Title: Heat Transfer as a Key Process in Earths Mantle: New Measurements, New Theory
1Heat Transfer as a Key Process in Earths Mantle
New Measurements, New Theory
Anne M. Hofmeister
2Collaborators
- Janet Bowey (U. College London)
- Bob Criss (Washington U.)
- Paul Giesting (Notre Dame)
- Gabriel Gwanmesia (U. Delaware)
- Brad Jolliff (Washington U.)
- Andrew Locock (Notre Dame)
- Angela Speck (U. Missouri Columbia)
- Brigitte Wopenka (Washington U.)
- Tomo Yanagawa (Kyushu U.)
- Dave Yuen (U. Minnesota)
3Outline
- Background
- Heat transfer via vibrations
- A model for klat
- Laser flash data on klat (T)
- Implications for magma genesis, Transition Zone
- Heat transfer via radiation
- A model incorporating grain size
- Does radiation or rheology have more impact?
- Implications for the Lower Mantle
- Merging Geological Geophysical Constraints
- Mantle convection is multiply layered.
- The global power is low with no secular delay
-
4Important Principles
Heat Light
lt 0 is destabilizing
gt 0 is stabilizing
Dubuffett et al.(2002)
Macedonio Melloni (1843)
Photo Credit www.Corbis.com
5What drives convection?
buoyancy
heat diffusion
viscous damping
vs.
which is more important?
6Jehovah
Baal
Thermal Conductivity
Rheology
Temperature Equation Quasi hyperbolic
nonlinear Parabolic Equation
Momentum Eq. Elliptic Eq.
Credit D. Yuen
7Thermal conductivity is most important property
because it controls the temperature, which then
determines the other physical properties.
k(T)
temperature
heat capacity
thermal expansivity
viscosity
density
8To model convection we need
k0 (ambient temperature and pressure)
9Why is a model for k needed?
because of crummy data!
10Heat Transfer via Vibrations (phonons)
Debye (1914) used Claussius kinetic theory of
gases to relate the thermal conductivity of a
solid to the collisions within its phonon gas
where ci is the heat capacity of the ith mode ui
is the group velocity ti is the mean free
lifetime between collisions
11The formula was not very useful because the
vibrations were treated as harmonic oscillators
(i.e., non-interacting).
Instead the vibrations interact through damping !
12The Lorentz Model A damped harmonic
oscillator has a lifetime
X Ae(-?t)cos (wt)
13Examples of vibrations
damped
underdamped
14Heat Transfer via Vibrations (phonons)
damped harmonic oscillator model
mean free gas theory
gives
(Hofmeister, 1999 2001)
where G is obtained from IR reflectivity data
15IR Spectrometer
16- Lifetimes (t 1/G)
- are obtained from IR peak widths
17Lets test the model against reliable data
18Compositional dependence of klat
19Compositional dependence of klat
20Pressure dependence of klat
21To understand Earth processes, we need to make
measurements at high T
http//www.math.montana.edu
22 A laser-flash apparatus
near-IR detector
furnace
Sample under cap
cap support
CO2 laser cabinet
23How a laser flash apparatus works
fayalite at 1000o C
CO2 laser pulse
fit
detector
Signal
emissions
t half
detector output
Sample in furnace
CO2 laser
Time, ms
24Advantages of LFA
Basalt
- Rapid and accurate
- Contact free no power losses from cracks
- Phonon component is separated from radiative
transfer effects
Heat transfer by phonons
Signal
500oC
Obsidian
signal
phonons
photons
500oC
time
25Once ?Dlat/?T 0, Dlat no longer effects
convection.
26More laser-flash results glass has low thermal
diffusivity
27Transient melting experiments
Change upon melting
28Results from laser-flash measurements
- The thermal diffusivity of melts or glasses is
lower than that of minerals or rocks - Thus, runaway melting is a possible mechanism for
magma generation in the upper mantle - D and klat (of minerals, rocks, and glasses) are
independent of T at high T - Thus, radiative transfer is the key process
inside Earths mantle
29Implications for Earths Mantle
30 Velocities in the Transition Zone cannot
be explained by adiabatic gradients or by steep
conductive temperature gradients
(super-adiabatic).
PREM (Anderson, 1989)
31k0 for mantle minerals
Low thermal conductivity is expected for the TZ,
as it is rich in garnet (e.g., Vacher et al.
1998). But, low k suggests a super-adiabatic T
gradient, which is not supported by seismic
velocities.
32Also, nearly constant temperatures suggest
buoyancy/ instability of the Transition Zone
Mantle avalanche ???
Alternatively, a chemical gradient exists across
the transition zone (Sinogeikin and Bass, 2002).
Then, the temperature gradient is
unconstrained. Layered mantle convection is
implied.
33Radiative Transfer
Hot Gas
Cool Dust
Shells in the Egg Nebula Credit R. Thompson (U.
Arizona) et al., NICMOS, HST, NASA
34The two types of radiative transfer
cold
direct
hot
Earth diffusive
Laboratory direct
990 K 1 km 1000 K
recorder heater
298 K 5 mm 800K
35Diffusive Radiative Transfer
- Earths mantle is internally heated and consists
of grains which scatter and partially
absorb light - Because the grains cannot be opaque,
- they cannot be blackbodies
- The light emitted
- the emissivity x the blackbody spectrum
- Emissivity absorptivity (Kirchhoff, ca. 1869).
We measure absorption with a spectrometer.
d
36Diffusive radiative transfer is calculated
from spectra from the near-IR through the
ultraviolet,accounting for scattering losses at
grain boundaries
Visible region from Taran and Langer
(2001) Ullrich et al. (2002)
interface reflectivity
37krad depends strongly and non-linearly on
grain-size (d) due to competing effects
1) small grains scatter light repeatedly,
providing a short mean free path, which
suppresses krad 2) small grains absorb light
weakly, providing a large mean free path, which
inhances krad 3) small grains emit weakly which
suppresses krad
38for 0.1 interface reflectivity
39Radiative transfer is large in the lower mantle,
which promotes stability
- But in the transition zone, the negative T
gradient of radiative transfer is destabilizing
for large grain sizes
40Does radiative transfer or viscosity affect
convection more?
work in progress by Tomo Yanagawa, Dave Yuen,
and Masao Nakada
41Vertical viscosity contrast is eg 107
k1
k 1 4T3
represents upper mantle
credit Tomo Yanagawa
42Vertical viscosity contrast is eg 103
k contrast is 5
represents Lower Mantle
credit Tomo Yanagawa
43Implications
- Radiative transport exerts greater control
over convection than viscosity - Blob-like convection in Upper Mantle
- An almost stagnant Lower Mantle
Is there evidence ?
44Tomography shows that the middle of the lower
mantle is less heterogeneous than the rest
Masters et al. (2000)
45Possible stratigraphies for layered convection
(categorized by different modes of heat transport)
Upper Mantle
Transition Zone
slab
Lower
Mantle
46Equatorial Section
N
Lower mantle L 2 flow
47Polar Section
48Does the Earths engine lack sufficient vigor to
produce whole mantle convection?
Strong radiative transfer in the lower mantle
limits strong convection.
- The current model for the global heat flux
assumed constant k and thus overestimated power
49Global Power
31 TW at mid-ocean
Half-space cooling model with constant k gives 44
TW. Analysis of the raw data gives 31 TW
50Geologic evidence for weak convection
- A global power of 31 TW is consistent with an
enstatite chondrite model of the Earth, which
also explains its O isotopes and huge Fe core
(Lodders, Javoy). - The long-standing existence of basaltic volcanism
of the oceanic crust implies near steady-state
heat expulsion. - MORB and hot-spot melting is runaway, requires
little excess heating. - Layered (weak) convection may address different
styles of upper and lower mantle
51Conclusions
- Variable thermal conductivity exerts great
control over convection, more than viscosity - Mantle convection is multiply layered
- Global power and estimated bulk compositions
agreeing implies that Earth cools as
radioactivity decreases - Radiative transport is a key process in the
Earth, as is surmised for the Universe