Geodynamics
Day
Lecturer
Lectures
2
BB
Temperature in the mantle
3
BB
Governing equations and approximate solutions
4
CLB
Numerical, analytical and laboratory models
5
CLB
Plates, slab and subduction
6
CLB
Plumes, hotspots,transition zone and CMB
9
CLB
Geological Constraints
10
BB
Composition and origin of the core
11
BB
Governing equations and the geodynamo
12
BB
Thermal and dynamical evolution of Earth's and planets
Numerical, Analytical
and Laboratory Models
Lecture 4: Geodynamics
Carolina Lithgow

Bertelloni
FAULTS!
Large range of Time

& Length

Scales
Mass

Momentum

Energy

Non

linear
What is right Constitutive Relation?
[
Tackley,
1999]
Governing Equations
Approaches
Static Processes
Dynamic Processes
Experimental

Laboratory
Observational

Modeling
Theoretical

Numerical Simulations
Present
Past
Problems in Mantle Geodynamics
Understanding Earth and Earth

like planets
Sources of energy: internal vs. basal heating
Constitutive law: How to make plates
Scales of flow: plates, plumes
Phase transitions and their effect
Layering: what happens to slabs
Heterogeneity: scales, nature, origin
Destruction of heterogeneity: mixing
Understanding Earth history
Present

Day
Gravity, Plate Motions (driving forces), Deformation
History
Past plate motions (driving forces), rearrangements
Thermal evolution
True Polar Wander
Geochemical variations
Plate Tectonics
Mantle Convection
[
Zhao et al
., 1997]
Mantle Convection and Plate Tectonics
[
Turcotte and Oxburgh
, 1967]
Plumes
[
Whitehead and Luther
, 1975]
How to construct a numerical model?
Numerical methods for PDE’s
Spectral, Finite element, Spectral element
Flexibility
Grids (geometry, adaptability)
Resolution
Material property contrasts
Speed!
Regional vs. Global
Boundary conditions
Resolution, Speed
Nature of problem
Inputs
Material properties (from mineral physics)
,
,
as a function of
Rheology (viscosity, but not only)
As a function
P dependence requires compressibility
Energy sources (from geochemistry, and …)
Rate of internal heating
Basal heating (heat flow coming out of the core)
Chemical Composition (from geochemistry in a broad sense)
Difficulties
Choice of rheological law (does it matter?)
Olivine rheology?
Making plates, asymmetric subduction
Lithosphere and mantle hard to treat together(Lagrangian vs Eulerian)
Full thermodynamics
Phase transitions (including melting)
Mixing
Tracer methods (substantial differences!)
Other methods better?
Characterizing mixing
[from
Louis Moresi
]
Recent Work
Mantle
Circulation
Model?
Slabs and Plumes: regional models
Geochemical
heterogeneity
[
Farnetani et al., 2002
]
[
Zhong et al.
, 2000]
[
Billen, 2004
]
Making plates
[
Bercovici
, 2003]
[
Tackley
, 2000]
Dynamics and chemical heterogeneity
[
Xie and Tackley
, PEPI, in press]
Why do experiments?
Fluid
dynamics
is
studied
both
theoretically
and
experimentally,
and
the
results
are
described
both
mathematically
and
physically
.
The
phenomena
of
fluid
motion
are
governed
by
known
laws
of
physics

conservation
of
mass,
the
laws
of
classical
mechanics
(Newton's
laws
of
motion),
and
the
laws
of
thermodynamics
.
These
can
be
formulated
as
a
set
of
nonlinear
partial
differential
equations,
and
in
principle
one
might
hope
to
infer
all
the
phenomena
from
these
.
In
practice,
this
has
not
been
possible
;
the
mathematical
theory
is
often
difficult,
and
sometimes
the
equations
have
more
than
one
solution,
so
that
subtle
considerations
arise
in
deciding
which
one
will
actually
apply
.
As
a
result,
observations
of
fluid
motion
both
in
the
laboratory
and
in
nature
are
also
essential
for
understanding
the
motion
of
fluids
.
Scaling analysis makes it possible to infer when two geometrically similar situations

of
perhaps quite different size and involving different fluids will give rise to the same type of
flow. Same Ra, ~ same Pr and you are in business.
For the Earth (why not just numerics?)
Benchmarking, reality check
Parameter Range (the higher the Ra #… the greater the resolution)
Large rheological variations
Thermochemical convection
Mixing
New physical phenomena?
Plumes and Entrainment
[
Jellinek and Manga
, 2002]
Slabs and trench rollback
[
Kincaid and Griffiths,
2003]
FAULTS!
Large range of Time

& Length

Scales
Mass

Momentum

Energy

Non

linear
What is right Constitutive Relation?
[
Tackley,
1999]
Governing Equations
Instantaneous Flow
Mantle Density Heterogeneity Model
[
Hager & O’Connell
, 1979]

Induced Viscous Flow

Can be solved analytically
For a spherical shell

Predict: Radial Stresses
Dynamic topography
Based on Geologic Information

Plate Motion History
Seismic Tomography

Convert velocity to density
[
Lithgow

Bertelloni and Richards,
1998]
[
Masters and Bolton
]
Geoid and Viscosity Structure
[
Forte and Mitrovica, 2001
]
Plate
Motions
[
Conrad and Lithgow

Bertelloni, JGR, in PRESS
]
Anisotropy
[
Gaboret et al.
, 2003; see also
Becker et al
, 2003]
Deformation
[
Lithgow

Bertelloni and Guynn,
2004]
Lithospheric Stress Field
Contribution from Mantle Flow
Past, Present and Future
What have we learned?

Mantle and Plates are an intimately coupled system

Deep mantle structure is important for the surface

Geological information provides quantitative constraints

Mixing is complicated!
Where are we now?

Circulation models

Generation of plates with exotic rheologies

Making real subduction zones!

Modeling isotopic and petrological heterogeneity

Modeling of observations in simple contexts (complications)
Where are we going?

Self

consistent modeling of mantle flow and lithospheric deformation

Connection to surface processes (sea

level; climate)

Understanding deep Earth structure and consequences
(seismology via mineral physics)

Feedback between geodynamic models and tectonics
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