Shear Heating in Extensional Detachments: Implications for the Thermal History of the Devonian Basins of W Norway

Tectonophysics 608 (2013) 1073–1085

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Shear heating in extensional detachments: Implications for the thermal history of the Devonian basins of W Norway

Alban Souche ⁎, Sergei Medvedev 1, Torgeir B. Andersen 1, Marcin Dabrowski 2

Physics of Geological Processes (PGP), University of Oslo, P.O. Box 1048, Blindern, 0316 Oslo, Norway article info abstract

Article history: The supra-detachment basins in western Norway were formed during Lower to Middle Devonian in the Received 9 July 2012 hangingwall of the extensional system of detachments known as the Nordfjord-Sogn Detachment Zone Received in revised form 27 May 2013 (NSDZ). The basins experienced elevated peak temperatures (up to 345 °C adjacent to the main detachment Accepted 4 July 2013 fault) during the terminal stages of the extension. In this study, we show that the heat generated by the de- Available online 12 July 2013 formation of the rocks within the shear zone of the detachment, also known as shear heating, played a role in the thermal evolution of the entire region during the extension and could have induced the elevated peak Keywords: ﬂ Shear heating temperatures of the supra-detachment basins. We numerically analyse the in uence of the rheology and Supra-detachment basins the deformation style within the shear zone, the rate of exhumation of the footwall, and the thickness of Numerical modelling the sedimentary accumulation on the top of the system. The model reproduces the elevated temperatures Post-Caledonian extension recorded in the supra-detachment basins where locally 100 °C and 25% of the total heat budget can be attrib- uted to shear heating. We show that this additional heat source may increase the peak temperatures of the hangingwall as far as 5 km away from the detachment. © 2013 Elsevier B.V. All rights reserved.

1. Introduction 1) The footwall records higher-grade synkinematic metamorphism and younger metamorphic cooling ages than the hangingwall. The Large-scale extensional detachments, resulting from gravitational footwall is often referred to as a metamorphic core complex, and collapse of over-thickened crust, or extension driven by plate motions, in extreme cases the entire crust may be stretched off to expose have been recognized and documented in a number of places and pro- mantle rocks (Manatschal, 2004; Wernicke, 1985). vide a major mechanism to exhume large segments of the lower crust 2) The shear zone is usually characterized by the ductile deforma- and mantle (Dewey, 1988; Lister et al., 1986; Manatschal, 2004; Wernicke, 1985). The main geological feature of such crustal-scale exci- tion with normal-sense kinematic indicators in the mylonites, sion is the juxtaposition of lower and upper crustal rocks across rela- which are commonly capped by brittle fault rocks. In the case of tively narrow (100 m to a few kilometre thick) damage and shear the Nordfjord-Sogn Detachment Zone, the mylonites may be sever- zones (e.g. Andersen and Jamtveit, 1990; Norton, 1986). Based on geo- al kilometers thick and associated with displacement in the order of logical observations, the ‘simple shear model’ or modiﬁed versions of it, 100 km (Andersen and Jamtveit, 1990; Hacker et al., 2003). explains the excision of the lithosphere along low angle normal faults 3) In the upper stratigraphic level of the hangingwall, syntectonic and shear zones. However, despite the general acceptance of this supra-detachment basins develop along active faults (e.g. low- model, several important questions remain regarding the dynamics angle-normal faults, listric normal faults or strike-slip transfer faults) and the overall thermal evolution of crustal-scale detachments. and are commonly found in tectonic contact with the shear zone A detachment consists of a footwall (“lower plate”), a shear zone, (Andersen, 1998; Osmundsen et al., 1998, 2000; Seguret et al., 1989). and a hangingwall (“upper plate”). The thermal evolution of a crustal-scale detachment has to be considered with two distinct aspects: fast exhumation and highly- localized deformation. Pressure-temperature-time (PT-t) paths of the ⁎ Corresponding author at: Institute for Energy Technology (IFE), Instituttveien 18, footwall metamorphic core complexes typically indicate fast decom- NO-2007 Kjeller, Norway. Tel.: +47 22 85 60 48. pression at near-isothermal conditions during exhumation from the E-mail address: [email protected] (A. Souche). lowertotheuppercrustlevel(Labrousse et al., 2004). The time window 1 Present address: Centre for Earth Evolution and Dynamics (CEED), University of bracketing such isothermal exhumation is only a few million years Oslo, P.O. Box 1048, Blindern, 0316 Oslo, Norway. 2 ﬁ Present address: Computational Geology Laboratory, Polish Geological Institute – (Hacker et al., 2010; Johnston et al., 2007) and is signi cantly smaller National Research Institute, Wrołcaw 53-122, Poland. than the time required for thermally equilibrating the crust by diffusion

(several tenths of Myr, e.g., Turcotte and Schubert, 2002). Therefore, the The other characteristic feature controlling the thermal evolution thermal structure of the crust after fast exhumation of a high- to of the detachment zone results from the relative movement between ultra-high-pressure [(U)HP] terrane might be strongly perturbed by in- the foot- and the hangingwall. Large strain can accumulate inside the teraction between a “hot” footwall and a “cold” hangingwall. shear zone of the detachment, and this may have a signiﬁcant effect

a 5 E 6 E

Bremangerlandet Hornelen

Frøya Gjegnalunds- Svelgen Sandane breen Kalvåg Hornelen basin Ålfobreen Hyen

Hovden

Florø 61.6 N Håsteinen basin

Askrova Trondheim

Førde

Kvamshesten basin Norway Bygstad Dale Bergen Oslo

Fure Værlandet Fjaler Sørbøvåg

Hyllestad

61.2 N Solund basin Leirvik Devonian basins (hangingwall)

Sula Lavik Hardbakke Major detachment faults

Ytre Sula Caledonian nappes (hangingwall / shear zone)

10 km Western Gneiss Region (footwall)

b Erosion W E Devonian basins

Burial depth basins >10 km Exhumation of the footwall? Shear heating?

Fig. 1. a) Geological map of the Nordfjord-Sogn Detachment Zone in western Norway. b) Schematic cross section (E-W) across the detachment. Heat flux introduced at the base of the Devonian basins can come from the exhumation of the footwall or from shear heating in the shear zone. A. Souche et al. / Tectonophysics 608 (2013) 1073–1085 1075 on the heat budget of the system in form of shear heating (Brun and Hacker et al., 2003 (peak) Hacker et al., 2003 (retro) Cobbold, 1980; Burg and Gerya, 2005; Campani et al., 2010; Hartz and 2.5 Johnston et al., 2007 (peak) Podladchikov, 2008; Leloup et al., 1999; Schmalholz et al., 2009; HP Johnston et al., 2007 (retro) (WGR) Scholz, 1980). Shear heating rate depends on the non-elastic strain Average of error ellipses (1σ) rate and the deviatoric stress experienced by rocks during deforma- 2 HP tion. The amount of shear heating produced in a geological system (Caledonian nappes) is difficult to measure and modelling provides a viable tool for ~60 km assessing the role of shear heating. 1.5 We base our study on the geological observations of the “Isothermal” decompression Nordfjord-Sogn Detachment Zone (NSDZ) of western Norway. In the ~40 km peak conditions top stratigraphic level of the detachment, several supra-detachment 1 basins formed (Fig. 1) as response to repetitive tectonic motions dur- HP ing the exhumation of the footwall (Osmundsen et al., 1998; Seguret Pressure (lithostatic) [GPa] (retrograde overprints) ~20 km et al., 1989; Seranne et al., 1989; Steel et al., 1977). These supra- 0.5 detachments basins are commonly named the Devonian basins due to the presence of Devonian plant fossils in the sediments (Høegh, 0 1945; Kolderup, 1916, 1921, 1927). The special feature of the Devoni- 400 500 600 700 800 an basins is the documented low-grade metamorphism (Seranne and Temperature [oC] Seguret, 1987; Souche et al., 2012; Svensen et al., 2001; Torsvik et al., 1988). Souche et al. (2012) showed that the temperature conditions Fig. 2. Peak and retrograde Caledonian metamorphism from the WGR and HP Caledo- at the burial depth of 9.1 km was as high as 345 °C which can be trans- nian nappes exposed beneath the Solund and Hornelen basins. Thermobarometry data lated to a geothermal gradient of 38 °C/km. Additionally, the peak from Hacker et al. (2003) and Johnston et al. (2007). temperatures in the Devonian basins increase with proximity to the detachment contact and thus suggest that the lateral variation of and Dallmeyer, 1992; Cuthbert, 1991; Fossen and Dallmeyer, 1998; maximum temperatures was controlled by a dynamically evolving Young et al., 2011). system, most likely linked to the detachment. Was shear heating con- The mylonites of the NSDZ have a maximum thickness of 5.5 km tributing to the heat budget in the system? Could it have an impact on north of the Hornelen basin, but the precise original thicknesses cannot the lateral variation of the peak temperatures within the supra- be accurately determined because of excision by later faults. Marques detachment basins? et al. (2007) estimated the shear strain partitioning in the NSDZ and In this study, we analyse the thermal evolution of the detachment showed that the lower parts of the mylonites experienced considerable zone and estimate the contribution of shear heating on the heat bud- flattening across the foliation in addition to simple shear (ratio of sim- get of the area. We first present a compilation of available geological ple to pure shear ~1). The upper ~2 km of the mylonites are, however, data from the NSDZ to build a well-founded geological model that can characterized mainly by simple shear, with a shear strain of approxi- be studied numerically. We compare the results of our numerical mately 20 (Andersen and Jamtveit, 1990; Hacker et al., 2003; Marques studies with independent observations from the supra-detachment et al., 2007), used here as the bulk shear strain along the NSDZ. basins of western Norway and discuss the importance of the shear heating in this particular geological setting. 2.2. The hangingwall peak temperatures

2. Geological constraints of the model Following fluid-inclusion and mineralogical studies of the basins (Svensen et al., 2001), a recent study using Raman spectroscopy of car- 2.1. Footwall conditions and strain partitioning in the detachment bonaceous material (RSCM) from Devonian plant fossils (e.g. Souche et al., 2012) documents high peak temperatures from the Solund, The NSDZ is one of the largest extensional detachments in the world, Hornelen, and Kvamshesten basins. The temperatures locally reached with a displacement of 70 to 100 km (Andersen and Jamtveit, 1990; 345 °C for an estimated burial of 9.1 km in the Kvamshesten basin Hacker et al., 2003). The extension was initiated during the latest stages (Table 1). This suggests a geothermal gradient of approximately of the Caledonian continent-continent collision when the crust reached 38 °C/km, which is clearly at variance with commonly accepted geo- its maximum thickness and partially crystallized to (U)HP eclogites in thermal estimates for a thickened orogenic crust or even for a crust in the Late Silurian to Early Devonian (Hacker et al., 2012; Krogh et al., early stages (415-395 Ma) of post-orogenic extension (Fossen, 2010; 2011; Kylander-Clark et al., 2009). The eclogites are found in the WGR Gabrielsen et al., 2005; Hacker, 2007; Spengler et al., 2009). Souche et (Fig. 1), which constitutes the exhumed footwall of the NSDZ. Petrolog- al. (2012) concluded that the elevated basin temperatures could only ical and thermochronological studies of the footwall give consistent be explained by an additional heat source introduced at the base of PT-paths (Fig. 2) with a common near-isothermal decompression from peak-pressure conditions within maximum 10 Ma (Hacker et al., Table 1 2003, 2010; Johnston et al., 2007; Kylander-Clark et al., 2009; Root et Burial depth and peak temperature estimates of the Devonian basins of W Norway. al., 2005; Young et al., 2011). The HP rocks exposed structurally below the basins (here we use Fluid-inclusion and Raman spectroscopy of mineralogical studies (*) carbonaceous material (**) data from near the Solund and Hornelen basins) provide useful constraints regarding the Caledonian metamorphism (Fig. 2) and the ki- Burial T (average) T (local) Distance from nematic evolution of the NSDZ (Hacker et al., 2003; Johnston et al., depth(***) the detachment 2007; Young et al., 2007). We take the maximum burial of the HP Hornelen 9.1 ± 1.6 km 250 ± 20 °C 295 ± 30 °C at 1 km units to represent the initial depth (~60 km) where the exhumation Kvamshesten 9.1 ± 1.6 km 250 ± 20 °C 345 ± 30 °C at 1 km Solund 13.4 ± 0.6 km 315 ± 15 °C 284 ± 30 °C at 8 km started along the shear zone. Based on the decompression path of 295 ± 30 °C the HP units, we constrain our model to account for 40 km of vertical 301 ± 30 °C exhumation bringing the HP rocks to a depth of 20 km, at which the *Svensen et al. (2001);**Souche et al. (2012); (***) The burial depth is estimated from retrograde mineral assemblages and their cooling age have been de- lithostatic pressure assuming a constant rock density of 2600 kg/m3 (Svensen et al., termined by 40Ar/39Ar geochronology (Andersen, 1998; Chauvet 2001). 1076 A. Souche et al. / Tectonophysics 608 (2013) 1073–1085 the hangingwall during the extension. This conclusion also is in agree- Normal sense reactivation of the detachment fault along the ment with previous description of ductile deformation of the basin-fill Solund and Kvamshesten segments (Fig. 1) in the Permian, and sediments adjacent to the detachment, which could suggest elevated again in the Late Jurassic has been documented by palaeomagnetic temperatures in this area (Braathen et al., 2004; Norton, 1987). and geochronological studies of fault breccias along the NSDZ (Andersen et al., 1999; Eide et al., 1997; Torsvik et al., 1992), and 2.3. Model: constraints and simplifications may have contributed to some exhumation. In this study, we assume that the Devonian basins reached their peak temperature conditions The different geological aspects presented in the previous sections during or shortly after the major post-Caledonian extension and allow us to build a simplified geological model of the evolution of the were not influenced by later reactivation of the detachment faults. detachment zone used in the numerical analysis (Fig. 3). The initial configuration of the model (Fig. 3a) corresponds to the thickened 3. Model Caledonian crust with a Moho depth set to 70 km corresponding to approximately twice the average thickness of continental crust. We 3.1. Governing equations assume that the deformation was initiated by the development of a lithospheric-scale shear zone with a constant dip angle α = 30° We analyze the thermal evolution in the model by solving the (Andersen and Jamtveit, 1990; Norton, 1986). transient heat balance equation: The active deformation within the shear zone and the exhumation of the footwall is considered within a time window denoted t*.Afterthat ∂T ! ρC þ v ∇T −∇ ðÞk∇T ¼ H þ H ð1Þ time the system still. We assume constant rates of deformation for sim- p ∂t r s plicity. During deformation, the footwall translates upward along the detachment and accounts for the exhumation of the lower crustal body where T is the temperature, t is the time, k is the thermal conductiv- ! (hf = 40 km) from 60 to 20 km depth (marked by a star in Fig. 3 aand ity, v is the rock velocity, ρ is the rock density, Cp is the rock specific b). At the same time, the hangingwall translates downward along the de- heat capacity, and Hr is the radiogenic heat production (see character- tachment and creates accommodation space in the basin formed at the istic values in Table 2). The shear heating term Hs is the product of the surface. We assume immediate erosion and sedimentation processes so deviatoric stress τ and the non-elastic strain rateγ˙ (Brun and Cobbold, that the model does not produce variations in topography. At time t*, 1980; Burg and Gerya, 2005; Turcotte and Schubert, 2002) so that: the lower crustal body is at 20 km depth and the basin is at maximum ¼ τ γ˙ ð Þ depth (bmax). Accordingly to the estimated burial depth of the Devonian Hs 2 basins (Table 1), we consider two values for bmax,10km(forthe Hornelen and Kvamshesten basins) and 15 km (for the Solund basin). The hangingwall and footwall translate along the detachment with- An important element of the model is the style of deformation out internal deformation. All the deformation is accommodated with- within the shear zone. Despite observations of Marques et al. in the shear zone and thus shear heating (Eq. (2)) is only used in the (2007) on the significant component of pure shear within the lower shear zone. parts of the NSDZ (Section 2.1), we assume simple shear only. This Completing the mathematical model of thermal evolution requires simplification reduces the number of model parameters, which are the specification of initial and boundary temperature conditions, ve- poorly constrained and might be related to the earlier stages of exhu- locities and rheological relationship. The assumption of constant mation (Andersen et al., 1994). Thus, simple shear (Fig. 3c) accom- translation during exhumation (Section 2.3) gives the velocities with- modates the total relative displacement between the foot- and in the foot- and the hangingwall by dividing the total displacements hangingwall. According to the observations and measurements by t*. The initial and boundary temperature of the system and speci- along NSDZ (see Section 2.1), we set a bulk shear strain (γbulk)of20 fication of Eq. (2) for the shear zone are discussed below. at time t*. Given γbulk, α, and the total displacement between the foot- and hangingwall, we estimate the thickness of the shear zone 3.2. Initial geotherm to be D=5-5.5 km depending on bmax, which is consistent with the observations (Marques et al., 2007). The initial thermal situation before the extension has to be consid- The assumption of uniform translation (and thus, without any de- ered in the geological framework of the Caledonian orogeny (peak formation) of the foot- and hangingwall is a simplification of our condition data points on Fig. 2). Thus, to obtain the initial thermal model. We have, however, tested the importance of the lateral state, we perform an auxiliary modelling of the evolution of the lith- stretching of the units, and found that a moderate extension does osphere during the Caledonian collision. In this experiment we as- not cause significant changes of the peak temperatures in vicinity of sume that, prior to collision, the lithosphere was in steady state and, the detachment zone. during the orogeny, the lithosphere thickened uniformly by pure

a) Initial configuration (t=0) b) Final configuration (t=t*) c) Model geometry (not to scale)

0 α 0 α=30° b basin α upper crust max bmax 20 20 γ =20 Moho bulk 32 hf 40 40 =40 km h α f D lower crust depth [km] 60 60 α γ 70 Moho D = (bmax+hf)/sin( )/ bulk mantle lithosphere 20 km 20 km 80 80

Fig. 3. a) Initial and b) ﬁnal conﬁguration of the different rock units in the model. The maximum basin depth bmax = 10-15 km. The total vertical motion of the footwall hf =40km. c) Sketch of the translation motion between the foot- and the hangingwall units along the constant dipping shear zone (α = 30°). All the deformation is accommodated inside the shear zone with a resulting bulk shear strain γbulk = 20 at time t*. The thickness of the shear zone D is estimated to be 5-5.5 km. A. Souche et al. / Tectonophysics 608 (2013) 1073–1085 1077

Table 2 Thermal and rock properties of the different units of the model.

Parameters symbol Unit Value

sediments upper crust lower crust mantle

Thermal conductivity* k W/(m.K) a = 0.64; b = 807 a = 1.18; b = 474 a = 0.73; b = 1293

Specific heat capacity Cp J/(kg.K) 1000 1000 1000 1000 Rock density ρ Kg/m3 2600 2700 2900 3300 3 −6 −6 −7 −8 Radioactive heat production** Hr W/m 1.2 × 10 1×10 4×10 2×10 *k=a+b/(T+350), where T is the temperature expressed in °C (after Clauser and Huenges (1995)). ** after Hasterok and Chapman (2011). shear. We used a 1D computer code LiToastPhere (Hartz and setups but where shear heating was ignored (M30, M35 and M40). Podladchikov, 2008) to perform the calculations. The shear heating models are warmer by an average of 100 °C, illus- We consider the Caledonian continent-continent collision to last trating the importance of this heat source during deformation. The re- for 25 My (Corfu et al., 2006; Johnston et al., 2007; Torsvik and sults also illustrate greater dependence on the initial conditions and Cocks, 2005) and to result in 100% thickening of the crust (double rock properties for the models without shear heating. of the original thickness) which corresponds to an average strain We use the preferred temperature profile M35-sh (Fig. 4) to build rate of 8.7 × 10-16 s-1. The model lithosphere consists of three layers, the initial temperature distribution. We also use this profile to con- composed of a wet quartzite upper crust, a diabase lower crust, and a strain the bottom boundary condition during the model evolution. dry dunite mantle (Ranalli, 1995). The initial thickness of the upper As the footwall moves upward during exhumation, the material in- crust is set to 16 km (Hasterok and Chapman, 2011). The lower coming into the system assumed to sustain its temperature initially crust extends to the Moho discontinuity with initial depths of 30, 35 prescribed by M35-sh. This assumption ignores the thermal relaxa- and 40 km (corresponding to the model “Mxx”). The initial depth of tion of the deep lithosphere after Caledonian orogeny, which is ap- the mantle lithosphere is set to 140 km (Artemieva, 2006). The ther- proximately valid for fast exhumation considered here. mal properties used in the calculations are listed in Table 2. We performed a series of numerical tests varying the initial Moho 3.3. Kinematic of the shear zone depth and the amount of radioactive heat production and considering the influence of shear heating. We compare the model results with Restoring the exact distribution of velocities and stress field within the data of the peak metamorphic conditions of the Caledonian the shear zone is beyond the scope of this study. Instead, we approxi- nappes below the Solund basin and the Hornelen basins (Fig. 2). mate the velocities within the shear zone using two end-member ap- The best fit geotherm is obtained with the model M35-sh (Fig. 4), proaches, in which either shear strain rate (γ˙ -cst) or shear stress (τ-cst which accounts for shear heating during the deformation of the lith- model) is kept constant across the shear zone. The two kinematic osphere. Fig. 4 also presents model results obtained with similar models correspond respectively to an upper and lower bound on the estimate of shear heating expressed by Eq. (2). Whereas the γ˙ -cst model 3 forces uniform deformation and thus active heat production even in τ 100% thickening (pure shear) in 25Ma strong areas of the shear zone, the -cst model results in localized defor- Strain rate = 8.7e-16s-1 mation of weaker parts of the detachment, and thus produces less heat. It is important to keep in mind that neither the γ˙ -cst nor the τ-cst 2.5 ~ 88 km M30 models reproduce exactly the actual deformation process within the M35

M40 Nordfjord-Sogn Detachment and the main purpose in using these two virtual kinematic models is to deliver an upper and lower bound on the shear heating effect.

2 ~ 72 km M40-sh 3.3.1. Rheology M35-sh No shear heating Shear heating The shear zone accumulates the entire deformation in the model M30-sh (Fig. 3c) and hosts the production of shear heating. This deformation occurs in the range of 0-60 km, and thus involves the transition from 1.5 ~ 54 km brittle to ductile behaviour of rocks. The brittle behaviour is described by Byerlee’s relationship: Pressure (lithostatic) [GPa] y τ ¼ − μ ∫ ρ ð Þ 1 ~ 37 km By 1 p f g dy 3 0 Geological data (peak conditions): Hacker et al. (2003) Johnston et al. (2007) See Table 2 for definitions and values of parameters used. This Average of error ellipses (1σ) constitutive relationship assumes no deformation for the stress 0.5 400 500 600 700 800 values below critical, τBy, which increases with depth (Fig. 5). We Temperature [oC] approximate Eq. (3) using a power law relationship (after Nanjo et al., 2005; Turcotte and Glasscoe, 2004) Fig. 4. 1D model predictions (solid and dash lines) versus pressure-temperature (PT) qffiffiffiffiffiffiffiffiffiffiffi ! estimates of the HP units in the footwall of the Nordfjord-Sogn Detachment Zone τ nb (Hacker et al., 2003; Johnston et al., 2007). Different model setups are compared for τ ¼ τ nb γ˙ =γ˙ γ˙ ¼ γ˙ ð Þ By b c or b τ c 4 different Moho-depth indicated by “Mxx”, and with or without shear heating indicated By by “-sh”. The grey shades represent the spread of the curves “M35” and “M35-sh” by varying the radioactive heat production by ±25%. We observe a good fit between where γ˙ is a critical strain rate and γ˙ is the strain rate of the brittle the representative PT data and those predicted by the model when the bulk deforma- c b fi γ˙ tion of the lithosphere is taken into account. Without shear heating during collision, deformation. Here we de ne c as the bulk strain rate imposed by the entire system is too cold in comparison to the geological data. the motion of the foot- and the hangingwall (γbulk/t *). For large 1078 A. Souche et al. / Tectonophysics 608 (2013) 1073–1085

a b τ shear stress [MPa] 0 100 200 300 400 0 τ γ = 2.1x10-13

After exhumation (Wet Quartzite) 10 Brittle/Ductile Transition zone

τ ite) By 20 artz Qu 2015 et 10 5 (W ial tit =1 In b n Depth [km] ) tzite uar ry Q (D Brittle failure ial tit 30 In

0 γ γ c 40

Fig. 5. a) Brittle failure approximated by power law relationship between shear stress and shear strain rate. The power law expression (Eq. (3)) approaches Byerlee’s brittle failure ˙ (where τBy(y) is function of depth) for large power law exponent (nb = 20 in this study). b) Depth distribution of the shear stress within the shear zone (γ-cst model and t* =3 My). A single stress proﬁle is drawn for dry and wet quartzite at the initial conditions. The brittle-ductile transition is smoothed (illustrated by yellow) because of the use of approximation presented on Fig. 5a and Eq. (4). Lateral variation of the temperatures at the end of the exhumation (t*) scatters the shear stresses for a given depth as illustrated by the gray shade for the wet quartzite simulation.

power law exponent (nb = 20), the deviatoric stress is approximate- substituting Eqs. (4) and (5) into it. Our approximation to the shear ly equal to the critical stress τBy (yield strength) for a wide range of stress (Fig. 5b) follows the minimum of the two stress regimes and γ˙ strain rate values centered about the critical strain rate c. smoothes the transition zone. The ductile behaviour is described by a power-law for dislocation creep: 3.3.2. Constant shear strain model (γ˙ -cst model) The constant shear strain rate model results in a linear velocity qffiffiffiffiffiffiffiffiffiffi profile across the shear zone (Fig. 6a) defined by the hangingwall τ ¼ expðÞE=RTn nd γ˙ =A or γ˙ ¼ τnd A expðÞ−E=RT ð5Þ d d d and footwall velocities. The deformation is homogeneous and distrib- uted across the shear zone, without localization, and with the same γ˙ intensity in the “strong” or “weak” (thermally weakened) parts of where d is the strain rate of the ductile deformation. The Arrhenius term exp(E/RTnd) results in a strong decrease of the stress with temper- the shear zone. Therefore, we expect the shear heating term (Eq. ature and, for standard geotherm, with depth (Fig. 5b). The shear zone (2)) to be maximized using this kinematic model. exposed today between the Devonian basins and the WGR is mainly γ formed of Caledonian nappes represented by meta-sedimentary units γ˙ ¼ bulk ð Þ ⁎ 7 and some deformed slices of basement. The rheological weakness of t the meta-sediments is approximated by flow laws for wet and dry The corresponding shear stress, variable across and along the shear quartzite (see Table 3). zone, is determined at any points by substituting Eqs. (4) and (5) We assume the brittle and the ductile mechanism of deformation into Eq. (6) and solving it using Eq. (7). This approach insures a to act simultaneously on the total shear strain rate, and it allows us to mass conservation in the model but induces large variations of write: shear stress across the shear zone due to the variations of rheological properties. γ˙ ¼ γ˙ þ γ˙ ð Þ b d 6 3.3.3. Constant shear stress model (τ-cst model) τ fl For a given shear stress value across the shear zone, Eqs. (4) – (6) The motivation for the -cst model is to augment the ow pattern yield a strain rate profile. For a given strain rate value across the by avoiding large stress variation across the shear zone and allowing shear zone, a shear stress profile is obtained by solving Eq. (6) after for localization of the deformation. The localization has a direct impact on the distribution of heat produced by shear heating since large deformations mostly occur in “weak” parts of the shear zone. Table 3 Thus, the τ-cst model is used as end-member kinematic model mini- Material and rheological (Ranalli, 1995) parameters used in the numerical experiments. mizing the impact of shear heating as opposed to the γ˙-cst model. A Parameters Symbol Unit Value value of the shear stress τ, uniform across and variable along the − shear zone, is obtained by integrating Eq. (6) across the shear zone Gravity g m.s 2 9.81 ’ γ Friction coefficient μ - 0.7 (in the y direction, Fig. 6) and using the bulk strain rate ( bulk/t*)as

Pore ﬂuid factor Pf - 0.4 a constraint:

Power law exponent nb -20 −1 Gas constant R J.K 8.314 D D 0 ÀÁ0 Quartzite: Wet/Dry ∫γ˙dy ¼ ∫ γ˙ þ γ˙ dy Power law exponent n − 2.3/2.4 b d d 0 0 Pre-exponential multiplier A MPa-nd.s-1 3.2 × 10−6/6.7 × 10−6 "# ! ð8Þ D nb −1 3 γ τ 0 Activation energy for E kJ.mol 154E + 3/156 × 10 bulk D ¼ ∫ γ˙ þ τnd AexpðÞ−E=RT dy dislocation creep t⁎ τ c 0 By A. Souche et al. / Tectonophysics 608 (2013) 1073–1085 1079

0 20 km Brittle

Ductile 20 y’ x’

Depth [km] Line of zero velocity 40 Brittle-ductile transition

Velocities across the shear zone

60 a) b) c) d) Couette Poiseuille γ-cst +=τ-cst flow flow

Fig. 6. Typical velocity profiles of the two kinematic models. The profile (a) γ˙ -cst is derived for the constant shear strain model and gives a uniform linear velocity profile across the shear zone, constant in time. The profile (d) τ-cst is derived from the constant shear stress model (example of wet quartzite rheology at initial temperature distribution) and is the sum of Couette (b) and Poiseuille (c) flows in the shear zone. The profile (d) is calculated at each time step with the updated temperature and may change as the model evolves.

The strain rate profile is then calculated from Eqs. (4) and (5) and it the boundaries of the shear zone. However, significant rheological results in localized deformation in weak parts. Depending on the variations along the shear zone result in velocity fields characterized dominant deformation mechanism, rock weakens at the upper part by a non-vanishing divergence and lead to a violation of mass and of the shear zone in the brittle regime (where τBy is smaller, momentum conservation condition. To limit these effects, we aug- Eq. (3)) and at lower part of the shear zone in the ductile regime ment the kinematic profile by adding a Poiseuille flow contribution (where temperature is higher, Eq. (5)). Therefore, highly localized de- (Fig. 6c) determined by keeping the integrated mass balance con- formations occur along the boundary with the hangingwall in the stant along the shear zone. This results in a non-zero pressure gradi- upper part of the shear zone, and along the boundary with the foot- ent in the shear zone. We note that due to adding the Poiseuille flow wall in the lower part of the shear zone (Fig. 6b). component the original assumption of the constant shear stress The velocity profile resulting from the constant shear stress as- across the shear zone is not strictly satisfied. Yet, we choose to sumption (Couette flow, Fig. 6b) respects the no-slip conditions at refer to this model as τ-cst throughout the manuscript, as the strain

a) Initial conditions b) Exhumation of the footwall (t*=3 My) c) Thermal relaxation (30 My) 0 0 0 Basin Basin 15 15 20 20 HP unit 20 HP unit

32 Moho Moho 40 40 40

depth [km] 60 HP unit 60 60 70 Moho 20 km 20 km 20 km 80 80 80

o d e) Peak temperatures [ C] 0 782

C] maxima Basin o 350 15 20 HP unit 600 Moho contact shear zone 250 40 400

5 km away 60 200 150 10 km away 20 km 80 10 50

Temperature in the basin [ Shearing Thermal relaxation 13579 Time [My]

Fig. 7. Temperature distribution in the model (a) initial; (b) at the end of exhumation (3 My); (c) after thermal relaxation (30 My). (d) Temperature evolution in the markers located at the bottom of the basin taken at the contact, 5 km, and 10 km away from the shear zone (white circles in a-c). The arrows mark the temperature maxima and illustrate the scattered time for the peak conditions. e) Maximum temperature ﬁeld recorded during the entire simulation. The model used here is set with t* = 3 My, a dry quartzite rheology ˙ with γ-cst kinematic model, and bmax = 15 km. 1080 A. Souche et al. / Tectonophysics 608 (2013) 1073–1085

[J.m-3] Dry Quartzite Wet Quartzite 1010 0

AA BB A 15 B 9 20 10

8 Depth [km] Range for upper crust 10 radioactive heat production τ-cst γ -cst τ-cst γ -cst 20 km 60 107

Fig. 8. Distribution of total heat density produced by shear within the detachment zone for t* = 3 My (note the logarithmic colour-scale) and bmax = 15 km. Results are presented for τ-cst and γ˙ -cst models with dry and wet quartzite rheology. Shear heating produces 1-2 orders of magnitude more heat than the radioactivity of the upper crust during the same time interval. A, AA, B, and BB indicate the position of cross sections presented in Fig. 10. rates related to the Poiseuille flow are significantly smaller than the 3.4. FEM strategy total strain rates (Fig. 6c,d).Theresultingvelocityprofile of the τ-cst model is the sum of Couette and Poiseuille flowsasillustrated The model domain is 80 km deep and 120 km wide (Fig. 3). We Fig. 6d. use a triangular mesh generated with Triangle (Shewchuk, 1996, Dry Quartzite

0 0 γ -cst τ-cst 20 20 +143 oC +110 oC 40 40 3My

depth [km] 60 60

20 km 20 km 80 80

0 0 γ -cst τ-cst 20 20 [oC] o o 100

Duration of the detachment +81 C +67 C 40 40 10My

depth [km] 60 60 80

20 km 20 km 80 80 60 Wet Quartzite

0 0 γ -cst τ-cst 40 20 20 +92 oC +67 oC 20 40 40 3My

depth [km] 60 60 0

20 km 20 km 80 80

0 0 γ -cst τ-cst 20 20

o o Duration of the detachment 40 +49 C 40 +39 C 10My

depth [km] 60 60

20 km 20 km 80 80

Fig. 9. Temperature anomaly induced by shear heating for different kinematic models across the shear zone, for dry and wet quartzite rheology, for t* = 3 and 10 My, and for bmax = 15 km). The same colour code is used in all the plots. The numbers indicate the maximum difference in peak temperatures induced by shear heating. A. Souche et al. / Tectonophysics 608 (2013) 1073–1085 1081

2002) to discretise the model domain and accurately represent the 4.2. Heat produced by shear heating boundaries separating materials of different thermal properties. The mesh is updated at each time step accordingly to the subsidence of The distribution of total heat produced by shear heating within the basin on the top of the model. the detachment shear zone is presented in Fig. 8 (example presented Eq. (1) is implicitly solved with a finite element code using the for t* = 3 My). The results for γ˙ -cst model show a maximum heat Streamline Petrov-Galerkin scheme. A similar discretisation has been produced in the upper 10-20 km, which corresponds to the largest documented and used for geodynamical problems and we refer to the stress field at the brittle-ductile transition. The results for τ-cst paper of Braun (2003) for more technical details. Temperature and model are characterized by two areas with high heat production velocity fields are linearly interpolated using 3-nodes elements. (corresponding to areas of localized deformations), one in the upper The temperature-dependent thermal conductivity is calculated using brittle domain, and one in the lower ductile domain. Irrespective of temperatures from the previous time step. We consider zero flux on the different spatial distribution of the heat production in the two ki- the lateral boundaries and Dirichlet boundary conditions on the top nematic models, the amplitude remains within the same range. and bottom (Section 3.2). Shear heating may be locally two orders of magnitude higher than Shear zone related calculations are performed on an auxiliary reg- the heat produced by radioactive decay in the upper crust. This effect ular grid onto which the modelled temperature is projected. The reg- can be seen as a punctual heat source during the active deformation ularity of this grid allows accurate integration of Eqs. (4) – (6) and/or in the detachment zone. (8) across the shear zone to define the stress field, strain and strain rate. The resulting velocities and shear heating are then interpolated 4.3. Temperature anomaly produced by shear heating back to the main grid each time step. We illustrate (Fig. 9) the temperature anomaly produced by shear 4. Results heating by plotting the difference of modelled peak temperatures obtained with and without shear heating. For dry quartzite models We performed a systematic study by varying the time of the exhu- and t* = 3 Ma, shear heating can introduce more than 100 °C at the mation t* (3, 5, 10, and 15 My), the shear zone rheology (wet and dry base of the basin. The impact depends on the rheology and on t*, quartzite), the kinematic model of the shear zone γ˙ -cst and τ-cst), but remains significant (within 30-80 °C) for slower exhumation and the maximum basin depth bmax (10 and 15 km). All the simulations and weaker rheology in the shear zone. are repeated twice, with and without accounting for shear heating. In the model configurations presented here, a value of the pore

fluid factor of pf = 0.4 in Eq. (3) is assumed along the shear zone. 4.1. Temperature evolution and peak conditions The effect of pore-fluid pressure on the effective stress is still a matter of debate (e.g. Nur and Byerlee, 1971; Sibson, 1994). However, the For any t*, the exhumation of the footwall and the subsidence of the impact of varying the pore fluid pressure within acceptable range is hangingwall leads to an unsteady temperature field. Thermal relaxation not critical with respect to thermal effects related to shear heating. is reached by 20 to 30 My after t*. The different thermal stages of the The two kinematic models, γ˙ -cst and τ-cst, were introduced in model are illustrated in Fig. 7a-c. Note that for the similar initial and Section 3.3 as an upper and lower bound to estimate shear heating. final geometry and for the same distribution of the thermal properties Fig. 9 shows that for the same parameters, γ˙ -cst model is hotter of rocks, the initial and final geotherms (Fig. 7a and c) will be equiva- than τ-cst model. However, despite the large difference in the lent. The peak temperature profile (Fig. 7e), however, depends greatly model velocity profiles (Fig. 6), the estimated temperature anomaly on the parameters tested in our numerical experiments. produced by shear heating is on the same order. A difference of ap- To facilitate the comparison of our model results with geological proximately 30 °C separates at most the temperature anomaly observations (Section 2), we extract the peak temperature of each obtained from both models, which shows that the style of deforma- point during the evolution of the model up to thermal relaxation tion within the shear zone does not influence much the amplitude (Fig. 7e). The peak temperatures are reached at different time for dif- of the induced temperature anomaly in the system. ferent localities, often well after t=t*(Fig. 7d). 5. Comparison with geological observations

160 A AA (Dry Quartzite rheology) 5.1. Shear strain partitioning B BB (Wet Quartzite rheology) 140 Fig. 10 shows the strains along the cross sections A, AA, B, and BB 120 (Fig. 8) at the end of the simulations. Independent of the rheology and the cross section position, the strain across the shear zone, described 100 by the τ-cst model, localizes mostly along the upper part, beneath the

localized deformation localized deformation hangingwall with maximum strain higher than 200 and along the (Brittle regime) (Ductile regime) 80 basal part of the shear zone next to the footwall with maximum strain around 35-60. Strains higher than 100 are indeed speculated in the 60 Shear Strain upper part of the NSDZ (Hacker et al., 2003). However, there is no con- 40 vincing field evidence for high-strain environment at the base of the shear zone such as produced by the τ-cst model. This ductile shear local- Average shear strain = 20 20 (Model input) ization can be seen as an artefact of our simplified shear zone geometry (e.g., the strict rigidity of the footwall). The τ-cst model also produces a 0 543210 strain gap in the middle of the shear zone, reducing the effective thick- Shear zone thickness [km] ness of the shear zone. This is in contrast with the deformation pattern observed along the NSDZ, which exhibits continuous and large strain Fig. 10. Strain profiles across the shear zone for the τ-cst models. Two shear bands rep- (20) over several kilometres (Andersen and Jamtveit, 1990). resentative for brittle and ductile deformation are observed along upper (left) and bot- In contrast to τ-cst, the γ˙ -cst model satisfies the observations on tom (right) parts of the shear zone. The average strain across the shear zone is 20. The rheology and the position at which the cross sections are taken have a minor impact on continuous strain within the NSDZ, but lacks the high shear localiza- the style of final strain profile. See locations of cross sections on Fig. 8, t* = 3 My. tion in the upper part of the detachment. Although the two models 1082 A. Souche et al. / Tectonophysics 608 (2013) 1073–1085

Kvamshesten/Hornelen basins Solund basin Burial depth = 9.1 km Burial depth = 13.4 km a d GEOLOGICAL DATA MODEL RESULTS Svensen et al. 2001 Kvamshesten γ τ 340 380 -cst -cst Souche et al. 2012 t* = 3 My t* = 5 My t* = 10 My 300 Hornelen 340 C] o

260 300 Solund

the basin [ 220 260 Max temperature in Dry Quartzite Dry Quartzite 180 220 8 46 2 8 624 b e Kvamshesten 340 380

300 Hornelen 340 C] o

260 300 Solund

the basin [ 220 260 Max temperature in Wet Quartzite Wet Quartzite 180 220 8 624 8 624 c f Kvamshesten 340 380

300 Hornelen 340 C] o

260 300 Solund

the basin [ 220 260 Max temperature in No shear heating No shear heating 180 220 contact 8 624 8 624 contact distance from the detachment distance from the detachment [km] [km]

Fig. 11. Comparison of model temperatures and geological data for the Kvamshesten and the Hornelen basins (a-c, max. burial depth 9.1 km) and for the Solund basin (d-f, max. burial depth 13.5 km). Data from Svensen et al. (2001) present average peak temperatures for the entire basins, Souche et al. (2012) presents local peak temperatures. γ˙ -cst and τ-cst corresponds to the two kinematic models used for the shear zone. t* is the time window for the development of the detachment zone. (c) and (f) present the model results obtained without shear heating; (b) and (e) present the model results obtained with wet quartzite rheology for the shear zone, and (a) and (d) with dry quartzite. The maximum depth of the basin (bmax) was set to 10 km in (a-c) and 15 km in (d-f). differ in the style of deformation and in correlation to observations, The maximum reported burial depth of the Devonian sediments is the resulting heat produced within the shear zone based on those 9.1 km for the Kvamshesten and the Hornelen basins and 13.4 km models does not differ significantly. Thus, we can conclude that for the Solund basin (Svensen et al., 2001). Thus, we compare the exact reproduction of the flow within the shear zone has limited im- geological data with the modelled peak temperatures taken at 9.1 portance while considering the thermal budget of the NSDZ. (Fig. 11a-c) and 13.4 km (Fig. 11d-f). Fig. 11 presents the modelled temperature curves for three different t* and two kinematics within 5.2. Implications for the supra-detachment basins thermal history the shear zone (γ˙ -cst and τ-cst) in each sub-figure. All the results obtained without shear heating (Fig. 11c and f) In Fig. 11, we compare the modelled peak temperatures with show low peak temperatures and fail to reproduce the geological the geological data (Section 2.2). Svensen et al. (2001) documented av- data. In addition, these modelled temperatures show a relatively erage values for peak temperatures of 260 ± 20 °C for the entire small lateral variation through the basins. The lateral temperature Kvamshesten and Hornelen basins (horizontal lines on Fig. 11a-c) and variation does not exceed 40 °C in a range of 10 km away from the 315 ± 15 °C for the Solund basin (horizontal lines on Fig. 11d-f). detachment contact. That low thermal gradient illustrates the role Souche et al. (2012) reported the local estimates of peak temperature played by the hot rising footwall on the heating of the basin. This of the sediments as a function of the distance to the detachment (data heat source is not sufficient to induce significant variations of the points on Fig. 11). peak temperatures in the supra-detachment basins. A. Souche et al. / Tectonophysics 608 (2013) 1073–1085 1083

2.5 Model results: Geological data: Markers before exhumation Johnston et al., 2007 (peak) No shear heating Johnston et al., 2007 (retro) γ-cst model Corresponding samples 2 HP τ-cst model Average of error ellipses (1σ) (Caledonian nappes)

~60 km “Isothermal” 1.5 decompression ~50 km

~40 km HP 1 Pressure [GPa] (retrograde overprints) ~30 km

~20 km 0.5

~10 km

0 200 250 300 350 400 450 500 550 600 650 700 750 Temperature [oC]

Fig. 12. Comparison of retrograde overprints (Johnston et al., 2007) with PT-t paths from numerical models of our study. All the model results are obtained for t* = 3 My, a dry quartzite rheology, and bmax = 15 km.

The models including shear heating (Fig. 11a, b, d and e) show sig- calculate pressure, which makes our pressure estimates as upper bounds nificantly higher peak temperatures and a stronger dependence on (as the background extensional stress may induce underpressure) and the proximity to the shear zone. Wet quartzite models, however, do conclusions of this section more robust. Markers initially shallower than not show good qualitative agreement with observations (Fig. 11b 45 km exhibit strong thermal overprint related to shear heating. The tem- and e). Dry quartzite models (Fig. 11a and d) result in higher temper- perature increase during the exhumation of these markers, up to 100 °C, ature rise and compare well to geological observations. The tempera- compares with some of the geological data but is observed at much ture curves for γ˙ Z -cst models (any t*) and τ-cst models (t* b 5 My) shallower depths in the model. In contrast, markers initially deeper than show good correlation to the average peak temperatures of Svensen 45 km, comparable to the initial decompression depth of the HP units, et al. (2001) and to the local estimates of Souche et al. (2012). monotonically cool during decompression. The results obtained with dry quartzite (Fig. 11a and d) show The model results show the limited effect of shear heating in pro- about 100 °C or more of lateral variation of peak temperatures within ducing temperature increase at the early stage of the decompression 10 km distance from the detachment. This clearly indicates the signif- of the HP units found in the NSDZ. Either these units were originally icance of shear heating by locally increasing the temperature in the at shallower depth and were subjected to overpressure (Petrini and sediments at the vicinity of the detachment fault. These models re- Podladchikov, 2000), or were possibly affected by heat generation produce the geological data of 295 °C in the Hornelen basin. In com- during retrograde metamorphism reactions (Connolly and Thompson, parison to a maximum of 220 °C calculated without shear heating, 1989; Haack and Zimmermann, 1996). shear heating alone accounts for as much as 25% of the thermal budget of the sediments. 6. Conclusions Figs. 9 and 11 show that the influence of shear heating depends greatly of the distance to the shear zone, and is in accordance with We have developed a simple numerical model to understand the the geological observations from Souche et al. (2012). The numerical thermal budget and the role of shear heating in crustal-scale exten- results of the present study show that rocks located more than sional detachments. Using geological observations of the NSDZ we 5-10 km away from the detachment are not affected by shear heating. have developed a conceptual model of evolution of such a system. The model was augmented by constraining the non-steady-state 5.3. PT-t path and retrograde overprint of rocks within the shear zone geotherm associated with the end of Caledonian orogeny. We have built two simplified kinematic models for the deformation within The studies of PT-t paths representative for the exhumation of HP the shear zone. The model results were tested against peak tempera- units within the NSDZ show isothermal or temperature-increasing ture conditions documented within three Devonian basins of western decompression (Hacker et al., 2003; Johnston et al., 2007; Labrousse Norway. Our numerical study has shown: et al., 2004) illustrated in Fig. 12. Can shear heating lead to temperature increase or support isothermal condition during exhumation of 1. Shear heating within the highly-deformed NSDZ can generate a the HP units? Below we demonstrate that shear heating is unlikely temperature increase up to 100 °C in the detachment shear zone an explanation for such an effect and other mechanisms should be and is a necessary mechanism to explain the elevated peak tem- found to explain the phenomenon. peratures within the Devonian basins of western Norway. We compare these observations with our model results. We select 2. Shear heating may account for 25% of the thermal budget of the several markers with initial depth between 60 and 25 km and reconstruct supra-detachment basins and may affect the peak temperatures 5 their PT-t paths. In our estimations, we use lithostatic condition to to 10 km away from the detachment shear zone. 1084 A. Souche et al. / Tectonophysics 608 (2013) 1073–1085

3. The amount of shear heating produced in the system is predomi- Hacker, B.R., Kylander-Clark, A.R.C., Andersen, T.B., Kooijman, E., 2012. Laser-Ablation Split-Stream (LASS) Petrochronology of the Ultrahigh-Pressure Western Gneiss nantly dependent on the exhumation rate and the rheological pa- Region. Abstract, IGC-34; 2012-08-06 - 2012-08-1. rameters of the rocks forming the shear zone. Hartz, E.H., Podladchikov, Y.Y., 2008. Toasting the jelly sandwich: The effect of shear 4. Shear heating has a limited impact on the documented heating heating on lithospheric geotherms and strength. Geology 36, 331–334. Hasterok, D., Chapman, D.S., 2011. Heat production and geotherms for the continental during decompression of the HP units in the NSDZ. lithosphere. Earth and Planetary Science Letters 307, 59–70. Høegh, O.A., 1945. Contributions to the Devonian flora of western Norway III. Norsk Acknowledgements Geologisk Tidsskrift 25, 183–192. Johnston, S., Hacker, B.R., Ducea, M.N., 2007. Exhumation of ultrahigh-pressure rocks beneath the Hornelen segment of the Nordfjord-Sogn Detachment Zone, western The Norwegian Science Council provided basic funding though a “Cen- Norway. Geological Society of America Bulletin 119, 1232–1248. tre of Excellence” grant to Physics of Geological Processes. Statoil and Det Kolderup, C.F., 1916. Bulandets og Værlandets konglomerat og sandstensfelt. Bergens norske viteskapsakademi are thanked for a Vista grant to AS. Det norske Museums Aarbok 1915-16. Naturvidenskabelig Række 26. Kolderup, C.F., 1921. Kvamshestens devonfelt. Bergens Museums Aarbok 1920-21. oljeselskap is thanked for research grant to SM. The two reviewers, Prof. Naturvidenskapelig Række 1–96. Taras Gerya and Prof. Stefan Schmalholz, are thanked for their comments Kolderup, C.F., 1927. Hornelens devonfelt. Bergens Museums Aarbok 1926. and suggestions that helped improving the manuscript. Naturvidenskapelig Række 1–56. 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