Continental Collision and the Dynamic and Thermal Evolution of the Variscan Orogenic Crustal Root Ð Numerical Models

Journal of Geodynamics 31 (2001) 273±291 www.elsevier.nl/locate/jgeodyn

Continental collision and the dynamic and thermal evolution of the Variscan orogenic crustal root Ð numerical models

J. Arnold a,*, W.R. Jacoby a, H. Schmeling b, B. Schott c aInstitut fuÈr Geowissenschaften, Johannes Gutenberg-UniversitaÈt Mainz, Saarstr. 21, D-55099 Mainz, Germany bInstitut fuÈr Meteorologie und Geophysik, Johann Wolfgang Goethe-UniversitaÈt Frankfurt, Feldbergstr. 47, D-60323 Frankfurt/M, Germany cFaculty of Earth Sciences, Utrecht University, Budapestlaan 4, 3584 CD Utrecht, The Netherlands

Received 1 February 2000; received in revised form 5 September 2000; accepted 5 September 2000

Abstract Orogeny is modelled numerically by treating continental collision within full convection solutions, in order to better understand some aspects of the Variscan structures and processes. Three dierent approaches are taken: (1) collision where one `continental plate' is `pushed' against another across a zone of weakness; (2) gravitational instability of a lithospheric mantle root leading to delamination, slab break-o and crustal root reduction; (3) melting in the lower part of a crustal orogenic root. The ®rst approach demonstrates that thick (but in the models: cool) roots can accumulate, in which upper crustal rocks are carried to great depth and mantle material may be carried towards upper crustal levels. The second approach shows that lithospheric root break-o can lead to rapid crustal uplift and thinning of the lower crust if its viscosity is suciently low. The third approach suggests that internal heating in a thickened crust may lead to melting and granit formation, however, only after a long geological time (in the order of 100 Ma), while delamination and asthenospheric heat advection may achieve this in shorter time periods (in the order of 10 Ma). The dierent models tested all demonstrate that crustal root formation and destruction by uplift and exhumation can be achieved in geologically short time periods (1±10 Ma). # 2001 Elsevier Science Ltd. All rights reserved.

1. Introduction

One of the motivations for this work is to understand why and how the Variscan belt has lost its crustal root (Meissner and Tanner, 1993; Enderle et al., 1997). While other Palaeozoic orogens, such as the Urals, have preserved a thick crustal root accompanying moderate topography

* Corresponding author. E-mail address: [email protected] (J. Arnold).

(Stadtlander et al., 1999), the present Variscan crust, with similarly moderate topography, is generally rather ``thin'', around 30 km (Blundell, 1992). There is no doubt that some of the exposed continental Variscan rocks had experienced high pressure metamorphism that docu- ments a former sizeable crustal root (Masonne, 1999). We approach the problem via numerical experiments of continental collision. We do not attempt to simulate details, but hope to approach `reality' with meaningful approximations. The European Variscan belt represents a multi-terrane collage assembled in late Paleozoic time, culminating between 350 and 300 Ma. A general feature seems to be extensive high-pressure (HP) metamorphism during the Lower Carboniferous in several parts of the orogen, followed by rapid uplift and exhumation of metamorphic core complexes. During this time, HT/LP metamorphism occurred with increasing volcanic activity indicating high heat ¯ow and extension in the upper crust which has been removed by erosion and denudation. The study is guided by recent observations (Franke, 2000) of a now better known region: the SE±NW section from the Moldanubian, crossing the Erzgebirge to the foreland in the NW, or the Saxothuringian belt including the mid-German Crystalline High (Fig. 1). Deep burial and subsequent uplift with extension, volcanism, high heat ¯ow and crustal melting occurred at 340 Ma within an extremely short interval of de®nitively <10 Ma, perhaps 2 Ma (Willner, 1998; O'Brien, 1999). Marine sedimentation occurred on the Moldanubian basement (Tepla-Barandian) contemporaneous with deep convergence and shallow extension (Zulauf et al., 1998). HP granulite

Fig. 1. Sketch of the Variscan belt in Central Europe showing the section by which the presented models are guided (modi®ed after Franke, 1992). J. Arnold et al. / Journal of Geodynamics 31 (2001) 273±291 275 facies metamorphism is dated, both in the Saxonian granulites (Reinhardt et al., 1998) and in the Erzgebirge (Masonne, 1999), at 340 Ma and time-equivalent sedimentation and volcanism is documented in the upper crust overlying the HP rocks. The apparent con¯ict (Franke, 1998) may be resolved by this study. Convergence, collision and extension in the upper crust during very short spatial and temporal scales may have a modern analogy in the region forming the Alboran sea and surrounding mountain ranges. Occasional deep earthquakes (Tandon et al., 1998) indicate ongoing subduction of a piece of delaminated and detached mantle lithosphere while mountain ranges are presently formed and uplifted and a marine basin forms in-between; Docherty and Banda (1995) point out that here adjacent coeval compression and extension have occurred from Miocene to Recent. They envision the development of the Alboran sea basin through a south-easterly migration of a delaminating continental lithosphere to explain the younger extension in the eastern basin. Evi- dence for the migration comes from tectonic inversion in the eastern Alboran sea basin north of Al-Mansour Seamount. This is an interesting similarity to the marine sedimentation on the Moldanubian basement (Tepla-Barandian) contemporaneous with deep convergence and shallow extension (see above). Both regions share similar features and hopefully modelling sheds light on both situations. In a ®rst attempt, 1D conductive and advective heat transfer (Haugerud, 1989) has been modelled for the Erzgebirge evolution by E. Sebazungu (see Willner et al., 1997, where regional information is given; Willner et al., 2000) to understand especially the metamorphic structure as a consequence of thrusting, uplift and lateral extension and denudation of the upper crustal block within <10 Ma. The petrological data on the òbserved' pTt-paths of sandwiched metamorphic units (Willner et al., 1997: a HT/HP unit between two lower-pT units in the Erzgebirge) can be reproduced with crustal uplift rates for the thrust-up block, from top to bottom, of 2.2, 3.4 and 8.9 mm/a, and 1.3 mm/a for the low-grade ramp. Thermal anomalies in the middle crust can be modelled by sandwiching hot material between cooler units. A ®nal HT/LP overprint of the low- grade ramp occurred during the last stage of exhumation. The model is one of tectonic and ero- sional denudation during ongoing convergence in deeper levels. The crustal root disappears when the gravitationally unstable mantle lithosphere delaminates and breaks o during ongoing continental convergence. This will be discussed in Section 2 mostly based on results by Schott and Schmeling (1998), after the build-up of the crustal orogenic root, modelled mostly by J. Arnold and presented here. To test tectonic models and ideas, 2-d numerical FD-calculations are carried out. The approach is that of convection modelling in a dynamically, rheologically and thermally consistent way, by solving on a grid of points by ®nite dierences the equations of mass, momentum and energy conservation. Two regimes are investigated: `compressive' and èxtensional' (Schott et al., 2000b). In the ®rst case compressional forces, e.g. ``ridge push'', are required to push one plate down (`collision') and initiate delamination when it gains its own instability. The compressive regime with dense lithospheric mantle sinking causes crustal thickening and surface uplift, and the uplift causes the upper crust to spread. This is implied by the observation that uplift rates become greater with increasing structural depth indicating lateral extension. The PTt paths are clockwise; the retrograde branch shows isothermal decompression even with some heating (Willner et al., 1997; Nega et al., 1999). The second case is for crustal root destruction, and lithospheric extension may prevail while it is dominated by the cold and dense mantle lithosphere 276 J. Arnold et al. / Journal of Geodynamics 31 (2001) 273±291 sinking that causes delamination. The extension is generated by the obliquely descending heavy slab `pulled' down by gravity and somewhat `guided' by the ìmmobile' surrounding mantle. An important aspect is that around 340 Ma the entire central portion of the Variscan orogen was aected by a HT/HP metmorphism closely postdated by large masses of granitoids between 330 and 320 Ma. Melting in the orogenic crustal root may be due to radiogenic heating of the stacked material (Gerdes et al., 1997) and/or due to asthenospheric rise after delamination. Sev- eral authors (Kalt et al., 1998; O'Brien, 1999) object to the ®rst suggestion and think that an external heat source is required. H. Schmeling has recently completed the numerical realisation of partial melting and melt segregation in a convecting mantle (Schmeling, 2000) and has applied it to the present study in an attempt to resolve this question.

2. Method

The aim of numerical modelling of collisional processes is to catch some essential features and to test geodynamic hypotheses to ®nd out how crust and mantle may behave in nature in accor- dance with the laws of physics, i.e. the conservation laws for mass, momentum and energy and especially the rheological properties of the various crust and mantle units. This is a ¯uid dynamic convection approach. The governing conservation equations are solved on an equidistant grid in a rectangular box (®nite dierences) with the routine FDCON (Schmeling, 1989). The biharmonic idealized Navier±Stokes equation for the stream function is solved on 61Â61 or 61Â121 grids (and larger ones) by using the Cholesky decomposition. The extended Boussinesq approach is used. The heat equation is solved on 241Â241 or 241Â481 grids (and larger ones) by an alternate- direct-implicit method (Schmeling and Bussod, 1996). Velocities are linearly interpolated between the ®ne and coarse grids. In addition to this, ¯ow paths of tracers are calculated by a Runge±Kutta integration method of 4th order combined with a predictor±corrector method. This Lagrangian formulation has two purposes: (1) to carry information about physical properties as the locally assumed rheological law, and (2) to estimate synthetic PTt-paths and to reconstruct the deformation history of units of geological interest. Modelling with melting in the orogenic crustal root has been carried out by solving the full set of equations for two phase ¯ow of the partially molten system (see Schmeling, 1998, for the details). However, since a relatively high viscosity has been chosen for the felsic magma (1010 Pas), only negligable melt segregation occurs at the melt fractions obtained. The rheology of crust and mantle is assumed to be temperature, and pressure dependent and diers in the crust (upper and lower) and mantle (for details see Tables 1±4). Particulars are presented in the following section. Generally the total strain rate is the result of several deformation

Table 1 Crustal rheology parameters (Wilks and Carter, 1990)

Thickness (km) Density (kg/m3) Rheology A (PaÀn sÀ1) Q (kJ/mol) n

. À21 Upper crust 15 2800 Granite dominated 3.98 10 Quc=134 2.6 . À29 Lower crust 15 3000 Quartzite/feldspar dominated 1.0 10 Qlc=139 3.4 J. Arnold et al. / Journal of Geodynamics 31 (2001) 273±291 277

Table 2 Mantle rheology parameters (Bai et al., 1991) i Density (kg/m3) A (PaÀn sÀ1 atmÀm) mE(J/mol) V (m3/mol) n

1 3400 2.1 10À17 0.02 5.4.105 1.5.10À5 3.5 2 3400 5.2 10À16 0.23 5.4.105 1.5.10À5 3.5

Table 3 Model parameters of reference lithosphere for the thermal evolution models

Unit Thickness (km) Density (kg/m3) Radiogenic heat generation (mW/kg)

Upper crust 15 2600 6.16.10À10 Lower crust 15 2800 1.36.10À10 Lithospheric mantle Temperature dependent 3300 3.1.10À13

Table 4 Rheology parameters for the thermal evolution models

A (PaÀn sÀ1) E (kJ/mol) V (m3/mol) n

Crust, westerly granite 3.98.10À21 Q=139 10À5 3.4 Mantle, wet Anita bay dunite 1.0.10À29 Q=444 10À5 3.35 mechanisms, where each contribution can be expressed by an empirically derived power law (Schmeling and Bussod, 1996). In some models the crust is regarded isoviscous, with some assumption of weaker regions, e.g. in a `collision zone'. Two sets of models were calculated. The ®rst set focuses on convection in the upper mantle with free or no slip boundary conditions (see subsections ``Crustal root formation'' and ``Dela- mination of the mantle lithospheric root''). The main questions relate to the plate movements (``free'' at the surface) and to the structure and properties of the rock units involved in the collision. The bottom at the upper/lower mantle boundary is not very critical to the problem and its rheology is anyway uncertain. The thermal boundary conditions are 0C (surface) and constant heat ¯ux of 20 mW/m2 (bottom). The adiabatic temperature gradient is about 0.32 K/km. The potential mantle temperature is 1200C. A conductive temperature pro®le is assumed to 100 km depth, resulting in a high-viscosity lithosphere. Crustal radiogenic heating decays exponentially with depth, the characteristic length scale is 30 km, contributing approximately 20 mW/m2 to the surface heat ¯ow. With chondritic radiogenic heating in the upper mantle the surface heat ¯ux is about 53 mW/m2. Thermal diusivity varies with depth and has a local minimum in the mantle lithosphere. The second set of models (see subsection ``Late orogenic thermal evolution of the crust and melting'') focusses on the thermal and mechanical evolution of the thickened crust after delamination of the mantle lithosphere, and extends only to 120 km depth. In these models melt generation is included. The critical problems are those of the boundary conditions, the physical conditions for delamination and mechanical decoupling, the crustal response to buoyant instability and thermal 278 J. Arnold et al. / Journal of Geodynamics 31 (2001) 273±291 eects as melt segregation and shear heating in the lower crust as a result of delamination (Schott et al., 1999).

3. Results of modelling

3.1. Crustal root formation

To model crustal root formation by collision, convection is restricted to the upper mantle (scaling depth 670 km, aspect ratio 2), and the average heat ¯ow is as stated above. Crustal rheology is given by : " AÁneÀ Q=RT 1 : where " is the uniaxial strain rate, A is a constant, Á is the dierence between the maximum and minimum stress, Q is the activation energy, R is the gas constant and T is the absolute temperature. The parameters are given in Table 1. The inclined `weakness' zone (see Fig. 2) in the model has a ®xed kinematic viscosity of 1017 Pas and a thickness of 30 km. The rheology of the mantle is characterised by olivine (temperature, stress dependent). Two deformation mechanisms, each expressed by a power law (Schmeling and Bussod, 1996; para- : : : meters from laboratory data for single-crystals from Bai et al., 1991), contribute to "tot "1 "2 both as : " AÁnPm eÀ EPV=RT 2 i O2

A is a pre-exponential constant, P is pressure, P is the partial pressure of oxygen with exponent O2 m, E is activation energy, V activation volume. Partial pressure of oxygen is assumed to be buf- fered at quartz-fayalite-magnetite and corrected for pressure and temperature as in Schmeling and Bussod (1996). The two sets of parameters are listed in Table 2. An upper limit has been assumed for the viscosity (locally) of 1025 Pas; this is relevant only in the upper left-hand model corner (Fig. 2) where mantle material reaches the surface (T=0). The information on material properties (upper, lower crust, mantle) is carried in the numerical model by markers. Mantle markers (carrying mantle properties) are black in the initial lithosphere, light gray elsewhere in order to delineate the model evolution; the instantaneous lithosphere is determined by the pT conditions. Temperature dependence of density is incorporated in the solution with the extended Boussinesq approximation (Schmeling and Bussod, 1996). We initiate collision by imposing a 2 cm/a convergence velocity on the model lithosphere on the left-hand side using an initially enforced convection cell (by a vertical pro®le of the stream function as a kinematic internal ``boundary condition'', see Schott et al., 2000b). The right-hand side lithosphere is held ®xed by its large viscosity. In the present model run no slab break-o occurs, because the steady push from the left does not allow high tensile stresses to develop in the subducting lithosphere. A `snapshot' of the evolution of the collision at about 56 Ma model time is shown in Fig. 2 presenting the marker distribution, the viscosities (note the assumed inclined weakness zone of J. Arnold et al. / Journal of Geodynamics 31 (2001) 273±291 279

Fig. 2. Snapshot of continental collision as part of mantle convection at 56 Ma model time: (a) marker ®elds distin- guishing upper and lower crust, mantle lithosphere and asthenosphere; for better visualization the markers have been simpli®ed by ``smooth'' grey tones; (b) viscosity as assumed in the inclined weakness zone or as determined by Eqs. (1) and (2), scaled with a reference viscosity of 1018 Pas; (c) temperature distribution. low viscosity), and temperature. The marker ®elds have been ``smoothed'' by relating a colour scale to the locally dominant spatial marker frequencies. They distinguish upper and lower crust and the initial lithosphere, while new rheological lithosphere forms from upwelling and cooling asthenosphere, as evident in the high-viscosity `lid' forming at the left-hand side spreading axis. The shallow slab descent is in¯uenced by the model region and the boundary conditions. The most interesting aspects are those of crustal root formation and deformation shown with markers in a `zoomed-up' 300Â450 km model box (Fig. 3) for three model times (27, 56, 90 Ma). The crustal root reaches a thickness of >100 km with a `tail' of lower crustal material dragged down to >200 km between the two mantle `plates'. The sti upper crust remains undeformed 280 J. Arnold et al. / Journal of Geodynamics 31 (2001) 273±291

Fig. 3. Enlarged crustal root as it develops at three time steps: (a) 27 Ma; (b) 56 Ma; (c) 90 Ma. The upper crustal material is shown with gray markers, the lower crust light gray, the lithoshere (as it existed at model time zero) black, and the asthenosphere and newly formed lithosphere light gray. Note that the rheology of lithosphere and asthenosphere is governed by Eq. (2). The isotherms are also plotted. until it enters the weak zone where it is entrained into the orogenic deformation forming a `double vortex' partially displacing (ductile) lower crust. This is clearest at 90 Ma: upper crust is `sucked' down (at x=1300 km) with upwelling on both sides, 150 km apart (note the isotherms). The downward `¯ux' of upper crustal material splits to both sides. Near the ùpper plate', lower crust and some mantle are carried to shallow levels. The double vortex is driven by both the sti upper J. Arnold et al. / Journal of Geodynamics 31 (2001) 273±291 281 crust and the descending mantle plate. The deformation of the crustal root has a chaotic char- acter. Crustal material is piled up, the root deepens and broadens (to 400 km width), the structures become more complex, upper crustal material is pushed deeper and `slivers' of mantle are carried higher. The isotherms (especially at 90 Ma) demonstrate some kind of internal crustal root convection driven mechanically by the plate convergence. The low viscosity lower crust allows mantle to separate or delaminate, and only mantle lithosphere is juxtaposed with the lower crust shielded from asthenospheric heat advection, hence remaining `cool'. This is dierent from the kind of delamination modelled in the next sections where the lower crust is directly exposed to hot asthenosphere. Thermal eects, as HT/HP metamorphism, melting and granite intrusion may result from heating by subduction of a ridge, which in a scenario of terranes and small transient ocean basins could happen frequently. In Fig. 3 the 90 Ma frame shows that younger and hotter lithosphere is about to arrive. Advection of hot asthenosphere through slab break-o and radiogenic heating of the lower are explored in the next subsections. The weak zone is assumed `àd hoc'' to permit `collision'; the poor spatial resolution requires the weak zone to be broader (about 30 km across) than it appears to be in reality. The weak zone is assumed at ®xed grid points and in¯uences the ¯ow, e.g. by not being able to shift as a whole; this must be considered in interpreting the resulting ¯ow patterns. Another caveat concerns the upper impermeable model boundary preventing surface uplift, erosion and denudation. However, the low viscosity in the collision region appears principally `realistic' as crustal material is `softer' than òld' oceanic lithosphere and deformation and associated viscous heating will lower the eective viscosity; young orogens show high heat ¯ow (but the models do not capture this thermally; the isotherms at 90 Ma show only moderate uplifts on either side of the downwelling).

3.2. Delamination of the mantle lithospheric root

In this subsection an overview is given over the results of delamination modeling by Schott and Schmeling (1998). The idea is that of a gravitational instability of the mantle lithosphere, leading to its delamination and subsequent detachment. In this model this is accomplished by assuming a cool mantle lithospheric root as the initial condition (Fig. 4a). Delamination of the mantle lithosphere is likely to occur over a wide range of lower crustal viscosity of 1020±1023 Pas, but with increasing viscosity of the lower crust, the negative buoyancy forces of the mantle lithosphere (=slab length) must increase. However, it is also found, that the ability of the delaminated mantle lithosphere to detach is sensitive to the lower crustal viscosity, and slab detachment is likely to occur for lower crustal viscosities larger than 1022 Pas. In the case of a detaching lithospheric slab (Fig. 4Band C), the time elapsing from the onset of delamination to the slab detachment is of the order of 3 Ma, which is very short on a geological time scale (Schott and Schmeling, 1998), but in agreement with the ``observed'' short time scale of uplift and exhumation (Willner, 1998; Willner et al., 1997). Delamination and the rise of hot asthenosphere to the base of the crust allows the crustal root to ¯atten out within the same time span, leading to an extensional stress regime in the isostatically relaxing crust. Due to the lattice- preferred orientation of olivine, the mineral axis would align with the axis of maximum extension, which is perpendicular to the strike of the orogen in case of lithospheric delamination. This orientation would be preserved in the newly forming mantle lithosphere, when that asthenosphere 282 J. Arnold et al. / Journal of Geodynamics 31 (2001) 273±291

Fig. 4. Composition (upper crust Ð light gray, lower crust Ð black, mantle-lithosphere Ð dark gray, asthenosphere Ð gray) and temperature (isotherms) during the delamination and detachment of the mantle-lithosphere: (A) initial state; (B) delamination of the mantle-lithosphere; (C) slab is detached. Note the short time-span of only 3 Ma between delamination (B) and detachment (C). J. Arnold et al. / Journal of Geodynamics 31 (2001) 273±291 283 is cooling, and should be detactable as fossile seismic anisotropy, as found in the Appalachians (Levin et al., 2000). Note, that with a temperature dependent viscosity, there is no convective removal of the thickened mantle lithosphere as described by Houseman et al. (1981), because the cold part of the model ¯uid has a much too high viscosity. If the mantle lithosphere is not delaminating a stagnant lid develops (Buck and TocksoÈ z, 1983). The delamination model self-consistantly predicts the existence of largely thickened crust (LT- HP) coupled to the delaminating mantle lithosphere and showing near-surface compression; in the vicinity thin isostatically relaxing or already relaxed crust is being underplated by hot asthenosphere (LP-HT), showing near-surface extension (Fig. 4, B,C). The gravitational potential energy, which is released during the isostatic rebound of the thickened crustal root is likely to be partly converted into heat by viscous dissipation. Hence, the crustal root is not isostatically relaxing as a whole and areas of crustal ¯ow, counter to the delamination movement, can show signi®cant dissipative heating in the lower crust (Schott et al., 2000a). This might be an important additional heatsource for late orogenic evolution after delamination. In the case of a laterally heterogeneous lithosphere the delaminating mantle lithosphere will detach, if a highly viscous lower crust or a weak mantle lithosphere is reached. Delamination of the mantle lithosphere does not necessarily lead to an upwelling asthenosphere underplating the crust if additional forces from e.g. mantle drag can provide a large scale compressional regime (Schott et al., 2000b). There is ample evidence for hot Variscan rocks now exposed in the whole study area (Franke, 2000) and the question is how the heat got up. Delamination is a possibility to supply heat within short time scales of some Million years, another possibility could be radiogenic heat in the thick immature sedimentary pile, in this case, heat is supplied within some 100 Ma under realistic conditions but need not come from the mantle. This is discussed in the next subsection.

3.3. Late orogenic thermal evolution of the crust and melting

While the collisional stage of the Variscan orogeny started at the end of the Devonian, the high temperature events and extension occurred within 5±20 Ma during the ®nal collision stage. For example, Gerdes et al. (1998) assume crustal stacking of the southern Bohemian zone between 360 and 345 Ma and present arguments for batholith intrusion at 330±320 Ma. For the north- western part of the Bohemian Massif the collision has been dated at 370 Ma, followed by a gravitational collapse and HT-HP and HT-LP metamorphism at 355±345 Ma (Zulauf, 1997; Zulauf et al., 1998). Crustal stacking of the southern Saxothuringian occurred between 375 and 340 Ma while intrusions and extension have been dated between 340 and 330 Ma (Gaitzsch, 1998). To address the question of the heat source from a thermo-mechanical point of view, we present a 1D thermal model of a stacked continental crust, and then discuss a 2D thermo-mechanical model. Since there are no reliable data about the thermal structure of the colliding terranes (Laurentia, Avalonia and Gondwana) prior to collision, we assume a typical continental structure (Table 3). The thermally relevant assumptions are brie¯y discussed since they dier slightly from the models presented above. The radiogenic heat generation of the dierent layers have been taken from Van Schmus (1989, 1995), and are in general agreement with estimates of radiogenic heat sources of the Mesozoic and Cenozoic continental crust (Cermak et al., 1991). Together with a mantle heat ¯ux at the base 284 J. Arnold et al. / Journal of Geodynamics 31 (2001) 273±291 of the lithosphere of 28.4 mW/m2 the model reference lithosphere has a steady state surface heat ¯ux of 58.2 mW/m2, which is about the average value of Paleozoic or Mesozoic continents (Stein,

1995). A temperature dependent heat capacity, cp, has been chosen (Navrotsky, 1995) because upper lithospheric temperatures are below or about the Debye temperature. The heat capacity varies from 780 J/(kg K) at 0C to 1320 J/(kg K) at 1200C. A temperature and depth dependent thermal diusivity has been chosen for crustal rocks according to Clauser and Huenges (1995) and for mantle rocks according to Katsura (1995). Variations in range between 1.4.10À6 near the surface and 0.5.10À6 m2/s within the upper mantle. In the conductive cases below is raised up to 3 10À6 m2/s for temperatures above 1300C to mimic advective heat transport within the underlying asthenosphere. Tests with constant and variable cp and have been carried out for a

Fig. 5. (a) Thermal evolution of a 1D model of a stacked continental crust. At the time t=0 Ma, a 30 km thick crust with the equilibrium temperature distribution of Fig. 2 has been stacked on top of another 30 km thick crust, resting on a mantle lithosphere. Due to radiogenic heating (see Table 3) the thickened lithosphere heats up, as indicated by the geotherms at the dierent times. Thermal parameters and cp are temperature dependent. The two dashed lines indicate typical solidus temperatures within the underthrusted crust. (b) Same as (a), but with elevated asthenospheric temperatures beneath 65 km at the time t=0 Ma. This initial condition may be the consequence of fast delamination of a mantle lithosphere. J. Arnold et al. / Journal of Geodynamics 31 (2001) 273±291 285 cooling half space, showing that to ®rst order their variations cancel out. On the other hand, accounting for the temperature dependence of only one of these parameters introduces signi®cant errors into the temporal behaviour of the temperature distributions. In a ®rst experiment the thermal evolution of an instantaneously stacked crust is studied in 1D (Fig. 5a). The steady-state temperature pro®le of the reference lithosphere has been taken as initial temperature before stacking and is still visible in parts (0 Ma curve). It takes about 3 Ma until the crustal package is warmed up to values comparable to the time prior to stacking. Due to doubling of the radiogenic heat sources within the new thickened crust, the upper part of crust 2 is heated to 600C after 100 Ma, and the lower part reaches 800C after 170 Ma (as indicated by the dashed lines). At least such temperatures are needed to melt the underlying crust in the presence of water (Wyllie, 1984) and to explain the HT-HP metamorphic rocks of the Moldenubian zone (O'Brien and Carlswell, 1993) or the HT-LP gneisses and migmatites of Bayerischer Wald (SW-Bohemian Massif) (Kalt et al., 1998). This result is in contrast to the thermal models of a stacked crust obtained by Gerdes et al. (1998). Their reference lithosphere contains somewhat higher radiogenic heat sources, resulting in a steady state heat ¯ux of 75 mW/m2 which is representative for anomalously warm Cenozoic continents (Stein, 1995). Because the heat sources were distributed over greater depth compared to our models and to other typical depths distributions (see e.g. compilation by Cermak et al., 1991), signi®cantly higher crustal temperatures were obtained (For a given amount of crustal heat sources and a given basal heat ¯ux, crustal temperatures stronlgy depend on the depth of the heat sources). As an additional heat source we propose advection due to asthenospheric ascent up to a level immediately beneath the thickened crust (Zulauf, 1997; Schott and Schmeling, 1998). Because our dynamical models show (Schott and Schmeling, 1998) that the process of delamination and asthenospheric rise can be very fast (< 2 Ma), we choose a stacked crust as the initial condition (as in Fig. 5a), i.e. we introduce the emplacement of a shallow asthenosphere by increasing the initial temperature instantaneously to 1300C everywhere below 65. The temporal evolution of that 1D model is shown in Fig. 5b. Now the additional asthenospheric heat source eectively heats up the underlying crust, and crustal melting temperatures are exceeded already after 15 Ma (horizontal dashed lines). Signi®cant melting has to be expected already at 30 Ma and later. This is still a purely conductive model, including the cooling of the asthenosphere which slows down crustal heating. In nature, ascent of hot asthenosphere involves thermal convection, which will advect hot mantle material into shallow depths for a longer time period (see below). It is interesting to study the thermal, mechanical and rheological evolution of a 2D thermo- mechanical model of a lithosphere-asthenosphere system, in which the crust is stacked similarly as in the 1D model above. Fig. 6 shows the initial condition of that model, consisting of a 2-layer overthrust crust (black and dark green markers), a 2-layer underthrust crust (light green and orange markers) and a lithospheric-asthenospheric mantle (red markers) beneath. The sides of the model are symmetric, i.e. no lateral shortening or widening is applied. As initial thermal condition the temperature of the reference crust has been chosen for the two crustal units (Fig. 6, bottom). Mimicking a situation immediately after delamination of the mantle lithosphere, a hot shallow asthenosphere is introduced by choosing 1300C for all depths greater than 65 km. The temperature dependent thermal parameters are chosen as in the 1D models above (except for (T) for mantle material, which is now taken from Katsura (1995) also at asthenospheric temperatures); the thermal expansivity is 3.7.10À5 KÀ1. In addition to the heat equation also the equations 286 J. Arnold et al. / Journal of Geodynamics 31 (2001) 273±291 of conservation of mass and momentum are solved. A temperature and depth dependent power law rheology has been chosen according to : " AÁneÀ EPV=RT 3 : where " is the strain rate, A is a pre-exponential factor, Á is the stress dierence, P is the pressure, E is the activation energy, V activation volume, R is the gas constant and T is the absolute temperature. The assumed numerical values are given in Table 4 after Kirby and Kronenburg (1987) and Chopra and Paterson (1984), resulting in a relatively weak lithosphere. Crustal melting occurs if the temperatures in the thickened crust exceed the solidus temperature of granite, assumed at 760C. The degree of melting is assumed to increase linearly with temperature until the liquidus temperature is reached, chosen at 1100C. Other melting parameters include the latent heat of melting of 300 kJ/kg and the melt density of 2450 kg/m3.

Fig. 6. Initial condition of a 2D thermo-mechanical model of a stacked crust. (a) Marker ®eld indicating the position of the upper and lower crusts of the overthrust and underthrust crusts. (b) Initial temperature ®eld. Note the uniform hot temperatures beneath 65 km, mimicking the shallow asthenosphere. J. Arnold et al. / Journal of Geodynamics 31 (2001) 273±291 287

Fig. 7. State of the 2D thermo-mechanical model after 71.5 Ma. (a) Marker ®eld showing the position and deformation of the crustal and mantle units. (b) Melt fraction. (c) Temperature ®eld. (d) Logarithmic viscosity ®eld, scaled with the reference viscosity of 1021 Pas. 288 J. Arnold et al. / Journal of Geodynamics 31 (2001) 273±291

As expected from the 1D model (Fig. 5b) also the 2D model heats up fast, and melting temperatures are exceeded in the lowermost part of the thickened crust after 25.8 Ma. After 36 Ma the degree of melting has reached 14%, and the thickness of the molten region is 11 km. Due to buoyancy forces of deep crustal material and melt, the crustal root begins to ¯atten by ductile deformation. This deformation is possible, because the chosen rheologies lead to relatively low eective viscosities: 1020À21 Pas in the mantle and 1021À22 Pas in the crustal root. At later times (71 Ma), further radiogenic and advective heating due to a convecting asthenosphere has increased the degree of melting to 24% (Fig. 7). The total crustal thickness has reached approximately the average value of 45 km (this rather large value is a consequence of not allowing crustal material to escape to the sides of the model). Most of the crustal deformation has taken place in the underthrust crust, the overthrust crust is almost undeformed due to the strong rheology at low temperatures. Within the underthrust crust the marker ®eld shows characteristic parabola shaped features at both sides of the crustal root indicating a channel type of lower crustal ¯ow, similar to the models of Schmeling and Marquart (1990), Henk (1998) or Koyi et al. (1999). Although buoyancy forces are present in the partially molten lower crust, the viscosity of the overburden is too high to allow diapiric ascent. This is in agreement with the ®ndings of Bittner and Schmeling (1995), who showed, that ecient diapiric ascent is only possible if the viscosity of the overburden is of the order of 1019 Pas or lower. External tectonic forces might lead to weak- ening of the crust e.g. along fault zones, thereby enhancing the potential of diapiric ascent (Zulauf et al., 1998). The question arises whether asthenospheric rise might be associated with mantle melting and basaltic underplating. In the Variscan belt only small amounts of mantle melts have been recog- nized (e.g. Gerdes et al., 1997, 1998). Our models show that after delamination of the mantle lithosphere the asthenosphere may rise up to levels of 60±70 km (Schott, 1998; Schott and Schmeling, 1998). Thermodynamic calculations by Iwamori et al. (1995) show that upwelling of dry mantle does not lead to melting at all below 60 km depth if the potential temperature of the mantle is less than 1350C, and in case of wet conditions only small degrees of melting are possible (assuming fractional melting). Thus, asthenospheric rise associated with delamination of the mantle lithosphere is an eective mechanism to place hot but essentially subsolidus mantle material beneath the thickened crust, and does not predict large volumes of mantle melts. Even in case of signi®cant magmatic underplating, entrainment of basaltic melts within granitic intrusions is predicted to be of minor importance as long as the basaltic melts are suciently denser than the overlying granitic partial melts and the solid overburden (Cruden et al., 1995).

4. Summary and conclusions

The crustal models show (1) that the build up of a complex root is possible if the lower crust has a low viscosity; (2) that the root may `¯ow' apart and `disappear' if slab delamination and break-o occurs and (3) that extensive melting is possible within a rather short time period within a few tens of million years while delamination and hot asthenospheric rise occurs within 1±10 Ma. However, radiogenic heating alone may be insucient, additional heating from shallow asthenosphere is needed. Another possible heat source may be subduction of very young lithosphere (`ridge subduction'). J. Arnold et al. / Journal of Geodynamics 31 (2001) 273±291 289

Numerical models help understanding the complex, sometimes apparently contradictory, orogenic processes, as e.g. contemporaneous plate convergence and upper crust extension. Adjusting the models to geological data is, however, only approximately possible and sometimes, as in this case, requires the models to be `split' into dierent approaches in order to catch dierent geological aspects: orogenic root formation and destruction without and with melting. More uni®ed modelling is perhaps desirable, but may have the disadvantage of becoming too complex for the results to become clear.

Acknowledgements

This work was carried out and funded within the framework of the ``Schwerpunktprogramm'' ``Orogenic Processes Ð Quanti®cation and Modeling in the Variscan Belt'' coordinated by W. Franke. His enthusiasm made us work hard on the modelling and ®nancial support of J. Arnold and B. Schott by Deutsche Forschungsgemeinschaft made it possible. Computational support and assistance by E. Sebazungu and K. Regenauer-Lieb is gratefully acknowledged. A. Willner introduced us into the geological complexities of Erzgebirge.

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