# Research Methods - Thermochronology

## Thermal modeling using the software code HeFTy

3-D thermokinematic numerical modeling using the software code PECUBE

During the last years research efforts have been devoted to understand the coupling between tectonics and erosion (Beaumont et al., 1999; Braun, 2002, 2003, 2005; Ehlers and Farley, 2003; Ehlers 2005; Braun et al., 2006). Quantification of the rate at which landforms adapt to a changing tectonic and deeper heat flow environment has become an important research object.

In addition, the increased understanding how change in surface topography affects warping isotherms in the uppermost crust allow further interpretation of thermochronological data (Fig. 6, Turcotte and Schubert, 1982; Stüwe et al., 1994; Macktelow and Grasemann, 1997; Stüwe and Hintermüller, 2000; Braun 2002).

The new finite-element code PECUBE solves the 3D heat transport equation in a crustal/lithosphere block (e.g. bound by faults) that undergoes uplift and surface erosion and is characterized by an evolving, finite-amplitude surface topography (Fig. 7, Braun, 2003, 2005; Braun et al. 2006).

High resolution Landsat (30 m) and Radarsat images are the base for the digital elevation model that is included in the 3D thermokinematic modeling. Thermal input parameters for the thermokinematic modeling are heat diffusivity, heat production and temperature at the base of the defined crustal segment.

The T-histories of rocks, which are exhumed to the Earth’s surface, are derived from the computed crustal thermal structure. These t-T paths are used to calculate artificial closure ages of the apatite fission track and apatite (U-Th)/He system for each particle and plot those values on the recent topographic map.

The computer code statistically compares in the 3-D space the real thermochronological data with the artificial generated thermochronological data and calculates a misfit. PECUBE is a subroutine of the software code CADI that generates new input parameters out of a defined parameter space for the PECUBE software and thereby tries to minimize the misfit.

Related to the amount of input parameters and the necessary calculations to fulfil statistic requirements the calculations are performed on a cluster such as the Heidelberger HELICS-cluster.

Thermal processes in normal-fault bounded rages that influence thermochronological ages (modified after Bauer et al., 2010, Geology Today; cp also Ehlers et al., 2003)

Flow chart describing various input options of PECUBE as well as input parameters and output fields (a) the general operating mode of PECUBE (modified after Braun, 2003a) and (b) a more detailed sketch illustrating the operating mode of the inverse approach of PECUBE (modified after Braun, 2003a), (from Grobe, 2011).

Quantification of thermal parameters such as heat generation and thermal diffusivity as well as the temperature at the base of the defined crustal segment are necessary for the 2-D and 3-D thermokinematic modeling.

The heat generation can be estimated on the basis of rock density (ρ) and abundances of U (CU), Th (CTh), and K(CK) by applying the equation of Rybach (1988):

To avoid large uncertainties in the calculation of the thermal field, the thermal conductivity/diffusivity of the rocks should be known from laboratory measurements. This holds especially true for sedimentary rocks.