A geochronological perspective on erosion - Cin Download

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A geochronological
perspective on erosion
Francis Albarede
Where it all began: the Swiss Alps
(Jäger, Niggli, & Wenk, Beiträge sur Geologischen Karten der Schweiz, 134, 1967)
K-Ar mica ages
Hunziker et al. (1992)
Rb-Sr mica ages
Hunziker et al. (1992)
Zircon fission-track ages
What were the questions then?
• Why geochronological ages are distinctively
younger in the metamorphic core of the Alps?
• Which dynamic for mountain ranges?
• What does a geochronological age date?
• Closure temperature vs paragenetic PT
estimates
• What is the magnitude of erosion rate?
What are the questions now?
• What is the record of continental crust erosion
over different time scales, Quaternary,
Cenozoic, Phanerozoic?
• What is the ratio between mechanical erosion
and chemical weathering?
• What is the record of CO2 consumption by
weathering?
Early thermal models
PTt trajectories of Massif Central granulites
Contrary to the Alps, granulite exhumation seems too
fast (3-5 km/m.y.) to be driven by erosion only and
must correspond to a tectonic event.
Final retrogressive
paragenesis
(Albarede, BSGF 1976)
Initial granulite
paragenesis
England and Thompson (1984)
Bringing geological evidence
and thermal models of
tectonic and erosion together
(Thompson and Ridley, 1987)
Modeling tectonics and erosion amounts to
reconstructing a flow field in the crust.
The flow field is strongly temperature-dependent.
Material conservation (Euler equation)
velocity
If the medium is incompressible
vx
vz
The forms of the heat
transport equation
Lagrangian
Eulerian
advective
‘with the stream’ ‘on the ground’ transport
derivative
derivative
conductive
transport
Heat
generation
K is thermal diffusivity (m2/s), A the heat production rate (J/m3/s)
and cP is the heat capacity
Eulerian fishermen
A Lagrangian fisherman
Rock and mineral samples are the
‘Lagrangian buoys’ of metamorphic geology !
Heat transport at steady state
In one dimension and at steady-state (u=-vz>0), this
equation becomes:
Selecting a characteristic length l, we define
the Peclet number as:
so
K is thermal diffusivity (m2/s), A the heat production rate (J/m3/s)
and cP is the heat capacity
Erosion rates, at last!
0.63 T∞
becomes
or
The thermal boundary layer thickness l= k/u
~0.63 T∞ therefore gives a straightforward
indication of the erosion rates.
The slope of these lines is u/k
14
12
ln T∞/(T∞-T)
10
8
1 km/a
6
0.5 km/a
4
0.1 km/a
2
0
0
50
100
150
200
z km
250
300
350
Effect of phase changes
• Mineral reactions do not have a
significant effect on dT/dz.
• Melting flattens the path in the zT plot, while crystallization makes
it steeper or may even reverse it.
• The apparent effect of melting
and crystallization is to multiply
heat capacity cp by 1 + (L/c p DT),
where L is latent heat, DT is the
melting range, and L/cp ~ 300 K.
melting
crystallization
Brower (EPSL 2004)
Is rugged topography an issue ?
Turcotte and Schubert (1982)
The thermal effect of topography dies out
with a length scale of l/2p: a mountain
with a foothold of 10 km produces no
thermal effect below ~2 km.
The velocity field in the crust
constrains erosion rates
Anomalous temperature
gradient recorded by
mineral assemblages
Tectonics is an integral part of the velocity field
Erosion rates can therefore be
calculated:
1. from PT estimates in metamorphic series
2.from the PTt path of a particular sample (go to
cooling age theory)
3. from alterations of the heat flow
A PT metamorphic grid
Kerrick et al. (EPSL,2001)
Example of a conductive cooling path
of Maine plutons
Heizler et al. (AJS, 1988)
Advective cooling: Münchberg eclogites,
Variscan Bohemia
Duchêne et al. (AJS 1988)
The cooling age theory
Martin H. Dodson (1932-2010)
Bulk Closure Temperature Equation
Tc =
E
é ART 2 D ù
R ln ê 2 c 0 ú
ë a E(dT / dt) û
Where
Tc
=
closure temperature
D 0, E =
diffusion parameters
R
=
gas constant
A
=
geometric term (55 for a sphere, 27 for a
cylinder, 8.7 for a plane sheet)
a
=
effective diffusion dimension
dT/dt =
cooling rate
Diffusion is a thermally activated
process
Energy
threshold
activation
energy E
Position
The closure temperature Tc is the temperature of a system at the time of its
measured date (Dodson, 1973).
Loss of nuclides from a sphere
Constant T and therefore constant D. The fraction F of nuclide remaining at t is:
(radius a, diffusion coefficient D). If T varies, and therefore D
as D(T(t)), let us define t as
The fraction of nuclide remaining at t is:
Approximation valid for F>0.15:
The critical assumptions that made
Dodson’s model successful
1. A hyperbolic cooling rate
which is a good approximation
2. A time scale q
The system is assumed to cool fast
enough for the transition to be very
short relative to the rate of decay. A
‘closure’ tc and therefore a closure
temperature Tc and a closure age tc are
assumed.
t>tc
t<tc
Defining the closure temperature Tc
The dimensionless arameter tc is assumed to be constant (although geometry
dependent) and therefore
For a spherical mineral tc =1/55 =1/A.
In the widely used form:
E
Tc =
é ART 2 D ù
R ln ê 2 c 0 ú
ë a E(dT / dt) û
D0 and Ei are experimentally determined for
each element in each mineral
Slope = -Ei/R
Intercept: ln D0
Farley (2000): helium diffusion in apatite
Hodges (1991)
Mineral
Ea
gas (kJ/mol) Do (m2/s) a (mm) for Tc geo
Apatite
Zircon
He
He
138
164
3.16E-03
1.95E-05
75
75
Titanite
He
174
8.77E-04
250
Monazite
He
202
1.25E-03
75
Plagioclase
K Feldspar
Ar
Ar
168
177
1.42E-04
1.84E-07
500
500
sph
sph
189
295
213
330
240
370
39.7
33.9
Biotite
Muscovite
Hornblende
Quartz
Ar
Ar
Ar
Ar
197
264
276
43
7.5E-06
2.3E-04
6.0E-06
3.1E-19
500
500
500
500
cyl
cyl
sph
sph
313
449
532
183
347
487
577
276
384
529
628
411
36.8
40.5
38.0
9.0
Tc
Tc
Tc
E/RTc
Dc
Reference
1 °C/Myr 10 °C/Myr 100 °C/Myr
44.8 1.1E-22 "best estimate" of Farley (2000)
sph
58
73
90
40.5 5.1E-23 ave of Reiners et al. (2004), Cherniak
cyl
167
190
215
and Watson (2010)
42.4 3.3E-22 ave of Shuster et al. (2004), Cherniak and
sph
173
196
220
Watson (2009), Reiners and Farley
(1999)
45.3 2.6E-23 ave of Cherniak and Watson (2009),
sph
216
239
264
Boyce et al. (2005), Farley (2007)
8.1E-22 Cassatta et al. (2009) (average)
3.6E-22 ave of Clay et al. (unpub.), Foland
(1974), Wartho et al. (1999) (low T)
7.5E-22 McDougall and Harrison (1999)
6.1E-22 Harrison et al. (2009)
1.8E-22 Harrison (1981)
3.7E-23 Thomas et al. (2008) & Watson and
Cherniak (2003)
Baxter (RMG72, 2010)
Reiners (AREPS,2006)
Pb model ages in the crust
Cherniak (CMP, 1995)
• Tc depends on the cooling rate and grain size.
• Lead in the crust is largely held in K-feldspar.
• Pb-Pb model ages reflect the onset of melting or more
probably the ‘softening’ temperature of the crust.
10
6
Pb diffusion in K-feldspar
400
500
600
700
10 4
o
C
C
o
C
o
C
o
Cooling rate K Ma
-1
10 2
10
10
0
-2
10 -4
10 -6
10 -8 -5
10
10
-4
10
mineral radius m
-3
10
-2
Pb model ages of Europe
U-Pb zircon
Lu-Hf garnet
K-Ar amphibole
Pb-Pb feldspars
K-Ar and Rb-Sr muscovite
K-Ar K-feldspar
Fission-track zircon
U-He apatite
Cooling and uplift history of the Lepontine Central Alps
Hurford (CMP, 1986)
Mean cooling patterns north of the Insubric Line.
Hurford (CMP 1986)
Direct determination of erosion rates
dz/dT in the French Alps
apatite fission tracks
Tc=104°C
zircon fission tracks
Tc=230°C
Same samples!
Van der Beck et al. (EPSL, 2010)
Coast Plutonic Complex in
south-eastern Alaska
(Reiners, AREPS 2006)
Apparent variations in erosion rates
are most often assigned to geological
history.
ZFT (red, 230-300°C)
ZHe (orange, 183°C)
AFT (light blue, 104°C)
AHe (dark blue, 70°C)
Erosion rate may also have remained
constant and we may see an effect of
lateral advection (gravity, tectonics) at
shallow depth and to some extent of
topography.
Zircon FT
Zircon He
Apatite FT
Apatite He
The concept of closure applies to all
mineral equilibria
Farewell Symphony
(Haydn, 1772)
Decreasing temperature
The impact on the interpretation of parageneses and on
geothermobarometry is important and largely ignored in the literature.
Examples: Fe-Mg in clinopyroxene (Tc~800°C), Fe-Mg in garnet (700°C),
O in quartz (500°C).
Mineral equilibrium is a dream!
Limitations to the concept of closure
temperature
Dodson (1986):
During the early stages of cooling
rapid diffusion ensures that the
concentration everywhere stays close
to the equilibrium value as it changes
with temperature. However, the rate
of diffusion diminishes rapidly with
decreasing temperature, so the
concentration in the interior begins
to lag behind that at the surface.
Eventually the system ‘closes’
initially at the centre, and
subsequently nearer to the outside,
the concentration approaches a limit
at which the whole grain is effectively
isolated from its surroundings, except
for an infinitesimal surface layer.
Trying to fix it for 30 years
•
Dodson (1986). Define a closure
temperature at each point x inside the
mineral. G(x) is the ‘closure’ function.
•
Ganguly and Tyrone (1999). An arbitrary
diffusion profile at t=0.
Lagrangian (conductive) cooling
Rocks at different depth had different Tc because they come from different
depths.
Rate of cooling at the cooling temperature
Alternatively, it is in principle possible to map T∞ (deep crust) using the rates
u of erosion
Inversion of 39Ar-40Ar
degassing spectra
decay scheme
g
40K
40
Ar* 
le 40
( K )(elt  1)
lt
 40 Ar *  lt  
t  ln  40    1
lt  K  le  
1
Unknowns:
40Ar* : radiogenic 40Ar from 40K decay (isotope dilution)
40K : a small fraction of total K (measure K conc.
and use abundance %)
40Ar-39Ar
Dating
- based on K-Ar dating
- bombard sample with fast neutrons, 39K -->
39Ar
Converting 39K into 39Ar brings the following advantages:
1. You can obtain K (39Ar) and 40Ar data from the same sample
2. Ar isotopic ratios are the only measurements required (high precision)
3. You can measure Ar ratios as you slowly heat the sample

t  ln  J
lt 
1
Ar * 
 1
39
Ar

40
where
elT  1
J  40
Ar * / 39 Ar
So…
Older samples have higher 40Ar*/39Ar values
and
Altered regions of samples have lower 40Ar*/39Ar values
due to loss of 40Ar*
J calculated from bombarding and
measuring samples of known age (T)
Principles of the 39Ar-40Ar method
(Merrihue and Turner, 1964)
Harrison and Zeitler (2005)
Retrieving the distribution of Ar isotopes from the
monomineralic anorthosite 15145
(Albarede, EPSL 1978)
Turner (1972)
Radiogenic 40Ar concentration profile in plagioclase
(Albarede, EPSL 1978)
Inversion of K-feldspar 39Ar-40Ar
degassing spectra: the Multiple Diffusion Domain Theory
(Harrison et al., RMG 2005)
The stepwise
outgassing
experiment is also a
diffusion experiment
Fraction of a uniformly distributed
isotope(e.g., 39Ar) left at t:
while
The multiple diffusion domain (MDD)
theory of Lovera et al. (1989) assumes
that a crystal is made of multiple
fractions of domains with different radii
and identical activation energy.
Different strategies: least-square fit,
Monte-Carlo search.
Harrison et al. (2005)
Thermal history
reconstruction from 39Ar40Ar spectra
(Harrison et al., RMG 2005)
A contribution of this class:
a relationship between
temperature T∞ in the deep
crust and erosion rate
Paradox: For a given Tc, T∞ increases as
the inverse of the squared erosion
rate. This only means that it takes
longer to cool hotter material by
conduction than cooler layers.
The rise of hot deep crust is associated
with erosion rates in the order of ~0.1
km a-1. Faster erosion rates bring cold
crust to the surface.
Leaky chronomometers
(Albarede, GRL, 2003; Guralnik,
EPSL, 2013)
an
tl
e:
con
tinuously open
open
open
s t: e
piso
d
ically
o pe n
closure temperature interval
closed
cr u
These chronometers remain above
their closure temperature under
conditions at which they are neither
entirely open, nor entire closed.
Temperature
m
Some geochronometers spend their
life above their cooling temperature.
They are only useful when the rocks
are erupted very fast (volcanic
xenoliths, UHP metamorphism).
Time
closed
Significance of the
thermobarometric mantle
geotherms relative to mineral
closure temperatures
Closure temperatures with respect to
Fe-Mg exchange are in the order of
800°C. What is the behavior of Sm-Nd
and Lu-Hf chronometers under such
conditions?
Bell et al. (Lithos, 2003)
Open system behavior of
leaky chronometers
176Lu-176Hf and 147Sm-143Nd apparent
ages on garnet peridotite inclusions in
South African kimberlites
(Bedini et al., EPSL, 2004)
Albarede’s (2003) solution for leaky chronometers
P: parent isotope, D* radiogenic isotope, radial coordinate r, radius a
Dodson’s change of variable
Solution for T>Tc
Age deficit DT:
Evolution of DT, the difference between the crystallization age and
the apparent 147Sm-143Nd age, with time t for a 1 mm spherical
pyrope crystal as a result of volume diffusion. Open circles: closure
temperatures. (Albarède, 2003)
Relationship between the cooling rate and the temperature T0 at t = 0 deduced
from the 147Sm-143Nd age deficit DT of a 1 mm pyrope crystal formed at 2.9 Ga.
Cooling rate -dT /dt = aT02 . Open circles: closure temperature
Application to garnet Sm-Nd ages of peridotite
inclusions in kimberlite from South Africa
Bedini et al., EPSL, 2004)
Application to garnet Sm-Nd ages of peridotite
inclusions in kimberlite from other regions
Had enough of equations?