Earth System Science II – EES 717
The Earth Interior – Mantle Convection &
Plate Tectonics
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)
Physiology of ‘solid ‘ Earth – driving
mechanism for plate tectonics
Plate Tectonics is the surface
expression of the mechanism by which
heat escapes the Earth’s interior
Origin of heat in the Earth’s interior
1. radioactive decay
2. residual heat from Earth’s formation
and to a lesser extent, heat contribution from
the growth of the inner core which drives the
convection in the outer core
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
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.
Forces acting on the plates
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)
Go to handout for 3 primary forces now.
How Well Convection Explains Plate Tectonics:
Section 3 of BYR
What Convection Can not explain thus far:
Section 4 of BYR
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.).
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.
The Wilson Cycle – how continents might come
together and drift apart in a regular rather
than random pattern
EES 717
2.5. Influence of TemperatureDependent Viscosity
Spring 2010
Hanii Takahashi
• 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!
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
3
2.5
exp(1/T)
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)
2
1.5
1
0.5
0
0
20
40
T
60
• 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.
Induces heat plug that
Colder, stronger, less mobile
forces fluid interior to
warm up
Hotter, weaker, more mobile
T difference bw
fluid interior & surface
fluid interior & underlying medium
Hence, there are larger T jump across the top boundary layer and smaller
jump across the bottom
• 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
• 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.
• There are three different regime of convection
with VT (Christensen,1984a; Solomatov,1995)
which depends on Rayleigh number.
VT weakly : convection is nearly isoviscous . Nearlyisoviscous 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 Earth’s 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….
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
Is the movement of the plates continuous? Not so
clear.
 Intermittent Plate Tectonic?