Shear heating in extensional detachments: Implications for the …folk.uio.no/torgeir/pdfpapers/Souche_shearheating.pdf · Devonian basins of W Norway ... hangingwall of the extensional

Shear heating in extensional detachments: Implications for the thermal history of theDevonian 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

a b s t r a c ta r t i c l e i n f o

Article history:Received 9 July 2012Received in revised form 27 May 2013Accepted 4 July 2013Available online xxxx

Keywords:Shear heatingSupra-detachment basinsNumerical modellingPost-Caledonian extension

The supra-detachment basins in western Norway were formed during Lower to Middle Devonian in thehangingwall of the extensional system of detachments known as the Nordfjord-Sogn Detachment Zone(NSDZ). The basins experienced elevated peak temperatures (up to 345 °C adjacent to the main detachmentfault) during the terminal stages of the extension. In this study, we show that the heat generated by the de-formation of the rocks within the shear zone of the detachment, also known as shear heating, played a role inthe thermal evolution of the entire region during the extension and could have induced the elevated peaktemperatures of the supra-detachment basins. We numerically analyse the influence of the rheology andthe deformation style within the shear zone, the rate of exhumation of the footwall, and the thickness ofthe sedimentary accumulation on the top of the system. The model reproduces the elevated temperaturesrecorded 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 thehangingwall as far as 5 km away from the detachment.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Large-scale extensional detachments, resulting from gravitationalcollapse of over-thickened crust, or extension driven by plate motions,have been recognized and documented in a number of places and pro-vide a major mechanism to exhume large segments of the lower crustand mantle (Dewey, 1988; Lister et al., 1986; Manatschal, 2004;Wernicke, 1985). Themain geological feature of such crustal-scale exci-sion is the juxtaposition of lower and upper crustal rocks across rela-tively narrow (100 m to a few kilometre thick) damage and shearzones (e.g. Andersen and Jamtveit, 1990; Norton, 1986). Based on geo-logical observations, the ‘simple shear model’ or modified versions of it,explains the excision of the lithosphere along low angle normal faultsand shear zones. However, despite the general acceptance of thismodel, several important questions remain regarding the dynamicsand the overall thermal evolution of crustal-scale detachments.

A detachment consists of a footwall (“lower plate”), a shear zone,and a hangingwall (“upper plate”).

1) The footwall records higher-grade synkinematic metamorphismand younger metamorphic cooling ages than the hangingwall. Thefootwall is often referred to as a metamorphic core complex, andin extreme cases the entire crust may be stretched off to exposemantle rocks (Manatschal, 2004; Wernicke, 1985).2) The shear zone is usually characterized by the ductile deforma-tion with normal-sense kinematic indicators in the mylonites,which are commonly capped by brittle fault rocks. In the case ofthe Nordfjord-Sogn Detachment Zone, the mylonites may be sever-al kilometers thick and associated with displacement in the order of100 km (Andersen and Jamtveit, 1990; Hacker et al., 2003).3) In the upper stratigraphic level of the hangingwall, syntectonicsupra-detachment basins develop along active faults (e.g. low-angle-normal faults, listric normal faults or strike-slip transfer faults)and are commonly found in tectonic contact with the shear zone(Andersen, 1998; Osmundsen et al., 1998, 2000; Seguret et al., 1989).

The thermal evolution of a crustal-scale detachment has to beconsidered with two distinct aspects: fast exhumation and highly-localized deformation. Pressure-temperature-time (PT-t) paths of thefootwall metamorphic core complexes typically indicate fast decom-pression at near-isothermal conditions during exhumation from thelower to the upper crust level (Labrousse et al., 2004). The timewindowbracketing such isothermal exhumation is only a few million years(Hacker et al., 2010; Johnston et al., 2007) and is significantly smallerthan the time required for thermally equilibrating the crust by diffusion

Tectonophysics xxx (2013) xxx–xxx

⁎ Corresponding author at: Institute for Energy Technology (IFE), Instituttveien 18,NO-2007 Kjeller, Norway. Tel.: +47 22 85 60 48.

E-mail address: [email protected] (A. Souche).1 Present address: Centre for Earth Evolution and Dynamics (CEED), University of

Oslo, P.O. Box 1048, Blindern, 0316 Oslo, Norway.2 Present address: Computational Geology Laboratory, Polish Geological Institute –

National Research Institute, Wro!caw 53-122, Poland.

TECTO-125967; No of Pages 13

0040-1951/$ – see front matter © 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.tecto.2013.07.005

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Please cite this article as: Souche, A., et al., Shear heating in extensional detachments: Implications for the thermal history of the Devonian basinsof W Norway, Tectonophysics (2013), http://dx.doi.org/10.1016/j.tecto.2013.07.005

http://dx.doi.org/10.1016/j.tecto.2013.07.005

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(several tenths ofMyr, e.g., Turcotte and Schubert, 2002). Therefore, thethermal structure of the crust after fast exhumation of a high- toultra-high-pressure [(U)HP] terranemight be strongly perturbed by in-teraction between a “hot” footwall and a “cold” hangingwall.

The other characteristic feature controlling the thermal evolutionof the detachment zone results from the relative movement betweenthe foot- and the hangingwall. Large strain can accumulate inside theshear zone of the detachment, and this may have a significant effect

Exhumation of the footwall?Shear heating?

Erosion

>10 km Burial depth basins

W E

b

Devonian basins

Værlandet

Hornelen basin

Kvamshesten basin

Håsteinen basin

Solund basin

Ytre Sula

Hardbakke

Lavik

Leirvik

Hyllestad

Sørbøvåg

Bygstad

Førde

Florø

Hovden

Kalvåg

FjalerFure

Dale

ÅlfobreenHyen

Sandane

Bremangerlandet

Askrova

FrøyaSvelgen

Sula

Gjegnalunds-breen

Hornelen

a

10 km

5 E 6 E

61.6

N61

.2 N

Norway

Oslo

Trondheim

Bergen

Devonian basins (hangingwall)

Caledonian nappes(hangingwall / shear zone)

Western Gneiss Region (footwall)

Major detachment faults

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 ofthe Devonian basins can come from the exhumation of the footwall or from shear heating in the shear zone.

2 A. Souche et al. / Tectonophysics xxx (2013) xxx–xxx



on the heat budget of the system in form of shear heating (Brun andCobbold, 1980; Burg and Gerya, 2005; Campani et al., 2010; Hartz andPodladchikov, 2008; Leloup et al., 1999; Schmalholz et al., 2009;Scholz, 1980). Shear heating rate depends on the non-elastic strainrate and the deviatoric stress experienced by rocks during deforma-tion. The amount of shear heating produced in a geological systemis difficult to measure and modelling provides a viable tool forassessing the role of shear heating.

We base our study on the geological observations of theNordfjord-Sogn Detachment Zone (NSDZ) of western Norway. In thetop stratigraphic level of the detachment, several supra-detachmentbasins formed (Fig. 1) as response to repetitive tectonic motions dur-ing the exhumation of the footwall (Osmundsen et al., 1998; Seguretet al., 1989; Seranne et al., 1989; Steel et al., 1977). These supra-detachments basins are commonly named the Devonian basins dueto the presence of Devonian plant fossils in the sediments (Høegh,1945; Kolderup, 1916, 1921, 1927). The special feature of the Devoni-an basins is the documented low-grade metamorphism (Seranne andSeguret, 1987; Souche et al., 2012; Svensen et al., 2001; Torsvik et al.,1988). Souche et al. (2012) showed that the temperature conditionsat the burial depth of 9.1 kmwas as high as 345 °Cwhich can be trans-lated to a geothermal gradient of 38 °C/km. Additionally, the peaktemperatures in the Devonian basins increase with proximity to thedetachment contact and thus suggest that the lateral variation ofmaximum temperatures was controlled by a dynamically evolvingsystem, most likely linked to the detachment. Was shear heating con-tributing to the heat budget in the system? Could it have an impact onthe lateral variation of the peak temperatures within the supra-detachment basins?

In this study, we analyse the thermal evolution of the detachmentzone and estimate the contribution of shear heating on the heat bud-get of the area. We first present a compilation of available geologicaldata from the NSDZ to build a well-founded geological model that canbe studied numerically. We compare the results of our numericalstudies with independent observations from the supra-detachmentbasins of western Norway and discuss the importance of the shearheating in this particular geological setting.

2. Geological constraints of the model

2.1. Footwall conditions and strain partitioning in the detachment

TheNSDZ is one of the largest extensional detachments in theworld,with a displacement of 70 to 100 km (Andersen and Jamtveit, 1990;Hacker et al., 2003). The extensionwas initiated during the latest stagesof the Caledonian continent-continent collision when the crust reachedits maximum thickness and partially crystallized to (U)HP eclogites inthe Late Silurian to Early Devonian (Hacker et al., 2012; Krogh et al.,2011; Kylander-Clark et al., 2009). The eclogites are found in the WGR(Fig. 1), which constitutes the exhumed footwall of the NSDZ. Petrolog-ical and thermochronological studies of the footwall give consistentPT-paths (Fig. 2) with a common near-isothermal decompressionfrom peak-pressure conditions within maximum 10 Ma (Hacker et al.,2003, 2010; Johnston et al., 2007; Kylander-Clark et al., 2009; Root etal., 2005; Young et al., 2011).

The HP rocks exposed structurally below the basins (here we usedata from near the Solund and Hornelen basins) provide useful con-straints regarding the Caledonian metamorphism (Fig. 2) and the ki-nematic evolution of the NSDZ (Hacker et al., 2003; Johnston et al.,2007; Young et al., 2007). We take the maximum burial of the HPunits to represent the initial depth (~60 km) where the exhumationstarted along the shear zone. Based on the decompression path ofthe HP units, we constrain our model to account for 40 km of verticalexhumation bringing the HP rocks to a depth of 20 km, at which theretrograde mineral assemblages and their cooling age have been de-termined by 40Ar/39Ar geochronology (Andersen, 1998; Chauvet

and Dallmeyer, 1992; Cuthbert, 1991; Fossen and Dallmeyer, 1998;Young et al., 2011).

The mylonites of the NSDZ have a maximum thickness of 5.5 kmnorth of the Hornelen basin, but the precise original thicknesses cannotbe accurately determined because of excision by later faults. Marqueset al. (2007) estimated the shear strain partitioning in the NSDZ andshowed that the lower parts of the mylonites experienced considerableflattening across the foliation in addition to simple shear (ratio of sim-ple to pure shear ~1). The upper ~2 km of the mylonites are, however,characterized mainly by simple shear, with a shear strain of approxi-mately 20 (Andersen and Jamtveit, 1990; Hacker et al., 2003; Marqueset al., 2007), used here as the bulk shear strain along the NSDZ.

2.2. The hangingwall peak temperatures

Following fluid-inclusion and mineralogical studies of the basins(Svensen et al., 2001), a recent study using Raman spectroscopy of car-bonaceous material (RSCM) from Devonian plant fossils (e.g. Souche etal., 2012) documents high peak temperatures from the Solund,Hornelen, and Kvamshesten basins. The temperatures locally reached345 °C for an estimated burial of 9.1 km in the Kvamshesten basin(Table 1). This suggests a geothermal gradient of approximately38 °C/km, which is clearly at variance with commonly accepted geo-thermal estimates for a thickened orogenic crust or even for a crust inearly stages (415-395 Ma) of post-orogenic extension (Fossen, 2010;Gabrielsen et al., 2005; Hacker, 2007; Spengler et al., 2009). Souche etal. (2012) concluded that the elevated basin temperatures could onlybe explained by an additional heat source introduced at the base of

HP (Caledonian nappes)

HP (retrograde overprints)

HP (WGR)

~60 km

~20 km

~40 km

Temperature [oC]

0.5

1.5

2

2.5

Pre

ssur

e (li

thos

tatic

) [G

Pa]

1

0

Hacker et al., 2003 (peak)Hacker et al., 2003 (retro)Johnston et al., 2007 (peak) Johnston et al., 2007 (retro)

peak conditio

ns“Isothermal”

decompression

400 500 600 700 800

Average of error ellipses (1!)

Fig. 2. Peak and retrograde Caledonian metamorphism from the WGR and HP Caledo-nian nappes exposed beneath the Solund and Hornelen basins. Thermobarometry datafrom Hacker et al. (2003) and Johnston et al. (2007).

Table 1Burial depth and peak temperature estimates of the Devonian basins of W Norway.

Fluid-inclusion andmineralogical studies (*)

Raman spectroscopy ofcarbonaceous material (**)

Burialdepth(***)

T (average) T (local) Distance fromthe detachment

Hornelen 9.1 ± 1.6 km 250 ± 20 °C 295 ± 30 °C at 1 kmKvamshesten 9.1 ± 1.6 km 250 ± 20 °C 345 ± 30 °C at 1 kmSolund 13.4 ± 0.6 km 315 ± 15 °C 284 ± 30 °C

295 ± 30 °C301 ± 30 °C

at 8 km

*Svensen et al. (2001); **Souche et al. (2012); (***) The burial depth is estimated fromlithostatic pressure assuming a constant rock density of 2600 kg/m3 (Svensen et al.,2001).

3A. Souche et al. / Tectonophysics xxx (2013) xxx–xxx



the hangingwall during the extension. This conclusion also is in agree-ment with previous description of ductile deformation of the basin-fillsediments adjacent to the detachment, which could suggest elevatedtemperatures in this area (Braathen et al., 2004; Norton, 1987).

2.3. Model: constraints and simplifications

The different geological aspects presented in the previous sectionsallow us to build a simplified geological model of the evolution of thedetachment zone used in the numerical analysis (Fig. 3). The initialconfiguration of the model (Fig. 3a) corresponds to the thickenedCaledonian crust with a Moho depth set to 70 km corresponding toapproximately twice the average thickness of continental crust. Weassume that the deformation was initiated by the development of alithospheric-scale shear zone with a constant dip angle α = 30°(Andersen and Jamtveit, 1990; Norton, 1986).

The active deformation within the shear zone and the exhumation ofthe footwall is considered within a time window denoted t*. After thattime the system still. We assume constant rates of deformation for sim-plicity. During deformation, the footwall translates upward along the de-tachment and accounts for the exhumation of the lower crustal body(hf = 40 km) from 60 to 20 km depth (marked by a star in Fig. 3 a andb). At the same time, the hangingwall translates downward along the de-tachment and creates accommodation space in the basin formed at thesurface. We assume immediate erosion and sedimentation processes sothat the model does not produce variations in topography. At time t*,the lower crustal body is at 20 km depth and the basin is at maximumdepth (bmax). Accordingly to the estimated burial depth of the Devonianbasins (Table 1), we consider two values for bmax, 10 km (for theHornelen and Kvamshesten basins) and 15 km (for the Solund basin).

An important element of the model is the style of deformationwithin the shear zone. Despite observations of Marques et al.(2007) on the significant component of pure shear within the lowerparts of the NSDZ (Section 2.1), we assume simple shear only. Thissimplification reduces the number of model parameters, which arepoorly constrained and might be related to the earlier stages of exhu-mation (Andersen et al., 1994). Thus, simple shear (Fig. 3c) accom-modates the total relative displacement between the foot- andhangingwall. According to the observations and measurementsalong NSDZ (see Section 2.1), we set a bulk shear strain (γbulk) of 20at time t*. Given γbulk, α, and the total displacement between thefoot- and hangingwall, we estimate the thickness of the shear zoneto be D = 5-5.5 km depending on bmax, which is consistent with theobservations (Marques et al., 2007).

The assumption of uniform translation (and thus, without any de-formation) of the foot- and hangingwall is a simplification of ourmodel. We have, however, tested the importance of the lateralstretching of the units, and found that a moderate extension doesnot cause significant changes of the peak temperatures in vicinity ofthe detachment zone.

Normal sense reactivation of the detachment fault along theSolund and Kvamshesten segments (Fig. 1) in the Permian, andagain in the Late Jurassic has been documented by palaeomagneticand geochronological studies of fault breccias along the NSDZ(Andersen et al., 1999; Eide et al., 1997; Torsvik et al., 1992), andmay have contributed to some exhumation. In this study, we assumethat the Devonian basins reached their peak temperature conditionsduring or shortly after the major post-Caledonian extension andwere not influenced by later reactivation of the detachment faults.

3. Model

3.1. Governing equations

We analyze the thermal evolution in the model by solving thetransient heat balance equation:

ρCp!T!t ! v! ""T

! "#" " k"T# $ % Hr ! Hs #1$

where T is the temperature, t is the time, k is the thermal conductiv-ity, v! is the rock velocity, ρ is the rock density, Cp is the rock specificheat capacity, and Hr is the radiogenic heat production (see character-istic values in Table 2). The shear heating term Hs is the product of thedeviatoric stress τ and the non-elastic strain rateγ̇ (Brun and Cobbold,1980; Burg and Gerya, 2005; Turcotte and Schubert, 2002) so that:

Hs % τ γ̇ #2$

The hangingwall and footwall translate along the detachment with-out internal deformation. All the deformation is accommodated with-in the shear zone and thus shear heating (Eq. (2)) is only used in theshear zone.

Completing the mathematical model of thermal evolution requiresthe specification of initial and boundary temperature conditions, ve-locities and rheological relationship. The assumption of constanttranslation during exhumation (Section 2.3) gives the velocities with-in the foot- and the hangingwall by dividing the total displacementsby t*. The initial and boundary temperature of the system and speci-fication of Eq. (2) for the shear zone are discussed below.

3.2. Initial geotherm

The initial thermal situation before the extension has to be consid-ered in the geological framework of the Caledonian orogeny (peakcondition data points on Fig. 2). Thus, to obtain the initial thermalstate, we perform an auxiliary modelling of the evolution of the lith-osphere during the Caledonian collision. In this experiment we as-sume that, prior to collision, the lithosphere was in steady state and,during the orogeny, the lithosphere thickened uniformly by pure

0

40

60

80

20

20 km

upper crust

lower crust

Moho70

32

mantle lithosphere

dept

h [k

m]

0

40

60

80

20

20 km

Moho

basinbmax"

hf D

bmax

#bulk=20

"=30°

"

"

hf =40 km

D = (bmax+hf)/sin(")/#bulk

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

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 = 40 km.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 theshear 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.




shear. We used a 1D computer code LiToastPhere (Hartz andPodladchikov, 2008) to perform the calculations.

We consider the Caledonian continent-continent collision to lastfor 25 My (Corfu et al., 2006; Johnston et al., 2007; Torsvik andCocks, 2005) and to result in 100% thickening of the crust (doubleof the original thickness) which corresponds to an average strainrate of 8.7 ! 10-16 s-1. The model lithosphere consists of three layers,composed of a wet quartzite upper crust, a diabase lower crust, and adry dunite mantle (Ranalli, 1995). The initial thickness of the uppercrust is set to 16 km (Hasterok and Chapman, 2011). The lowercrust extends to the Moho discontinuity with initial depths of 30, 35and 40 km (corresponding to the model “Mxx”). The initial depth ofthe mantle lithosphere is set to 140 km (Artemieva, 2006). The ther-mal properties used in the calculations are listed in Table 2.

We performed a series of numerical tests varying the initial Mohodepth and the amount of radioactive heat production and consideringthe influence of shear heating. We compare the model results withthe data of the peak metamorphic conditions of the Caledoniannappes below the Solund basin and the Hornelen basins (Fig. 2).The best fit geotherm is obtained with the model M35-sh (Fig. 4),which accounts for shear heating during the deformation of the lith-osphere. Fig. 4 also presents model results obtained with similar

setups but where shear heating was ignored (M30, M35 and M40).The shear heating models are warmer by an average of 100 °C, illus-trating the importance of this heat source during deformation. The re-sults also illustrate greater dependence on the initial conditions androck properties for the models without shear heating.

We use the preferred temperature profile M35-sh (Fig. 4) to buildthe initial temperature distribution. We also use this profile to con-strain the bottom boundary condition during the model evolution.As the footwall moves upward during exhumation, the material in-coming into the system assumed to sustain its temperature initiallyprescribed by M35-sh. This assumption ignores the thermal relaxa-tion of the deep lithosphere after Caledonian orogeny, which is ap-proximately valid for fast exhumation considered here.

3.3. Kinematic of the shear zone

Restoring the exact distribution of velocities and stress field withinthe shear zone is beyond the scope of this study. Instead, we approxi-mate the velocities within the shear zone using two end-member ap-proaches, in which either shear strain rate (γ̇-cst) or shear stress (τ-cstmodel) is kept constant across the shear zone. The two kinematicmodels correspond respectively to an upper and lower bound on the es-timate of shear heating expressed by Eq. (2). Whereas the γ̇-cst modelforces uniform deformation and thus active heat production even instrong areas of the shear zone, the τ-cstmodel results in localized defor-mation of weaker parts of the detachment, and thus produces less heat.It is important to keep in mind that neither the γ̇-cst nor the τ-cstmodels reproduce exactly the actual deformation process within theNordfjord-Sogn Detachment and the main purpose in using these twovirtual kinematic models is to deliver an upper and lower bound onthe shear heating effect.

3.3.1. RheologyThe shear zone accumulates the entire deformation in the model

(Fig. 3c) and hosts the production of shear heating. This deformationoccurs in the range of 0-60 km, and thus involves the transition frombrittle to ductile behaviour of rocks.

The brittle behaviour is described by Byerlee’s relationship:

τBy % 1#pf

# $μg $

y

0

ρdy #3$

See Table 2 for definitions and values of parameters used. Thisconstitutive relationship assumes no deformation for the stressvalues below critical, τBy, which increases with depth (Fig. 5). Weapproximate Eq. (3) using a power law relationship (after Nanjo etal., 2005; Turcotte and Glasscoe, 2004)

τ % τBy%%%%%%%%%%%γ̇b=γ̇c

nbq

or γ̇b % ττBy

!nb

γ̇c #4$

where γ̇c is a critical strain rate and γ̇b is the strain rate of the brittledeformation. Here we define γ̇c as the bulk strain rate imposed bythe motion of the foot- and the hangingwall (γbulk/t *). For large

Table 2Thermal 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 = 1293Specific heat capacity Cp J/(kg.K) 1000 1000 1000 1000Rock density ρ Kg/m3 2600 2700 2900 3300Radioactive heat production** Hr W/m3 1.2 ! 10#6 1 ! 10#6 4 ! 10#7 2 ! 10#8

*k=a+b/(T+350), where T is the temperature expressed in °C (after Clauser and Huenges (1995)). ** after Hasterok and Chapman (2011).

Temperature [oC]

0.5400 500 600 700 800

1.5

2

2.5

3

Pre

ssur

e (li

thos

tatic

) [G

Pa]

100% thickening (pure shear) in 25MaStrain rate = 8.7e-16s-1

~ 88 km

~ 72 km

~ 54 km

~ 37 km

Geological data (peak conditions): Hacker et al. (2003) Johnston et al. (2007)

Average of error ellipses (1!)

1

No shear heating Shear heatingM35

-shM40-sh

M30

-sh

M35M

30

M40

Fig. 4. 1D model predictions (solid and dash lines) versus pressure-temperature (PT)estimates of the HP units in the footwall of the Nordfjord-Sogn Detachment Zone(Hacker et al., 2003; Johnston et al., 2007). Different model setups are compared fordifferent Moho-depth indicated by “Mxx”, and with or without shear heating indicatedby “-sh”. The grey shades represent the spread of the curves “M35” and “M35-sh” byvarying the radioactive heat production by ±25%. We observe a good fit betweenthe representative PT data and those predicted by the model when the bulk deforma-tion of the lithosphere is taken into account. Without shear heating during collision,the entire system is too cold in comparison to the geological data.




power law exponent (nb = 20), the deviatoric stress is approximate-ly equal to the critical stress τBy (yield strength) for a wide range ofstrain rate values centered about the critical strain rate γ̇c.

The ductile behaviour is described by a power-law for dislocationcreep:

τ % exp E=RTnd# $%%%%%%%%%%γ̇d=A

ndq

or γ̇d % τndA exp #E=RT# $ #5$

where γ̇d is the strain rate of the ductile deformation. The Arrheniusterm exp(E/RTnd) results in a strong decrease of the stresswith temper-ature and, for standard geotherm, with depth (Fig. 5b). The shear zoneexposed today between the Devonian basins and the WGR is mainlyformed of Caledonian nappes represented by meta-sedimentary unitsand some deformed slices of basement. The rheological weakness ofthe meta-sediments is approximated by flow laws for wet and dryquartzite (see Table 3).

We assume the brittle and the ductile mechanism of deformationto act simultaneously on the total shear strain rate, and it allows us towrite:

γ̇ % γ̇b ! γ̇d #6$

For a given shear stress value across the shear zone, Eqs. (4) – (6)yield a strain rate profile. For a given strain rate value across theshear zone, a shear stress profile is obtained by solving Eq. (6) after

substituting Eqs. (4) and (5) into it. Our approximation to the shearstress (Fig. 5b) follows the minimum of the two stress regimes andsmoothes the transition zone.

3.3.2. Constant shear strain model (γ̇-cst model)The constant shear strain rate model results in a linear velocity

profile across the shear zone (Fig. 6a) defined by the hangingwalland footwall velocities. The deformation is homogeneous and distrib-uted across the shear zone, without localization, and with the sameintensity in the “strong” or “weak” (thermally weakened) parts ofthe shear zone. Therefore, we expect the shear heating term (Eq.(2)) to be maximized using this kinematic model.

γ̇% γbulk

t⁎#7$

The corresponding shear stress, variable across and along the shearzone, is determined at any points by substituting Eqs. (4) and (5)into Eq. (6) and solving it using Eq. (7). This approach insures amass conservation in the model but induces large variations ofshear stress across the shear zone due to the variations of rheologicalproperties.

3.3.3. Constant shear stress model (τ-cst model)The motivation for the τ-cst model is to augment the flow pattern

by avoiding large stress variation across the shear zone and allowingfor localization of the deformation. The localization has a direct im-pact on the distribution of heat produced by shear heating sincelarge deformations mostly occur in “weak” parts of the shear zone.Thus, the τ-cst model is used as end-member kinematic model mini-mizing the impact of shear heating as opposed to the γ̇-cst model. Avalue of the shear stress τ, uniform across and variable along theshear zone, is obtained by integrating Eq. (6) across the shear zone(in the y’ direction, Fig. 6) and using the bulk strain rate (γbulk/t*) asa constraint:

$D

0

γ̇dy0 % $D

0

γ̇b ! γ̇d& '

dy0

γbulk

t⁎D % $

D

0

ττBy

!nb

γ̇c ! τndAexp #E=RT# $" #

dy0#8$

$ shear stress [MPa] 0 100 200 300 400

Dep

th [k

m]

0

10

20

30

40

# = 2.1x10-13

Brittle failure

Intitial (

Dry Quartzite)

Intitia

l (Wet Quartzite

)

After exhumation (Wet Quartzite)

Brittle/DuctileTransition zone

$

#

$By

#c

nb=1

2015 10 5

0

a b

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 (γ̇-cst model and t* = 3My). 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 ap-proximation 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 illustratedby the gray shade for the wet quartzite simulation.

Table 3Material and rheological (Ranalli, 1995) parameters used in the numerical experiments.

Parameters Symbol Unit Value

Gravity g m.s#2 9.81Friction coefficient μ - 0.7Pore fluid factor Pf - 0.4Power law exponent nb - 20Gas constant R J.K#1 8.314

Quartzite: Wet/DryPower law exponent nd # 2.3/2.4Pre-exponential multiplier A MPa-nd.s-1 3.2 ! 10#6/6.7 ! 10#6

Activation energy fordislocation creep

E kJ.mol#1 154E + 3/156 ! 103




The strain rate profile is then calculated from Eqs. (4) and (5) and itresults in localized deformation in weak parts. Depending on thedominant deformation mechanism, rock weakens at the upper partof the shear zone in the brittle regime (where τBy is smaller,Eq. (3)) and at lower part of the shear zone in the ductile regime(where temperature is higher, Eq. (5)). Therefore, highly localized de-formations occur along the boundary with the hangingwall in theupper part of the shear zone, and along the boundary with the foot-wall in the lower part of the shear zone (Fig. 6b).

The velocity profile resulting from the constant shear stress as-sumption (Couette flow, Fig. 6b) respects the no-slip conditions at

the boundaries of the shear zone. However, significant rheologicalvariations along the shear zone result in velocity fields characterizedby a non-vanishing divergence and lead to a violation of mass andmomentum conservation condition. To limit these effects, we aug-ment the kinematic profile by adding a Poiseuille flow contribution(Fig. 6c) determined by keeping the integrated mass balance con-stant along the shear zone. This results in a non-zero pressure gradi-ent in the shear zone. We note that due to adding the Poiseuille flowcomponent the original assumption of the constant shear stressacross the shear zone is not strictly satisfied. Yet, we choose torefer to this model as τ-cst throughout the manuscript, as the strain

Ductile

Brittle

+ =Couette Poiseuille

60

Dep

th [

km]

20 km0

40

20

Line of zero velocity

Brittle-ductile transition

Velocities across the shear zone

a) b) c) d)

$-cst#-cst

y’x’

flow flow

Fig. 6. Typical velocity profiles of the two kinematic models. The profile (a) γ̇-cst is derived for the constant shear strain model and gives a uniform linear velocity profile across theshear 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 thesum 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.

0

40

60

80

20

20 km

MohoHP unit

15

b) Exhumation of the footwall (t*=3 My)0

40

60

80

20

20 km

MohoHP unit

15

c) Thermal relaxation (30 My)

350

150

250

50

1 3 5 7 9Time [My]

Shearing Thermal relaxation

maxima

Tem

pera

ture

in th

e ba

sin

[o C]

10 k

m a

way

5 km

awa

ycont

act s

hear

zon

e

0

40

60

80

20

20 km

MohoHP unit

15

e) Peak temperatures782

600

400

200

10

[oC]

40

60

80

20

20 kmMoho70

32

HP unit

a) Initial conditions

dept

h [k

m]

0 BasinBasin

Basin

d

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 lo-cated 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 thescattered 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 rheologywith γ̇-cst kinematic model, and bmax = 15 km.




rates related to the Poiseuille flow are significantly smaller than thetotal strain rates (Fig. 6c, d). The resulting velocity profile of theτ-cst model is the sum of Couette and Poiseuille flows as illustratedFig. 6d.

3.4. FEM strategy

The model domain is 80 km deep and 120 km wide (Fig. 3). Weuse a triangular mesh generated with Triangle (Shewchuk, 1996,

108

[J.m-3]

107

109

1010

Range for upper crust radioactive heat production

60

Dep

th [

km]

20 km

20

A

AA BB

B15

0 Dry Quartzite Wet Quartzite

$-cst # -cst

$-cst # -cst

Fig. 8. Distribution of total heat density produced by shear within the detachment zone for t* = 3My (note the logarithmic colour-scale) and bmax = 15 km. Results are presentedfor τ-cst and γ̇-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 sametime interval. A, AA, B, and BB indicate the position of cross sections presented in Fig. 10.

40

80

100

60

[oC]

0

40

60

80

20

20 km

0

40

60

80

20

20 km

dept

h [k

m]

3My

0

40

60

80

20

20 km

+143 oC

+92 oC

0

40

60

80

20

20 km

dept

h [k

m]

+81 oC

10M

y

0

20

+49 oC

# -cst 0

40

60

80

20

20 km

0

40

60

80

20

20 km

dept

h [k

m]

3My

Dur

atio

n of

the

deta

chm

ent

0

40

60

80

20

20 km

+110 oC

+67 oC

0

40

60

80

20

20 km

dept

h [k

m]

+67 oC

10M

y +39 oC

Wet Quartzite

$-cst

$-cst

$-cst

$-cst

# -cst

# -cst

# -cst

Dur

atio

n of

the

deta

chm

ent

Dry Quartzite

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 forbmax = 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.




2002) to discretise the model domain and accurately represent theboundaries separating materials of different thermal properties. Themesh is updated at each time step accordingly to the subsidence ofthe basin on the top of the model.

Eq. (1) is implicitly solved with a finite element code using theStreamline Petrov-Galerkin scheme. A similar discretisation has beendocumented and used for geodynamical problems and we refer to thepaper of Braun (2003) for more technical details. Temperature andvelocity fields are linearly interpolated using 3-nodes elements.The temperature-dependent thermal conductivity is calculated usingtemperatures from the previous time step. We consider zero flux onthe lateral boundaries and Dirichlet boundary conditions on the topand bottom (Section 3.2).

Shear zone related calculations are performed on an auxiliary reg-ular grid onto which the modelled temperature is projected. The reg-ularity of this grid allows accurate integration of Eqs. (4) – (6) and/or(8) across the shear zone to define the stress field, strain and strainrate. The resulting velocities and shear heating are then interpolatedback to the main grid each time step.

4. Results

We performed a systematic study by varying the time of the exhu-mation t* (3, 5, 10, and 15 My), the shear zone rheology (wet and dryquartzite), the kinematic model of the shear zone γ̇ -cst and τ-cst),and themaximumbasin depth bmax (10 and 15 km). All the simulationsare repeated twice, with and without accounting for shear heating.

4.1. Temperature evolution and peak conditions

For any t*, the exhumation of the footwall and the subsidence of thehangingwall leads to an unsteady temperaturefield. Thermal relaxationis reached by 20 to 30 My after t*. The different thermal stages of themodel are illustrated in Fig. 7a-c. Note that for the similar initial andfinal geometry and for the same distribution of the thermal propertiesof rocks, the initial and final geotherms (Fig. 7a and c) will be equiva-lent. The peak temperature profile (Fig. 7e), however, depends greatlyon the parameters tested in our numerical experiments.

To facilitate the comparison of our model results with geologicalobservations (Section 2), we extract the peak temperature of eachpoint during the evolution of the model up to thermal relaxation(Fig. 7e). The peak temperatures are reached at different time for dif-ferent localities, often well after t = t* (Fig. 7d).

4.2. Heat produced by shear heating

The distribution of total heat produced by shear heating withinthe detachment shear zone is presented in Fig. 8 (example presentedfor t* = 3 My). The results for γ̇ -cst model show a maximum heatproduced in the upper 10-20 km, which corresponds to the largeststress field at the brittle-ductile transition. The results for τ-cstmodel are characterized by two areas with high heat production(corresponding to areas of localized deformations), one in the upperbrittle domain, and one in the lower ductile domain. Irrespective ofthe different spatial distribution of the heat production in the two ki-nematic models, the amplitude remains within the same range.

Shear heating may be locally two orders of magnitude higher thanthe heat produced by radioactive decay in the upper crust. This effectcan be seen as a punctual heat source during the active deformationin the detachment zone.

4.3. Temperature anomaly produced by shear heating

We illustrate (Fig. 9) the temperature anomaly produced by shearheating by plotting the difference of modelled peak temperaturesobtained with and without shear heating. For dry quartzite modelsand t* = 3 Ma, shear heating can introduce more than 100 °C at thebase of the basin. The impact depends on the rheology and on t*,but remains significant (within 30-80 °C) for slower exhumationand weaker rheology in the shear zone.

In the model configurations presented here, a value of the porefluid factor of pf = 0.4 in Eq. (3) is assumed along the shear zone.The effect of pore-fluid pressure on the effective stress is still a matterof debate (e.g. Nur and Byerlee, 1971; Sibson, 1994). However, theimpact of varying the pore fluid pressure within acceptable range isnot critical with respect to thermal effects related to shear heating.The two kinematic models, γ̇ -cst and τ-cst, were introduced inSection 3.3 as an upper and lower bound to estimate shear heating.Fig. 9 shows that for the same parameters, γ̇ -cst model is hotterthan τ-cst model. However, despite the large difference in themodel velocity profiles (Fig. 6), the estimated temperature anomalyproduced by shear heating is on the same order. A difference of ap-proximately 30 °C separates at most the temperature anomalyobtained from both models, which shows that the style of deforma-tion within the shear zone does not influence much the amplitudeof the induced temperature anomaly in the system.

5. Comparison with geological observations

5.1. Shear strain partitioning

Fig. 10 shows the strains along the cross sections A, AA, B, and BB(Fig. 8) at the end of the simulations. Independent of the rheology andthe cross section position, the strain across the shear zone, describedby the τ-cst model, localizes mostly along the upper part, beneath thehangingwall with maximum strain higher than 200 and along thebasal part of the shear zone next to the footwall with maximum strainaround 35-60. Strains higher than 100 are indeed speculated in theupper part of the NSDZ (Hacker et al., 2003). However, there is no con-vincing field evidence for high-strain environment at the base of theshear zone such as produced by the τ-cstmodel. This ductile shear local-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 astrain gap in the middle of the shear zone, reducing the effective thick-ness of the shear zone. This is in contrast with the deformation patternobserved along the NSDZ, which exhibits continuous and large strain(20) over several kilometres (Andersen and Jamtveit, 1990).

In contrast to τ-cst, the γ̇ -cst model satisfies the observations oncontinuous strain within the NSDZ, but lacks the high shear localiza-tion in the upper part of the detachment. Although the two models

543210Shear zone thickness [km]

She

ar S

trai

n

0

20

40

60

80

100

140

120

Average shear strain = 20(Model input)

160

localized deformation

(Brittle regime)

localized deformation

(Ductile regime)

A AA

B BB

(Dry Quartzite rheology)

(Wet Quartzite rheology)

Fig. 10. Strain profiles across the shear zone for the τ-cst models. Two shear bands rep-resentative for brittle and ductile deformation are observed along upper (left) and bot-tom (right) parts of the shear zone. The average strain across the shear zone is 20. Therheology and the position at which the cross sections are taken have a minor impact onthe style of final strain profile. See locations of cross sections on Fig. 8, t* = 3 My.




differ in the style of deformation and in correlation to observations,the resulting heat produced within the shear zone based on thosemodels does not differ significantly. Thus, we can conclude thatexact reproduction of the flow within the shear zone has limited im-portance while considering the thermal budget of the NSDZ.

5.2. Implications for the supra-detachment basins thermal history

In Fig. 11, we compare the modelled peak temperatures withthe geological data (Section 2.2). Svensen et al. (2001) documented av-erage values for peak temperatures of 260 ± 20 °C for the entireKvamshesten and Hornelen basins (horizontal lines on Fig. 11a-c) and315 ± 15 °C for the Solund basin (horizontal lines on Fig. 11d-f).Souche et al. (2012) reported the local estimates of peak temperatureof the sediments as a function of the distance to the detachment (datapoints on Fig. 11).

The maximum reported burial depth of the Devonian sediments is9.1 km for the Kvamshesten and the Hornelen basins and 13.4 kmfor the Solund basin (Svensen et al., 2001). Thus, we compare thegeological data with the modelled peak temperatures taken at 9.1(Fig. 11a-c) and 13.4 km (Fig. 11d-f). Fig. 11 presents the modelledtemperature curves for three different t* and two kinematics withinthe shear zone (γ̇-cst and τ-cst) in each sub-figure.

All the results obtained without shear heating (Fig. 11c and f)show low peak temperatures and fail to reproduce the geologicaldata. In addition, these modelled temperatures show a relativelysmall lateral variation through the basins. The lateral temperaturevariation does not exceed 40 °C in a range of 10 km away from thedetachment contact. That low thermal gradient illustrates the roleplayed by the hot rising footwall on the heating of the basin. Thisheat source is not sufficient to induce significant variations of thepeak temperatures in the supra-detachment basins.

Hornelen

340

300

260

220

340

300

260

220

180

340

300

260

22046

340

300

260

220

18028

Max

tem

pera

ture

in

the

basi

n [o C

]M

ax te

mpe

ratu

re in

th

e ba

sin

[o C]

Max

tem

pera

ture

in

the

basi

n [o C

]

340

300

260

220

340

300

260

220

18046 28

46 28

46 28

46 28

46 28

contact

distance from the detachment[km]

Kvamshesten/Hornelen basinsBurial depth = 9.1 km

contact

Solund basinBurial depth = 13.4 km

Dry Quartzite

Svensen et al. 2001 GEOLOGICAL DATA

380

380

Dry Quartzite

Wet Quartzite Wet Quartzite

Souche et al. 2012

Kvamshesten

Hornelen

Kvamshesten

Hornelen

Kvamshesten380

distance from the detachment[km]

t* = 3 Myt* = 5 Myt* = 10 My

# -cst $-cst

Solund

Solund

Solund

No shear heating No shear heating

a

b

c

d

e

f

MODEL RESULTS

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. γ̇-cst andτ-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 resultsobtained 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 maximumdepth of the basin (bmax) was set to 10 km in (a-c) and 15 km in (d-f).




The models including shear heating (Fig. 11a, b, d and e) show sig-nificantly higher peak temperatures and a stronger dependence onthe proximity to the shear zone. Wet quartzite models, however, donot show good qualitative agreement with observations (Fig. 11band e). Dry quartzite models (Fig. 11a and d) result in higher temper-ature rise and compare well to geological observations. The tempera-ture curves for γ̇Z -cst models (any t*) and τ-cst models (t* b 5 My)show good correlation to the average peak temperatures of Svensenet al. (2001) and to the local estimates of Souche et al. (2012).

The results obtained with dry quartzite (Fig. 11a and d) showabout 100 °C or more of lateral variation of peak temperatures within10 km distance from the detachment. This clearly indicates the signif-icance of shear heating by locally increasing the temperature in thesediments at the vicinity of the detachment fault. These models re-produce the geological data of 295 °C in the Hornelen basin. In com-parison to a maximum of 220 °C calculated without shear heating,shear heating alone accounts for as much as 25% of the thermal bud-get of the sediments.

Figs. 9 and 11 show that the influence of shear heating dependsgreatly of the distance to the shear zone, and is in accordance withthe geological observations from Souche et al. (2012). The numericalresults of the present study show that rocks located more than5-10 km away from the detachment are not affected by shear heating.

5.3. PT-t path and retrograde overprint of rocks within the shear zone

The studies of PT-t paths representative for the exhumation of HPunits within the NSDZ show isothermal or temperature-increasingdecompression (Hacker et al., 2003; Johnston et al., 2007; Labrousseet al., 2004) illustrated in Fig. 12. Can shear heating lead to tempera-ture increase or support isothermal condition during exhumation ofthe HP units? Below we demonstrate that shear heating is unlikelyan explanation for such an effect and other mechanisms should befound to explain the phenomenon.

We compare these observations with our model results. We selectseveralmarkerswith initial depth between60 and 25 kmand reconstructtheir PT-t paths. In our estimations, we use lithostatic condition to

calculate pressure, which makes our pressure estimates as upper bounds(as the background extensional stress may induce underpressure) andconclusions of this section more robust. Markers initially shallower than45 kmexhibit strong thermal overprint related to shear heating. The tem-perature increase during the exhumation of these markers, up to 100 °C,compares with some of the geological data but is observed at muchshallower depths in the model. In contrast, markers initially deeper than45 km, comparable to the initial decompression depth of the HP units,monotonically cool during decompression.

The model results show the limited effect of shear heating in pro-ducing temperature increase at the early stage of the decompressionof the HP units found in the NSDZ. Either these units were originallyat shallower depth and were subjected to overpressure (Petrini andPodladchikov, 2000), or were possibly affected by heat generationduring retrograde metamorphism reactions (Connolly and Thompson,1989; Haack and Zimmermann, 1996).

6. Conclusions

We have developed a simple numerical model to understand thethermal budget and the role of shear heating in crustal-scale exten-sional detachments. Using geological observations of the NSDZ wehave developed a conceptual model of evolution of such a system.The model was augmented by constraining the non-steady-stategeotherm associated with the end of Caledonian orogeny. We havebuilt two simplified kinematic models for the deformation withinthe shear zone. The model results were tested against peak tempera-ture conditions documented within three Devonian basins of westernNorway. Our numerical study has shown:

1. Shear heating within the highly-deformed NSDZ can generate atemperature increase up to 100 °C in the detachment shear zoneand is a necessary mechanism to explain the elevated peak tem-peratures within the Devonian basins of western Norway.

2. Shear heating may account for 25% of the thermal budget of thesupra-detachment basins and may affect the peak temperatures 5to 10 km away from the detachment shear zone.

350 400 450 500 550 600 650 700 7500

0.5

1

1.5

2

2.5

~60 km

~20 km

300250200

“Isothermal”decompression

HP (retrograde overprints)

~40 km

~30 km

~10 km

~50 km

Markers before exhumationNo shear heating #-cst model $-cst model

Corresponding samplesJohnston et al., 2007 (retro)Johnston et al., 2007 (peak)

Model results: Geological data:

Temperature [oC]

Pre

ssur

e [G

Pa]

Average of error ellipses (1!) HP (Caledonian nappes)

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 dryquartzite rheology, and bmax = 15 km.




3. The amount of shear heating produced in the system is predomi-nantly dependent on the exhumation rate and the rheological pa-rameters of the rocks forming the shear zone.

4. Shear heating has a limited impact on the documented heatingduring decompression of the HP units in the NSDZ.

Acknowledgements

TheNorwegian ScienceCouncil providedbasic funding though a “Cen-tre of Excellence” grant to Physics of Geological Processes. Statoil and Detnorske viteskapsakademi are thanked for a Vista grant to AS. Det norskeoljeselskap is thanked for research grant to SM. The two reviewers, Prof.Taras Gerya and Prof. Stefan Schmalholz, are thanked for their commentsand suggestions that helped improving the manuscript.

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Shear heating in extensional detachments: Implications for the …folk.uio.no/torgeir/pdfpapers/Souche_shearheating.pdf · Devonian basins of W Norway ... hangingwall of the extensional