Mantle Geophysics and Tectonophysics
Topics:
 Heat transport within the Earth
 Mantle convection
 Elastic (seismic) properties
 The CMB
 The upper mantle – lithosphere
 Crust and surface expression of mantle circulation
A simple Earth model
Heat conduction through the lithosphere
The Earth is cooling... losing internal energy.
Heat is being released from the Earth's interior at a
rate of about 44TW. Averaged over the surface of the
Earth, this amounts to a heat flow of about 70mW/m2
through the crust .
Heat energy diffuses through the crust and
lithosphere by conduction according to Fourier's Law
of Thermal Conduction.
With magmas at volcanoes and spreading ridges,
heat is being advected to the surface. Actually, this
accounts for only a fraction of the heat that is brought
to the surface and radiated through the atmosphere
into space.
Global distribution of heat flow
Temperature through the lithosphere and crust
For a lithosphere with 100km depth (i.e., an average gradient
of 12K/km), the average lithospheric thermal conductivity: k
~ 4 W m-2 K-1 .
Measured conductivities of surface rocks: k ~ 2-3 W m-2 K-1 .
Thermal diffusion (conductive)
Thermally driven mantle convection
 The contribution of diffusive cooling of the mantle
is insignificant in comparison to convective heat
transport through the mantle.
 The mantle behaves like a viscous fluid on long
timescales; being a fluid, it can flow and can be
driven into convection by a temperature gradient.
 Heat flows out of the depths of the cooling Earth
transported through the mantle between the D'' layer
and the base of the lithosphere by convective fluid
motions rather than conduction. This is the more
effective means of moving heat through a fluid.
How does convection work?
Adiabatic compression
Consider a cube of mantle material under pressure
Adiabatic temperature gradient
Mantle temperature?
If the actual temperature gradient
exceeds the adiabatic gradient?
If the actual temperature gradient (i.e. the increase of
temperature with depth) exceeds the local adiabatic
temperature gradient, then any infinitesmal displacement of a
volume of mantle material will be enhanced through bouyancy
if displaced upwards or negative bouyancy if displaced
downwards.
We have “convection”!
The process of convection removes heat from depth in the
mantle to the base of the lithosphere where it is conducted out
to the surface. The interior cools; the actual temperature
gradient reduces.
The process of convection pulls the entire mantle
temperature toward the adiabatic gradient. If the temperature
gradient falls to the adiabatic or below, convection ceases!
Temperature gradient in the mantle
Vigourous convection in the mantle pulls the actual
temperature gradient toward the adiabatic gradient.
If the temperature at the base of the lithosphere is 1500K
as corresponds to Hawaiian lava eruptions, then the
adiabatic gradient to top of the D'' layer would account for
a base temperature in excess of about 2100K depending
on the distributed thermal expansivity, αp , and heat
capacity, Cp, throughout the mantle.
Heat “conducts” into the fluid mantle through the D''
boundary layer.
Vigour and Rayleigh Number
Convection can be driven by internal or bottom heating. Surely,
both contribute.
The Rayleigh number measures the ratio of the forcing-toretardation of the convection.
For internal heating:
For bottom heating:
Here, η is the local viscosity, Tsx, the local adiabatic excess. d is
mantle thickness, base of lithosphere to D''.
The 660km spinel-perovskite transition
adiabat
The negative
Clapyron slope shows an
endothermic effect as the
mantle rises through the
660km transition. The
absorbed heat
contributes a slight
cooling and relative
density increase that
retards convection.
The effect reverses for a
descending lithospheric
plate or slab.
Layered mantle convection?
 There is/was a long-standing debate concerning the
possibly layered convection in the mantle.
 There is general agreement that the 660km phase
change does retard sinking subducting plates and
bouyant rising melts during convection.
 There is also general agreement that plates can and
do penetrate through 660 and that rising plumes and
convective sheets rise through 660.
 Seismic tomography shows that we have a pooling
of material around 660 as would be expected of
layered convection while there remains sufficient
penetration to involve the whole mantle in the
convective process.
from seismology.harvard.edu
D'' – postperovskite transition
 Recently, it has been determined that the perovskite
mineral phase of [Mg, Fe]SiO3 compresses into a denser
postperovskite phase (same stoichiometry?) at about
120GPa pressure and 2500K temperature.
This condition is interpreted to be the cause of the
seismic, velocity-slowing anomaly of the D'' layer.
This is not entirely out-of-line with our adiabatic
temperature estimate; we don't have tight measures of
thermal expansivity, αp , and heat capacity, Cp, throughout
the mantle.
The missing ingredient: Kie Hirose
Boundary layers – lithosphere and CMB-D''
Heat conducts into the mantle from the core through
the D'' boundary layer.
Heat is carried through the mantle to the base of of the
lithosphere via convection.
Heat is conducted through the lithosphere to the crust
and surface.
Convection moves heat with a smaller temperature
gradient than does conduction. The temperature
gradients across the D'' layer and lithosphere are much
greater than through the 2900km of the mantle!
Heat conduction through D''
The D'' layer is between 100 and 200 km thick.
It's area is about ¼ that of the Earth's surface area.
The heat flow from the core into the mantle is variously
estimated* to be ~9 TW. The heat flux, then, is about 40 mW m-2.
If the thermal conductivity is similar to that of the lithosphere,
~4 W m-2 K-1, the temperature gradient through the D'' layer takes
us to a temperature of 3500-4000 K.
*See Don Anderson: Energetics of the Earth
http://www.mantleplumes.org/Energetics.html
The outer and inner core
Temperature and
pressure within
Earth
The outer core is convecting vigourously; its
temperature gradient must be very close to adiabatic.
Still, we don't have good constraints on the thermal
properties of the liquid outer core.
Temperature at the inner-core/outer-core boundary?
Probably about 4500 K.
Assuming an essentially iron-nickel inner core and
adiabatic equilibrium, the inner core's central
temperature is estimated to be about 5500 K.
Mao and Hemley, 2007
Part II
Seismotectonics
 Kanimori (1977) estimated that earthquakes release (use)
about 5 x 1017 J per year. The theoretical limit of the annual
energy available from the convective heat engine is about 5.4
x 1020 J per year. The work “done” by earthquakes accounts
for only about 0.1% of the annual energy available to the
convection engine.
 What else?
 Moving masses laterally across the geoid requires no work
apart from the resistance or friction of the motions. Lifting
masses above the geoid requires work. On long time scales,
we believe that the topography of the Earth is approximately
stable: uplift and erosion are in balance. The energy required
to uplift the topography must somehow be provided by the
convection engine.
Seismotectonics
 The heat engine that is expressed in mantle convection works on
the body and surface of the Earth.
 It is not an especially thermodynamically “efficient”: its
theoretically limiting efficiency is determined by the temperature
differences at the bottom and top of the circulating mantle.
 We might expect, then, that the convection engine could
accomplish “work” at the rate of about 17TW. This is a
tremendous power to move and uplift continents, spread ocean
basins, lift mountain-building magmas above the surface and
fracture surface rocks in earthquakes.
Powering mantle convection
The mantle engine's power derives from several
possible sources:
 A chondritic Earth should contain enough U, Th and K
to account for much of the heat flow from the surface.
Fe
32.0 %
O
29.7
Si
16.1
Mg
15.4
Ca, Al, Na
3.5
K
160 ppm (0.0187 40K)
Th
0.055
U
0.015
McDonough, 2003
Powering mantle convection - II
The mantle engine's power derives from several
possible sources:

A chondritic Earth should contain enough U, Th and K
to account for much of the heat flow from the surface.
40K
> 40Ar*,
232Th
40Ca
> 208Pb
235U,238U >
207Pb,206Pb
2.79 x 10-5 W/kg
2.69 x 10-5
9.71 x 10-5
 Total present-day instantaneous combined radiogenic
heat source estimate for the BSE (bulk silicate Earth):
Anderson, 2009
12.7 – 31TW.
* It has been argued that the atmospheric mass of argon (1.29% of the
atmospheric mass) entirely derives from the decay of 40K during the history of
the Earth. Presently, 40K comprises 0.0117% (atom count) of natural K.
40K
-> 40Ar, 40Ca
Core convection and the geodynamo
 Compensation for the continuing dissipation of the
geomagnetic field requires a continuous power input of ~0.54TW (various estimates) to maintain the field.
 The convective engine of the core provides this power input.
Thebelieve
temperature
under which
this engine
operates is
If we
ourgradient
temperature
profile,
we might
(we have)
estimated to range
from about
to 4300K.
accept
Andersons's
9mW/m2
heat 5100K
flow from
the
 The
theoretically
limiting
core
into
the mantle
... efficiency of this engine – it is this
engine that drives the geodynamo – is then:
Caveat
But! Note that our argument is really a circular one.
 ~77% of the power available in the convective engine is
We
have obtained
our temperature
on the
basis
ofout
exhausted
into the mantle.
This corresponds
to a heat
flow
Anderson's
heat
estimate:
~9TWand possibly more
of the core into
the flow
mantle
of at least 1.8TW
than 14TW if all the available power of the convection drive
feeds the geodynamo. There are myriad other losses.
Powering core convection
We tread on very soft ground of assumption here.
 Latent heat of fusion of inner core: depends upon the rate
and history of freezing of the core. We may argue that the
core started freezing 3.5Ga or as recently as 1Ga.
 Radioactive isotopes in the core and, preferentially,
incorporated into the inner core. 40K is the best candidate.
 Chemical differentiation releasing light elements into the
outer core as Fe-Ni crystallize to form the inner core.
 A small metallic fissile U-Th core at the centre of the inner
core... probably fanciful but possibly testable.
 Fossil primordial heat assembled during accretion.
Properly, simply the continuing cooling of the overlying
mantle... sometimes seen as “entropy increase”.
0.1 - 1TW
0.1 - 1TW
0.1 - 1TW
0 - 1TW
Probably enough
Formation of the oceanic crust and lithosphere
The ocean basin deepens with distance from the spreading
ridge as a consequence of isostatic adjustment
Ocean bathymetry
GEBCO
The ocean ridges are the shallowest regions of the
basins; they are also the youngest!
Mathematical-physical theory
v
Mathematical-physical theory - II
v
Mathematical-physical theory - III
Mathematical-physical theory - IV
Much manipulation (Sandwell; 2001 ) takes us here:
To
Surface temperature
0 C
Tm
Mantle temperature
1300 C
Tl
Boundary temperature
1100 C
D
Thermal diffusivity
8 x10-7 m2/s
k
Thermal conductivity
3.3 W/m/K
The error function: erf(x)
Explore this special function on Wolfram|Alpha
What happens at a subduction trench?
We have seen how the oceanic crust and upper-mantle
lithosphere form and deepen as the plate spreads from a
ridge.
The Earth remains finite in area so that lithospheric plate has
to be consumed back into the volume of the Earth
somewhere... Where? Along “subduction zones”. How
does subduction work?
Forces acting of lithospheric plates
Exploring some tectonic stories and maps
http://pubs.usgs.gov/gip/dynamic/understanding.html
http://earthquakescanada.nrcan.gc.ca/zones/cascadia/mega-eng.php
http://earthquakescanada.nrcan.gc.ca/zones/cascadia/strain-eng.php
http://denali.gsfc.nasa.gov/dtam/data/ftp/gtam.gif
http://denali.gsfc.nasa.gov/dtam/data/ftp/dtam.gif
http://denali.gsfc.nasa.gov/dtam/seismic/
http://www.gps.caltech.edu/~dla/images/n_polar.jpg
http://www.gps.caltech.edu/~dla/images/s_polar.jpg
http://www.gps.caltech.edu/~dla/images/oblique.jpg
Part III
Plate tectonics!
Global topography
Why continents?
...from Scholl
Formation of continents
...from McCulloch and Bennett
206Pb/238U
Accretion of the continents
207Pb/235U
From Assynt's Geology
Rino, et al., 2004
Uranium – lead geochronology
Jack Hills Zircons
Peck, et al., UWisconsin
Global crustal thickness
WikiMedia Commons
The plate-tectonic paradigm
by Vigil, USGS
The plates!
WikiMedia Commons