Continental-scale rheological heterogeneities and …328 A. Tommasi, A. Vauchez / Tectonophysics 279 (1997) 327–350 1. Introduction Continental collision zones often extend far in-land

ELSEVIER Tectonophysics 279 (1997) 327–350

Continental-scale rheological heterogeneities and complex intraplatetectono-metamorphic patterns: insights from a case-study and

numerical models

Andrea Tommasi *, Alain VauchezLaboratoire de Tectonophysique, ISTEEM, CNRS/Universite de Montpellier II, F-34095 Montpellier cedex 5, France

Accepted 2 May 1997

Abstract

Continental plates are built over long periods of time through successive extensional and compressional cycles. Theyare therefore rheologically heterogeneous. This heterogeneity should significantly influence the mechanical response ofthe continental lithosphere during collision processes. The study of the Neoproterozoic Borborema shear zone systemof northeast Brazil highlights a systematic link between marked changes in its tectono-metamorphic pattern and thepre-existing structure of the plate, that is characterized by juxtaposition of continental domains either comprisingan old basement (Palaeo- to Eoproterozoic) or accreted during an extensional event between 1.0 and 0.7 Ga. InNeoproterozoic time, when the shear zone system was developed, these domains displayed different geotherms andlithospheric thicknesses, and therefore contrasted rheological behaviours. We use numerical models simulating themechanical evolution of a continental plate comprising multiple thermally-induced rheological heterogeneities submittedto compression to investigate how these heterogeneities may affect strain localization and the distribution of deformationregimes and vertical strain within the plate. From the very beginning of the deformation, weak and stiff heterogeneitiesinduce strain localization, due to a lower initial effective viscosity or to stress concentrations at their tips, respectively.Shear zones propagate from the heterogeneities and finally coalesce, forming a network of high-strain zones boundingalmost undeformed blocks. Within this network, shear zones transfer strain between the different heterogeneities and modelboundaries. The evolution of the system depends essentially on the geometrical distribution of heterogeneities and on theirstrength contrast relative to the surrounding lithosphere. The resulting finite-strain field is heterogeneous and displays rapidlateral variations in vertical and/or rotational deformation. Such a heterogeneous strain distribution may induce contrastedmagmatic, metamorphic and uplift evolutions within an orogenic belt, as observed in the Borborema shear zone system andother collisional belts.

Keywords: continental deformation; rheological heterogeneity; shear zones; numerical modeling; inversion tectonics; NEBrazil

Ł Corresponding author. Fax: 33-67143603; e-mail: [email protected]

0040-1951/97/$17.00 1997 Elsevier Science B.V. All rights reserved.PII S 0 0 4 0 - 1 9 5 1 ( 9 7 ) 0 0 1 1 7 - 0

328 A. Tommasi, A. Vauchez / Tectonophysics 279 (1997) 327–350

1. Introduction

Continental collision zones often extend far in-land and display significant spatial variation of strainintensity, deformation regime, and vertical strain.These complex tectono-metamorphic patterns mayresult from particular plate boundary configura-tions, like oblique convergence and indentation (e.g.,Sumatra and New Zealand margins and the India–Asia collision). They may also be induced by a vari-ation of the bulk stress field through time, due tochanges in convergence direction or velocity, to anincrease of buoyancy forces resulting from a largelithospheric thickening (e.g., Molnar and Tappon-nier, 1988), or to activation of processes like mantledelamination (e.g., England and Houseman, 1989).Finally, in old orogens, where information on con-vergence directions and original plate geometry isoften lost and knowledge of the timing of the de-formation and metamorphism is limited to sparsegeochronological data, complex kinematic patternsand metamorphic histories were frequently taken asevidence of polycyclic evolution.

Boundary conditions-related processes are essen-tial for producing heterogeneous strain fields withinthe assumption, often implicit in conceptual geody-namic models, that plates react to external solicita-tions as homogeneous media. However, this assump-tion is highly questionable for continental plateswhose evolution involves successive accretions anddispersions resulting in domains with different agesand tectonic histories. This mosaic-like structure im-plies that continental plates display lateral variationsof lithospheric thickness and composition, geother-mal gradients and structural fabric. This heterogene-ity is clearly illustrated by maps of surface heat flowand lithospheric thickness of present-day continentalplates, as shown in Fig. 1 for western Europe, or bytomographic images of the uppermost mantle layerbeneath continental plates (e.g., Grand, 1994; Poletand Anderson, 1995; VanDecar et al., 1995).

What is the effect of these heterogeneities onthe mechanical response of a continental plate sub-jected to a continental collision? From the analysisof a case-study, the Borborema shear zone systemof northeast Brazil, and numerical models simu-lating the mechanical evolution of a continentalplate comprising multiple thermally-induced rheo-

Fig. 1. An example of heterogeneous continental lithosphere:lithospheric thicknesses inferred from P-wave residuals (Babuskaand Plomerova, 1992) and surface heat flows (Hurtig et al., 1991)in Europe.

logical heterogeneities, we investigate the effect ofthese heterogeneities on strain localization and shearzone development, and on the spatial organizationof deformation regimes and vertical strains. Then,we discuss the implications of this process for thetectono-thermal evolution of collisional belts.

2. Intraplate rheological heterogeneities

Intraplate rheological heterogeneities may be in-duced by lateral variations in structural fabric, crustalthickness, and geothermal gradient. Ancient high-deformation zones should induce a local anisotropyin the mechanical properties of the lithosphere(Vauchez et al., 1997a). However, limited experimen-tal data prevent a quantification of this anisotropy.Ranalli (1986) and Dunbar and Sawyer (1989) in-vestigated the effect of a lateral variation in crustalthickness on the strength of the lithosphere. Theyshow that for similar geothermal gradients, domainswith a thickened crust will display lower lithosphericstrengths than those characterized by a normal crustdue to replacement of stiff upper mantle materialby weaker crustal rocks. Although this may resultin a significant perturbation of the finite-strain field(e.g., Dunbar and Sawyer, 1989), we will focus onthe mechanical effect of lithospheric-scale thermalheterogeneities.

Intraplate thermal heterogeneities are commonlyassociated with the existence, within a continental

A. Tommasi, A. Vauchez / Tectonophysics 279 (1997) 327–350 329

plate, of old blocks displaying a thicker lithosphereand a lower geothermal gradient than the surround-ing lithosphere, and of younger and thinner domains,showing higher geothermal gradients. These lateralvariations in geothermal gradients within a continen-tal plate should induce changes in rheology, becauseunder lithospheric P–T conditions and geologicalstrain rates rock-forming minerals deform domi-nantly by dislocation creep, which is exponentiallydependent on temperature. Thus lateral variations ingeothermal gradients should imply either an increaseor a decrease of the integrated yield strength of thelithosphere (Fig. 2), which corresponds to the forcesupported by a lithospheric column of unit width(England, 1983).

2.1. Stiff intraplate heterogeneities — cratons

Continental plates develop by successive accre-tion around cratonic nuclei (e.g., African, SouthAmerican and North American plates). Seismic to-mography data (e.g., Grand, 1994; Polet and Ander-son, 1995) suggest that these cratonic nuclei have adeep, cold lithospheric root. Moreover, in spite ofthe long time elapsed since the episode responsiblefor the main assembly of these continents (¾600 Mafor the African and South American plates), these

Fig. 2. Geothermal gradient (dotted line), one-dimensionalstrength profile (solid line) and lithospheric strength for dif-ferent geodynamic settings characterized by typical surface heatflows (top right): (a) a cratonic block, (b) a normal lithosphere,(c), and (d) a thinned lithosphere. Geotherms are calculated us-ing thermal conductivities, kc D 2:5 W m�1 K�1 and km D 3:35W m�1 K�1 for crustal and mantle rocks, respectively, and asurface heat production, Hs D 2ð10�6 W m�3, which decreasesexponentially with a length scale of 10 km (a, b, and c) or 7.5km (d). Strength profiles are calculated using: the Sibson (1974)frictional law for the upper crust, a quartzite flow law (Patersonand Luan, 1990) for the quartz-rich upper to middle crust, afelsic granulite flow law (Wilks and Carter, 1990) for the lowercrust, and the Aheim dunite flow law (Chopra and Paterson,1981) for the upper mantle. For the cratonic block (a), the crustis considered as entirely formed by felsic granulite. zM indicatesMoho depth. (b), (a), (c), and (d) correspond to the thermaland compositional profiles used for calculation of the integratedrheological parameters (Table 1) for the normal lithosphere, thestiff domain, the weak domain (in low viscosity contrast mod-els), and the weak domain (in high viscosity contrast models),respectively.


cratonic nuclei (e.g., the Archaean Kapvaal craton;Nyblade and Pollack, 1993) still display lower sur-face heat flows than adjacent terranes. They shouldtherefore have cold geotherms and a higher stiffnessthan the surrounding terranes (Fig. 2a), representinglong-lived stiff rheological heterogeneities.

2.2. Weak heterogeneities — continental rifts

The continental lithosphere is deeply modifiedduring extensional episodes. Both diffuse extension,as observed in the Basin and Range Province, orrifting processes result in lithospheric thinning, lo-cally increased geothermal gradients, and, therefore,lowered lithospheric strengths. On the other hand,crustal thinning raises the crust–mantle transition, in-ducing lower temperatures and higher yield stressesin the uppermost mantle of thinned areas; this leadsto an increase in bulk lithospheric strength. Sincecrustal and mantle thinning have opposite effects,the lithospheric strength of extensional areas willdepend on the ratio between mantle and crustal ex-tension. For vertically uniform stretching, England(1983) has shown that after an initial decrease in theaverage strength due to lithosphere attenuation, con-ductive cooling of the lithosphere leads to a rapid in-crease in lithosphere strength for strain rates <10�14

s�1. However, geophysical surveys (e.g., Davis etal., 1993; Achauer et al., 1994; Gao et al., 1994)and petrological studies on rift-related magmatism(Thompson and Gibson, 1994) suggest that in mostrecent rifts, like the Rio Grande, the East African andthe Baikal rifts, the lithosphere attenuation is largerthan the observed crustal thinning.

In that case, continental rifts may represent hotand weak heterogeneities (Fig. 2c,d,e). Such hetero-geneities certainly have a shorter time span than coldones. Morgan and Ramberg (1987) using the modelof McKenzie (1978) calculated that the thermal re-laxation of a palaeorift occurs in a time interval of70–200 m.y. depending on the equilibrium thicknessof the lithosphere (100 and 200 km, respectively).For narrow rifts, lateral heat conduction will play animportant role, resulting in shorter durations of thethermal anomaly. However, the model by McKenzie(1978) simulates only the thermal relaxation withinthe rifted zone. Comparison between modelled ther-mal evolutions of thinned and normal lithospheres

(Sahagian and Holland, 1993) suggests that smallthermal contrasts may be maintained for longer timespans. Moreover, post-extension subsidence and sedi-mentation induce deepening of the crust–mantle tran-sition and at least partially counteract the strength-ening effect of lithospheric cooling. Thus, since forsimilar crustal thicknesses even very small variationsin geothermal gradient may still affect the lithosphericstrength (compare Fig. 2b and 2c), strength contrastsassociated with an intracontinental rift may remainactive during several hundreds of million years.

3. The Borborema shear zone system

The Borborema shear zone system of northeastBrazil (Fig. 3) is composed of NE-trending, dextraltranscurrent shear zones, from which E–W-trending,dextral strike-slip shear zones branch off (Vauchez etal., 1995). These E–W-trending shear zones displaysinuous trends and terminate in metasedimentarybelts, forming compressional horsetail structures.The connections between the different high-strainzones (NE–SW- and E–W-trending shear zones andmetasedimentary belts) are continuous, displayinga progressive rotation of foliations and lineations,and the deformation within the different high-strainzones was roughly synchronous (Feraud et al., 1993;Monie et al., 1996). Deformation regimes vary withthe orientation of the high-strain zones: whereas N–S-trending metasedimentary belts display a domi-nant normal shortening, NE-trending belts deformedby dextral transpression, and E–W shear zones arecharacterized by dominant dextral shear. This sug-gests that the shear zone network behaved as amechanically coherent system subjected to a homo-geneous continental-scale stress field, characterizedby roughly E–W compression (Vauchez et al., 1995).

From these observations, we infer that this com-plex strain field records the effect of pre-existingintraplate rheological heterogeneities in the mechan-ical behaviour of the plate. South of the BorboremaProvince, the Sao Francisco craton displays a thickerlithosphere (200–400 km; Grand, 1994; VanDecar etal., 1995) and a lower average surface heat flow thanthe surrounding Pan-African belts .42 š 5 mW/m2

and 55 š 4 mW/m2, respectively; Vitorello et al.,1980). Its termination should therefore induce a sig-nificant variation in the rheological properties of the


Fig. 3. Schematic map of the Borborema shear zone system (location in inset) showing the geometrical distribution of shear zones(black) and metasedimentary belts (dark grey). Abbreviations are: Tsz, Tatajuba shear zone; Pesz, West Pernambuco shear zone; Pasz,Patos shear zone; and CGsz, Campina Grande shear zone. Numbers indicate the U/Pb ages (in Ga) of different domains of the centralBorborema Province (Sa, 1992; Van Schmus et al., 1995).

lithosphere. Moreover, isotopic data (Van Schmus etal., 1995; B.B. Brito Neves, pers. commun., 1995)strongly suggest that the lithosphere of the centralBorborema Province is heterogeneous and resultsfrom the juxtaposition of continental domains eithercomprising an old basement (Palaeo- to Eoprotero-zoic) or formed of rocks accreted between 0.7 and1.0 Ga during an extensional event responsible forthe production of large volumes of juvenile crust.These younger domains, that correspond roughly tothe present-day metasedimentary belts, may haveacted as low-strength intraplate heterogeneities dur-ing the subsequent continental collision.

4. Numerical modelling

The study of the Borborema shear zone systemsuggests that intraplate rheological heterogeneities

may significantly modify the response of the conti-nental lithosphere to collision processes. We investi-gated the physical validity of this hypothesis throughnumerical models of the mechanical evolution of arheologically heterogeneous lithosphere subjected tocompressional tectonic forces.

This approach has been used already to study theeffect of single rheological heterogeneities in con-vergent environments. Vilotte et al. (1984, 1986),England and Houseman (1985), and Vauchez et al.(1994) investigated the effect of stiff inclusions ofdifferent shapes and sizes on the strain localizationand distribution of vertical strains within a collisionalbelt. Chery et al. (1991) and Wdowinski and Bock(1994) used vertical plane-strain models to show theinfluence of a low-strength domain on the distribu-tion of thickening within a compressional margin.

Finally, Tommasi et al. (1995), using plane-stress


map-view models based on the Borborema shearzone system of northeast Brazil, investigated the ef-fect of a single low-viscosity inclusion on the propa-gation of a shear zone developed at the tip of a stiffdomain. The present models are a continuation ofthis study. They aim to analyse the interactions be-tween multiple rheological heterogeneities and focuson the effect of the heterogeneities on strain local-ization, on the spatial organization of deformationregimes, and on vertical strain distribution.

4.1. Topology and boundary conditions

The topology of the different models is based onan extreme simplification of the conceptual modeldeveloped for the Borborema shear zone system. TheBorborema Province is simulated by a 2500ð2500km quadrilateral plate modelled by a mesh of ¾2600seven-nodded isoparametric elements (Fig. 4). Therheological heterogeneities are modelled by quadri-lateral blocks: a 500ð2000 km stiff block located atthe southeastern boundary of the model, represent-ing the craton, and/or 500ð100 km lower-viscosityblocks located in the central domain of the model,corresponding to basins (the present-day metasedi-mentary belts). Since we do not know precisely the

Fig. 4. Topology and boundary conditions (represented by engi-neering symbols) for the models. A stiff block within the ‘normallithosphere’ (unshaded) is represented in dark grey, whereas low-strength domains are displayed in light grey.

pre-deformation configuration of the system, sev-eral geometrical distributions of heterogeneities weretested.

An eastward displacement at constant velocity isset on the western boundary of the plate, simulat-ing the convergence of two continental plates. Thesouthern and eastern boundaries are only free toglide laterally (reflective conditions), simulating theextension of similar terranes south- and eastwardof the modelled domain. Geological constraints arelacking for the northern boundary. In most experi-ments, it is set free to move either normal or parallelto its trace, but, in order to test the effect of a freeboundary on the results, we also performed tests inwhich reflective conditions were also applied to thenorthern boundary.

Both plane strain and plane stress approximationshave been used, but only the plane stress resultsare presented, since this approximation accounts forvertical deformations, especially thickening in thelow-viscosity domains, as it is often observed innatural basins (inversion tectonics). Vertical defor-mations are overestimated, however, because gravityforces are not taken into account in this formulation(that correspond to an Argand number, Ar D 0; Eng-land and McKenzie, 1982). Finally, mesh refinementtests show that the main results do not depend onmesh size.

4.2. Physical formulation

Numerical modelling was performed using afinite-element program developed by Daudre (1991)in which a Lagrangian formulation of the equationsof continuum mechanics is solved for plane strainor plane stress approximations. The deformation ofthe lithosphere is modelled by a Stokes flow of anon-linear incompressible viscoplastic material thatfollows a Norton law and a Von Mises plasticitycriterion.

The different domains of the models simulate ter-ranes with different continental accretion ages andtectonic histories: a cratonic domain surrounded by ayounger lithosphere in which basins have formed.These domains are characterized by contrastinggeothermal gradients and compositional structuresand display different rheological profiles (Fig. 2).Integration of the deviatoric stress over the litho-


Table 1Model parameters (derived from the rheological profiles shown in Fig. 2)

Definition Stiff domain (Fig. 2a) Main lithosphere (Fig. 2b) Weak domain a (Fig. 2c) Weak domain a (Fig. 2d)

N¦y (Pa) Plasticity limit 1.62ð108 1.35ð107 1.14ð107 5.97ð106

N (Pa-n s-1) Fluidity 1.46ð10-59 1.02ð10-50 9.66ð10-49 1.24ð10-49

n Stress exponent 4.5 4.5 4.5 4.5

a In models with a low viscosity contrast.b In models with a high viscosity contrast.

sphere thickness gives the strength of the lithospherefor each domain (England, 1983). The rheologicalbehaviour of the lithosphere is approached throughvertically integrated rheological parameters: ¦ y and y , that depend on the local geothermal gradient andcompositional structure of the lithosphere (Tommasiet al., 1995) and therefore have different values foreach domain (Table 1).

Consequently, the constitutive equation is:

¦i j D 2¼P"i j C Ži j P (1)

where ¦i j is the Cauchy stress tensor, P"i j is thestrain rate tensor, P is the pressure, and Ži j is theKronecker delta. The effective viscosity ¼ is definedby:

¼ D ¦ y C

� NP" p

3

�1=n!=NP"p

3

where NP" is the 2nd invariant of the strain rate tensor,and n, ¦ y , and are material parameters: n is thestress exponent, is the vertically integrated fluiditythat takes into account the mantle contribution tothe lithospheric strength, and ¦ y is the verticallyintegrated plasticity limit that integrates the uppercrust contribution.

5. Models results

Models output at each time step is a set of tensorscharacterizing the material flow (strain rate, spin, fi-nite deformation and rotation). How can we correlatethese results to the natural deformation of conti-nents? As observed in the Borborema shear zonesystem, the major displacements in continental col-lision zones are localized in large-scale shear zones,that are characterized by an association of simpleand pure shear.

In the models, strain localization is indicated bylateral variations in strain rate leading to the de-velopment of high-strain zones. Deformation withinthese zones may be characterized by a combinedanalysis of finite strain (both horizontal and verti-cal) and rotation fields. A shear zone, i.e., a zonedisplaying significant simple shear, is marked by anassociation of high strain rate and spin or high finitestrain and rotation (see the kinematic description ofa simple shear deformation in Appendix A). Shearsense is indicated by the sign of spin (or rotation):in our models positive rotations correspond to dex-tral shear. The vertical finite-strain field records thepure shear deformation component: positive verticalstrains correspond to a thickening of the model andnegative ones to a thinning.

5.1. Models comprising a stiff and/or a single weakheterogeneity: previous results

The presence of a rheological heterogeneity, ei-ther stiff or weak, deeply modifies the otherwisehomogeneous deformation field induced by normalconvergence. As already observed in previous work(Vilotte et al., 1984, 1986; England and Houseman,1985; Vauchez et al., 1994), stress concentration atthe tips of a stiff inclusion induces strain localiza-tion, leading to initiation of shear zones (Fig. 5a,b).Confinement effects are also observed; they inducea heterogeneous distribution of vertical strains andlocal thickening in the domain squeezed between theconverging boundary and the stiff block (Fig. 5c).Within the stiff inclusion, strain is very small, andfor large viscosity contrasts between the stiff domainand the surrounding lithosphere, the former displaysan almost rigid behaviour.

A single weak heterogeneity also induces signifi-cant strain localization. However, since strain is con-



centrated within the weak heterogeneity (Fig. 5d), theeffect on the deformation pattern is dependent on theability of the heterogeneity to accommodate the im-posed displacements, i.e., on its orientation relative tothe convergence direction and on its viscosity contrastrelative to the surrounding medium. A weak inclusionwith its long axis oblique to the convergence directionundergoes a transpressional deformation, indicated bylarge positive vertical strains (Fig. 5f) and finite-rota-tion values (Fig. 5e). The shearing deformation prop-agates outside the heterogeneity, generating transcur-rent shear zones in the surrounding lithosphere. How-ever, for a similar displacement, strain rate gradientsin the surrounding medium are less important thanthose induced by a stiff inclusion (compare Fig. 5aand 5d), i.e., a low-viscosity heterogeneity inducesa more limited strain localization in the surroundingmedium than a stiff one.

The mechanical response of a lithosphere con-taining both a stiff block and a weak inclusion ischaracterized by an interplay of the effects of thetwo heterogeneities (Tommasi et al., 1995). Strainlocalization is enhanced relatively to single-hetero-geneity models (compare Fig. 5g with Fig. 5a and5d). The deformation field induced by the presenceof the stiff block is modified, since part of the con-vergence is accommodated by the weak inclusion:the shear zone developed at the corner of the stiffdomain is rotated and propagates towards the weakinclusion, functioning as a strain-transfer zone. Ro-tational deformations are also enhanced (Fig. 5h).Strain regimes within the high-strain zones dependon their orientation relative to the bulk stress field(Fig. 5h and 5i).

Fig. 6 displays the finite-rotation field for a modelin which reflective boundary conditions were appliedto the northern limit. The only effect of this change inboundary conditions is a less effective propagationof the shear zone system north of the low-viscos-ity domain, the rotation field remaining otherwise

Fig. 5. Results for models comprising a single stiff (a–c), a single weak heterogeneity (d–f), or a weak and a stiff heterogeneity (g–i)after 120 km of convergence. (a), (d), and (g) Second invariant of the Almansi–Euler finite-strain tensor (logscale). (b), (e), and (h)Finite-rotation contours; counterclockwise rotations are displayed in white. (c), (f), and (i) Contours of vertical finite strain; thinnedregions are displayed in white. Insets at the top right of each column show the geometry and boundary conditions for each model.Interpretative sketches displaying shear zones (dotted lines) and compressive domains (direction of shortening is indicated by solidarrows) developed in the models are shown at the bottom left of each column; sizes of the arrows and thickness of the lines representschematically the relative strain intensity within each shear zone.

unchanged (compare to Fig. 5h). Thus strain local-ization and shear zone reorientation result essentiallyfrom the presence of rheological heterogeneities anddo not depend on the existence of a free boundary.

5.2. Models comprising a stiff and two weakheterogeneities

The temporal evolution of the finite-strain androtation fields (Figs. 7 and 8) of a model with mul-tiple heterogeneities highlights that, from the verybeginning of the convergence, both weak and stiffheterogeneities induce strain localization, due to thelower initial effective viscosity of the weak domainsand stress concentrations at the tips of stiff inclu-sions. Shear zones oriented roughly at 45º to thebulk compression initiate at the tips of the hetero-geneities. As these shear zones propagate, they arerotated due to the interplay between the effects of thevarious rheological heterogeneities, and finally coa-lesce, forming a system of branched shear zones thatlink the heterogeneities and limit almost undeformedblocks (Fig. 9).

As in models with a single low-viscosity hetero-geneity, strain regimes within high-deformation zones(weak blocks and strain transfer zones) are variableand depend on their orientation relative to the bulkstress field and on local stresses induced by the het-erogeneities. The low-viscosity domains display atranspressional deformation characterized by right-lateral shear (Fig. 9b) and normal shortening accom-modated dominantly by thickening (Fig. 9c). More-over, the convergence-transverse weak domain dis-plays higher thickening/horizontal simple shear ra-tios than the convergence-oblique one. Strain transferzones deform dominantly by right-lateral shear, withsubsidiary pure shear deformation accommodated bythickening in the NE-trending branch of the shearzone system for large convergence values (¾200 km).

The final configuration of the shear zone system is


Fig. 6. Finite-rotation field for a model comprising a weak and a stiff heterogeneity after 120 km of convergence. In this experimentreflexive conditions were applied to the northern boundary.

variable. It may be characterized either by a balanceddevelopment of its various branches or by a domi-nance of one branch over the others. This final con-figuration is controlled by interactions between thevarious rheological heterogeneities and the boundaryconditions and depends, therefore, on the spatial dis-tribution of heterogeneities and on their rheologicalcontrast relative to the surrounding medium. A qual-itative comparison of the finite-rotation fields after 5km and 200 km of convergence (Fig. 8f and Fig. 10)indicates that the final deformation pattern is alreadyprefigured at the first stages of the evolution of the sys-tem. This suggests that the interactions between thevarious rheological heterogeneities and the boundaryconditions are active from the very beginning of thedeformation and control its entire evolution.

5.3. Effect of the geometrical distribution ofheterogeneities

Depending on the location and orientation ofthe heterogeneity responsible for its development,

a branch of the shear zone system may accommodatemost of the deformation of the system, hinderingthe evolution of the other branches. In most models,the southern strain transfer zone is better developedthan the northern one (Figs. 9, 11 and 12: rightpanel). This suggests that, for a similar viscositycontrast between the weak domains and the sur-rounding lithosphere, strain, and especially shearing,is more efficiently transferred to the weak domainnearest to the tip of the stiff domain.

Strain transfer between the weak heterogeneitiesalso depends on their location and orientation. Be-tween two low-viscosity heterogeneities, respectivelynormal and oblique to the convergence direction,strain transfer occurs over a relatively large area(Fig. 9a) characterized by an association of thick-ening (Fig. 9c) and a variable proportion of right-and left-lateral shearing (Fig. 9b). In contrast, modelswith two convergence-oblique weak heterogeneitiesdevelop a branched shear zone system. The system iscomposed of two (Fig. 12) or three NNE- to ENE-trending branches (Fig. 11), depending on the align-


Fig. 7. Temporal evolution of the finite strain of a model comprising multiple heterogeneities. Second invariant of the Almansi–Eulerfinite-strain tensor (logscale) after 5 km (a), 40 km (b), 80 km (c), 120 km (d), 160 km (e), and 200 km (f) of convergence.


Fig. 8. Temporal evolution of the rotational deformation of a model comprising multiple heterogeneities. Finite rotations after 5 km (a),40 km (b), 80 km (c), 120 km (d), 160 km (e), and 200 km (f) of convergence.


Fig. 9. Results for a model comprising a stiff and two weak heterogeneities after 120 km of convergence. (a) Second invariant ofthe Almansi–Euler finite-strain tensor (logscale). (b) Finite-rotation contours; counterclockwise rotations are displayed in white. (c)Contours of vertical finite strain; thinned regions are displayed in white. (d) Interpretative sketch displaying shear zones (dotted lines)and compressive areas (direction of compression is indicated by solid arrows) developed in the models; the sizes of the arrows andthickness of the lines represent schematically the relative strain intensity within each shear zone. Inset shows the geometry and boundaryconditions of the model.

ment of the weak domains relative to the shear zoneinitiated at the tip of the stiff domain. Strain intensityvaries within the system: shear strains are larger in

the strain transfer zones connecting the stiff block tothe southernmost weak domain and the northernmostweak domain to the free boundary. This suggests that


Fig. 10. Finite-rotation field for a model comprising multipleheterogeneities after 5 km of convergence. Note difference inscale with Fig. 8.

these shear zones form an en-echelon system in whichdeformation is transferred between the two weak do-mains through a compressive jog.

5.4. Effect of the rheological contrast between theheterogeneities and the surrounding medium

The rheological contrast between the weak het-erogeneities and the surrounding medium controlsthe finite-strain field. In models with high initial vis-cosity contrasts, strain localizes preferentially withinthe weak domains. These domains consequently dis-play the highest horizontal and vertical strains, andthe strain transfer zone that links the nearest low-viscosity domain accommodates more shear strain(Figs. 9, 11 and 12: right panel). On the other hand,in models with low viscosity contrast, the higheststrains occur either within the weak domains or atthe tip of the stiff block, and all the strain transferzones show similar development (Fig. 12: left panel).This suggests that the distance between the variousheterogeneities has a larger effect when the viscositycontrast is high.

Fig. 11. Effect of the geometrical distribution of rheologicalheterogeneities in the shear zone development. Finite rotationsafter 200 km of convergence. Top right inset shows the geom-etry and boundary conditions of the model. Bottom right insetdisplays an interpretative sketch displaying shear zones (dottedlines) and compressive areas (direction of shortening is indicatedby solid arrows) developed in the model; sizes of the arrows andthickness of the lines represent schematically the relative strainintensity within each shear zone.

Moreover, in models with a high viscosity con-trast, the weak domains deform faster than the sur-rounding medium, and kinematic continuity con-straints induce the development of left-lateral rota-tions at their NW and SE tips. For favourable modelgeometries, as in Fig. 12b, these left-lateral rotationdomains coalesce, generating a sinistral shear zonelinking the two low-viscosity domains. For a lowviscosity contrast, although the weak domains stilldeform faster than the surrounding medium, the vari-ation in strain between the two media is smaller, andthe left-lateral shear zone is not so well developed(Fig. 12: left panel). This allows, in some specialconfigurations (Figs. 7 and 8), the formation of anarcuate dextral shear zone connecting the two weakdomains. This shear zone displays a complex de-formation regime characterized by an association ofpure and simple shear, and by a decrease of the dex-


Fig. 12. Effect of the initial viscosity contrast between the weak domain and the surrounding medium on the development of shearzones; contours of finite rotation after 120 km of convergence. Integrated rheological parameters (Table 1) for the weak domain in (leftpanel) and (right panel) are calculated using the lithospheric strength of Fig. 2c and Fig. 2e, respectively. The rheological parametersfor the other domains are kept constant. Top left inset shows the geometry and boundary conditions for the two models. Bottom rightinsets display an interpretative sketch displaying shear zones (dotted lines) and compressive areas (direction of compression is indicatedby solid arrows) developed in each model; the sizes of the arrows and thickness of the lines represent schematically the relative strainintensity within each shear zone.

tral shearing component along the shear zone awayfrom the weak domains.

6. Comparison between models and theBorborema shear zone system

6.1. Strain distribution

The strain patterns obtained in the models repro-duce some fundamental characteristics of the Bor-borema shear zone system (Fig. 3). The northerntermination of the Sao Francisco craton (i.e., the tipof the stiff heterogeneity) is marked by the devel-opment of a continental-scale, NE-trending, dextraltranscurrent zone. Sinuous dextral strike-slip shearzones branch off from this major deformation zone,transferring the deformation to the metasedimentary

belts (ancient basins regarded as representing weakinclusions), in which they terminate. The strain dis-tribution is heterogeneous: shear zones and severelydeformed metasedimentary belts border blocks, suchas the domain delimited by the Patos shear zoneand the Oros and Serido belts, that are significantlyless deformed. From the structures developed in themodels only the sinistral shear zones initiated at thenorthwestern tip of the weak inclusions are not ob-served in the Borborema shear zone system. Sincethe development of these sinistral shear zones is sig-nificantly reduced in models with a low viscositycontrast between the weak inclusions and the sur-rounding material, we infer that the strength contrastinduced by the basins in the Borborema Provincewas moderate. This is in agreement with the timeinterval between the last extensional episode and the


compression that generated the shear zone system (atleast 100 Ma).

Although there is a good qualitative relationshipbetween modelling results and the Borborema shearzone system, strain localization is less well devel-oped in the models than in the natural case: shearzones thickness is typically ¾100 km in the modelsand 20–30 km at most in the Borborema Province.This discrepancy is at least partially due to thevery simple flow law used in the models, that in-tends to simulate the bulk rheological behaviour ofa column of lithospheric material. This flow lawis characterized by a low stress exponent and doesnot take into account softening processes leadingto strain localization in nature, like development ofa lattice preferred orientation, changes in deforma-tion mechanisms associated to an effective grainsize reduction or synkinematic mineralogical trans-formations (Poirier, 1980), or partial melting. Strainlocalization in the models is therefore only inducedby local stress concentrations or viscosity contrastsand cannot be as effective as in natural deforma-tion. Another factor that should be considered is thatthe Borborema Province data provide informationon the width of the shear zones in the middle crust

Fig. 13. Schematic structural map of the central domain of the Borborema shear zone system. Pasz D Patos shear zone, CGsz D CampinaGrande shear zone, T D Teixeira Batholith, 1 D post-Proterozoic sediments, 2 D Brasiliano granites, 3 D migmatites and in-situ granites,4 D metasediments, 5 D basement, 6 D strike-slip shear zone, 7 D foliation, 8 D stretching lineation, 9 D HT-mylonites. Inset shows thedistribution of deformation regimes. Arrows represent pure and simple shear components of the deformation in the various high-strainzones, and their size indicates the relative magnitude of each component.

while models mostly simulate the behaviour of thelithospheric mantle. Natural shear zones likely widenwith depth; if similar depths should be compared dis-crepancy between model and reality would probablydiminish.

6.2. Strain regimes

The models display significant lateral variationsof strain regime within short distances (<100 km).In the Borborema shear zone system (Fig. 13), strainregime also changes significantly over short dis-tances. As in the models, the relative amount ofshortening and shearing within the metasedimentarybelts depends on their orientation relative to theconvergence direction: whereas the N–S-trendingOros belt displays dominant flattening strains (Sa,1992), the NE-trending Serido belt is characterizedby a partitioning of the deformation into dextralstrike-slip zones and domains where coaxial straindominates. The sinuous Campina Grande shear zone(CGsz) also displays significant variations in defor-mation regime accompanying a change in orientationfrom E–W to NE–SW (Vauchez et al., 1995): in theE–W-trending branch, asymmetric microstructures


consistently indicate right-lateral shearing, whereasthe NE-trending branch is characterized by narrowdextral shear zones cutting across domains with pre-dominance of symmetric microstructures suggestiveof dominant pure shear (Fig. 13). This association offlattening and shearing suggests dextral transpressionwithin this zone.

Finally, in some models (Figs. 7 and 8), a com-plex strain transfer zone develops to accommodatechanges in flow direction imposed by the spatialdistribution of heterogeneities. This switch in flowdirection takes place over a large area through anarcuate shear zone. Within this structure, not onlythe strain distribution is heterogeneous, but the strainregime varies along the shear zone: simple sheardeformation decreases relative to pure shear. A sim-ilar structure is observed in the Borborema shearzone system: at the connection between the Tatajubaand Patos shear zones, a change in flow directionfrom NE–SW to E–W is accommodated througha strike-slip duplex in which arcuate shear zonesbound almost undeformed blocks (Fig. 14). Withinthis structure, the dip of the foliation decreases to-ward the outer boundary and the lineations show

Fig. 14. Hand-drawing from Landsat images of the connection between the E–W-trending Patos shear zone and the NE-trending Tatajubaand Potengi shear zones.

moderate plunges, suggesting a thrusting componentassociated with the dominant dextral simple shear(Vauchez et al., 1995; Corsini et al., 1996).

6.3. Vertical strains—effect on uplift andmetamorphic evolution

Although vertical strains are clearly overestimatedin the models (because Ar D 0), the results in-dicate large lateral variations in vertical strains.Whereas some regions, such as the weak blocksand the domain confined between the stiff blockand the converging boundary, tend to thicken sig-nificantly, a large part of the model suffers littlevertical strain (Fig. 9c). Heterogeneity of the verti-cal strain field may produce contrasted metamorphicand uplift histories within a collisional belt. Themetamorphic evolution of rocks within domains sub-jected to significant thickening should reflect syn-collisional thickening followed by thermal relaxation(England and Thompson, 1984). Post-orogenic upliftrates should be higher in these domains, due to eithera more effective erosion (higher topography) or totectonic denudation processes (late-orogenic exten-


sion due to thermal weakening of the thickened crust,Gaudemer et al., 1989, or lithospheric delamination,England and Houseman, 1989). On the other hand,zones undergoing thinning should display a syn-col-lisional extensional deformation during which P–T–t patterns should record either an initial isother-mal uplift followed by a rapid cooling (pure shearextension) or linear depth–temperature paths withmoderate dT=dP (simple shear extension; Ruppelet al., 1988) and then the effects of sedimentationand subsidence. Finally, areas where vertical strain isnegligible (undeformed blocks or domains showingdominant strike-slip motions) should remain quitestable during the post-orogenic evolution of the belt,showing very low uplift rates.

The correlation between the modelled verticalstrain field and the metamorphic pattern of theBorborema Province is, however, not straightfor-ward. Detailed metamorphism studies of this areaare lacking. However, significant lateral variationsin synkinematic metamorphic conditions have beenobserved. Deformation within the NE-trending shearzones of the western domain occurred under higherpressure conditions .T > 700ºC and P ³ 600–800 MPa) than those recorded by shear zonesand metasedimentary belts of the eastern domain(Vauchez et al., 1995). This suggests higher upliftrates and exposure of deeper crustal levels in thewestern domain. Even inside a specific high-strainzone, lateral variations in metamorphic grade maybe observed. In the E–W-trending shear zones de-veloped under high-temperature, low-pressure meta-morphic conditions .T ³ 650–750ºC and P ³ 500MPa), the highest temperatures and the most ex-tensive partial melting are observed at the con-nections between shear zones and metasedimentarybelts. Synkinematic metamorphic conditions signif-icantly decrease northward in the Serido metased-imentary belt, away from the connection with thePatos shear zone, from high amphibolite (with par-tial melting) to greenschist facies. This suggeststhat shallower levels are exposed in the northernpart of the belt, but pressure determinations, neededto confirm this hypothesis, are not available. Sim-ilarly, from the E–W-trending West Pernambucoshear zone northward, synkinematic metamorphicconditions decrease from upper-amphibolite facies(¾700ºC and 600–700 MPa) in the shear zone

(Vauchez and Egydio-Silva, 1992) to greenschist fa-cies in the Cachoeirinha–Salgueiro belt. On the otherhand, the Oros belt displays a northward increase ofsynkinematic metamorphic conditions: its southerndomain has been deformed under greenschist- toamphibolite-facies conditions, whereas in its north-ern domain metamorphic assemblages record synk-inematic granulite-facies conditions. This could beexplained by development of a compressional defor-mation regime at the connection between the Orosbelt and the NE-trending Senador Pompeu shearzone. Unfortunately, such lateral variations in defor-mation regime within a high-strain zone cannot bereproduced in the present models, because the useof a homogeneous mesh limits the possible resolu-tion within high-strain domains; we are only able todescribe phenomena on a scale ½ 50 km.

Lateral variations in thermal history may signifi-cantly affect age determinations, since most isotopicsystems, like 40Ar/39Ar, measure ages of cooling be-low closure temperatures. Within a collisional beltthis may result in age variations between the dif-ferent domains of the belt even when deformationwas roughly synchronous. If the thermal evolutionof the belt is not significantly disturbed by heatadvecting events, such as emplacement of large vol-umes of magmas, cooling rates will depend on upliftrates. Regions with faster denudation rates will tendto display older ages. 40Ar/39Ar ages obtained inamphiboles and biotites of mylonites of the variousshear zones of the Borborema system span over morethan 30 Ma; ages in amphiboles and biotites froma NE-trending shear zone of the western domainare clearly older (¾570 and ¾560 Ma, respectively;Monie et al., 1996) than those measured in mylonitesfrom the eastern Patos shear zone (540–530 Ma inamphiboles and 525–500 Ma in biotites; Feraud etal., 1993). This suggests an earlier and faster coolingof the western domain that could be associated witheither a larger thickening in the western part of thesystem or the extensive magmatism and partial melt-ing that accompanied the deformation at the Patosshear zone–Serido belt junction.

Pre-existing intraplate rheological heterogeneitiescontrol the shear zone distribution. They may therebyinfluence syn-collisional magma emplacement, be-cause shear zones may act as preferential channelsfor magmas to circulate (e.g., Clemens and Mawer,


1992). Lithospheric-scale transcurrent shear zones,like those developed in the models, are especiallygood candidates to tap and channel melts at differentdepths because deformation within these zones in-duces a continuous transformation of the rocks fabricthat is likely to locally enhance the vertical perme-ability of the crust. Large volumes of synkinematicmagmas emplaced as vertical sills within the shearzones, and elongated syn- to late-kinematic plutonsemplaced at their margins argue for a close rela-tionship between shearing deformation and magmaemplacement within the Borborema shear zone sys-tem (Vauchez et al., 1995, 1997b; Neves et al., 1996).Moreover, within sinuous shear zones like those de-veloped in the models, changes in the shear zoneorientation may induce local variations in the stressfield, giving rise to features like extensional bendsthat would form privileged sites for magma emplace-ment. For instance, the right-lateral step-over formedby the Patos and Campina Grande shear zone systemis occupied by a large (100 kmð30 km) magmaticbody, the Teixeira batholith (Fig. 13).

6.4. Model limitations

Although there is a good qualitative agreementbetween our models and the deformation field of theBorborema shear zone system, the present modelsonly simulate the main characteristics of the studiedprocess: the effect of pre-existing structure of acontinental plate on its thermo-mechanical evolution.Lithospheric deformation is a 3D process. A morerealistic description of its evolution can only bedone through 3D-modelling that takes explicitly intoaccount lateral variations of lithospheric structureand geothermal gradient. However, even in a 2Dhorizontal plane approach, two important points stillneed to be developed: the integration of gravityforces and a mesh refinement in high-strain domains.

Integration of gravity forces to our horizontal-plane stress models through a parameter like theArgand number (England and McKenzie, 1982) isessential to the study of the deformation regimes inthe low-viscosity domains. In the Borborema shearzone system, although the metasedimentary belts dis-play evidences of crustal thickening, stretching lin-eations within these domains are systematically par-allel to their elongation, suggesting that shortening

was mainly accommodated by horizontal motions.How such a system can accommodate significantshortening without material loss remains however anunanswered question. On the other hand, remeshingof the high-strain domains would allow us to sim-ulate more realistic gradational transitions betweenthe different domains of the models. Moreover, thepresent resolution of the models does not allow todiscriminate homogeneous from localized deforma-tion or to visualize lateral variations in strain regimewithin a high-strain zone. A finer mesh would entitlestudy of strain localization and kinematics varia-tion within a specific high-strain zone (in particularwithin its sinuous domain) or in jogs between en-echelon shear zones.

7. Comparison with data from other orogenicbelts

A consistent relationship between the presenceof intraplate rheological heterogeneities and strainlocalization has been observed in several other oro-genic belts. Vilotte et al. (1984, 1986) and Englandand Houseman (1985) explained the formation ofthe Altyn Tagh fault on the southeastern margin ofthe Tarim shield during the India–Asia collision bynumerical models investigating the effect of a stiffinclusion on the thermo-mechanical evolution of aplate submitted to an indentation. In southeast Brazil,the southern termination of the Sao Francisco cra-ton (Fig. 15) is also marked by a southward change

Fig. 15. Schematic map of Ribeira–Aracuaı belt (light shading)showing the dominant kinematics for its southern and northerndomains. Inset shows location of the belt.


in deformation regime in the Ribeira–Aracuaı beltfrom dominant E–W shortening and thickening, ac-commodated by orogen-normal thrusting, to dextralshearing in a continental-scale, NE-trending tran-scurrent shear zone (Vauchez et al., 1994). Thischange in deformation regime is accompanied by asouthwestward decrease in metamorphic conditionsaway from the Sao Francisco craton. Such a variationin exposure levels may be interpreted as resulting ofa differential uplift within the belt due to a decreasein thickening away from the stiff block.

Present-day stress-field analysis in the Baikal riftregion (Petit et al., 1996) also points to a consistentrelationship between changes in the tectonic regimeand the pre-existing structure of the plate. This studyshows that although there is a general agreementbetween average local SHmax directions and the re-gional ones, suggesting that the India–Asia collisionis responsible for both the wrench-compressionaltectonics in Mongolia and the extensional regime inthe Baikal, in the south Baikal rift, at the tip of thecraton, the tectonic regime changes abruptly fromwrench-compressional to extensional. Moreover, Pe-tit et al. (1996) observe that the rift either follows thesuture between the Siberian craton and the Palaeo-zoic Sayan–Baikal folded belt (when its orientationis favourable as in the south Baikal rift) or propa-gates into the folded zone (as in the north Baikalrift, where the northeastward propagation of the riftinto the shield is hindered). They suggest thereforethat the pre-existent structure of the Asian plate mustplay an important role in the development of the riftsystem.

Inversion tectonics (i.e., normal shortening of pre-existing basins during later compressional episodes)is a common process (e.g., Cooper and Williams,1989). The present models show however that, aslong as the thermal anomaly associated with thelithospheric thinning subsists, the basins representlithospheric-scale weak heterogeneities and their ef-fect is not restricted to the crust. In this case, theymay significantly affect the final deformation pat-tern, guiding strain localization and controlling thedevelopment of shear zones. For instance, in theNorthern Appalachians, rift basins developed duringthe early stages of convergence have probably in-fluenced the final deformation pattern of the NorthAmerican plate, controlling the location and geome-

try of thrust fronts and dextral strike-slip shear zonesthat accommodate the Middle Devonian to Permianaccretion of Avalon and Meguma terranes (Kepieand Dostal, 1994, fig. 5).

In the Alpine belt of North Africa, the GreatKabylia massif is located farther south than the othercrystalline massifs of the belt; it is bounded on itswestern and eastern sides by two transcurrent faults,respectively, dextral and sinistral, that accommo-dated the differential motion of the massif relativeto the remainder of the belt. Saadallah et al. (1996)show that the southern front of the Great Kabyliamassif, the Djurdjura range, is marked by a zoneof intense deformation in which developed a trans-pressive duplex flower structure. They also arguethat this high-strain zone formed over a sedimentarybasin characterized, at least in its northern part, bya thinned crust. These observations suggest that thepresence of the basin controlled the southward prop-agation of the Alpine deformation in this region. It isnoteworthy that this zone displays a high Quaternaryseismicity (Boudiaf, 1996), suggesting that it stilllocalizes strain.

Finally, a significant lateral variation of defor-mation regime is observed in the late Palaeozoicintracontinental deformation of Central Africa. Itdisplays a complex intraplate structural pattern char-acterized by roughly coeval rifting, strike-slip, andthrusting events, that is interpreted as resulting fromthe reactivation of pre-existing basement structureswith different orientations due to a northward con-vergence at the southern margin of the Gondwanaplate (Daly et al., 1990).

8. Conclusions

Numerical modelling shows that pre-existing rhe-ological heterogeneities favour the development ofa heterogeneous strain field, characterized by signif-icant lateral variations in strain intensity, deforma-tion regimes and vertical strains, even in a systemwith simple, time-independent boundary conditions.Both weak and stiff heterogeneities in models in-duce an almost instantaneous strain localization dueto the lower initial effective viscosity of the do-mains characterized by higher geothermal gradientsand to stress concentrations at the tips of stiff in-clusions. Shear zones initiate at the tips of the


heterogeneities. Their propagation is controlled bythe interplay between the effects of the various rhe-ological heterogeneities, and they finally coalesceforming a shear zone system, in which they act asstrain transfer zones between the different hetero-geneities and/or the free boundary. In some models,preferential development of one branch of the shearzone system relative to the others indicates thatthe evolution of the system is sensitive to the in-teractions between the different heterogeneities andthe boundary conditions. These interactions dependon the geometrical distribution of heterogeneitiesand on the strength contrast between the hetero-geneities and the surrounding lithosphere. The initialviscosity contrast relative to the surrounding litho-sphere controls the strain intensity within the het-erogeneities; high viscosity contrasts result in moreheterogeneous strain distributions. The finite-strainfield involves a network of high-strain zones bound-ing almost undeformed blocks and displays lateralvariations in vertical and/or rotational deformationover short distances. While strain transfer zones aregenerally characterized by a dominant simple sheardeformation, weak domains in the models deformby an association of pure and simple shear, that iscontrolled by their orientation relative to the con-vergence direction: those normal to the convergencedirection deform by dominant normal shortening andthickening with subsidiary shearing, whereas thoseobliquely oriented record transpression. Althoughthe simple shear deformation propagates outwardsfrom the weak domains, forming the strain transferzones, the pure shear deformation remains mostly lo-calized within them. The limits of the weak domainsare therefore generally characterized by significantvariations in vertical strain.

The existence of intraplate rheological hetero-geneities is an intrinsic consequence of the long-last-ing evolution of continental plates through multipletectonic cycles. The similarity between model andnatural strain fields suggests that, in a convergentenvironment, a control of the finite-strain field by in-traplate rheological heterogeneities is not only phys-ically possible, but it certainly represents an essentialparameter governing the tectono-metamorphic evo-lution of collisional belts. Significant variations instyle and intensity of deformation may therefore oc-cur over short distances even in a collisional belt

resulting from a normal convergence between plateswith simple geometry. Their effect on the defor-mation patterns and, thus, on the metamorphic anduplift histories developed during a continental con-vergence should be therefore carefully assessed inthe study of collisional belts, especially in attemptsto unravel ancient geodynamic evolutions.

Acknowledgements

We thank Bertrand Daudre for providing usCREEP, and Jean Chery, Jean-Marc Lardeaux andChristian Teyssier for their thoughtful reviews andconstructive criticism. A.T. was supported duringthis work by a Ph.D. fellowship of the Conselho Na-cional de Desenvolvimento Cientıfico e Tecnologico(CNPq, Brazil). This work is a contribution toEEC project number CI 1-0320-F-CD ‘Ductile ShearZones in the Pan-African Belts from Northeast Braziland Associated Phanerozoic Sedimentary Basins’.

Appendix A

The characterization of a shear zone in the models maybe illustrated by the kinematic description of a simple sheardeformation characterized by a displacement parallel to one ofthe reference axes (Fig. 16). This coordinate system correspondsto the one generally used in the study of natural shear zones.

The function F describes a flow parallel to axis e1:

x D F.X; t/ D .X1 C 2kt X2; X2/ (A1)

The transformation gradient is then:

F D r� D0@1 2kt

0 1

1A (A2)

The polar decomposition F D RU gives the stretch U and therotation R components of the flow (Hassani, 1994):

U D 1p1C k2t2

0@ 1 kt

kt 1C 2k2t2

1A (A3)

R D 1p1C k2t2

0@ 1 kt

�kt 1

1A (A4)

The velocity gradient l, the strain rate d, and the spin w areexpressed as:

l D @v@xD0@0 2k

0 0

1A (A5)

d D0@0 k

k 0

1A and w D0@ 0 k

�k 0

1A (A6)


Fig. 16. Kinematic description of the simple shear x D F.X; t/ D .X1 C 2kt X2; X2/ at a time t D 1=k (adapted from Hassani, 1994).Rotation/sense of shear convention is inversed relative to the models (in which positive rotations correspond to dextral shear).

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Documents

Continental-scale rheological heterogeneities and …328 A. Tommasi, A. Vauchez / Tectonophysics 279 (1997) 327–350 1. Introduction Continental collision zones often extend far in-land