Download Geodynamics

Geodynamics
Causes and consequences of plate
motion
Quantitative geodynamics
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Forces acting on the plates
Cooling plate model of the oceanic lithosphere
Stresses in the plates
Mantle convection
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Thermal convection
Rayleigh number
Convection in the Earth’s mantle
Geochemical evidence
Geophysical evidence
Heat transfer
• Heat provides the energy that drives all the
tectonic activity.
• Plate tectonics is ultimately driven by the
transfer of heat from the core and mantle to
the Earth’s surface
• Three main mechanisms of heat transfer
– Conduction
– Convection
– Radiation
Rappel (1)
Rappel (2)
Rappel (3)
Heat flow
Example of terrestrial heat flow
measurement
Example of terrestrial heat flow
measurement
Kelvin and the age of the Earth
Cooling of a conductive Earth
Continental heat flow
Crustal heat generation by
radioactivity
Crustal radioactivity
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Heat production (μW m-3)
Depends on composition
Crustal rocks (0.2 -> 3 μW m-3 )
Scale:heat production x thickness = heat flux
“Average crust” = 0.65-0.95 μW m-3
Oceanic heat flow
Surprise!
Sea floor spreading => Oceanic
lithosphere is cooling
Velocity scale
for heat transport?
Compilation of all oceanic heat flux
data, grouped by age
Heat flow should decrease with age!
Heat flow data are noisy because of
hydrothermal convection
In sedimented areas,
fractures are sealed,
the heat flux follows
the cooling model
Measurements on
very young sea floor
near the JdF ridge.
Away from
outcropping
basement, follows t-1/2
Measurements
in selected areas
for all ages
Follow exactly t-1/2 for sea
floor ages younger than
80My
Heat flux does not
decrease any more for
ages older than 80My
Is there a better way to see that
plate is cooling?
Sea floor bathymetry increases because
density changes as lithosphere cools
down?
Bathymetry fits the cooling plate
model -> 80Ma
Bathymetry vs age
But plates can be rejuvenated when
they pass over a hot spot
What about ages > 80 Ma
Global heat flow map
Energy Budget of the earth
• Continental heat loss
14TW
• Oceanic heat loss =
32TW (including
hotspots)
• Total = 46TW
• Crustal heat generation
6-8TW
• Mantle heat generation
12-14TW
• Cooling of the core 614TW
• Cooling of the mantle
must provide ~ 1022TW (16TW = rate of
cooling ~100 K Gy-1)
Stresses acting on the plates
• Plate boundaries
• Ridge push
• Slab pull
• Transforms
• Viscous drag at the base of the plate
Ridge push
Slab pull
Transforms. San Andreas thermal
paradox
• Friction along the fault
produces heat.
• Heat flux
measurements do not
show much heating
along San Andreas fault
• For mid-oceanic ridges
transforms, plate is hot
and ductile at shallow
depth.
Viscous drag
Summary
• Slab pull is the dominant force acting on
plates
• Ridge push may be important on plates that
include no subduction zone
• Transforms are probably negligible in first
order
• Viscous drag maybe variable
• Internal stresses are not always negligible
Stress indicators
• To determine the tectonic stress orientation
different types of stress indicators are used in
the World Stress Map. They are grouped into
four categories:
– earthquake focal mechanisms
– well bore breakouts and drilling induced fractures
– in-situ stress measurements (overcoring, hydraulic
fracturing, borehole slotter
– young geologic data (from fault slip analysis and
volcanic vent alignments
Intraplate stresses
Convection in the Earth
• Early model
proposed by
Holmes
• Radioactivity in
continents
cause heating
of mantle and
trigger
convection and
continental
breakup
Early plate tectonics models?
Debate on the organization of
convection
What drives the plates?
• Convection in the mantle, but many questions
are open:
– How is convection organized?
– Role of 670km discontinuity
– One or two reservoirs?
– Role of plates in mantle convection
– Hot spots, plumes, and convection
• Geophysics 1 – Geochemistry 1
Well organized cells?
• It was first thought that
mantle convection is
organized.
• Ridge = ascending
current
• Trench = descending
current
• Geometry of plates
shows that it must be
different!
Or is it more complicated?
With plumes feeding the asthenosphere?
Perhaps like this?
like a lava lamp!
Rayleigh-Benard convection
• Fluid heated from
below
• Important forces?
• Gravity
• Friction
Necessary (but not sufficient)
condition
• Temperature gradient
must be super adiabatic
• Adiabatic gradient in
mantle is ~ 0.5 K km-1
• It is achieved but…
• Condition is not
sufficient!
Forces acting on fluid
• Ratio of 2 forces is a
dimensionless number
• Reynolds number (Re) is
extremely small for Earth’s
mantle < 10-15. Inertia is
unimportant.
• Rayleigh number (Ra) is the
ratio of gravity forces that
maintain movement and
frictional forces that oppose
it
• If Ra is large, gravity rules
and convection occurs.
Another definition of Rayleigh number
• Ra = τconduction/τconvection
• If Ra is large, cooling by
convection is much
more efficient than by
convection
• τconduction= L2/κ for
mantle
• Τconvection = L / v (crude
estimate). Need to use
Ra definition
Critical Rayleigh number
• Convection possible when Ra >
critical value
• Depending on wavelength,
convection occurs or does not.
• Critical value depends on
geometry
• On the order 1,000
Viscosity of the mantle
Mantle viscosity
• Order of time constant can
be obtained from
dimensional analysis.
• It must depend on viscosity
and pressure differences in
mantle
• Viscosity = Pa s
• Pressure = Pa
• Time = viscosity/Pressure
• Exact form requires to write
down the equations.
Rayleigh number for the mantle
affects the form of the convection
Increasing Ra
670 km discontinuity?
Isotope tracing
• Crust is enriched in Rb
relative to mantle
• Crust is depleted in Sm
• Sr87/Sr86 increases faster in
crust than mantle
• Nd143/Nd144 increases faster
in mantle
• Negative correlation
• Model age (age of
extraction from mantle
reservoir)
What about mantle convection?
Isotope geochemistry shows different
mantle sources for magmas
• MORBs are depleted
relative to OIBs (source
of hot spot in lower
mantle?)
• OIBs are very
heterogeneous
• More isotopic systems =
more reservoirs
With Pb isotopes, the mantle contains
many reservoirs
Thank God, we have geophysics!
Seismic tomography shows lateral variations in
velocity (due to temperature?)
• Interpretation of seismic tomography in the
mantle is that velocity differences are mostly
due to temperature differences
• For the same pressure and composition,
higher velocities imply colder rocks
Tomographic images of subduction zones show
the slab penetrating in the lower mantle
One alternative model?
• Lava lamp model was
popular because it allows
two reservoirs not
separated by 670
discontinuity
• It solves the problem of
missing heat sources (the
MORB source is too
depleted in radioelements).
• Thermal and compositional
effects cancel, so it cannot
be tested
Conclusions
• Geochemistry suggests mantle not very well
mixed
• Seismic tomography shows 670km
discontinuity is not a barrier for convection
and mantle may be mixed
• Models of mantle convection
• Avalanches? Intermittent mixing. (see also some of the
tomography).
• Lava lamp type of model?
Summary
• Stress at plate boundaries.
• slab pull is the largest
• large enough to drive plate motion
• Mantle Ra >>> critical
• Lithosphere is thermal boundary layer (conduction vs
convection in the mantle)
• Geochemistry sees compositional heterogeneities
• Geophysics sees mostly temperature differences
• Slabs penetrate into lower mantle