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## Thermokinematic modeling

The result of the structural‐kinematic modeling consists of a set of velocity fields, each describing the deformation pattern for one time interval of the section restoration. These velocity fields serve as input for the thermo‐kinematic model PECUBE (Braun, 2003; see also Braun et al., 2012).

PECUBE is designed to solve the three‐dimensional heat‐transport equation in a crustal block submitted to a specific tectonic and topographic scenario. The code uses a finite‐element approach to derive the time‐temperature (t T) paths of individual rock particles ending up at the surface at the end of the model run. These t T paths are subsequently used to compute apparent ages for a range of thermochronometers, using standard thermochronological age‐ prediction models (Braun et al., 2012).

We have implemented a new feature in PECUBE so that it can use a set of velocity fields as input files for the calculation of particle paths. The standard kinematic input for PECUBE consists, for each modeled time‐step, of a fault geometry and the velocities of the hanging‐ and footwall with respect to the fault (cf. Braun et al., 2012). We have replaced this input by a set of velocity vectors derived from the structural‐kinematic model for each time‐step. The two‐ dimensional velocity fields derived from the structural‐kinematic modeling are extrapolated in the third dimension, normal to the section, to allow direct comparison with the observed thermochronological data and correctly take into account the influence of topography.

Since the calculated t T paths are highly sensitive to surface topography, the predicted thermochronological ages will be affected by the implemented topographic evolution scenario Zoltán Erdős Ph.D. Thesis (Braun, 2002; Braun et al., 2006). The influence of the surface topography is strongest for thermochronometric systems characterized by low closure temperatures (e.g. apatite fission‐ track and (U‐Th)/He systems; Braun et al., 2006). Since the paleotopography of a mountain belt is extremely difficult to determine, it is common practice to use the present‐day surface topography throughout the modeled time‐period, thereby supposing topographic steady state (e.g. Herman et al., 2010; Robert et al., 2011; Whipp et al., 2007). In case this simplification is not sufficient, PECUBE includes a set of options allowing simple parametric amplification or reduction of the topography (e.g. Glotzbach et al., 2011; Valla et al., 2010). Basic sedimentation scenarios can also be implemented (Fillon and van der Beek, 2012). These options enable testing different topographic evolution scenarios for the same set of velocity fields. In our models, we have used a digital elevation model of the present‐day surface topography downgraded to a resolution of 300 m. The crustal blocks and the deposits have spatially uniform material properties, typical for the continental crust (Table 1). For a more detailed description of the use of PECUBE we refer the reader to Braun (2003) and Braun et al. (2012).

Table 1. Reference thermal and kinematic parameters used in PECUBE modeling. Bold values for basal temperature and crustal heat production those used in the reference model and are set to obtain a surface heat flow of 70 mW m‐2 and a corresponding geothermal gradient of 33 °C km‐1 (e.g. Fernandez and Banda, 1989; Fernandez et al., 1998; Fillon and van der Beek, 2012).

**Thermochronometric age predictions**

PECUBE predicts thermochronometric ages from the time‐temperature histories of rock particles using forward kinetic models (Braun et al., 2012). Apatite (U‐Th)/He (AHe) ages are Erdős et al. 2014

predicted using the numerical scheme presented in Wolf et al. (1998) and the kinetic parameters proposed by Farley (2000). Apatite (AFT) and zircon (ZFT) fission‐track ages can be predicted using several different models and parameterizations. For AFT ages, we have used the model presented by Green et al. (1989) with kinetic parameters modified by Stephenson et al. (2006), while for the ZFT system we have used the annealing model of Galbraith and Laslett (1997) with the annealing parameters proposed by Rahn et al. (2004). We acknowledge that more elaborate models exist both for AFT and AHe age predictions (e.g. Flowers et al., 2009; Gautheron et al., 2009; Ketcham et al., 2007), which take into account compositional controls on annealing/diffusion rates. However, as Fillon and van der Beek (2012) pointed out previously, the characteristics of the observational dataset justify the use of the simpler age‐ prediction models. In particular, for the AHe data Gibson et al. (2007) and Metcalf et al. (2009) reported effective uranium concentrations of a few tens of ppm, which is within the range where the kinetic parameters of Farley (2000) can be used (Flowers et al., 2009; Gautheron et al., 2009). As concerns the AFT data, Gibson et al. (2007) Metcalf et al. (2009) and Sinclair et al. (2005) reported kinetic indicators close to that of Durango apatite, on which the kinetic parameters of Stephenson et al. (2006) have been calibrated. Moreover, the rapid cooling inferred from the age‐elevation profiles (cf. Section 2.3) will minimize any compositional effects on the AFT and AHe ages.

To evaluate the consistency of the restoration with the observed data, predicted thermochronological ages at the sampling location are extracted by interpolation and are compared to the observed ages. An objective function that takes into account the error on the observed ages allows quantifying the fit between the predicted and observed ages (Glotzbach Zoltán Erdős Ph.D. Thesis et al., 2011). The resolution with which the input parameters of the forward models are constrained could, in principle, be assessed by inverse modeling (cf. Braun et al., 2012; Glotzbach et al., 2011; Valla et al., 2010), but these require running large numbers of individual forward models with slightly varying parameters, which is not possible in this case due to the complexity of the structural‐kinematic model.

For the available K‐feldspar 40Ar/39Ar data, we have used the thermal histories predicted by multi‐diffusion domain modeling presented in Metcalf et al. (2009). We compare these t T paths qualitatively to the t T paths extracted from our PECUBE models.

### Structuralkinematic modeling results

The objective of the structural‐kinematic modeling was to reproduce the section restoration presented by Muñoz (1992), in order to verify that it can be quantitatively balanced and to derive a set of velocity fields describing the movement of the crustal blocks through time.

The results of the modeling are compared with the original restoration in Figure 5. The model matches the restoration well for the 30‐Ma and the 36‐Ma time slices, except for the detailed geometry of the Axial‐Zone thrust sheets discussed below, but for the 50‐Ma time slice the mismatch becomes significant. The Muñoz (1992) restoration implies internal deformation of the Orri thrust‐sheet between 36 Ma and 50 Ma, thinning and elongating it significantly during retrodeformation. As a result, our model requires less convergence for the restoration of the Orri thrust‐sheet than the original reconstruction. Moreover, the Muñoz (1992) restoration implies 20% thickening of the Nogueres thrust sheet by internal deformation between 50 Ma and 60 Ma. Due to the accumulation of internal deformation and the uncertainties arising from the drawing method, such as the small changes in the area of crustal blocks, we could not restore the section beyond its 50‐Ma state.

Figure 5. Result of the structural‐kinematic modeling using 2D‐Move for the same four time slices as shown in Figure 2. For comparison, the resulting crustal‐scale geometry is plotted on top of the section restoration by Muñoz (1992) and Beaumont et al. (2000).

**Thermokinematic modeling results**

All the presented thermo‐kinematic models utilize the same set of displacement fields derived from the structural‐kinematic modeling. Material and thermal properties used in the thermo‐ kinematic modeling are given in Table 1. The t T paths predicted for the locations of K‐ feldspar 40Ar/39Ar samples are plotted together with the t T histories inferred by Metcalf et al. (2009) in Figure 6, while the predicted AFT and AHe ages are plotted together with the observed ages in age‐elevation plots (Figures 7 and 9).

#### Reference model

In the reference model, the present‐day topography is kept constant through time, while adopted thermal parameters were the same as those used previously by Fillon and van der Beek (2012).

The reference model does not predict reset ZFT ages in the Nogueres and Marimaña massifs but the two samples from the southern side of the Orri thrust‐sheet (from the Maladeta and Barruera units) have predicted ages of ~46 Ma, in contrast to observed ages of 49 and 104 Ma, respectively (Sinclair et al., 2005); the model therefore predicts these to have cooled from somewhat too high temperatures.

**Table of contents :**

**Preface **

Acknowledgements

List of Publications

Authorship statement

Abstract

Résumé

Introduction

State of the art

Aims and Research Objectives

Study area

Modeling approach

Structuralkinematic

modeling

Thermokinematic

modeling

**Thermomechanical**

modeling

Summary of papers

Paper 1

Paper 2

Paper 3

Conclusions

Surface processes and mountain building

Extensional inheritance and mountain building

Interaction of thinskinned

and thickskinned

tectonics

Consistency of the ECORS crosssection

restoration with thermochronology data

The effects of surface processes on the Pyrenean orogeny

The effects of extensional inheritance on the Pyrenean orogeny

Future perspectives

**References **

Papers

Paper I

Paper II

Paper III