Earth System Science II – EES 717

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Earth System Science II EES 717 The Earth
Interior Mantle Convection Plate Tectonics
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Anatomy of Earth
Layering based on different criteria 1. Density
(crust, mantle, core) 2. Chemical composition
(consistent with density) 3. Mechanical behavior
of materials (lithosphere, asthenosphere, mantle,
core)
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Physiology of solid Earth driving mechanism
for plate tectonics
Plate Tectonics is the surface expression of the
mechanism by which heat escapes the Earths
interior
Origin of heat in the Earths interior 1.
radioactive decay 2. residual heat from Earths
formation and to a lesser extent, heat
contribution from the growth of the inner core
which drives the convection in the outer core
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Mantle Convection
Two possible patterns of mantle convection 1.
smaller cells may be generated separately within
the upper mantle and within the lower mantle or,
2. the whole mantle below lithosphere may be
involved in a single, larger pattern of
convection cells, depending on the nature of the
lower/upper mantle transition zone. If the
transition zone marks a change in chemical
composition ? 1. If the transition zone results
from mineralogical changes that take place
quickly relative to the rate of convection ? 2
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Onset of Thermal Boundary Layer Instability
The fluid is initially of the same temperature 1.
Starting at time 0, the fluid is cooled from the
above with boundary temperature of 0 at the
surface. The top thermal boundary layer thickens
with time. After a certain period of time, the
thermal boundary layer becomes unstable as
Rayleigh number characterizing the top boundary
layer reaches a critical level. Cold downwellings
develop from the thermal boundary layer, which
limits the thickening of the boundary layer. The
downwellings also cool the mantle.
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Forces acting on the plates
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And the forces are
F1 mantle drag friction between the convecting
asthenosphere and the overlying rigid
lithosphere F2 gravitational push generated
by high topography of MOR on the rest of oceanic
plate F3 pull on the opposite end of the
plate into a subduction zone due to the
increasing density of the oceanic lithosphere as
it cools F4 the elastic resistance of the
oceanic plate to being bent into a subduction
zone F5 the tendency of the overriding plate to
be drawn toward a subduction zone as the
subducting slab bends (otherwise it would move
away from the overriding plate) F6 friction
between the subducting slab and the overlying
lithosphere F7 tendency of the oceanic plate to
sink as it cools and becomes denser (we can call
that negative buoyancy)
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Go to handout for 3 primary forces now. How
Well Convection Explains Plate Tectonics
Section 3 of BYR
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What Convection Can not explain thus far
Section 4 of BYR
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• A Primer on Convection
• A system cooled from above or heated from within
  will develop an upper thermal boundary layer
  which drives the system.
• The thermal boundary layer (plate, slab) is the
  only active element.
• All upwellings are passive, and diffuse.
• For large Prandtl number (the mantle) the
  mechanical boundary layers are the size of the
  mantle.
• The scale of thermal boundary layers (plate
  thickness) is controlled by the Rayleigh number
  (Ra), which for the top is of the order of
  hundreds of km.
• Ra is controlled both by physical properties
  (conductivity, expansivity etc.) and environment
  (heat flow, temperature gradients etc.).

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• A Primer on Convection
• Both of these, physical factors and environment,
  cause Ra to be orders of magnitude lower at the
  base of mantle than at top. Therefore convective
  vigor is orders of magnitude less at the base of
  mantle.
• The mechanical and thermal boundary layers at the
  base of mantle are therefore of the order of
  thousands of kilometers in lateral dimensions.

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The Wilson Cycle how continents might come
together and drift apart in a regular rather than
random pattern
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EES 717 2.5. Influence of Temperature-Dependent
Viscosity  Spring 2010 Hanii Takahashi
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• Mantle material have temperature dependent
  viscosity (VT) for subsolidus flow. In this
  section, we will learn how VT plays a significant
  role in plate-mantle system.
• Subsolidus flow occurs by
• diffusion creep
• dislocation power-law creep
• The mobility of the molecules depends on thermal
  activation!

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• Viscosity law of silicates contain the factor of
  eHa/RT (Arrhenius factor)
• where Ha activation enthalpy, R gas const, and
  T temperature
• A little change in T lead huge change in
  viscosity
• Viscosity become very sensitive at lower
  temperature

Viscosity may changes as much as 7 orders in the
top 200 hundred km on the mantle. (King, 1995
Beaumont, 1976 Watts et al., 1982)
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• VT on mantle convection make top colder thermal
  boundary much stronger than the rest of the
  mantle.
• Plate-like thermal convection
• Less plate-like thermal convection
• VT lead asymmetry between upwelling and
  downwelling.

Hence, there are larger T jump across the top
boundary layer and smaller jump across the
bottom
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• VT causes a significant change in the lateral
  extent of convection sell.
• The top thermal boundary is cool enough to become
  negatively buoyant and sink
• Travel horizontally a long distance
• Causes the upper thermal boundary layer and its
  convection cell to have extremely large lateral
  extents relative to the layer depth
• This effect has been verified in lab (Weinstein
  and Christensen, 1991 Giannandrea and
  Christensen, 1993 Trackley, 1996a Ratcliff et
  al., 1997)
• VT can explain the large aspect convection cells
  of mantle convection (we will discuss more
  later)

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• Top thermal boundary layer with VT(strongly
  dependent) can become completely immobile because
  too strong to move.
• The large aspect ratio effect vanishes
• Top boundary layer successfully impose a rigid
  lid on the rest of the underlying viscous
  convection with a no-slip to boundary condition
• Convection has cells which are as wide as they
  are deep
• The planform can assume various simple geometries
  (Fig.3), although hexagons or squares might be
  not well assumed because of asymmetry between
  upwelling and downwelling
• However, the immobilization of the top layer
  leads to convection that is unlike the Earth.

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• There are three different regime of convection
  with VT (Christensen,1984a Solomatov,1995) which
  depends on Rayleigh number.
• VT weakly convection is nearly isoviscous .
  Nearly-isoviscous or low-viscousity-contrast
  regime
• VT moderately convection develops a sluggish
  cold top boundary layer with mobile and large
  horizontal dimension. Sluggish convection regime
• VT strongly convection assumes much of the
  appearance of isoviscous convection below a rigid
  lid. Stagnant lid regime it is the most likely
  regime for Earths plates

• However, mobile plates shows that the
  lithosphere-mantle system has effects which
  mitigate the demobilization of the top thermal
  boundary layer caused by VT
• It is not clear that extreme Arrhenius-type
  mantle or lithosphere viscosity occurs from a
  practical standard point..discuss later.

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Conclusions

• To consider the effect of VT is very important
  regard to the concept of self-regulation in
  solid-sate convection.
• If mantle viscosity is too high or convection to
  be strong enough to remove the heat generated
  internally, then mantle will simply heat up until
  the viscosity is reduced sufficiently.
• There is a more profound role for VT and
  consideration of long-term evolution of the
  plate-mantle system must account for the extreme
  sensitivity of heat flow to inthernal temperature
  through viscosity variabilityDavies, 1980
  schubert et al., 1980

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Is the movement of the plates continuous? Not so
clear. ? Intermittent Plate Tectonic?