Transcript Conductive Thermal Transfer

GEO 5/6690 Geodynamics
08 Sep 2014
Last Time: Conduction; Radiogenic Heating;
Critical Thinking Skills
Material Properties of Rocks:
• Thermal Conductivity k:
- Temperature sensitive; composition dependent
- Mafic rocks have lower k at low T but higher k at
high T than granitic rocks
• Heat Production A: (In T&S, H)
- Radioactive decay of crustal K, Th, U adds to surface
heat flow; heat production A (W/m3) is a source
- Only composition-dependent
- A(granites) >> A(mafics) >> A(mantle rocks)
- Normal crustal fractionation processes 
~exponential decay of A with depth
Read for Wed 10 Sep: T&S 132-149
© A.R. Lowry 2014
Roy et al. “wrap-up”:
Food for thought:
• If elevation increased by heating after
Laramide, where should it have risen?
• And what should it have looked like
before flat-slab subduction?
He isotope ratio figure provided by Crossey et al. for the
EarthScope 2010-2020 Science Plan… Black dots are
travertines; color contour is P-velocity at 100 km depth.
Recall surface heat
flow…
> 50 mW/m2
requires advection;
For advection by
rifting alone, >90
mW/m2 requires a
strain rate in excess
of 3x10-15 s-1.
Eastern Basin-Range
is ~1x10-15 s-1; Rio
Grande Rift is much
less than that!
13C suggests ~1/3 total CO2 is
deep-derived, with ~1/4 of that
from “mantle” and 3/4 from “crust”;
3He/4He
also suggests a
contribution from the mantle
coupled with an important
contribution from the crust.
So important questions include:
• What is the transfer mechanism
across the ductile lower crust?
• Does the combination of “crustal”
and “mantle” signatures reflect
mixing, or residence time?
• What are the flux rates?
• How much heat was lost along
the way?
We derived our equation relating heat flow q and
the geothermal gradient assuming no heat
dT
sources…
q  k
dz
More realistically in the Earth, expect that all rock
acts as a heat source due to radioactive decay
of U, Th,K etc. For a material with heat
production A (W/m3),  q  A and the 1D
solution becomes:
 T
A


2
k
z
2
Material Properties of Rocks:
Similarly can measure A of
rock from U, Th, K
concentrations (inferred
by measuring radioactive
decay products).
A is high in granitic rocks
(particularly near top
of intrusions), lower in
lower crustal rocks,
very low in the mantle.
Brady et al
Lithos 2005
K
Th
U
Surface radiogenic element concentrations (averaged over
10-km scales)
US Geological Survey has flown aero-spectral gamma at
relatively high resolution (<1 km pixel) over the entire
conterminous United States… Measurements are integrative so
are representative of properties of surface rocks. Can these be
used to draw inferences about deeper rocks also?
Combined
radiogenic
heat
production
can be
estimated
from (T&S eqn 4-8):
If heat production truly
decays exponentially
with depth, i.e.,
A  A0 explrad z

for some length-scale
parameter lrad,
then if heat flux at the
base of the lithosphere
q0 is constant, we would
expect:
qs  q0  lrad A0
Here solved for slope &
intercept of line fit
averaged within
500X500 km windows.
Other complications: What about topography?
T h

Two effects:
• Temperature depends on
altitude per “lapse rate”
• Heat flow “refracts” toward
heat sinks (i.e., surface)
For periodic boundary, first
effect is attenuated as
2 x  2 z 
T cos
exp

     

Second expresses in
temperature as:
2 x  2 z 
q0  A0 lrad

h0 cos
exp

     
k
Other complications: What about topography?
So can Fourier transform
observed topography and surface T variations and solve!