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See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/227820275 On the thermomechanical evolution of compressional orogens Article in Geophysical Journal International · February 1997 DOI: 10.1111/j.1365-246X.1997.tb01561.x CITATIONS 114 READS 25 2 authors: Geoffrey E. BattUniversity of Western Australia 49 PUBLICATIONS 1,179 CITATIONS SEE PROFILE Jean BraunUniversity Joseph Fourier - Grenoble 1 204 PUBLICATIONS 4,927 CITATIONS SEE PROFILE All content following this page was uploaded by Geoffrey E. Batt on 20 April 2015. The user has requested enhancement of the downloaded file. All in-text references underlined in blueare linked to publications on ResearchGate, letting you access and read them immediately. Geophys. zyxwvusrqponm . Int. zyxwvusrqpo 1997) 128,364-382 On the thermomechanical evolution of compressional orogens z . E. Batt and J. Braun Research School of Earth Sciences, Australian National University, Canberra ACT 0200, Australia Accepted 1996 September 24. Received 1996 September 20; in srcinal form 1996 September 5 SUMMARY We present results from a newly developed fully coupled thermomechanical model of the continental crust in which crustal shortening at a convergent plate boundary is driven by a basal velocity discontinuity which represents delamination and subduction in the underlying mantle. This new dynamical model incorporates complex rheologies (elasticity, thermally activated creep and brittle frictional behaviour), allows for extremely large deformation, and is coupled along its top boundary to a complex erosion/ sedimentation model. The model is based on the ‘dynamic Lagrangian remeshing’ (DLR) method, which uses Lagrangian spatial discretization of the crust and therefore allows for an accurate tracking of rock particles as they travel through the deforming orogen; this information is, in turn, used to produce synthetic PTt paths. We have used this model to predict the distribution of apparent ages for a wide range of isotopic systems at the surface of an actively deforming orogen. We have also predicted other geophysical and geological observables, such as the metamorphic grade of exposed rocks (regarded here as a first-order approximation for total denudation), topography, surface heat flux, and the thickness of sediment deposited in the adjacent foreland basins. Results clearly demonstrate that the highest exhumation rates (and thus the youngest isotopic ages) are found in regions of maximum topography near the centre of the orogen, but that the most deeply exhumed rocks are found on the side of the orogen, in the vicinity of the retro-shear zone, a crustal-scale ‘fault’ which accommodates most of the crustal shortening within the orogen. It is also in this region that the isotopic systems characterized by the greatest closure temperatures display the youngest ages and the highest grade metamorphic rocks are found. These conclusions are derived from the assumption of uniform erosion across the orogen; in cases where rainfall (and thus erosion) is orographically controlled, the tectonic style of the orogen is different from the uniform erosion case, as is the distribution of isotopic ages and metamorphic grades across the orogen. Key words: crust, orogeny. 1 INTRODUCTION Abnormal temperature gradients are commonly observed in regions of active compressional tectonics (Zeitler et al. 1982; Holm, Norris zyxwvutsrq Craw 1989; Clark & Jaeger 1992; Tippett & Kamp 1993; Winslow et al. 1994); indirect evidence is also becoming available suggesting that a similar palaeothermal regime was present in ancient collision zones (Dunlap et a . 1995). Many explanations have been proposed to account for this anomalous thermal regime, including magmatic activity and underplating (England Richardson 1977), dissipation of mechanical energy (Barr & Dahlen 1990) and tectonic heat transport (England Richardson 1977; Allis 1981; Koons 1987). In this work, we are attempting quantitatively to assess the efficiency of the latter mechanism. Because temperature increases rapidly with depth in the Earth’s crust, the vertical movement of rocks in tectonically active regions must cause some degree of thermal disturbance; the details of the thermal perturbation are strongly dependent on the assumed distribution of (a) the deformation within the orogen, and (b) the erosion along its upper surface (England & Thompson 1984; Koons 1987; Barr & Dahlen 1990; Royden 1993; Ruppel Hodges 1994). The large-scale features of many present and past com- pressional orogens are well explained by a relatively simple mechanical model (Willett, Beaumont & Fullsack 1993). In this model (Fig. l), continental collision is seen as the final stage in the evolution of a closing oceanic basin following subduction of the oceanic plate beneath one of the two continents (or continental fragments). As the mantle part of 364 zyxwvuts 997 RAS Thermomechanical evolution of compressional orogens 365 (a) zyxwvutsrq ECTONIC SEITING Compressional Continent II zyxwvutsrq orogen Continent I I I stepup I shear I zones I Strenath Retro -side / \ Pro -side Low-strength decollement zyxwvuts oho mantle (b) FULLY COUPLED THERMO-MECHANICAL MODEL Irregular apatlal dlscre~lzatlon T=To \ egional 1s0stat1c compensation \ Visco-eiasto-plastic msterlal o represent frictional brittle behaviour and power-law thermally activated creep zyxwvutsrqpon Figure 1. (a) Simplified description of the assumed tectonic setting at a collisional plate boundary in which subduction of the subcontinental mantle is accommodated by thrusting in the overlying crust. (b) Schematic description of the numerical model and boundary conditions used to represent the tectonic setting described in (a). one of the two lithospheric continental plates continues to subduct, it delaminates from the overlying lighter crust which, in turn, is forced to accommodate the plate convergence by deforming. Many studies (Beaumont & Quinlan 1994; Beaumont, Fullsack & Hamilton 1994; Braun & Beaumont 1995; Upton, Koons & Chamberlain 1995; Shi, Allis Davey 1996) have shown that, following mantle delamination, crustal deformation is accommodated by thrusting along a major thrust plane (the retro-shear of Willett zyxwvutsr t al. 1993), which dips at approximately 45 in the opposite direction to the palaeo- subduction zone (Fig. 1). The crust behaves as a doubly vergent accretionary wedge, the geometry of which is determined by the internal strength of the crust and the strength of the dkcollement between the crust and mantle. In particular, this model is regarded by many as the most likely explanation for the dynamics of the continental collision along the Australian-Pacific plate boundary in central South Island, New Zealand (Beaumont, Fullsack Hamilton 1992; Allis & Shi 1995; Braun & Beaumont 1995; Stern 1995; Upton zyxwv t al. 1995; Beaumont et. al 1996). The purpose of this work is to determine and analyse the thermal consequences of crustal deformation driven by delamination of the underlying mantle. Previous work Shi ef zyxwvutsrq l. 1996 Koons 1987; Barr Dahlen 1990) has demonstrated that crustal-scale thrusting accompanied by surface erosion may lead to rapid exhumation of rocks and significant per- turbation of the pre-orogenic geotherm. We present here the results of a fully coupled thermomechanical model of crustal deformation from which we predict patterns of isotopic age for rocks that have travelled through the model orogen. These predictions can be directly compared to observed age patterns derived from several isotopic systems by making the assump- tion that the 'age' of a sample/mineral is related to the thermal history it has experienced on its way to the Earth's surface (Dodson 1973). We have produced a large series of numerical simulations in which crustal rheology, surface erosion parameters and the velocity of convergence have all been varied. Here, we will show the results of a number of those model simulations to highlight the relative importance of several model parameters. In addition to the various isotopic ages, our model also predicts deformation patterns within the crust, the depth of the brittle-ductile transition, the exhumation depth of rocks exposed at the surface of the model, topography and surface heat flow. In this paper, we initially provide the reader with a first- order estimate of the magnitude of the thermal perturbation produced by tectonic deformation and surface erosion, by presenting the analytical solution to a simplified version of the problem. We then describe the thermomechanical numerical model that will allow us to propose more realistic predictions, presenting the results of a 'reference' numerical experiment, and investigate how sensitive the model results are to the various parameters used, concentrating on the assumed rheology, the initial geothermal gradient and patterns of surface erosion. Finally, we compare some of the model predictions with existing geological and geochronological data from several compressional orogens. 2 SIMPLE ANALYTICAL SOLUTION When a crustal layer of thickness L is subject to uniform uplift and denudation at a velocity zy the steady-state vertical temperature distribution within the layer is given by (see Appendix A) where T is the dimensionless temperature scaled by the tem- perature at the base of the layer (T= T/T, and Z is the dimensionless vertical coordinate scaled by the thickness of the layer (Z=z/L) and measured from the surface held at a constant nil temperature. is the dimensionless heat pro- duction (see Appendix A). The Peclet number, Pe, is a dimen- sionless number that characterizes a system in which conduction competes with advection in transporting heat. Pe is defined as VL Pe=--, K where K is the average diffusivity of crustal rocks. Table 1 shows the value of Pe for various tectonic systems. The surface heat flux anomaly predicted by eq. (1) is qA E = 4c (3) 997 RAS, GJI 128, 364-382 366 G. E. Butt and J. Braun Table 1. zyxwvutsrqpo eclet zyxwvutsrqpo Pe) numbers calculated for a variety of parameter combinations, assuming a thermal diffusivity of 25 kmz Myr-'. The Peclet number is a measure of the relative importance of advection versus conduction in transporting heat. Where Pe zyxwvuts , advection is the dominant process and the thermal structure of the system will be significantly perturbed by tectonic transport. Denudation rate (km/Myr) 3 5 10 Tectonic style 1 0.04 0.12 0.2 0.4 thin-skinned 3 0.12 0.36 0.6 1.2 thinskinned Layer thickness (km) 10 0.4 1.2 2 '4 thrust nappe 30 1.2 3.6 6 12 crust a1 100 4 12 20 40 lithospheric Pe for Pe 2 10 zyxwvutsr zyxwvutsrqpo 1 +f (4) This simple relationship is illustrated in Fig. 2 where the predicted heat flux anomaly is shown as a function of Pe for various values of the heat production parameter, f. Fig. 2 clearly shows that in regions where advection of heat by tectonic transport and erosion dominates over conduction (i.e. where Pe 2 ), the surface heat flux is strongly perturbed. This simple relationship (eq. 6) is, however, based on the assumption of one-dimensionality. Tectonic systems are charac- terized by complex 2-D and 3-D geometries. In the following sections, we investigate the character of this heat anomaly in detail, using more realistic deformation and erosion patterns derived from a 2-D thermomechanical model of the Earth's crust. 3 THE NUMERICAL METHOD The crust is regarded here as a non-linear viscoelastoplastic material which deforms as a Maxwell viscoelastic body until stress levels reach a critical value and brittle failure takes place. The viscosity of the material is stress-dependent and thermally activated, following a 'classical' Arhenius relationship derived from laboratory experiments on rock samples. We shall con- sider two types of rheology: a quartz-dominated rheology (Rl) based on the quartzite rheology of Paterson & Luan (1990) and a feldspar-dominated rheology (R2) based on the Adirondak granulite rheology of Wilks & Carter (1990). A detailed discussion on the suitability of such laboratory-derived rheological laws for use in large-scale crustal deformation experiments is given in Tommasi (1995). Brittle deformation is represented by an associative plastic flow law derived from Griffith's failure criterion. This failure criterion may be easily expressed in terms of the invariants of the stress tensor, J i 2T,p=O, (7) where JZD s the second invariant of the deviatoric part of the stress tensor and p is the pressure. In our model, the pressure incorporates the lithostatic pressure (resulting from deformation driven by the imposed boundary conditions). Predicted 1 D Heat zyx nomaly zy 8.0 6.0 4.0 2 0 0.0 I I I 0 2 4 zyxwv 8 10 Pe Figure 2. Predicted heat flux anomaly as a function of Pe (the Peclet number = vL/K , haracterizing an actively deforming compressional orogen. The heat flux anomaly is calculated as the ratio of the heat flux predicted by a 1-D balance between the vertical advective and conductive heat transport and the conductive heat flux obtained by assuming no vertical tectonic transport. The various curves correspond to different values of the dimensionless heat production factor, .f = pHLz/k/kT,. See text for further explanation. zyxw 997 RAS, GJI 128, 364-382 Thermomechanical euolution of compressional ovogens 367 Justification for the use of Griffith's failure criterion to model the brittle behaviour of crustal rocks is given in Braun (1994) and Braun zyxwvutsrq Beaumont (1995). Geometrical effects arising from finite deformation are also incorporated in the model: the midpoint strain is used in place of the infinitesimal strain and the Green-Naghdi rate of stress change in place of the time derivative of stress (Hughes Winget 1980). In the following numerical experiments, deformation of the crust is driven by an imposed velocity discontinuity at the base of the model (Fig. 2). Such a discontinuity represents delamination of the underlying mantle (Willett et al. 1993). The equations of mechanical equilibrium and heat transfer by conduction and advection are solved by the finite-element method (Bathe 1982) using linear triangular elements. To permit large deformation, the 'dynamical Lagrangian remeshing' (DLR) method is used (Braun & Sambridge 1994). The DLR method was improved on by allowing for dynamical mesh refinement through the insertion of nodes in regions of large deviatoric strain. Simultaneously, nodes were removed from the numerical mesh to simulate erosion along the top surface. During addition and removal of nodes, a simple algorithm is used to prevent the break-up of compositional boundaries (such as the boundary between upper and lower crust in the numerical experiments with layered crustal rheology). This algorithm implies the injection of nodes along the com- positional boundaries where the Delaunay triangulation used in DLR causes the boundary to break up. zyxwvut Temperature C) zyxwvuts 100 200 300 400 500 zyxwv 10 zyxwvutsr E Y 5 0 Q, 0 zyxwvu 2 30 zyxwvutsrq igure 3. Initial temperature profile for the crust as assumed in the numerical experiments. Erosion and sedimentation rates along the surface of the model are computed using a 1-D model of mass transport by diffusive and river processes similar to that described in Kool & Beaumont (1994). Erosion by river processes is derived from an assumed precipitation function which may be orographically determined; one can therefore predict asymmetrical erosion patterns resulting from the rain shadow effect of a tectonically growing mountain range. The crustal layer is assumed to rest on a relatively strong mantle lithosphere of finite flexural strength. This is incor- porated in the model by linking the deformation of the base of the crustal layer to a thin elastic plate which supports loads created by variations in thickness of the crustal layer. 4 AN EXAMPLE OF CONTINENTAL COLLISION In the first numerical experiment, a 30 km thick crustal layer is subjected to 100 km of shortening over a period of 10 Myr. The velocity of convergence is constant at 10 km Myr-'. The rheology is assumed to be viscoelastic-plastic throughout the crust, with ductile behaviour based on the viscosity derived for feldspar-rich rocks (R2). The initial geotherm is shown in Fig. 3; the temperature at the base of the crust is assumed to be fixed at 500°C. The choice of such a boundary condition is discussed in Appendix B. Heat generation by the decay of radiogenic elements is assumed to be constant throughout the crustal layer. More sophisticated models of the distribution of heat- generating radionuclides could be used but would not signifi- cantly modify the results presented here. The model parameters are listed in Table 2. We also assume that erosion is relatively efficient at removing material at the surface of the orogen, so that the system reaches equilibrium in a few million years. The exact value of the parameters used in the erosion model are of little significance. They have been set to yield a maximum topography of 2-3 km and have uniform value across the simulated orogen; in later experiments we will investigate the effect of introducing non- uniform erosion via an orographically controlled rainfall pattern. 4.1 Predicted deformation The predicted deformation of the crustal layer and its thermal evolution are depicted in Fig. 4. Along the base of the crust, deformation is ductile. The very large strain created along the boundary at the singularity propagates through the basal ductile layer to initiate the formation of crustal-scale brittle shear zones. During the first stages of deformation (Fig. 4a), the shear zones dip at approximately 45" in opposite directions. We refer to those shear zones as the pro- and retro-shear zones, following the convention of Willett et al. (1993). By definition, the mantle on the pro-side of the orogen undergoes subduction, whereas the mantle on the retro-side of the orogen is 'stable' and resists subduction. In our numerical model, the Figure 4. Results of the first numerical experiment; (a)-(c) Grey-shaded contour plots of the logarithm of the second invariant of the deviatoric part of the strain rate tensor at 1, 4 and 10 Myr since the beginning of tectonic deformation, respectively. Dark shading indicates a large strain rate, light shading corresponds to low strain rates. The arrows indicate the instantaneous particle velocities at some selected grid points. The dark thick lines correspond to the predicted stratigraphy in the sedimentary basins forming on either side of the orogen. (d)-(f) Grey-shaded contour plots of the predicted temperature at times 0.2, 4 and 10 Myr, respectively. Dark shading corresponds to low temperatures and light shading corresponds to high temperatures. The thin black lines are stratigraphic horizons that were horizontal prior to the onset of tectonic activity. 997 RAS, GJI 128, 364-382
