[Tectonics]
Supporting Information for
[Alpine
exhumation of the central Cantabrian Mountains, Northwest
Spain]
[C. Fillon1,2, D. Pedreira3, P.A. van der Beek1, R.S. Huismans4, L. Barbero5, J.A. Pulgar3]
[1 ISTerre, Université Grenoble Alpes, CNRS, 1381 rue de la Piscine, 38041 Grenoble cedex, France
2
GET, Observatoire Midi Pyrénées, Université de Toulouse, CNRS, IRD, 14 avenue E. Belin, F-31400
Toulouse, France
3
Departamento de Geologia, Universidad de Oviedo, Oviedo, Spain
4
Department of Earth Sciences, Bergen University, Bergen N-5007, Norway
5
Departamento de Ciencias de la Tierra, Facultad de Ciencias del Mar y Ambientales. Universidad de
Cadiz, Spain]
Contents of this file
Text S1
Introduction
This supporting information contains details on the methodology used in the article to model
the low-temperature thermochronology dataset. The thermo-kinematic model is deriving heat
transfer equation in three dimensions in a crustal block that experiences exhumation through a
prescribed geometry (flat-ramp fault system here). The thermochronological data produced by
a tectonic scenario are then compared to the measured ones and assessed by a misfit function.
Text S1.
3D thermal modeling of the data
Model description
The thermo-kinematic modeling is based on Pecube (Braun, 2003; Braun et al., 2012), a
finite-element code that solves the heat-transfer equation (Carslaw and Jaeger, 1959) in 3
dimensions, following this formulation:
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With T(x,y,z,t) the temperature (°C), ρ the rock density (kg.m-3), c the heat capacity (J.kg1 -1
.K ), v the rock uplift velocity with respect to the base of the crustal block (km.Myr-1 ),
and H the radioactive heat production (W.m-3). This equation is solved in a crustal block
for a prescribed exhumation (rock advection) and topographic history. In this version of
the code, rock advection is controlled by one or several faults, carrying a velocity field,
with a variable geometry. For each node, Pecube calculates time-temperature paths for
particles that end up at the surface. Thermochronological age-prediction models are used
to calculate thermochronometric ages that are compared to the input dataset. Here, we use
the AFT annealing model of Stephenson et al. (2006), the ZFT annealing model of
Tagami et al.(1998), and the AHe diffusion model of Farley Farley (2000).
The calculated ages are then compared to the input data to estimate the fit of the model.
The statistic evaluation of this misfit is defined by the objective function (Braun et al.,
2012; Glotzbach et al., 2011) :
2
m  o 
   i i 
 i 
i1
n

(2)
With µ the misfit value, n the number of data and, for each data point i, oi the observed
value (age or mean track length), mi the modeled (predicted) value, and σi the observed (1
) error.This approach is very useful to set first-order constraints on exhumation
scenarios but a precise evaluation of each parameter (such as exhumation rates and
topographic parameters at different timesteps) requires an inverse approach.
For inverse modeling, Pecube was coupled with the Neighborhood Algorithm
(Sambridge, 1999a, b). This approach defines an optimal model (i.e a best-fitting set of
parameters) within a predefined parameter space, and then evaluates the level of
constraint that the data resolve for each parameter. At the end of the sampling stage, we
thus have a large collection of models that converge to an optimal combination of
parameter values as a function of their misfit, but these solutions are strongly dependant
on the calibration of the sampling stage itself. To more quantitatively assess these results,
a Bayesian estimate of parameter values is calculated during the appraisal stage by resampling the models and calculating the marginal posterior probability density function
(L) of each parameter, following the equation (Sambridge, 1999a):
The PDF directly provides a measure of the distribution of likely parameters value , in
most of the case with one or two peak-values. From the PDFs, we can graphically infer
the optimal parameter value (peak) and deduce its incertitude by taking the values at the
half-gaussian height of the peak.
References
Braun, J., 2003, Pecube: a new finite-element code to solve the 3D heat transport
equation including the effects of a time-varying finite amplitude surface
topography: Computers & Geosciences, v. 29, p. 787-794.
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Braun, J., van der Beek, P., Valla, P., Robert, X., Herman, F., Glotzbach, C., Pedersen, V.,
Perry, C., Simon-Labric, T., and Prigent, C., 2012, Quantifying rates of landscape
evolution and tectonic processes by thermochronology and numerical modeling
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Carslaw, H. S., and Jaeger, C. J., 1959, Conduction of Heat in Solids,3rd Edition. ,
Clarendon Press, Oxford.
Farley, K. A., 2000, Helium diffusion from apatite: general behavior as illustrated by
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