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?