doi:10.1144/SP324.9 2009; v. 324; p. 111-124 Geological Society, London, Special Publications

 C. Glotzbach, C. Spiegel, J. Reinecker, M. Rahn and W. Frisch  

transect, Central Alpsthermochronology and thermal modelling along the Gotthard What perturbs isotherms? An assessment using fission-track 

Geological Society, London, Special Publications

serviceEmail alerting

article to receive free email alerts when new articles cite thisclick here

requestPermission to seek permission to re-use all or part of this article click here

SubscribePublications or the Lyell Collection

to subscribe to Geological Society, London, Specialclick here

Notes  

Downloaded by University of Minnesota on 29 March 2010

London © 2009 Geological Society of

What perturbs isotherms? An assessment using fission-track

thermochronology and thermal modelling along

the Gotthard transect, Central Alps

C. GLOTZBACH1,2*, C. SPIEGEL1,3, J. REINECKER1, M. RAHN4 & W. FRISCH1

1Institute of Geoscience, University Tubingen, Sigwartstrasse 10, 72076 Tuebingen, Germany2Present address: Laboratoire de Geodynamique des Chaınes Alpines, Universite Joseph

Fourier, BP53, 38400 Grenoble, France3Present address: FB 5 – Geoscience, University Bremen, Postfach 330 440,

28334 Bremen, Germany4Institute of Mineralogy – Geochemistry, University Freiburg, Albertstrasse 23b,

79104 Freiburg, Germany

*Corresponding author (e-mail: christoph.glotzbach@bvra.ujf-grenoble.fr)

Abstract: Interpretation of low-temperature thermochronological data usually relies on assump-tions on the shape of isotherms. Recently, a number of thermal modelling approaches investigateand predict the theoretical influence of topography on isotherms. The application and proof of thesepredictions is not well confirmed by measured data. Here we present apatite fission-track (AFT)data from samples collected along the Gotthard road tunnel and its corresponding surface line totest these predictions. AFT ages broadly cluster around 6 Ma along the tunnel. No correlation oftunnel ages with superimposed topography is seen, which means that topography-induced pertur-bation of isotherms under given boundary conditions (topographic wavelength 12 km; relief1.5 km; exhumation rate 0.45 km Ma21) can be neglected for the interpretation of AFT ages.Thus, in areas characterized by similar topographies and exhumation rates, apparent exhumationrates deduced from the age–elevation relationship (AER) of AFT data need no correction for topo-graphy-induced perturbation of isotherms. Three-dimensional (3D) numerical thermal modellingwas carried out incorporating thermally relevant parameters and mechanisms, such as topography,geology, thermal conductivities and heat production. Modelling reveals a strong influence on theshape of isotherms caused by spatially variable thermal parameters, especially heat productionrates. Therefore, not only topography has to be considered for interpreting low-temperature ther-mochronological data, but also other parameters like heat production rates.

Supplementary material: 1. Electron microprobe analyses, 2. Topography and model extend,3. Model parameters are all available online at http://www.geolsoc.org.uk/SUP18380.

The first geological applications of low-temperaturethermochronology commonly assumed that criticalisotherms (e.g. 110 8C for apatite fission track)remain horizontal in relation to topography(Schaer et al. 1975). Thermal modelling, however,predicts that in areas with pronounced relief near-surface isotherms will be influenced by topographywith compressed isotherms beneath valleys andwider-spaced isotherms beneath ridges (e.g. Stuweet al. 1994). The impact for the interpretation oflow-temperature thermochronological data, espec-ially apatite fission track (AFT) and (U–Th)/Hedata, was investigated recently (Stuwe et al. 1994;Mancktelow & Grasemann 1997; House et al.1998, 2001; Stuwe & Hintermuller 2000; Braun2002; Foeken et al. 2007). On the other hand,bending of isotherms carries potential information

to reveal minimum ages of topography and the evol-ution of palaeorelief (House et al. 1998; House et al.2001; Braun 2002; Foeken et al. 2007).

A widely used technique to derive exhumationrates utilizes the correlation of ages of a single isoto-pic system, e.g. AFT or apatite (U–Th)/He, withelevation, the so-called age–elevation relationship(AER) (Wagner & Reimer 1972; Schaer et al.1975; Stuwe et al. 1994). The great advantage, incontrast to the mineral-pair method (Wagner et al.1977), is that no estimation of the geothermal gradi-ent has to be made. However, this proxy is only validunder certain assumptions (e.g. Parrish 1983): (1)during and after passing the closure isotherm allsamples followed a vertical exhumation pathwayand no tectonic displacement exists betweensamples; (2) all samples are kinetically uniform;

From: LISKER, F., VENTURA, B. & GLASMACHER, U. A. (eds) Thermochronological Methods: From PalaeotemperatureConstraints to Landscape Evolution Models. Geological Society, London, Special Publications, 324, 111–124.DOI: 10.1144/SP324.9 0305-8719/09/$15.00 # Geological Society of London 2009.

and (3) the closure isotherm is fixed with respect tosome geographical reference horizon, e.g. sea level.

A drawback of many studies is that sample pro-files are more horizontal than vertical, and thusdeduced exhumation rates from such profiles areaffected by topography-induced perturbation of iso-therms. The magnitude of isotherm perturbationincreases with topographic wavelength, relief andexhumation rate (Stuwe et al. 1994). Hence, inmountainous regions the assumption that AFT rel-evant isotherms are flat is probably not fulfilled. Inthis case only vertical profiles (along a borehole orsteep cliff) give correct values of exhumationrates. Resulting apparent exhumation rates of AERplots from ‘near’-vertical profiles have to be cor-rected for the effect of isotherm perturbation dueto topography. This leads to the question of the geo-morphic and structural–kinematic boundary con-ditions that cause isotherm perturbation. Based onnumerical modelling and analytical solutions(Stuwe et al. 1994; Mancktelow & Grasemann1997; Stuwe & Hintermuller 2000; Braun 2002),exhumation rates of �0.5 km Ma21 along with atopographic wavelength of �10 km and a relief of�2 km are threshold values for perturbing the110 8C isotherm.

The aim of this study is to estimate the pertur-bation of isotherms under a given framework ofexhumation rate, topographic wavelength, reliefamplitude, rock properties and geothermal gradientby applying AFT thermochronology. AFT age vari-ations along the tunnel transect give evidence asto whether the 110 8C isotherm was perturbed and,if so, to what extent. For this we sampled the Got-thard road tunnel as well as the correspondingsurface line directly above the tunnel. The Gotthardroad tunnel is located in central Switzerland and hasa length of 16.3 km (Fig. 1). Present-day uplift ratesrange between 0.7 mm year21 in the north and1.1 mm year21 in the south of the tunnel (Kahle1997) (Figs 1b & 2a). The Gotthard transect ischaracterized by more or less ENE–WSW-trendingridges and valleys with a topographic wavelength of12 km and relief of up to 1.5 km (Fig. 1b). Publishedexhumation rates constrained by AFT data fromthe Gotthard Massif range between 0.45 and0.5 km Ma21 between 10 and 6 Ma (Schaer et al.1975; Wagner et al. 1977; Michalski & Soom1990). These values suggest that the Gotthardtransect is close to the lower limit of the proposedparameter values given for a 110 8C isotherm pertur-bation. Thus, this study provides a natural benchmarkto verify topography-induced perturbation of iso-therms predicted by existing modelling approaches.

In addition, a new three-dimensional (3D) finite-difference thermal model for predicting the pos-itions of isotherms beneath topography is presented.Compared to previously published analytical

solutions (Stuwe et al. 1994; Mancktelow & Grase-mann 1997; Stuwe & Hintermuller 2000) our modelprovides the following advantages: (1) it incorpor-ates 3D topography; and (2) it includes temporallyand spatially variable parameters (e.g. thermal con-ductivity, internal heat production, exhumation rateand topography). Thus, the model provides infor-mation about the influence of different thermal par-ameters on predictions of the shape of near-surfaceisotherms, comparable to the program ‘Pecube’ ofBraun (2003).

Geological setting

The Gotthard road tunnel cross-cuts the entireGotthard Massif (GM) and the southern part of theAar Massif (AM). The GM forms an ENE–WSW-trending mountain range 80 km long and upto 12 km wide (Fig. 1a). The GM and AM belong tothe external Massifs of the Alps. They consist of pre-Variscan polymetamorphic basement intruded bylate Variscan granitoids and covered by Late Palaeo-zoic–Mesozoic sedimentary rocks (Fig. 1) (e.g.Labhart 1977, 1999; Schaltegger 1994). The bound-ary between GM and AM is marked by the heavilytectonized Urseren–Garvera zone, built up bysteeply dipping Permo-Carboniferous and Mesozoicmetasediments. The sedimentary cover of the GMand AM was mostly detached during the Alpineorogeny, forming parts of the Helvetic nappes.

Peak Alpine metamorphic conditions along thetunnel were reached at around 35–30 Ma, withgreenschist-facies conditions in the north andamphibolite-facies conditions in the south (Frey &Ferreiro Mahlmann 1999). The post-metamorphicevolution of the study area was mainly controlledby the northward movement of the Adriatic indenterand related thrusting in the external Alps (e.g.Schmid et al. 1996). Thrusting during the ‘Grindel-wald stage’ (22–12 Ma) propagated towards theforeland (Schmid et al. 1996), resulting in thrustingof the Gotthard Massif upon the Tavetsch and AarMassif around 20 Ma (ductile deformation) andsubsequent steepening of these structures (brittledeformation) (Wyder & Mullis 1998). It is likelythat brittle deformation continues up to thepresent, as indicated by post-glacial vertical move-ments that are common in the study area (Persaud& Pfiffner 2004; Ustaszewski et al. 2008).

Methods

Sample sets along the Gotthard transect werecollected and 31 AFT ages measured (Fig. 2a andTable 1). Minerals were separated using standardmagnetic and heavy liquid techniques. Apatiteswere mounted in epoxy, and their internal surfaces

C. GLOTZBACH ET AL.112

were excavated by grinding and polishing. After-wards the mounts were etched by 5 M HNO3 for20 s at 20 8C. Irradiation was carried out at theFRM-II reactor in Garching (TU Munchen,Germany). Mica detectors were etched to revealinduced tracks using 40% HF at 20 8C for 40 min.Fission-track counting was carried out with anoptical microscope (Axioscope 1, Zeiss) under1000� magnification using dry lenses. Sampleswere dated using the external detector method(Naeser 1978; Gleadow 1981) using the zeta cali-bration approach (Hurford & Green 1982, 1983),with a zeta of 354 + 7 years cm22 for dosimeterglass CN5 and Durango and Fish Canyon Tuffapatite age standards. Age determination, visualiza-tion and statistics were calculated and performedwith Trackkey 4.2 g (Dunkl 2000). All AFT agesare displayed as central ages and errors as +1s(Galbraith & Laslett 1993).

Measured Dpar values were used as kinetic par-ameters (e.g. Burtner et al. 1994), complementedby electron microprobe analysis on selected crys-tals, using a JEOL Superprobe with a beamcurrent of 30 nA, an acceleration voltage of 15 kVand a beam diameter of 10 mm.

Inferred shape of isotherms from AFT data

The aim of this section is to investigate the pertur-bation of measured AFT ages under the givenboundary conditions, especially with respect totopography.

Table 1 summarizes the results of AFT datingalong the tunnel and the corresponding surfaceline. Previously published AFT data for the Gott-hard area (Schaer et al. 1975; Wagner et al. 1977;Michalski & Soom 1990) are in good agreementwith our data and are therefore included in ourinterpretations (cf. Fig. 2b).

To make sure that measured variations of AFTages are, in fact, the result of the shape of thepalaeo-isotherm, the kinetic homogeneity of ourapatites was tested by etch-pit diameter (Dpar)measurements. Dpar values obtained for measuredsamples are small and relatively uniform, varyingbetween 1.1 and 1.6 mm (Table 1). Microprobe ana-lyses of 15 samples from different lithologies werecarried out, demonstrating that all samples areclose to the F-apatite end member, with Cl contentsof less than 0.1 wt%. Furthermore, analysedelements such as Si, Mn, Ce and Sr do not show

Fig. 1. (a) Geological sketch map of central Switzerland in Swiss coordinate system. The Gotthard road tunnel islocated in the centre, crossing the southern part of the Aar Massif (AM) and the Gotthard Massif (GM). (b) Shuttle RadarTopography Mission (SRTM) digital elevation model (DEM) of the study area. Contours are measured recent rock upliftrates in mm year21 from precise levellings (Kahle 1997).

WHAT PERTURBS ISOTHERMS? 113

Fig. 2. (a) Geological profile along the Gotthard road tunnel (modified after Keller et al. 1987) with published (open circles) and own samples (black dots) (Schaer et al. 1975;Wagner et al. 1977). All samples are directly located on the plane of the transect, except some samples plotted between the tunnel and surface line, and above the surface line. Theirdistance to the plane is: 750 m (A13), 280 m (A14), 890 m (A15), 300 m (A11), 780 m (KAW0203) and 420 m (KAW0205). The dotted line shows interpolated in situ rocktemperatures measured during excavation of the tunnel (Keller et al. 1987). (b) AFT ages along the tunnel (black) and on the surface (grey).

C.

GL

OT

ZB

AC

HE

TA

L.

114

Table 1. Apatite fission-track data from the Gotthard road tunnel and a surface line directly above the tunnel

Sample Geological unit Swiss grid(CH1903) (m)

Elevation(m)

Numberof grains

rs Ns ri Ni rd Nd P(x2)(%)

Dispersion Centralage+1s(Ma)

Dpar

(mm)U

(ppm)

X Y

TunnelMRP 250 Aare Granite 688290 168840 1082 20 0.800 27 21.100 671 10.45 4998 13.2 0.30 6.8 + 1.5 1.31 16MRP 249 Aare Granite 688020 167940 1093 30 0.501 104 8.899 1846 6.407 3310 93.8 0.00 6.4 + 0.7 1.34 16MRP 248 Aare Granite 687770 167240 1102 10 0.429 30 8.000 559 6.424 3310 78.5 0.01 6.1 + 1.2 1.12 16MRP 247 Aare Granite 687530 166590 1110 12 0.230 17 4.037 298 6.441 3310 97.6 0.00 6.5 + 1.6 1.13 8MRP 246 Aare Granite 687340 166060 1117 60 0.527 184 9.012 3145 6.45 3118 99.9 0.00 6.7 + 0.5 1.24 17MRP 245 Southern Gneiss Zone 687060 165240 1127 49 1.942 434 37.985 8491 6.655 3311 47.2 0.04 6.0 + 0.3 1.63 77MRP 244 Permo-Carboniferous 686850 164330 1138 50 1.604 571 30.145 10734 6.474 3310 84.1 0.04 6.1 + 0.3 1.32 57MRP 242 Northern Paragneiss Zone 686530 162770 1157 50 0.770 360 13.266 6202 6.491 3310 51.4 0.07 6.7 + 0.4 1.41 23MRP 241 Northern Paragneiss Zone 686430 162250 1163 50 0.763 328 13.140 5649 6.6 3311 92.3 0.00 6.8 + 0.4 1.47 22MRP 240 Gamsboden Granite Gneiss 686340 161790 1168 47 1.133 315 21.050 5852 6.516 3118 99.8 0.00 6.2 + 0.4 1.41 37MRP 239 Gamsboden Granite Gneiss 686240 161280 1174 33 0.754 215 14.658 4182 6.608 3311 25.6 0.04 6.0 + 0.5 1.25 25MRP 238 Gamsboden Granite Gneiss 686280 160790 1173 35 0.900 234 17.538 4559 6.508 3310 99.4 0.00 5.9 + 0.4 1.21 32MRP 237 Gamsboden Granite Gneiss 686360 160460 1172 50 1.165 431 23.019 8519 6.549 3118 97.8 0.00 5.9 + 0.3 1.41 41MRP 236 Gamsboden Granite Gneiss 686640 159460 1168 50 0.863 161 16.091 3003 6.524 3310 74.7 0.02 6.2 + 0.5 1.29 28MRP 235 Gamsboden Granite Gneiss 686820 158830 1166 50 0.754 277 13.656 5016 6.541 3310 77.8 0.03 6.4 + 0.4 1.41 25MRP 234 Gamsboden Granite Gneiss 686920 158500 1165 50 0.821 192 15.543 3637 7.055 3397 81.3 0.00 6.6 + 0.5 1.41 26MRP 233 Guspis Zone 687160 157770 1162 50 0.419 240 7.964 4562 6.558 3310 99.5 0.00 6.1 + 0.4 1.57 15MRP 232 Fibbia Granite Gneiss 687370 157150 1160 51 0.743 212 13.843 3951 6.574 3310 66.4 0.05 6.3 + 0.5 1.34 25MRP 231 Sorescia Gneiss 687670 156340 1157 50 1.755 725 36.502 15083 6.591 3310 60.8 0.09 5.6 + 0.3 1.26 66MRP 230 Tremola Serie 688030 155380 1153 25 0.123 27 2.304 504 6.582 3118 90.5 0.00 6.3 + 1.2 1.51 4MRP 229 Tremola Serie 688730 154050 1147 50 0.223 90 3.941 1589 6.615 3118 95.8 0.00 6.6 + 0.7 1.42 7

SurfaceMRP 278 Aare Granite 688180 168400 1265 50 0.806 168 16.205 3376 8.277 4059 50.4 0.11 7.3 + 0.6 1.32 23MRP 279 Aare Granite 687800 167320 1315 50 0.821 171 16.885 3516 8.303 4059 7.0 0.27 7.2 + 0.6 1.20 23MRP 290 Permo-Carboniferous 686730 163585 1510 50 0.994 420 19.662 8305 8.354 4059 4.1 0.20 7.5 + 0.4 1.26 27MRP 291 Gamsboden Granite Gneiss 686150 161390 1690 50 1.348 499 21.959 8131 6.391 3310 71.8 0.02 7.0 + 0.4 1.26 40CGP 11 Gamsboden Granite Gneiss 686240 160740 1725 44 1.230 467 19.488 7397 6.608 3310 32.5 0.10 7.4 + 0.4 1.28 33MRP 292 Gamsboden Granite Gneiss 686650 159420 2380 50 1.446 423 22.012 6439 8.430 4059 71.3 0.06 9.6 + 0.5 1.31 30CGP 05 Rotondo Granite 687129 157340 2580 36 0.898 197 11.761 2579 6.658 3310 59.6 0.09 9.0 + 0.7 1.30 21MRP 294 Sorescia Gneiss 687640 156530 2140 50 0.896 389 11.303 4905 6.374 3310 99.9 0.00 9.0 + 0.5 1.28 21CGP 07 Tremola Serie 688851 154073 1320 23 0.459 83 7.140 1291 6.624 3310 72.7 0.16 7.6 + 0.9 1.31 13MRP 276 Tremola Serie 689065 153820 1220 17 0.525 43 10.755 881 8.405 4059 54.6 0.01 7.3 + 1.2 1.59 14

rs (r i) are spontaneous (induced) track densities (105 tracks cm22); Ns (Ni) is number of counted spontaneous (induced) tracks; rd is dosimeter track density (105 tracks cm22); Nd is number of tracks counted ondosimeter; P(X2) is the probability obtaining Chi-square value (X2) for n degrees of freedom (where n is the number of crystals minus 1); dispersion is a real number, that gives an idea of the variability of thesingle grain age distribution, it is zero if all the data are identical, and increases as the data become more diverse; age +1 s is the central age +1 standard error (Galbraith & Laslett 1993); Dpar is the etch-pitdiameter of fission tracks, averaged from four measurements per analysed grain. Ages were calculated using the zeta calibration method (Hurford & Green 1983), glass dosimeter CN-5, and a zeta value of354.92 + 7.03 years cm22.

WH

AT

PE

RT

UR

BS

ISO

TH

ER

MS

?115

any significant variation, suggesting that apatites arekinetically uniform (for details see p. 1 of the sup-plementary material for this paper).

AFT ages of samples collected at the sameelevation can be used to predict the palaeoshape ofthe critical isotherm (House et al. 1998). Allsamples along the Gotthard tunnel are at approxi-mately 1.1 km elevation and yield AFT ages of6.2 + 0.6 Ma, overlapping within 1s-error limits(Fig. 2b). Individual samples characterized by lowU-content show larger 1s-error, especially thosefrom the northern and southern ends of the transect.

Surface samples yield AFT ages ranging from7.0 to 9.6 Ma. Surface samples collected at approxi-mately 1.3 km elevation along the Gotthard transect(CGP 07, MRP 276, MRP 278 and MRP 279)exhibit the same ages of 7.4 + 0.2 Ma. Thus, AFTage patterns on two structural elevation levels(c. 1.1 and c. 1.3 km) indicate that between 6.2and 7.4 Ma the 110 8C isotherm was flat, suggestingthat topography has no visible effect on the AFT agepattern along the tunnel. Small variations in agespartly coincide with stratigraphic–tectonic bound-aries (Fig. 2b), which can be explained by kineticor physical differences (such as heat productionand thermal conductivities).

Surface AFT ages show an increase withelevation (Figs 2b & 3). Slopes of AER were calcu-lated by weighting the ages according to their errors.Slopes and uncertainties were inverted to estimateexhumation rates with defined uncertainties(Reiners et al. 2003).

Regression bands were plotted with a 95% con-fidence interval, which allows prediction of theerror of the regression lines. The AER plot forsamples of the northern flank of the GotthardMassif (MRP 237, MRP 238, CGP 11 and MRP292) yields an apparent exhumation rate of0.35 + 0.1 km Ma21 for the period between 10

and 5 Ma (Fig. 3a). The horizontal and vertical dis-tance between the samples is 1.5 and 1.2 km,respectively. Samples of the southern flank (MRP229, MRP 276, MRP 294, CGP 07 and A14 ofSchaer et al. 1975) yield an apparent exhumationrate of 0.5 + 0.2 km Ma21 for the period between10 and 6 Ma (Fig. 3b). Here the horizontal and ver-tical distance between the samples is 4 and 1.6 km,respectively. Deduced apparent exhumation ratesare in good accordance with previously publisheddata (Schaer et al. 1975; Michalski & Soom1990). The presented data suggest that critical iso-therms are flat under the Gotthard transect anda correction for topography is not necessary.

Modelling the shape of isotherms

Although we demonstrated that in the specific caseof the Gotthard transect no topographic correctionis required, in the following section we test thetheoretical influence of topography and other ther-mally relevant parameters on near-surface iso-therms. We present numerical 3D finite-differencethermal models developed for a crustal block of14 � 26 � 10 km around the Gotthard road tunnel(an overview is provided on p. 2 of the supplemen-tary material). Modelling incorporates spatial and/or temporal varying parameters, namely topogra-phy, exhumation rates, thermal conductivity andheat production (for details see p. 3 of the sup-plementary material). The parameter values areeither taken from this study (exhumation rates) orfrom geophysical measurements (e.g. Busslinger &Rybach 1999). In the following, all mentionedisotherm perturbation values refer to the locationof the Gotthard road tunnel transect, and aredefined here as the maximum vertical deflection ofthe corresponding isotherm.

Fig. 3. AFT age–elevation relationship of surface samples (a) of the northern flank (MRP 292, CGP 11, MRP 237,MRP 238) and (b) of the southern flank (A14 from Schaer et al. 1975: MRP 294, MRP 276, CGP 07, MRP 229) of theGotthard transect.

C. GLOTZBACH ET AL.116

For simplification in the first step it is assumedthat heat transfer in the crust is controlled by con-duction only (Stuwe 2007). In this case Fourier’slaw of heat conduction can be used:

@T

@t¼ k �r2T (1)

where k is the thermal diffusivity with typical valuesof around 1026 m2 s21, T is temperature, t is timeand r is the nabla operator, describing here thespatial change of temperature in 3D (e.g. Stuwe2007). Equation (1) is modified to account for theeffect of exhumation and internal heat productiondue to radioactive decay, resulting in:

@T

@t¼ k � r2T þ u � @T

@zþ S

r � cp

(2)

where z is depth, S the heat production rate, r therock density and cp the specific heat. Initial andboundary conditions necessary for the solution ofthe differential equation (2) are as follows.

† The lower boundary of the model was placed at210 km from the surface and was fixed with aconstant vertical geothermal gradient, forwhich a value of 20 8C km21 was used basedon borehole and tunnel temperature measure-ments in or near the Gotthard road tunnel(Keller et al. 1987). To verify that this relatively‘shallow’ lower boundary allows the deflectionof isotherms caused by thermal relevant par-ameters (e.g. topography and exhumation), asimple 2D sinus-shaped topography was mod-elled analytically using the program ‘TERRA’(Ehlers et al. 2005) (Fig. 4). Used parametersfit those from the Gotthard transect. Position

of isotherms are unaffected by the depth ofthe lower boundary of the model.

† Topography was used as an upper-boundarycondition, discretized with a rectangular gridand converted into air temperature, dependingon elevation (Busslinger & Rybach 1999):

TAir ¼ T0 � a � h (3)

with TAir being the mean air temperature atsurface, T0 the air temperature at sea level, athe atmospheric lapse rate and h the elevation.Kohl et al. (2001) showed that ground surfacetemperature (GST) data collected from highelevations in Alpine terrain are best describedby the model of Niethammer (1910), withT0 ¼ 12 8C and a ¼ 4.6 8C km21. These val-ues were used to calculate GST for each nodebased on a Shuttle Radar Topography Mission(SRTM) digital elevation model (DEM). Weneglected the difference between air tempera-ture and the corresponding GST depending onexposition (slope and orientation), vegetation,snow cover and rock surface properties (e.g.Safanda 1999). Consequently, each node of theupper boundary is composed of an elevationand a corresponding GST.

† Lateral boundaries were fixed with no horizon-tal heat flow. For simplification a uniform dis-tance from node to node (Dx ¼ Dy ¼ Dz) of132.9 m was used, according to the spatial res-olution of the input DEM. Thus, the total meshwas built up by 1.55 � 106 nodes. A simplifiedgeological model was used for the modelling,which considered five geological units: AarMassif, Urseren Zone, Tavetsch Massif, Got-thard Massif and Schistes lustres (Fig. 1 andTable 2). Vertical boundaries between individ-ual geological units were assumed, consistentwith high dip angles observed at the surfaceand during tunnel construction (Fig. 2a). Thegeological units are characterized by differentphysical and thermal properties. The foliationdeveloped during Alpine metamorphismresults in a pronounced anisotropic thermalconductivity of all geological units, withratios of up to 1.5 between maximum (kk) andminimum (k?) values within one unit(Kappelmeyer & Haenel 1974; Kohl et al.2001). Input thermal conductivities are listedin Table 2. Rock radioactivity measurementswithin the tunnel (Keller et al. 1987) were usedto calculate the total heat production relatedto the radioactive decay of uranium, thoriumand potassium (Turcotte & Schubert 1982,equations 4–6). Resulting heat productionvalues ranged from 7.54 � 10211 to2.56 � 1029 W kg21 for individual geological

Fig. 4. Position of the 60 and 110 8C isothermsdepending on the depth of the lower boundary. Modelparameters are: steady-state topography with awavelength of 12.5 km and an amplitude of 0.5 km;exhumation rate of 0.45 km Ma21; lower boundary at210 km/2100 km with a temperature of 245 8C/1000 8C; upper boundary fixed by topography andsurface temperature calculated with 12 8C at 0 m and alapse rate of 4.6 8C km21; thermal diffusivity1 � 1026 m2 s21; density 2700 kg m23; specific heat1000 J kg21 K21; heat production 3 � 1026 W m23

with a skin depth of 10 km.

WHAT PERTURBS ISOTHERMS? 117

units, with 1.22 � 1029 W kg21 as an averagevalue. Modelling was carried out either withindividual values or an averaged heat productionrate extrapolated to the surroundings of the Got-thard road tunnel (Table 2). Tunnelling and geo-physical investigations revealed that the Aar andGotthard Massifs continue towards depth, poss-ibly by more than 10 km (Pfiffner & Heitzmann1997). Therefore, heat production rates areassumed to be constant with depth. Modellingwas conducted assuming both a steady-stateand time-varying topography, and a constantexhumation rate of 0.45 km Ma21 (mean valueof the AER plots in Fig. 3). To account for a time-varying topography nodes were added/removedand temperature adjusted (according to equation3) at the upper boundary during the modellingprogress. For instance, a change in elevationfrom 0 to 2000 m in 2 Ma, is implemented byadding one node (132.9 m) every 0.133 Ma(reaching an elevation of 1994 m after 2 Ma).A simple 2D thermal model was numericallycalculated and compared with an analytical sol-ution calculated with the program ‘TERRA’(Ehlers et al. 2005) (Fig. 5), proving the correct-ness of the used finite-difference thermalmodel approach.

From several performed model runs we presentfive solutions, which differ by the assumedthermal conductivity, heat production and topo-graphic evolution (Table 3). Models 1–3 were cal-culated until reaching a steady-state temperaturefield, which takes around 5 Ma depending on theparameterization. Models 4 and 5 were calculatedwith an initial steady-state temperature field, sub-sequently adapted during the modelling progressbecause of a changing topography.

To evaluate the influence of thermally relevantparameters (e.g. topography) on low-temperaturethermochronology in the following models,closure temperatures of 110 and 60 8C wereassumed for the apatite fission-track (e.g. Rahn &Grasemann 1999) and (U–Th)/He system (e.g.Ehlers & Farley 2003), respectively. AFT agedifferences along the tunnel are predicted, usingforward modelling of AFT ages with the programHeFTy (Ketcham et al. 2007) based on measuredkinetic parameters (Dpar) and generated time–temperature (tT) path for selected localities. There-fore, during modelling progress the temperaturesof selected localities were read out every 10 ka,yielding nearly continuous tT paths.

Figure 6 shows the predicted steady-state 110 8Cisotherm for different model runs, and the contoursof the corresponding 2D shape of the 60 and 110 8Cisotherms along the Gotthard road tunnel.

The benefit of model 1 is that we can estimate thenet influence of the topography on a chosen iso-therm because all other input parameters arespatially uniform. The modelled 110 8C isothermclearly demonstrates that small topographic featureshave no influence on the isotherm (Stuwe et al.1994; Mancktelow & Grasemann 1997). Thus,according to model 1, the shape of the isothermfollows the topography in a strongly dampenedfashion (Stuwe et al. 1994) and is clearly deformedbeneath the Gotthard Massif, with a perturbation of250 m. Resulting maximum AFT age differencealong the tunnel is 0.5 Ma (modelled ages rangefrom 6 to 5.5 Ma).

Table 2. Geological units with their anisotropic thermal conductivities (k)parallel and perpendicular to foliation and heat production values

Geological unit kk k? Heat production

(W m21 K21) (W m21 K21) (1029 W kg21)

Aar Massif 3.66* 2.83* 1.57–1.92Gotthard Massif 4.43* 2.95* 0.51–1.50Tavetsch Massif 3.61* 2.79* 1.92Urseren-Garvera zone 3.10* 2.45* 1.17Schistes lustres 3.10† 2.40† 0.51

*Kohl et al. (2001); †Kappelmeyer & Haenel (1974).

Fig. 5. Comparison between an analytical solution fromthermal modelling program TERRA (Ehlers et al. 2005)and the numerical model presented in this study for asimple 2D model. Model parameters are the same as inFigure 4, except a lower boundary at 210 km with atemperature of 220 8C.

C. GLOTZBACH ET AL.118

Incorporating spatially variable and anisotropicthermal conductivities (model 2) results in anoverall deeper 110 8C isotherm, because averageinput thermal conductivities are higher than thoseused for model 1. The shape of the 110 8C isothermin model 2 is similar to that from model 1, apartfrom a smaller isotherm perturbation of only150 m (Fig. 6). Areas characterized by low

thermal conductivities (Urseren zone and Schisteslustres, cf. Fig. 1) accumulate heat that bulge the110 8C isotherm. We conclude that the observeddifferences and anisotropy of thermal conductivitiesalong the Gotthard road tunnel (Table 2) do onlyweakly influence the shape of the near-surface iso-therms. For models 1 and 2, the corresponding per-turbation of the 60 8C isotherm is more or less twice

Table 3. Input parameters of individual model runs

ModelNo.

Topography Thermalconductivity

(W K21

m21)

Heatproduction(1029 W

kg21)

Rockuplift rate

(km Ma21)

Surfaceuplift rate

(km Ma21)

Exhumationrate

(km Ma21)

1 Recent, steady state 2.7 1.22 0.45 0 0.452 Recent, steady state Anisotropic,

cf. Table 21.22 0.45 0 0.45

3 Recent, steady state Anisotropic,cf. Table 2

Anisotropic,cf. Table 2

0.45 0 0.45

4 0 m to recent,increasing

Anisotropic,cf. Table 2

Anisotropic,cf. Table 2

0.45 0.10–0.27 0.18–0.35

5 Decreasing 2.7 1.22 0.45 20.10 to 20.22 0.55–0.67

Fig. 6. Three-dimensional models of the 110 8C isotherms with contours in metres below sea level calculated withparameters listed in Tables 2 and 3. The Gotthard road tunnel is marked by the white line. The corresponding position ofthe 60 and 110 8C isotherms with topography is shown in the graphs below. D AFT describes the variation of AFT agesalong the tunnel transect, predicted by the different model runs.

WHAT PERTURBS ISOTHERMS? 119

as high compared to the perturbation of the 110 8Cisotherm. However, the resulting AFT age differ-ence along the tunnel is only 0.2 Ma (modelledages range from 6.7 to 6.5 Ma).

From model 3, a laterally variable heat pro-duction was added, resulting in a more complex110 8C isotherm shape. Interestingly, the pro-nounced topography of the Gotthard Massif,forming an ENE–WSW-trending ridge in thesouthern tunnel section, is not mirrored by the110 8C isotherm. Evidently, differences in heat pro-duction values are capable of blurring the effect oftopography. As demonstrated by model run 1, thenet topographic effect is small. Thus, for model 3,the perturbation of the 110 8C can be nearly comple-tely attributed to the spatial variation of heatproduction, which here was assumed to persist tothe depth of 10 km. Owing to the lateral decreasein total heat production rate, the shape of the110 8C isotherm along the tunnel profile shows asteady decrease to the south, with a perturbation of550 m. The 60 8C isotherm runs more or lesshorizontally up to tunnel kilometre 12 and thendecreases towards the south with a total perturbationof 450 m. For this model run, variations of AFTages in the range of 1.2 Ma (modelled ages rangefrom 7.6 to 6.4 Ma) along the tunnel are predicted.The perturbation effect of topography and heatproduction at that depth becomes less pronouncedin the northern part of the transect. Thus, differencesin heat production are capable of compensating(northern section) and amplifying (southernsection) the perturbation of isotherms owing totopography (Fig. 6).

A palaeotopographic evolution with increasingrelief after 5 Ma, assuming isotropic thermal par-ameters, would result in flat isotherms at the timethe AFT samples cross the 110 8C isotherm, follow-ing the observation of model 1. In the extreme casethat the palaeotopography is flat at that time, result-ing AFT ages along the tunnel are all the same.Incorporating spatial variable heat production rates(model 4) results in increased isotherm perturbationwith depth, with perturbation values of the 60 and110 8C isotherms of 250 and 500 m, respectively(Fig. 6).

To investigate the effect of a possible palaeoto-pographic evolution with higher relief and peakelevations in Late Miocene times (6 Ma), whichdecrease to the present, model 5 was carried outassuming initial maximum elevations of 5 km anda relief of 3 km. The shape of resulting isothermsis comparable to that of model 1, however, withmore pronounced isotherm perturbations of 450 m(110 8C) and 750 m (60 8C). The doubling of thevertical isotherm perturbation with respect tomodel 1 corresponds to a doubling in the FT agedifference along the tunnel.

Influence of advective heat transport

on low-temperature isotherms

To investigate the impact of heat advection due tofaulting on isotherms and AFT ages simple 2Dnumerical modelling was carried out. A flat topogra-phy was assumed with two crustal blocks exhumedwith rates of 0.5 and 1 km Ma21 (Fig. 7a).

Fig. 7. (a) Two-dimensional numerical model with two crustal blocks separated by a perpendicular fault. Crustal blocksdiffer in their rock uplift rates and resulting exhumation rate assuming steady-state topography. Calculated 110 8Cisotherms for different time steps (0, 0.01, 0.1, 0.5 and 1 Ma) are displayed. The total shift of the 110 8C isotherm afterinfinite time is indicated by a dashed line. (b) Relationship between perturbation of the 110 8C isotherm and relativedisplacement along the fault.

C. GLOTZBACH ET AL.120

Assuming steady-state conditions and an exhuma-tion rate of 0.5 km Ma21, the 110 8C isotherm isat a depth of c. 3 km. Initiation of a perpendicularfault and increased exhumation (1 km Ma21) onone side of the fault results in a perturbation of iso-therms depending on the duration of displacement.Short-term movements (,0.1 Ma) result in a lesspronounced perturbation of the isotherm across thefault (,50 m) and a displacement of the crustalblocks of ,50 m. For small displacements heatadvection approximates relative rock uplift(Fig. 7b); hence advective heat flow dominates thetemperature field. For long-term movements,however, the role of diffusion increases. Thus theperturbation of the 110 8C isotherm is small as com-pared to the displacement (e.g. for a duration of1 Ma, a perturbation of 200 m corresponds to a rela-tive displacement of 500 m). Infinite displacementresults in a maximum possible isotherm pertur-bation of c. 320 m.

Discussion

In the following some essential requirements for theinvestigation of isotherm perturbation due to topo-graphy are discussed. In addition, we discuss themeasured AFT age pattern in light of the modelledpredictions of isotherm perturbation.

Advective and convective heat transport

In addition to the discussed thermally relevant par-ameters (e.g. heat production), near-surface temp-eratures are affected by advective and convectiveheat transport. Therefore, an important prerequisitefor investigations on isotherm perturbations is thatadvective and convective heat transport must be neg-ligible or quantifiable over geological timescales.

Advective heat transport may be caused bydeformation and spatial differences in rock upliftrates. Studies on brittle deformation structures andhydrothermal mineral precipitation along the Got-thard road tunnel showed that the main phase ofbrittle faulting had ceased before the structurallevel of the tunnel samples cooled below 190 8C(Luetzenkirchen 2002). First-order precise levellingof the Swiss national levelling network revealedonly a slight gradient of present-day vertical move-ments within the area of the Gotthard Massif(Fig. 1b), with rates of 0.8–1.0 mm year21 (Kahle1997). On a smaller scale, however, remotesensing analysis, field work and numerical model-ling demonstrate the activity of uphill-facingscarps in the Urseren valley as a response to isostaticvertical movements after the last Ice Age (Dahinden2001; Persaud & Pfiffner 2004; Hampel & Hetzel2006; Ustaszewski et al. 2008). AFT ages along

the Gotthard road tunnel show no jumps in ages(Fig. 2b), thus a differential vertical displacementof individual crustal blocks has been small and ishidden within the 1s-error of the AFT ages. Assum-ing an exhumation rate of 0.5 km Ma21 and anaverage AFT error of 0.6 Ma, only a vertical displa-cement of more than 300 m along a fault would besignificant. We conclude that vertical displacementsalong fault zones were small and therefore can beneglected for the last 6 Ma. Simple 2D thermal mod-elling of movements along a single vertical faultshow that a displacement of 300 m is capable ofgenerating a perturbation of the 110 8C isothermof approximately 150 m (Fig. 7). We cannotexclude the fact that mass advection along the Got-thard transect possibly led to a perturbation of iso-therms of less than 150 m, which in magnitude isclose to the net topography-induced isotherm per-turbation (see models 1 and 2, Fig. 6).

Convective heat transport may play an importantrole in the total heat transport in high mountainousareas (e.g. Whipp & Ehlers 2007). During construc-tion of the Gotthard road tunnel water inflowmeasurements were carried out, with maximumin situ measured rock temperatures of 32 8C(Fig. 2a) (Keller et al. 1987; Luetzenkirchen 2002).Except for an area in the central Gamsbodengranite-gneiss, which is assumed to be affected bya near-surface convective hydrothermal circuit(Pastorelli et al. 2001; Luetzenkirchen 2002),measured rock temperatures are correlated totopography.

We conclude that advective and convective heattransport are negligible, and that conductive heattransport dominates and controls the temperaturedistribution in the upper crust of the study area.

Predicted v. observed ages

A striking characteristic when comparing the mod-elled shape of isotherms and measured AFT agesalong the Gotthard transect is the incompatibilityof the more complex model 3, including spatiallyvariable thermal conductivities and heat productionrates. A possible explanation could be that measuredradioactivities in the rocks of the Gotthard roadtunnel and the resulting heat production rates arenot representative of the entire lithological unit,and, thus, cannot be extrapolated straightforwardly.Alternatively, perturbation of isotherms may becompensated for because of the spatially variableexhumation rates increasing to the south, which islikely when the deduced exhumation rates are con-sidered. Mean exhumation rates of between 10and 6 Ma are higher on the southern flank of theGotthard Massif compared to the northern flank(Fig. 3). The present-day uplift rates show thesame trend (Kahle 1997). Repeating model run 3

WHAT PERTURBS ISOTHERMS? 121

with exhumation rates increasing from north(0.45 km Ma21) to south (0.55 km Ma21) results inan AFT age pattern similar to that measured for thesurface and tunnel samples (Fig. 8). These exhuma-tion rates are optimized to match the measuredAFT ages and the AER-derived exhumation rates.Thus, small spatial differences in exhumation ratesare able to compensate for and mask the perturbationof isotherms resulting from other thermal par-ameters. Therefore, we conclude that measuredAFT age variations along the Gotthard road tunnel(6.2 + 0.6 Ma) do not preclude any presentedmodel or palaeotopographic evolution. The Gotthardtransect, however, is characterized by steady exhu-mation rates (Schaer et al. 1975; Wagner et al.1977), and more or less vertically oriented tectonicstructures and boundaries (Fig. 1b), facilitating thegeneration of a steady-state topography withspatially invariant ridges and valleys (Willett &Brandon 2002). But steady-state conditions arerarely achieved, especially relating to the LateNeogene climate change and the increased frequency

in climatic oscillations (Whipple & Meade 2006).Most probably, positive feedback between climatechange, weathering, erosion and isostatic reboundled to an increase in relief over the last millionyears (e.g. England & Molnar 1990; Molnar &England 1990). However, resolving the latestNeogene (,5 Ma) exhumation history of the Gott-hard Massif is beyond the scope of this paper andwill require the use of apatite (U–Th)/He data.

Conclusions

Apatite fission-track data along the Gotthard roadtunnel and its corresponding surface line are com-pared with 3D numerical thermal modellingresults. Modelling allows the interplay and relativeimportance of 3D topography, spatially variablethermal conductivities, heat production rates andexhumation rates on the shape of low-temperatureisotherms to be investigated. In addition, thepossible impact of advective and convective heattransport was examined.

Fig. 8. Measured AFT ages (black dots, with 1s age errors) and modelled AFT ages (grey squares) of (a) surfacesamples and (b) tunnel samples. Model parameters are that of model 3, but with the assumption that exhumation rateslinearly increase from north (0.45 km Ma21) to south (0.55 km Ma21).

C. GLOTZBACH ET AL.122

The following conclusions were obtained.

† The AER of AFT ages yielded exhumation ratesof 0.35 + 0.1 km Ma21 (northern flank of theGotthard transect) and 0.5 + 0.2 km Ma21

(southern flank), similar to previously pub-lished data (Schaer et al. 1975; Michalski &Soom 1990).

† Measured AFT ages from tunnel samples werearound 6.2 Ma (5.6–6.8 Ma), with no signifi-cant trend. A perturbation of AFT ages due totopography, with young ages correlating withmaximum overburden, is not visible along theGotthard road tunnel. Because AFT age errorsrange from 5 to 25% (0.3–1.6 Ma), a pertur-bation of approximately 0.6 Ma will mostlyremain hidden behind the data scatter.

† Modelling reveals that spatially variable heatproduction and exhumation rates strongly influ-ence the shape of near-surface isotherms, andneed to be considered for the interpretation oflow-temperature thermochronological data. Inthe specific case of the Gotthard transect, themodelled perturbation of the 110 8C isothermis in the range of 150–550 m (the correspond-ing difference in AFT ages along the tunnel isbetween 0.3 and 1.2 Ma), depending on theinput parameters and boundary conditions.

† This study illustrates that topography-inducedperturbation of isotherms can be neglectedfor the interpretation of AFT ages under thegiven boundary conditions (topographic wave-length 12 km; relief 1.5 km; exhumation rate0.45 km Ma21) and petrophysical parametersof the Gotthard transect, such as thermalconductivities.

This study was funded by the German Science Foundation(DFG), project SP 673/2. G. Hockh, D. Muhlbayer-Rennerand D. Kost (Universitat Tubingen) are gratefullyacknowledged for the mineral separation. Thanks also toT. Wenzel (Universitat Tubingen) for his support duringelectron microprobe analysis. M. Zattin and P. van derBeek are thanked for their constructive reviews ofthis manuscript.

References

BRAUN, J. 2002. Quantifying the effect of recent reliefchanges on age–elevation relationships. Earth andPlanetary Science Letters, 200, 331–343.

BRAUN, J. 2003. Pecube: a new finite-element code tosolve the 3D heat equation including the effects of atime-varying, finite amplitude surface topography.Computers & Geosciences, 29, 787–794.

BURTNER, R. L., NIGRINI, A. & DONELICK, R. A. 1994.Thermochronology of Lower Cretaceous source rocksin the Idaho–Wyoming thrust belt. AAPG Bulletin, 78,1613–1636.

BUSSLINGER, A. & RYBACH, L. 1999. Felstemperatur-prognose fur tiefliegende Tunnel. Tunnel, 1, 24–32.

DAHINDEN, T. 2001. Verschiebungsmessungen imGotthardgebiet. Diploma thesis, ETH Zurich.

DUNKL, I. 2000. Trackkey: a windows program for calcu-lation and graphical presentation of fission track data.Computers & Geosciences, 28, 3–12.

EHLERS, T. A. & FARLEY, K. A. 2003. Apatite (U–Th)/He thermochronometry: methods and applications toproblems in tectonic and surface processes. Earthand Planetary Science Letters, 206, 1–14.

EHLERS, T. A., CHAUDHRI, T. & KUMAR, S. 2005. Com-putational tools for low-temperature thermochron-ometer interpretation. Reviews in Mineralogy &Geochemistry, 58, 589–622.

ENGLAND, P. & MOLNAR, P. 1990. Surface uplift, upliftof rocks, and exhumation of rocks. Geology, 18,1173–1177.

FOEKEN, J. P. T., PERSANO, C., STUART, F. M. & TER

VOORDE, M. 2007. Role of topography in isothermperturbation: apatite (U–Th)/He and fission trackresults from the Malta tunnel, Tauern Window,Austria. Tectonics, 26, doi:10.1029/2006TC002049.

FREY, M. & FERREIRO MAHLMANN, R. 1999. Alpinemetamorphism of the Central Alps. SchweizerischeMineralogische und Petrographische Mitteilungen,79, 135–154.

GALBRAITH, R. F. & LASLETT, G. M. 1993. Statisticalmodels for mixed fission track ages. Nuclear Tracksand Radiation measurements, 21, 459–470.

GLEADOW, A. J. W. 1981. Fission-track dating methods:what are the real alternatives? Nuclear Tracks andRadiation Measurements, 5, 3–14.

HAMPEL, A. & HETZEL, R. 2006. Response of normalfaults to glacial–interglacial fluctuations of ice andwater masses on Earth’s surface. Journal of Geophysi-cal Research, 111, doi:10.1029/2005JB004124.

HOUSE, M. A., WERNICKE, B. P. & FARLEY, K. A.1998. Dating topography of the Sierra Nevada,California, using apatite (U–Th)/He ages. Nature,396, 66–69.

HOUSE, M. A., WERNICKE, B. P. & FARLEY, K. A.2001. Paleo-geomorphology of the Sierra Nevada,California, from (U–Th)/He ages in apatite. AmericanJournal of Science, 301, 77–102.

HURFORD, A. J. & GREEN, P. F. 1982. A users’ guide tofission track dating calibration. Earth and PlanetaryScience Letters, 59, 343–354.

HURFORD, A. J. & GREEN, P. F. 1983. The Zeta age cali-bration of fission-track dating. Chemical Geology(Isotope Geoscience Section), 41, 285–317.

KAHLE, H.-G. 1997. Recent crustal movements, geoid anddensity distribution; contribution from integrated satel-lite and terrestrial measurements. In: PFIFFNER, O. A.,LEHNER, P., HEITZMANN, P., MULLER, S. & STECK,A. (eds) Results of NRP 20; Deep Structure of the SwissAlps. Birkhaeuser, Basel, 251–259.

KAPPELMEYER, O. & HAENEL, R. 1974. Geothermicswith Special Reference to Application. GeoexplorationMonographs. Gebruder Borntrager, Stuttgart.

KELLER, F., WANNER, H. & SCHNEIDER, T. R. 1987.Geologischer Schlussbericht Gotthard-Strassentunnel.Beitrage zur Geologie der Schweiz: GeotechnischeSerie, 70.

WHAT PERTURBS ISOTHERMS? 123

KETCHAM, R. A., CARTER, A., DONELICK, R. A.,BARBARAND, J. & HURFORD, A. J. 2007. Improvedmodeling of fission-track annealing in apatite.American Mineralogist, 92, 799–810.

KOHL, T., SIGNORELLI, S. & RYBACH, L. 2001. Three-dimensional (3-D) thermal investigation below highAlpine topography. Physics of the Earth and PlanetaryInteriors, 126, 195–210.

LABHART, T. P. 1977. Aarmassiv und Gotthardmassiv.Sammlung geologischer Fuhrer, 63. Gebr. Borntrager,Berlin.

LABHART, T. P. 1999. Aarmassiv, Gotthardmassiv undTavetscher Zwischenmassiv: Aufbau und Entstehungs-geschichte. In: LOW, S. & WYSS, R. (eds) Vorerkun-dung und Prognose der Basistunnels am Gotthardund am Lotschberg. A. A. Balkema, Rotterdam, 31–43.

LUETZENKIRCHEN, V. H. 2002. Structural Geology andHydrogeology of Brittle Fault Zones in the CentralEastern Gotthard Massif, Switzerland. PhD thesis,ETH Zurich.

MANCKTELOW, N. S. & GRASEMANN, B. 1997. Time-dependent effects of heat advection and topographyon cooling histories during erosion. Tectonophysics,270, 167–195.

MICHALSKI, I. & SOOM, M. 1990. The Alpine thermo-tectonic evolution of the Aar and Gotthard Massifs,Central Switzerland: fission track ages on zircon andapatite and K–Ar mica ages. Schweizerische Minera-logische und Petrographische Mitteilungen, 70,373–387.

MOLNAR, P. & ENGLAND, P. 1990. Late Cenozoic upliftof mountain ranges and global climate change: chickenor egg? Nature, 346, 29–34.

NAESER, C. W. 1978. Fission Track Dating. US Geologi-cal Survey Open-File Report, 76–190.

NIETHAMMER, G. 1910. Die Warmeverteilung imSimplon. Ecologae Geologicae Helvetiae, 11, 96–120.

PARRISH, R. R. 1983. Cenozoic thermal evolution and tec-tonics of the Coast Mountains of British Columbia,1. Fission track dating, apparent uplift rates, and pat-terns of uplift. Tectonics, 2, 601–631.

PASTORELLI, S., MARINI, L. & HUNZIKER, J.-C. 2001.Chemistry, isotope values (dD, d18O, d34SSO4) andtemperatures of the water inflows in two Gotthardtunnels, Swiss Alps. Applied Geochemistry, 16,633–649.

PERSAUD, M. & PFIFFNER, O. A. 2004. Active defor-mation in the eastern Swiss Alps: post-glacial faults,seismicity and surface uplift. Tectonophysics, 385,59–84.

PFIFFNER, O. A. & HEITZMANN, P. 1997. Geologicalinterpretation of the seismic profiles of the CentralTraverse (lines C1, C2 and C3-north). In: PFIFFNER,O. A., LEHNER, P., HEITZMANN, P., MUELLER, ST.& STECK, A. (eds) Deep Structure of the Swiss Alps:Results of NRP 20. Birkhauser, Basel, 115–122.

RAHN, M. K. & GRASEMANN, B. 1999. Fission track andnumerical thermal modeling of differential exhuma-tion of the Glarus thrust plane (Switzerland). Earthand Planetary Science Letters, 169, 245–259.

REINERS, P. W., ZHOU, Z., EHLERS, T. A., XU, C.,BRANDON, M. T., DONELICK, R. A. & NICOLESCU,S. 2003. Post-orogenic evolution of the Dabie Shan,

eastern China, from (U–Th)/He and fission-trackthermochronology. American Journal of Science,303, 489–518.

SAFANDA, J. 1999. Ground surface temperature as a func-tion of slope angle and slope orientation and its effecton the subsurface temperature field. Tectonophysics,306, 367–375.

SCHAER, J. P., REIMER, G. M. & WAGNER, G. A. 1975.Actual and ancient uplift rate in the Gotthard region,Swiss Alps: a comparison between precise levellingand fission-track apatite age. Tectonophysics, 29,293–300.

SCHALTEGGER, U. 1994. Unravelling the pre-Mesozoichistory of Aar and Gotthard Massifs (Central Alps)by isotopic dating – a review. SchweizerischeMineralogische und Petrographische Mitteilungen,74, 41–51.

SCHMID, S. M., PFIFFNER, O. A., FROITZHEIM, N.,SCHONBRON, G. & KISSLING, E. 1996. Geophysi-cal–geological transect and tectonic evolution of theSwiss–Italian Alps. Tectonics, 15, 1036–1064.

STUWE, K. 2007. Geodynamics of the Lithosphere –Quantitative Description of Geological Problems.Springer, Berlin.

STUWE, K. & HINTERMULLER, M. 2000. Topography andisotherms revisited: the influence of laterally migratingdrainage divides. Earth and Planetary Science Letters,184, 287–303.

STUWE, K., WHITE, L. & BROWN, R. 1994. The influenceof eroding topography on steady-state isotherms.Application to fission track analysis. Earth and Plane-tary Science Letters, 124, 63–74.

TURCOTTE, D. L. & SCHUBERT, G. 1982. Geodynamics –Applications of Continuum Physics to GeologicalProblems. Wiley, New York.

USTASZEWSKI, M., HAMPEL, A. & PFIFFNER, O. A.2008. Composite faults in the Swiss Alps formed bythe interplay of tectonics, gravitation and postglacialrebound: an integrated field and modelling study.Swiss Journal of Geoscience, 101, 223–235, doi:10.1007/s00015-008-1249-1.

WAGNER, G. A. & REIMER, G. M. 1972. Fission tracktectonics: The tectonic interpretation of fission trackapatite ages. Earth and Planetary Science Letters, 14,263–268.

WAGNER, G. A., REIMER, G. M. & JAGER, E. 1977.Cooling ages derived by apatite fission track, micaRb–Sr and K–Ar dating: the uplift and coolinghistory of the Central Alps. Memorie Instituti Geologiaed Mineralogia Universita Padova, 30, 1–27.

WHIPP, D. M. & EHLERS, T. A. 2007. Influence ofGroundwater flow on thermochronometer-derivedexhumation rates in the central Nepalese Himalaya.Geology, 35, 851–854.

WHIPPLE, K. X. & MEADE, B. J. 2006. Orogen responseto changes in climatic and tectonic forcing. Earthand Planetary Science Letters, 243, 218–228.

WILLETT, S. D. & BRANDON, M. T. 2002. On steadystates in mountain belts. Geology, 30, 175–178.

WYDER, R. F. & MULLIS, J. 1998. Fluid impregnationand development of fault breccias in the Tavetschbasement rocks (Sedrun, Central Swiss Alps). Tectono-physics, 194, 89–107.

C. GLOTZBACH ET AL.124