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)

Insubric Line

Rb-Sr mica ages

Hunziker et al. (1992)

Insubric Line

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.

Initial granulite paragenesis

Final retrogressive paragenesis

(Albarede, BSGF 1976)

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)

vz

vx

velocity

If the medium is incompressible

The forms of the heat transport equation

Lagrangian‘with the stream’

derivative

Eulerian‘on the ground’

derivative

advective transport

conductive transport

Heatgeneration

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

K is thermal diffusivity (m2/s), A the heat production rate (J/m3/s) and cP is the heat capacity

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

Erosion rates, at last!

or

The thermal boundary layer thickness l= k/u ~0.63 T∞ therefore gives a straightforward indication of the erosion rates.

0.63

T∞

becomes

The slope of these lines is u/k

0 50 100 150 200 250 300 3500

2

4

6

8

10

12

14

z km

ln T

∞/(

T∞-T

)

1 km/a

0.5 km/a

0.1 km/a

Effect of phase changes• Mineral reactions do not have a

significant effect on dT/dz.• Melting flattens the path in the z-

T 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.

Brower (EPSL 2004)

melting

crystallization

Is rugged topography an issue ?

Turcotte and Schubert (1982)

The thermal effect of topography dies out with a length scale of /2 : l p 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 series2.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

Where

Tc = closure temperature

D0, 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

The closure temperature Tc is the tempe-rature of a system at the time of its measured date (Dodson, 1973).

Loss of nuclides from a sphereConstant 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:

1. A hyperbolic cooling rate

which is a good approximation

The critical assumptions that made Dodson’s model successful

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

In the widely used form:

For a spherical mineral tc =1/55 =1/A.

D0 and Ei are experimentally determined for each element in each mineral

Farley (2000): helium diffusion in apatite

Slope = -Ei/RIntercept: ln D0

Hodges (1991)

Mineral gasEa

(kJ/mol) Do (m2/s) a (mm) for Tc geo Tc Tc Tc E/RTc Dc  Reference1 °C/Myr 10 °C/Myr 100 °C/Myr

Apatite He 138 3.16E-03 75 sph 58 73 90 44.8 1.1E-22 "best estimate" of Farley (2000)Zircon He 164 1.95E-05 75 cyl 167 190 215 40.5 5.1E-23 ave of Reiners et al. (2004), Cherniak

and Watson (2010)Titanite He 174 8.77E-04 250 sph 173 196 220 42.4 3.3E-22 ave of Shuster et al. (2004), Cherniak and

Watson (2009), Reiners and Farley (1999)

Monazite He 202 1.25E-03 75 sph 216 239 264 45.3 2.6E-23 ave of Cherniak and Watson (2009), Boyce et al. (2005), Farley (2007)

Plagioclase Ar 168 1.42E-04 500 sph 189 213 240 39.7 8.1E-22 Cassatta et al. (2009) (average)K Feldspar Ar 177 1.84E-07 500 sph 295 330 370 33.9 3.6E-22 ave of Clay et al. (unpub.), Foland

(1974), Wartho et al. (1999) (low T)Biotite Ar 197 7.5E-06 500 cyl 313 347 384 36.8 7.5E-22 McDougall and Harrison (1999)Muscovite Ar 264 2.3E-04 500 cyl 449 487 529 40.5 6.1E-22 Harrison et al. (2009)Hornblende Ar 276 6.0E-06 500 sph 532 577 628 38.0 1.8E-22 Harrison (1981)Quartz Ar 43 3.1E-19 500 sph 183 276 411 9.0 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.

Pb model ages of Europe

U-Pb zircon

Lu-Hf garnet

K-Ar amphibole

K-Ar K-feldsparU-He apatite

Fission-track zircon

Pb-Pb feldsparsK-Ar and Rb-Sr muscovite

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 tracksTc=104°C

zircon fission tracksTc=230°C

Van der Beck et al. (EPSL, 2010)

Same samples!

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.

Apatite He

Apatite FT

Zircon He

Zircon FT

The concept of closure applies to all mineral equilibria

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!

Farewell Symphony(Haydn, 1772)

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

40K decay scheme

40 40* ( )( 1)te

t

Ar K e

40

40

1 *ln 1t

t e

Art

K

Unknowns: 40Ar* : radiogenic 40Ar from 40K decay (isotope dilution)40K : a small fraction of total K (measure K conc.

and use abundance %)

g

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 sample2. Ar isotopic ratios are the only measurements required (high precision)3. You can measure Ar ratios as you slowly heat the sample

40

39

1 *ln 1

t

Art J

Ar

40 39

1

* /

TeJ

Ar Ar

where

J calculated from bombarding and measuring samples of known age (T)

So…Older samples have higher 40Ar*/39Ar values

andAltered regions of samples have lower 40Ar*/39Ar values

due to loss of 40Ar*

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 experimentFraction 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 39Ar-40Ar 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)

Some geochronometers spend their life above their cooling temperature. They are only useful when the rocks are erupted very fast (volcanic xenoliths, UHP metamorphism).

These chronometers remain above their closure temperature under conditions at which they are neither entirely open, nor entire closed.

Significance of the thermobarometric mantle geotherms relative to mineral closure temperaturesClosure 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 chronometers176Lu-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 chronometersP: 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 = aT0

2 . 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?