
3000
2000
2500
3000
3500
4000
4500
4000
4500
Trench perpendicular location
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Terrane accretion is a witness to bendy subduction
55 Ma
45 Ma
RES?
PAC
YAK
TZ
SL
KULA
PAC
FAR
FAR
PAC
PAC
Hudson
Bay
Present
20 Ma
A
AD
N
CA .S.
U
PAC
JdF
PAC
JdF
PAC
PAC
25
Terrane accretion is a witness to bendy subduction
Terrane accretion may be
complicated but we can still observe:
Bro
Plate boundary changes
ok
Range
Accretion repeats
Docking is messy
s
Kalta
g
Fault
Ti
n
tin
Yukon-Tanana
NFF
Denali
Oroclines are part of the story
Alask
a
Ra
Upland
a
ng
e
Fa
Fau
lt
ul
t
Selwyn
basin
Fa
ul
es
t
F
BS
g
an
R
TF
Ca
ss
iar
der
Bor
rra
ne
ika
ch
Ke
CSF
KF
ugh
tro
Subduction zones must recover from
accretion for repetition to occur.
te
Z
CS
een
TkF
Qu
MT
arl
Ch
e
ott
t
ul
Fa
YF
Kootenay
terrane
F
FR
Does subduction actually step back
(re-initiate from scratch) in a 2D
sense or does this re-adjustment
require a 3D way of thinking ?
SR
PF
200
0
km
Figure 1. Terranes of the Canadian-Alaskan Cordillera. Inset shows terrane groupings and tectonic realms.
Colpron, M., Nelson, J. L., & Murphy, D. C. (2007). Northern
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Cordilleran terranes and their interactions through time. GSA Today.
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26
Pattern that repeats in the modern Earth
Z.-H. Li et al. / Earth and Planetary Science Letters 380 (2013) 98 111
map of the eastern Alpine Himalayan belt (modi ed from Hatzfeld and Molnar, 2010; Yin, 2010; Xu et al., 2012). Th
The red color indicates the continental collision zones. The blue color represents the lateral extrusion blocks in the ov
movement of continental plates and the extrusion of the overriding continental rocks in the Eurasia- xed reference fram
McClusky et al., 2000; Wang et al., 2001; Vernant et al., 2004; Zhang et al., 2004; Reilinger et al., 2010). MS: Mediterrane
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The state of the art today
Aspect
(Manual)
Models reproduce localised plate boundaries
Can follow evolving geometry
Looking at adaptive meshing for small-scales
Physics + chemistry
Reaching towards coupling !
surface / hydrosphere / atmosphere
User friendly ?!
ASPECT
Advanced Solver for Problems in Earth’s ConvecTi
Preview release, version 0.4.pre
(generated from subversion: Revision : 2273)
Wolfgang Bangerth
Timo Heister
with contributions by:
Markus Bürg, Juliane Dannberg, René Gaßmöller, Thomas Geenen, Eri
Kronbichler, Elvira Mulyukova, Cedric Thieulot
Underworld 2
Stag
Rhea (Burstedde et al)
SC 2010
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The “flying car future” — 20 years
Unrecognisable environments —
unlimited resources
unlimited streams of data
unfamiliar ways to interact with models and data
Algorithmic priorities will be very different
Assume any equations can be solved efficiently at sufficient resolution (?)!
( We are much less neurotic about loop unrolling etc than we were — let’s not look back ! )
Composing at the conceptual level of datasets / modelsets rather than operations
“A Model” will be an ensemble of models of today’s definition
To propagate errors, uncertainties etc, it is much better to think of a single model being a whole swarm !
of individual realisations
We can create metrics and comparison operators with this approach
Models (ensembles) will be richly tagged with evolving metadata
Google-style searches on models will be trivial!
( We probably couldn’t imagine how to automatically !
search text for arbitrary concepts 20 years ago )
Libraries / Catalogues of models will be possible / searchable given!
metrics etc!
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