Shear Zones – a Review MARK ⁎ Haakon Fossena,B, , Geane Carolina G

Home , Glarus thrust, Porphyroclast, Pure shear

Earth-Science Reviews 171 (2017) 434–455

Contents lists available at ScienceDirect

Earth-Science Reviews

journal homepage: www.elsevier.com/locate/earscirev

Shear zones – A review MARK ⁎ Haakon Fossena,b, , Geane Carolina G. Cavalcantec a Department of Earth Science/Museum of Natural History, University of Bergen, Allégaten 41, N-5007 Bergen, Norway b Instituto de Geociências, Universidade de São Paulo, Rua do Lago, 562, Cidade Universitária, São Paulo, SP CEP 05508-080, Brazil c Departmento de Geologia, Universidade Federal do Paraná, Av. Cel. Francisco Heráclito dos Santos, s/n, Centro Politécnico, 81531-980, Curitiba, PR CEP 81531-980, Brazil

ARTICLE INFO ABSTRACT

Keywords: Strain in the lithosphere localizes into tabular zones known as shear zones that grow from small outcrop-size Shear zones individual zones to large composite structures. Nucleation is related to distributed microscale flaws or mesoscale Kinematics structures such as fractures and dikes, and they soon establish displacement profiles similar to faults. Also similar Strain localization to faults, they grow in width and length primarily by segment linkage as they accumulate strain and displace- Vorticity ment, and this process typically results in shear zone networks. Consequently, mature shear zones are hetero- Crustal deformation geneous and composite zones characterized by anastomosing patterns and local variations in thickness and finite strain. Kinematic vorticity estimates suggest that most shear zones deviate from simple shear, and even if subsimple shear may be a useful reference model in many cases, finite strain data indicate that many shear zones involve three-dimensional combinations of coaxial and non-coaxial deformation, such as transpression and transtension. Strain geometry and kinematic vorticity can vary significantly within shear zone networks, which makes it difficult to estimate the bulk deformation type for a composite shear zone or shear zone network. However, perhaps the most challenging aspect is that of progressive deformation, i.e. to what extent and how flow parameters change during deformation (non-steady state deformation), which needs to be addressed by a combination of detailed field observations and numerical modeling.

1. Introduction during rifting (Powell and Glendinning, 1990; Butler et al., 2008; Bird et al., 2015; Phillips et al., 2016) and are important components in the The majority of strain accumulated in the mostly plastic or viscous context of plate tectonics (Bercovici and Ricard, 2012). part of the lithosphere, both in the crust and the mantle (e.g., Vauchez High-strain zones have been recognized in naturally deformed rocks et al., 2012; Snyder and Kjarsgaard, 2013), localizes into zones that since the 19th century (e.g., Reusch, 1888), and particularly since the show large variations in orientation, length, thickness, displacement, theory of thrusting was introduced (e.g., Bertrand, 1884; Geike, 1884; strain geometry, coaxiality, and deformation mechanisms. Such zones Törnebohm, 1888; Peach et al., 1907). However, even though strain in typically involve a significant component of simple shear, and are deformed rocks was discussed relatively early on (e.g., Harker, 1885), therefore called shear zones (Ramsay and Graham, 1970; Sibson, 1977; sound and quantitative analysis of shear zones in terms of geometry, Simpson and De Paor, 1993; Ramsay, 1980), although a component of strain and kinematics founded in mathematical analysis is relatively coaxial deformation (e.g., pure shear) is also commonly involved new, and basic aspects of such analyses were presented in a systematic (Ramberg, 1975a,b; Coward and Kim, 1981; Fossen and Tikoff, 1993; way by Ramsay (1967) and in a series of papers in the 1970s and1980s, Northrup, 1996). Shear zones separate less strained or unstrained notably Ramsay and Graham (1970), Ramberg (1975a,b), Coward portions of the lithosphere, and are the deeper counterparts to upper (1976), Cobbold (1977a,b), Berthé et al. (1979), Lister and Williams crustal faults and fault zones in contractional (thrust), extensional and (1979), Mandl et al. (1977), Sibson (1977), Ramsay (1980), Cobbold strike-slip settings alike (e.g., Sibson, 1977; Scholz, 1988; Wernicke, and Quinquis (1980), and Lister and Snoke (1984). The typical ap- 1985; Godin et al., 2006; Fossen, 2010; Ganade de Araujo et al., 2013; proach during this era was that of simple shear with or without addi- Cottle et al., 2015). They also represent rheological and mechanical tional shortening/dilation across the shear zone. Pure shear was then anomalies that may be reactivated or otherwise influence the structural combined with simple shear to create more general subsimple shear evolution during later stages or phases of deformation, for example zones, first in the pioneering work by Ramberg (1975a,b) and later by

⁎ Corresponding author at: Department of Earth Science/Museum of Natural History, University of Bergen, Allégaten 41, N-5007 Bergen, Norway. E-mail address: [email protected] (H. Fossen). http://dx.doi.org/10.1016/j.earscirev.2017.05.002 Received 19 January 2017; Received in revised form 6 May 2017; Accepted 6 May 2017 Available online 08 May 2017 0012-8252/ © 2017 Elsevier B.V. All rights reserved. H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

Fig. 1. Two shear zones at micro- and mapscale. a) Shear band in highly porous sandstone (thin section of core from the Njord Field, oﬀshore central Norway). Deformation oc- curred at shallow (few hundred meters) depth under un- consolidated conditions. b) Great Slave Lake shear zone (Canada), showing deﬂection of the Thelon-Taltson Magmatic Zone (TTMZ). Based on USGS map (2005).

Passchier (1986), Tikoff and Fossen (1993), and Simpson and De Paor fabric (Figs. 1 and 2a). The geometry, orientation and relative move- (1993), and then to combine pure and simple shear in a three-dimen- ment of the walls are the boundary conditions that control the de- sional way, particularly in the framework of transpression and transformation within the zone. However, several processes may change the tension (Sanderson and Marchini, 1984). In this work we will review boundary conditions over time, for example changes in compaction the most useful and fundamental aspects of shear zones, their evolution caused by pressure solution and related loss of material in the zone from incipient to large structures, and discuss challenges that need to be (thinning), strain localization where margins are left inactive (thin- studied in the future. ning), inclusion of larger or smaller portions of wall rocks (widening), and interaction between adjacent shear zones (widening by linkage). 2. Definition and classification Hence, terms such as widening, constant thickness and thinning shear zones are commonly used. A shear zone is a zone in which strain is clearly higher than in the A significant distinction can be made between plane strain zones and wall rock, and whose margins are defined by a change in strain, typi- non-plane strain zones, i.e. zones involving two- and three-dimensional cally seen by rotation of preexisting markers or formation of a new strain, respectively. Plane strain implies no change in length along the

Fig. 2. a) Schematic illustration of a simple shear zone, showing strain ellipses, new-formed foliation and two marker layers assumed to behave passively. b) Shear strain proﬁle through the zone. c) Graph showing relationships between shear strain (horizontal axis) and the orientation of the strain ellipse and the two markers shown in (a) as well as strain (R). d) Natural shear zone (based on photo by Giorgio Pennacchioni) from deformed granitoid rock in the Tauern Window, Italian Alps, and e) a shear strain map with three shear strain proﬁles estimated from foliation orientation, assuming simple shear. Displacement d is given in terms of the local shear zone thickness.

435 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455 intermediate (Y) principal strain axis, and thus many aspects of plane Correspondingly, a brittle shear zone shows discontinuous deformation strain can conveniently be dealt with by considering the plane con- where originally continuous markers are broken up by slip surfaces taining the maximum and minimum principal strain axes (X and Z) (shear fractures) that cause discontinuities in the displacement field (only the rotation of preexisting line and plane markers requires 3D (Fig. 4b). A completely brittle shear zone would have undeformed considerations in this case). Plane strain, whether simple, sub-simple or portions of rock between these slip surfaces. Ductile-brittle shear zones pure shear, plots along the diagonal of the Flinn diagram (Flinn, 1962), contain both continuous and discontinuous deformation. In this sense, while 3D deformations produce off-diagonal constrictional or flattening drag associated with faulting creates a ductile-brittle shear zone, even if strains. However, if volume change occurs by compaction across the the deformation mechanisms involved are purely frictional (e.g., shear zone in combination with a plane strain deformation (such as Homberg et al., 2017). simple shear), the resulting plane strain will plot in the flattening field (Ramsay and Woods, 1973). 3. From simple shear zones to zones of 3D strain Shear zones can further be classified according to their dominant micro-scale deformation mechanism, where plastic (or crystal-plastic) 3.1. Simple shear and the ideal (Ramsay-type) shear zone shear zones, also referred to as viscous shear zones, are dominated by crystal-plastic mechanisms (dislocation creep and twinning) and diffu- The ideal shear zone involves simple shear with or without addi- sion, while frictional or brittle shear zones are dominated by brittle de- tional compaction or dilation perpendicular to the zone (Ramsay, 1980) formation mechanisms (grain fracture, frictional sliding and grain ro- (compactional simple shear in Fig. 6). Ideal simple shear zones are easy tation). Brittle shear zones are generally known by other names, such as to deal with, as they have parallel planar walls and show simple rela- faults, fault zones or fault cores, and involve episodic seismic activity tions between displacement, strain and fabrics. If we place an x-y-z rather than the aseismic creep that characterizes strain accumulation in coordinate system with z perpendicular to the shear zone and x along plastic shear zones (Rutter et al., 2001). However, many shear zones the shear direction (Fig. 2a), then the simple shear deformation in- contain components of both plastic and brittle (frictional) deformation volved is conveniently expressed by the deformation matrix or de- mechanisms, and if the brittle component is significant, terms such as formation tensor brittle-plastic (Rutter, 1986), frictional-plastic, brittle-viscous (e.g., 1γ Fusseis and Handy, 2008) or frictional-viscous shear zones (e.g., Stipp D = ⎡ ⎤ 01 et al., 2002) may be appropriate. ⎣ ⎦ (1) Crystal-plasticity is controlled by mineralogy, temperature and This matrix transforms any point or vector to its new post-de- pressure, and further by the presence of fluids, strain rate and grain formational position by the linear transformation (homogeneous strain) size. Salt develops shear zones even at wet surface conditions, marbles x′ 1γ x at somewhat deeper crustal conditions, quartzites from close to 300 °C ⎡ ⎤ = ⎡ ⎤ ⎤ ⎣⎡z⎦ (Stipp et al., 2002), and feldsphatic rocks above ~450 °C (e.g., Sibson, ⎣z′⎦ ⎣01⎦ (2) 1977; Scholz, 1988). Hence, the complete transition from truly brittle The y-component remains constant for this transformation, meaning (frictional) to completely plastic shear zones can be wide. For con- that there is no shortening or stretching of any line exactly parallel to tinental rocks rich in quartz and feldspar, the transition stretches from the y-axis of the coordinate system. The full 3 × 3 matrix is 300 to 450 °C, as typically expressed by fractured feldspar in a matrix of recrystallized quartz deformed by dislocation creep (e.g., Tullis et al., ⎡10γ⎤ D = 1982; Viegas et al., 2016). Because large shear zones or shear zone ⎢010⎥ ⎢001⎥ (3) systems can transect the entire crust and in some cases even the entire ⎣ ⎦ lithosphere (e.g., Vauchez et al., 2012; Tikoff et al., 2013), they may, at The matrix product DDT gives the matrix (known as the left Cauchy- different depths, show the full range of microstructural or rheological Green tensor, or Finger tensor; Malvern, 1969, p.158, 174) whose ei- regimes or “facies”, as indicated in Fig. 3. Furthermore, many large genvectors represent the orientations of the principal strain axes, and high-grade crustal shear zones show evidence of later reactivation by whose eigenvalues correspond to their lengths (Flinn, 1979). D and DDT lower grade mylonitization and eventually brittle faulting during ex- can be used to calculate the rotation of lines and planes, the change in humation. length of lines, the orientation and magnitude of strain, and strain Finally, shear zones can be classified as ductile or brittle. These terms geometry (shape of the strain ellipsoid) (see Appendix A in Fossen, are being used in different ways by different parts of the structural 2016). This holds for any homogeneous deformation, not only for geology community. Some restrict the use of the term “ductile” to simple shear. temperature-dependent crystal-plastic deformation (Twiss and Moores, The most fundamental equations for perfect simple shear deforma- 2007), i.e. equivalent to the term plastic deformation described above. tion relate shear strain (γ) to the length and orientation (θ′) of the long However, as pointed out by Rutter (1986), an alternative and more (X) axis of the strain ellipse, as reflected by the trace of the new-formed descriptive definition considers ductile deformation as deformation foliation, and the change in orientation of passive planar markers (β → where no macroscopic fracture is involved, i.e. deformation that pre- β′, where β is the angle that the marker initially makes with the shear serves continuity of preexisting markers (e.g., Byerlee, 1968; Park, plane): 1997; van der Pluijm and Marshak, 2004; Paterson and Wong, 2005; γ = 2 tan(2θ′′ ), or θ= 0.5tan−1 (2 γ) (4) Fossen, 2016). This implies that ductile shear zones show a continuous displacement gradient across the zone (Fig. 4a), while brittle shear cot β′ =+ cot β γ (5) zones show displacement discontinuities (Fig. 4b). Hence, ductile and brittle deformation are also referred to as continuous and discontinuous (see Fig. 2 for a closer explanation). deformation, respectively. For compactional simple shear (Fig. 6), these relations change, de- The definition of ductile presented here is independent of depending on the amount of dilation (negative compaction) Δ: formation mechanism (Rutter, 1986), and is particularly used within 1 γΔ the fields of petroleum geology and experimental deformation of porous ⎡ ln(1+ Δ) ⎤ D = ⎢ ⎥ rocks (e.g., Wong and Baud, 2012; Homberg et al., 2017). All plastic ⎣01+ Δ⎦ (6) shear zones are ductile, but not all ductile shear zones are plastic. In 2γ(1+ Δ) particular, sediments and sedimentary rocks can develop ductile shear tan 2θ′ = 22 zones in which the grain-scale deformation is purely frictional (Fig. 5g). 1γ+−+ (1Δ) (7)

436 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

Fig. 3. a) Simplified diagram illustrating vertical variations in shear zones and shear zone fabrics (“facies”). The brittle-plastic transitions for quartz and feldspar and dominant recrystallization mechanisms (bulging, subgrain rotation and grain-boundary migration) are related to temperature, but also depend on strain rate and the amount of fluids present. b–d) Illustration of characteristic microfabrics in the three different regimes: b) brittle fracturing (brittle mechanisms); c) plastic with brittle feldspar (central grain) and small recrystallized quartz grains (dislocation creep); d) high-temperature recrystallization in the lower domain where both feldspar and quartz behave plastically and grain-boundary migration by diffusion is important.

strain may participate into shear bands separating back-rotated foliation domains, and complicating structures such as intrafolial folds may develop due to ﬂow perturbations and variations in ﬂow rate (Cobbold and Quinquis, 1980; Platt, 1983; Vollmer, 1988; Carreras et al., 2013).

3.2. General plane strain zones

It can be demonstrated that many shear zones are not simple shear, but involve an additional coaxial component. The deformation is still plane, provided that the pure and simple shear act in the same plane. Indications of non-simple shear include: 1) non-planar shear zone walls; 2) non-parallel shear-strain contours (Fig. 2e); 3) initial foliation at margins significantly different from 45°; 4) associated veins originating at an angle ≠ 45° to the shear zone (Fig. 7); 5) deflected markers not obeying the relationship shown in Fig. 2c(β′ curves); 6) a relationship between strain (R) and foliation deviating from the simple shear curve shown in Fig. 7 (θ′ curve); 7) porphyroclasts showing conflicting sense of rotation; 8) sets of differently oriented shear bands showing opposite senses of shear. Fig. 4. Shear zone end members based on (dis)continuity of markers, displacement field In terms of progressive deformation or flow, non-simple shear zones and strain gradient. a) Continuous or ductile deformation, where displacement and strain differ from simple shear zones in terms of coaxiality, which is described varies gradually through the zone. b) Perfect discontinuous or brittle end member where by the kinematic vorticity number Wk.Wk describes the relationship the displacement gradient is discontinuous. This end-member corresponds to a shear between the rotation and the change in shape of the strain ellipsoid. It is fracture. an instantaneous flow parameter, but for steady-state flow we can de- fi cot β+ γ ne Wk for an increment or the entire period of deformation, and thus cot β′ = ff 1Δ+ (8) relate Wk to simple and coaxial strain components (Tiko and Fossen, 1993). Hence, for plane strain deformation, Wk can be expressed in γ These relations are most easily applied to naturally deformed rocks terms of the amounts of pure (kx and kz) and simple shear ( ): for low to moderate strains. Once strain in a shear zone gets high, say Wkx= cos[arctan(ln(k kz ) γ)] (9) γ > 5, angles start to become difficult to measure (Ramsay, 1980). In fl addition, the foliation tends to de ect around heterogeneities, and where kx and kz are the stretches along the x and z coordinate axes,

437 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

Fig. 5. a) Fracture with selective eclogitization around the fracture, related to the inﬁltration of ﬂuids into the dry granulitic host rock along the fracture. b) Example of more advanced stage of (a), where a shear zone is established with a slightly wider alteration zone of eclogite. c) Lens of granulite enveloped by sheared rocks (eclogite). a–c represent three stages of shear zone development from the Caledonian Lindås Nappe near Bergen, Norway. d) Asymmetric structure extracted from mylonitic gneiss of the Nordfjord-Sogn Detachment Zone, Norway, formed by sinistral sense of shear. e) S-C structures in sheared granite from the Armorican Shear Zone, France. f) Shear zone developed on large vein, which is now converted into an ultramylonitic shear zone core. Caledonian Jotun Nappe, Norway. g) cm-scale ductile shear zone in the Aztec Sandstone, Nevada, where lamination can be traced continuously through the shear zone.

(straight ﬂow lines) that subdivide the particle paths into ﬂow com- partments (Passchier and Trouw, 2005),

Wk = cos α (10)

where α is the angle between the two ﬂow apophyses (Fig. 8c). Note that this relationship only holds for plane strain. Similarly, if the or-

ientation θ of the maximum instantaneous stretching axis ISA1 is known, for example from the initial orientation of the foliation along the margins of a shear zone or vein systems (Fig. 8),

Wk = sin 2θ (11)

The general plane strain deformation matrix is

γ(kxz− k ) ⎡kx ⎤ kΓ ln(k k ) ⎡ x ⎤ D = ⎢ xz⎥ = ⎢ 0kz⎥ ⎣ 0kz ⎦ ⎣ ⎦ (12)

where, for constant volume, kz = 1/kx. Fig. 6. Pure shear deformation expressed in a triangular diagram with pure shear, simple While Wk = 1 for perfect simple shear zones, it appears to be lower shear and orthogonal compaction as end members. (1 > Wk > 0) for most natural shear zones, and this deviation is typically explained by subsimple shear. Subsimple shear is a spectrum of deformations between simple and pure shear, and typical values of W respectively. Note that for non-steady flow (Wk changing during de- k estimated from natural shear zones range from 0.6 to 1 (e.g., Thigpen formation), this Wk will represent an average value for the interval in question. In terms of the two flow apophyses, i.e. the fixed directions et al., 2010a,b; Law et al., 2004; Zhang and Teyssier, 2013), although values close to 0 have been reported (Holcombe and Little, 2001)

438 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

θ (a) ISA 1 90

0.1

80 0.2 ISA 3 0.3 θ 70 0.4

0.5 60 0.6

0.7 50 (b) 0.8 90 3 θ α θ Wk=cos = cos(90-2 ) 40 80 0.9

) 70 30 Thickening shear zones α W =1 (simple , k 60 shear) θ α 20 Thinning 0.9 shear zones 50 0.8 0.60.6 0.7 0.50.5 1 10 0.40.4 40 2

0.30.3 Degrees ( 0.20.2 0.10.1 30 0 2.0 4.0 6.0 8.0 10 R =X/Z 2 XZ 20 θ Fig. 7. Relationship between the angle between the orientation of the trace of the strain XZ plane (foliation) (θ′) and the shear direction for different kinds of subsimple shear. 10 Values along the vertical axis represent the initial orientation (θ). 0 1 3 0.91.0 0.8 0.7 0.6 0.5 04 0.3 0.2 0.1 0.0 (Fig. 9). The consequence of having a pure shear component within the Simple Pure shear zone is that the shear zone material is extruded in the x direction. shear Wk shear However, if the pure shear component also affects the shear zone walls (c) 1 2 3 while the shear zone component does not, the effect is that both the Wk=0 Wk=0.75 Wk=1 walls and the shear zone lengthen during deformation. This situation α= α=90° corresponds in principle to the concept of stretching faults of Means 42° (1989, 1990), except that the stretching fault is replaced by a subsimple α=0° shear zone, forming a stretching shear zone. There are many different cases of stretching shear zones, depending on the coaxiality of the shear zone and the nature of the boundaries to its wall rock, but Fig. 10 shows (d) ISA 3 the principle for the case of conservation of continuity (completely ISA 1 ISA 1 ductile case; Fig. 10b) and a ductile-brittle case where a stretching fault ISA 1 occurs between an undeformed lower wall and the stretching shear zone (Fig. 10c). The concept of stretching shear zones has been applied θ= 45° ISA 3 θ= 24° θ=0° to spreading nappes and large-scale midcrustal flow during orogeny (e.g., Northrup, 1996; Law et al., 2004; Godin et al., 2006). Fig. 8. a) The orientation of the ISA (Instantaneous stretching axes) in a shear zone with θ α It should be noted that compactional simple shear (Fig. 6), defined by progressive vein formation. b) The orientations of and for various Wk values. c) The the matrix particle paths and orientations of flow apophyses (α) illustrated for three cases of plane strain. d) Illustration of the orientations of the ISA for the same cases. Fields of instantaneous extension are shown in black, while those of instantaneous contraction are ⎡1Γ⎤ 1Γ D = = ⎡ ⎤ shown in white. ⎣0kz⎦ ⎣01+ Δ⎦ (13) also produces Wk values different from 1, and can be estimated if both closer to 1 for higher shear strains. Hence, the effect of compaction on γ Δ shear strain ( ) and dilation ( ) are known (note that compaction is Wk is small in most high-strain zones. negative dilation): γ 3.3. 3D strain zones Wk = 2ln(1++ Δ)22 γ (14) Fabric and strain estimates from many shear zones show deviations

Hence, if compaction is significant, its effect on Wk, strain and fabric from not only simple shear but also plane strain in general (e.g., should be considered. In most shear zones in magmatic and meta- Hossack, 1968; Hageskov, 1985; Bhattacharyya and Hudleston, 2001; morphic rocks (excluding slates and phyllites), compaction is limited, Wells, 2001; Vitale and Mazzoli, 2009, 2010). This is shown in Fig. 11, and so is its effect on Wk. For example, if compaction generates a 20% where strain data from a variety of shear zone worldwide have been reduction in thickness (i.e., Δ = −0.2 and 1 + Δ = 0.8) over a shear compiled. Hence, for some shear zones strain must be treated in 3D. 3D strain of 2, the kinematic vorticity number Wk = 0.988, and gets even strain situations can be complex, and a general treatment of this subject

439 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

(a)

No strain

(b) 1 234 56 2

Pure shear 1

Stretching shear zone Pure shear (Wk=0.82) 1 234 56 (c) 2

1 Stretching Stretching fault shear zone No strain (Wk=0.82)

1 23456

Fig. 10. Schematic illustration of the concept of stretching fault and stretching shear zone. A grid with a crossing marker (a) is deformed so that the upper and lower layers (walls) deform by pure shear, and the middle layer (shear zone) by subsimple shear (Wk = 0.82 in this example) (b). In b), strain compatibility is preserved, and there is no discrete offset (the deformation is ductile). In c) the lower wall remains undeformed so Fig. 9. Statistical distribution of Wk estimates from a variety of sources, showing that that a stretching fault develops between the lower and middle layer. Note how the dis- even though simple shear deformation is recorded, subsimple shear with Wk close to 0.7 placement along this fault increases rapidly to the right. appears to be more common. Data from Bailey et al. (1994), Klepeis et al. (1999), Wallis (1992), Holcombe and Little (2001), Law et al. (2004, 2010), Xypolias and Kokklas (2006), Thigpen et al. (2010a,b), and Zhang and Teyssier (2013). In terms of strain, transpression/transtension develops non-plane strain that, for the Sanderson and Marchini model, is constrictional for is not possible here. However, a type of 3D deformation that has been transtension and flattening for transpression. Furthermore, constant Wk receiving much attention over the last decades is transpression/trans- transpression/transtension generates paths within the Flinn diagram tension, particularly since Sanderson and Marchini (1984) outlined a where the strain geometry (Flinn k-value, or degree of constriction or simple model that formed the basis for more in-depth exploration of this flattening) changes during deformation. L or L > S tectonites char- spectrum of deformation (e.g., Fossen and Tikoff, 1993; Robin and acterize transtension, with the lineation being oblique to the shear di- Cruden, 1994; Tikoff and Teyssier, 1994; Jones and Tanner, 1995; rection. In contrast to simple shear, the stretching lineation evolving Jones et al., 2004). The model is typically portrayed in the context of a during transtension will not rotate toward parallelism with the shear vertical shear zone, but is equally applicable to shear zones with other direction, but toward the flow apophysis that is oblique to the shear orientations, such as the horizontal shear zone portrayed in Fig. 12c, direction by an angle α. This angle also relates to Wk through Eq. (10), provided that the pure shear component acts orthogonal to the shear or to the simple and pure shear components through the equation zone. −1 The Sanderson and Marchini model involves an orthogonal combi- αtan[(lnk)γ]= (15) nation of simple and pure shear, as opposed to the case of subsimple shear (Fig. 12b) where the two components are applied in the same where k is the coaxial strain factor across the zone (> 1 for transten- plane. This produces strain along all three principal strain axes; trans- sion). pression if the pure shear component causes the zone to thin, and The lineation is less pronounced in the case of transpression, which transtension if the zone thickens. The model, in its simplest form, is one produces S > L or S-tectonites and strains in the lower part of the Flinn of homogeneous deformation between discontinuous boundaries, but diagram. However, the stretching lineation and the major principal the deforming volume can be subdivided into several smaller volumes strain axis X are perpendicular to the shear direction and parallel to the of homogeneous deformation (3 tabular volumes shown in Fig. 12c) or shear zone for Wk < 0.81, while for higher values of Wk it is generally even treated in terms of continuous deformation (Robin and Cruden, oblique to the shear direction and the shear zone. In the latter case X 1994). More general models can be constructed (Jones et al., 2004; and Y may change positions for Wk close to 0.81, but the lineation is Fossen and Tikoff, 1998), for instance with the simple shear plane being very weak in such cases. fl inclined with respect to the pure shear axes (Jones and Holdsworth, A model (Fig. 12d) where general attening rather than 2D pure 1998) (triclinic transpression), but many fundamental aspects of shear is combined with simple shear has also been suggested (e.g., Baird transpression and transtension in terms of strain and fabric develop- and Hudleston, 2007), and represents a spectrum of deformation be- ment are captured by the much simpler Sanderson and Marchini (1984) tween the Sanderson and Marchini transpression model and subsimple model, which is emphasized here. shear. An application of this model can be found in the context of shearing during gravity collapse (e.g., Merle, 1989).

440 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

ﬀ 100 Fig. 11. Strain data from shear zones from a range of di erent settings and lithologies, plotted in the Flinn diagram, showing that strain in general is non-plane. Data from Hossack (1968), Kligﬁeld et al. (1981), Simpson (1981), Choukroune and Gapais (1983), Davidson (1983), Lisle (1984), Gapais et al. (1987), James et al. Constriction (1989), Bailey et al. (1994), Bhattacharyya (2000), Wells (2001), Campanha and Sadowski (2002), Strine and Wojtal (2004), and Vitale and Mazzoli (2010).

k=1 (plane strain)

X/Y

Flattening

1 10 100 Y/Z Vitale & Mazzoli 2010 Granitoid, Italian Alps Vitale & Mazzoli 2010, foliation/fabrics Gapais et al. 1987 Xenoliths St Cast Granite Strine & Wojtal 2004 Grain shape data, Moine thrust Gapais et al. 1987 Xenoliths Granite Kligfield et al. 1981, reduct. spots, marble breccia Gapais et al. 1987 Xen Gotthard Granite Lisle 1984 Qtz conglomerate, thrust Choukroune & Gapais 1983 Xen Aar granite James et al 1989, feldspar aggregates, Australia Simpson 1981, Alps Hossack 1968 Qtz conglomerate, Caledonian thrust Simpson 1981 Granite, Alps Bhattacharyya 2000 Fsp aggregates, Seve Nappe Davidson 1983, granitic, feldspar grains Campanha & Sadowski 2002, grain shape, Ribeira Bailey et al. 1994 Granitic, Q/F, Blue Ridge Wells 2001, Elba Quartzite, Raft River Detachment

4. Shear zone initiation fractures can form immediately prior to plastic shearing, including in the tip region of shear zones as part of a continuous process that re- All rocks contain micro- to macroscale flaws or anisotropies that, presents a strain-controlled brittle-plastic transition. depending on their orientation and relative strength or viscosity, may In all cases where fractures act as shear zone precursors, fluids are or may not serve as nucleation points and guide shear zones as they thought to play an important role in the localization of plastic de- grow. In what appears to be homogeneous magmatic rocks in outcrop formation. Fractures are well known to be the main pathway for fluids or sample, shear zones seem to be able to form without utilizing pre- in the solid brittle crust, but are also important in the middle and lower existing macroscopic structures (Ramsay and Graham, 1970; Cobbold, crust where plastic deformation mechanisms dominate. High-tempera- 1977a,b; Poirier, 1980; Hobbs et al., 1990). This situation has been ture fracturing (> 500 °C) has been demonstrated (e.g., Goncalves explored by several authors by means of field observations (Ingles et al., et al., 2016), even for lower crustal conditions (Austrheim, 1987; Marsh 1999) and numerical and rock experimental work (Mancktelow, 2002; et al., 2011)(Fig. 5a–b). Hence, shear zone initiation may result from Mandal et al., 2004; Misra and Mandal, 2007), arguing that the pre- seismic activity, including pseudotachylite development (Austrheim sence of randomly scattered flaws represented by weak mineral phases and Boundy, 1994), even though their further development as shear are sufficient for shear zones to initiate. zones is aseismic. Once fractures create pathways for fluid flow, fluids Several other authors have found field evidence that shear zones can interact with minerals in the host rock and cause metamorphic reac- initiate on brittle fractures (Fig. 5a and f), with a transition to ductile tions that typically lead to wall softening and facilitate the transition to deformation through the activation of plastic deformation mechanisms plastic shearing. In the case shown in Fig. 5a–c, the transition is from (Segall and Simpson, 1986; Austrheim, 1987; Guermani and plagioclase-rich granulite to more hydrous eclogite. It should be noted, Pennacchioni, 1998; Pennacchioni, 2005; Pennacchioni and however, that in the case of early pseudotachylite formation, the tab- Mancktelow, 2007; Pennacchioni and Zucchi, 2013; Goncalves et al., ular geometry and fine grain-size of pseudotachylite may, regardless of 2016). Segall and Simpson (1986) interpreted such fractures to be fluid assistance, produce a surface heterogeneity that can localize formed during an earlier phase of deformation. Similarly, Mancktelow plastic deformation (e.g. Passchier, 1992; Pennacchioni and Cesare, and Pennacchioni (2005) demonstrated that the shear zones exploited 1997; Pittarello et al., 2013). Furthermore, not only fractures conduct already existing fractures, and that the fracture length controlled the fluids; evidence suggests that porosity can be created during plastic length of subsequent shear zones. In contrast, Austrheim (1987) re- deformation by grain-boundary sliding, creep cavitation, dissolution garded decimeter to meter-scale fractures to have formed during an and precipitation, giving rise to dynamic fluid flow (pumping) during early stage of shear zone development that permitted fluid-controlled deformation (Fusseis et al., 2009). weakening. Also Fusseis and Handy (2008) made the case that cm-scale In addition to the influence of fractures, shear zones preferentially

441 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

Fig. 12. Illustration of simple and subsimple (a) Simple shear (b) Subsimple shear shear (a–b, both plane strain) and two 3D deformations known as transpression (c) and a combination between simple shear and general ﬂattening (d), where material in the zone ex- trudes in all directions parallel to the zone. The shear zone (bluish color) is discretized into three homogeneously strained tabular bodies. Note that the models can be oriented in any orientation with respect to the horizontal and vertical directions. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.) Developed from Baird and Hudleston (2007).

develop along preexisting fabrics, layers, veins and dikes in ways that their central parts with displacement decreasing toward their tips depend on their rheological contrasts and orientations relative to the (Fig. 17a). Few data are available to quantify this relationship, but data regional stress ﬁeld. Typically strain is localized within weak layers or collected by Pennacchioni (2005) from outcrop-scale shear zones in structures, but can also be localized along lithologic boundaries such as granodiorite in the Adamello pluton, southern Alps, indicate that shear dike margins, which may result in paired shear zones of the type de- zone displacement distributions are quantitatively similar to those of scribed by Pennacchioni and Mancktelow (2007). faults, for which maximum displacement (Dmax) scales with length (L) (Fig. 17b) according to the expression

5. Shear zone growth n Dmax = cL , (16)

Shear zone growth is not explored to the same extent as fault where c is a constant and the exponent n is represented by a straight growth, but shear zones seem to show many of the same growth line in a log-log diagram (red lines in Fig. 17b). characteristics, at least qualitatively. Both shear zones and faults grow The Pennacchioni (2005) data define a relatively steep slope (n) in length as they accumulate displacement, although precise length when plotted in a log-log diagram (exponent ≈ 1.5, where ffi 1.56 data for shear zones are di cult to collect because they tend to connect Dmax = 0.017L )(Fig. 17b), which may suggest that displacement with other shear zones to form composite systems or networks (see accumulates fast relative to the rate of lengthening (tip propagation). below). This observation alone hints that in-plane growth from small to While the general (average) trend for faults is close to n = 1, higher larger structures purely by tip propagation is less important than exponents have been found for some fault populations (e.g., Marrett growth by linkage – a growth model that has been well established from and Allmendinger, 1991; Walsh and Watterson, 1988), which better fit studies of brittle faults (Trudgill and Cartwright, 1994; Dawers and the model where faults form by reactivation of preexisting structures Anders, 1995; Walsh et al., 2002, 2003; Soliva and Benedicto, 2004; (Walsh et al., 2002; Nicol et al., 2005). In this model, faults establish Soliva et al., 2006). A map of shear zones in a tonalitic rock from the their length at an early point and accumulate displacement with limited Alps, presented by Pennacchioni (2005) (Fig. 13), shows abundant tip propagation, resulting in a development from early flat-topped to examples of geometries consistent with growth by linkage, very similar bell-shaped displacement profiles. This development is well portrayed to structures found in brittle fault arrays. The result of such a process, in Fig. 17a, and we attribute this to the fact that these shear zone nu- when developed further, is a denser shear zone swarm such as that seen cleated on preexisting weak fractures. For a larger size range, however, in Figs. 14 and 15b, and eventually a major shear zone system at the we might expect a lower average exponent, perhaps closer to 1 as for 100 km scale, such as the Great Slave Lake shear zone (Fig. 1b) and the faults, as shown by the red lines in Fig. 17. This is because linkage will Pan-African Borborema province (Fig. 15a) and Ribeira belt (Vauchez episodically increase the length of the shear zones and cause a shift in et al., 2007; Ganade de Araujo et al., 2013). Such a schematic growth the growth path to the right in Fig. 17 (as indicated by the blue arrows evolution is envisaged in Fig. 16. in the elliptical inset figure), creating a relatively wide scatter (2–3 orders of magnitude for faults). In detail, Pennacchioni (2005) de- 5.1. Growth in length monstrates the presence of local displacement minima at stepovers and one or two cases of potential flat-topped profiles, again consistent with It is generally true that long shear zones have higher displacements growth through linkage (Peacock and Sanderson, 1991; Soliva and than short shear zones, and that they have maximum displacement near Benedicto, 2004; Fossen and Rotevatn, 2016).

442 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

Dikes

Shear zones

Quartz vein

5 m

Fig. 13. Surface map of shear zones in the Adamello tonalite, southern Alps (modiﬁed from Pennacchioni, 2005). The population shows a number of stepovers and bends (some are encircled) that indicate that they grow in length by linkage.

Fig. 14. Anastomosing system of mostly NW-SE striking shear zones in metagabbro, Archean Rainy Lake Zone, Canada. Modiﬁed from Carreras et al. (2010).

Anorthosite pods

Meta- gabbro

N 1 m

443 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

Fig. 15. Two systems of anastomosing and connecting shear zones (a) at very diﬀerent scales. a) Meter-scale anastomosing shear zone system from Cap de Creus (from Fusseis et al., 2006). b) The 100 km-scale late Proterozoic Borborema shear zone system of NE Brazil, interpreted by us from aeromagnetic data from the Brazilian Geological Survey (CPRM). Both systems show major shear zones connected by minor oblique zones, forming an S-C-style geometry. The Borborema example also has some antithetic shear components.

2 m

(b)

10 25 40

Recife

100 km

5.2. Thickness evolution

Shear zone thickness is another dimension that is influenced by strain and rheology. Considered over a large range of scales, and with a (a) considerable amount of variation, it is clear that shear zones with small offsets and lengths are thinner than larger ones, as demonstrated from Interaction the plot shown in Fig. 18 for shear zones from a variety of tectonic settings and lithologies. This relation suggests that shear zone growth involves thickening, which seems to contradict the common interpretation that shear zones strain soften as strain accumulates (see below). To explore this apparent contradiction, we will briefly review different models of shear zone growth, and discuss the importance of (b) growth by tip propagation versus growth by segment linkage.

5.3. Four reference models for shear zone thickness evolution

Several theoretical models have been proposed that relate evolution of shear zone thickness to strain and displacement accumulation (Means, 1984, 1995; Hull, 1988; Vitale and Mazzoli, 2008; Fossen, 2016). Four idealized models are presented here, each of which pro- (c) duces different displacement profiles across the zone (Fig. 19). It is emphasized that each one is idealized and should only serve as reference models. Type 1 thickens over time as strain propagates into the walls, leaving an inactive central part behind. Plateau-type displacement profiles characterize Type 1, which is different from Type 2, where strain increasingly localizes to the central part of the shear zone and a characteristic bell-type develops and evolves into a peak-type profile. Types 1 and 2 can be explained by strain hardening and weakening, respectively. Type 3 has constant active thickness (also attributable to weakening or confinement to a weak preexisting layer), while Type 4 (d) grows thicker while the whole shear zone remains active, and develops a bell-type profile that, unlike Type 2, does not grow into a peak-type profile (compare Fig. 19b and d). In practice, however, the actual shapes of the displacement profiles depend on the rate of strain hardening or softening, and on the kinematic vorticity number (Wk) (see Vitale and Mazzoli, 2008), and whether the strain is plane or three- dimensional. Fig. 16. Schematic illustration of the evolution of a shear zone network. a) Individual structures start to interact during growth. b) Some shear zones have connected to form 5.4. Weakening or hardening? more composite zones. c) All original components have linked to a continuous network. d) Network evolved to an anastomosing shear zone with lenses of less deformed protolith. The model is largely scale independent. There are several reasons why individual shear zones might behave

444 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

removal of dislocations (e.g., Shimizu, 2008). Grain boundary migration generally results in complete recrystallization and an interlobate texture with interfingering grain boundaries (e.g., Hirth and Tullis, 1992), but more straight grain boundaries within quartz ribbons and granoblastic feldspar-rich layers characterize some very high-temperature (≥700 °C) shear zones (Fig. 3d) (Hippertt et al., 2001; Passchier and Trouw, 2005). These three regimes, dominated by bulging, subgrain rotation and grain boundary migration are also known as regimes 1–3, respectively (Hirth and Tullis, 1992). The general reduction in grain size that particularly characterizes mylonitization in the low to medium-temperature regimes has itself been suggested to lead to softening (Warren and Hirth, 2006; Kilian et al., 2011; Bercovici and Ricard, 2012; Montesi, 2013; Platt, 2015). The reason is that it can promote a change in deformation mechanism from dislocation creep to diffusion creep and/or grain boundary sliding (e.g., Jiang et al., 2000; Bestmann and Prior, 2003). However, evidence that it may be of little importance has been put forward by De Bresser et al. (2001), who argue that significant weakening by grain size reduction can only occur by processes different from dynamic recrystallization, or if grain growth is inhibited by other mineral phases, such as micas. Recrystallization typically leads to the development of a preferred crystallographic orientation, which places mineral grains in orientations of easy slip and therefore weakens the rock. This effect is commonly referred to as geometric softening (e.g., Rutter et al., 2001; Ji et al., 2004; Passchier and Trouw, 2005). Metamorphic growth of weak mineral phases during shearing, such as mica growth on behalf of feldspar, is another well-known weakening factor known as reaction softening (Steffen et al., 2001; Gueydan et al., 2003; Passchier and Trouw, 2005; Oliot et al., 2010). Furthermore, hydrolytic weakening, which is caused by the introduction of water into the crystal lattice, reduces the intercrystalline rock strength, facilitates dissolution precipitation and accelerates grain boundary migration and grain boundary sliding (Chen and Argon, 1979; Kronenberg and Tullis, 1984; Hirth and Tullis, 1992; Kronenberg, 1994; Mancktelow and Pennacchioni, 2004; Finch et al., 2016). For example, “wet” quartz deforms at lower differential stresses than “dry” quartz (e.g., Hirth and Tullis, 1992; Gleason and DeSisto, 2008). Shear bands represent internal shear zone structures that involve local grain-size reduction (e.g., Viegas et al., 2016), hence the formation of shear bands in a shear zone may enhance shear zone weakening, particularly when coupled with slip on the main foliation (S) (Dennis and Secor, 1990). Shear heating may possibly increase the temperature enough to weaken the internal part of the shear zone (Brun and Cobbold, 1980), Fig. 17. a) Displacement-length data from amphibolite facies shear zones spanning from ff 3 to 21 m in length (Adamello tonalites, Italian Alps). Data from Pennacchioni (2005) and although the e ect may be limited (Platt, 2015). Finally, partial melting ff Ramsay and Allison (1979). b) Maximum displacement plotted against length for shear in migmatitic areas can create melt that has a lubricating e ect at zones shown in (a), together with data from faults and cataclastic deformation bands (see various scales (Handy et al., 2001; Cavalcante et al., 2016). Schultz and Fossen, 2002 for details). An exponential relationship (straight line re- All together, these factors generally favor shear zone softening and presenting an exponent ~1.5) is seen for the shear zones, which differs somewhat from maintenance or reduction of shear zone thickness (Type 2 and Type 3 that of faults and, especially, deformation bands. (For interpretation of the references to development: Fig. 19), while the data presented in Fig. 18 suggest that color in this figure, the reader is referred to the web version of this article.) they still manage to thicken as they develop. This apparent contradiction is similar to that of brittle faults, which have very weak fault as Type 2 and 3 zones, with no growth in thickness and with or without cores that theoretically should keep accumulating displacement localization to its central parts. One of these is dynamic recrystalliza- without thickening, but show a well-documented systematic increase in tion, i.e. recrystallization during shearing, which may change (usually thickness with increasing displacement when plotted over several or- soften) the rheological properties of the sheared rock. Considering the ders of magnitude. It is now generally accepted that fault zones grow in case of continental crust where quartz is abundant enough to control thickness due to linkage by tip interaction and coalescence (Fig. 16), as the deformation, recrystallization at relatively low temperatures typi- well as the formation of lenses and fault splays due to geometric cally occurs by bulging (important at 250–400 °C) and subgrain rotation complications along non-planar faults (Childs et al., 2009; Wibberley (~400–510 °C) (Fig. 3)(Stipp et al., 2002), leading to nucleation of et al., 2008). Shear zone evolution is in principle thought to occur in a new and smaller grains (Hirth and Tullis, 1992; Stipp and Kunze, 2007). similar way, where linkage and local complications due to geometric If recrystallization occurs by subgrain rotation, new grains have lower complications (bend in shear zone, deflection around heterogeneities) dislocation density and therefore deform at lower differential stress are important causes for shear zone widening with time. These are ty- (weakening) (Passchier and Trouw, 2005). At higher temperatures, pically temporal complications that may cause transient hardening that grain boundary migration dominates, which involves easy migration of can cause episodic widening in a generally weak shear zone. grain boundaries, grain growth and also strain softening through the Even when not considering network formation, most individual

445 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

Fig. 18. Displacement-Thickness (D-T) data extracted from ﬁeld data, 106 Jotun Nappe maps and publications in a range of magmatic and metamorphic rocks. Crosses represent thrusts, which behave diﬀerent from shear 105 Glarus Glencoul zones in general. Triangles represent shear zones in magmatic rocks that initiated from fractures. Data from Ramsay and Allison (1979), 104 Segall and Simpson (1986), Pennachioni (2005), Christiansen and Pollard (1997), Mazzolli et al. (2004) and Rosenberg and Schneider T=D/10 3 (2008). 10 T=D

102 T=10 D

Displacement (m) 10 Own estimates 1 Major thrusts Ramsay & Allison 1979 Segall & Simpson 1986 + Pennacchioni 2005 10–1 Christiansen & Pollard 1997 Vein systems (Mazzolli et al. 2004) Rosenberg & Schneider 2008 –2 10 10 10 10 1 10 10 10 10 10 –1 3 4 –2 2 5 –3 Thickness (m) faults and shear zones show evidence of thickening as they accumulate Furthermore, the walls may soften as fluids in the shear zone in- more strain and offset. For faults this can be caused by tectonic abrasion filtrate the walls, causing wall rock weakening through metamorphic of the wall rock, sometimes facilitated by bed-parallel slip (e.g., phase transformation and consequently shear zone widening (Type 1 or Watterson et al., 1998), and by geometric complications at fault bends. 4). It has been proposed that relatively high pressure within shear zones Fault core hardening by cementation is also possible. For shear zones, can effectively drive water into the hostrock, drying and thus hardening hardening can be related to by metamorphic growth of stronger mi- the shear zone core – a mechanism suggested as an explanation for the nerals, accumulation of dislocations, or dehydration or changes in deformation of km-thick ultramylonite zones (Finch et al., 2016). The formation mechanism (e.g., Oliot et al., 2010). Geometric complica- source of such fluids may be external, but fluids may also be released tions along individual shear zones can also cause local transient from hydrous minerals or during recrystallization of quartz and feldspar hardening. Such complications may be associated with relatively in the shear zone core (Mittempergher et al., 2014). competent objects of various kinds in the shear zone or locations of Finally, we would expect shear zones developing along preexisting linkage where duplexes or fold trains build up and cause widening of weak layers to be more likely to develop low D/T ratios. Thrusts typi- the zone (Woodcock and Fisher, 1986; Fossen and Rykkelid, 1990; cally form in such weak layers, of which the Glarus thrust in the Swiss Rykkelid and Fossen, 1992). Alps is an extreme example. This thrust-type shear zone involves

Fig. 19. Four different types of shear zones based on thickness and activity through time, where the black-gray fields represent active portions of the shear zone. a) Type 1, where the zone widens and leaves the central part inactive. b) Type 2 where strain localizes to the central part of the zone. c) Type 3, which maintains its thickness and is everywhere active at any given time. d) Type 4, where the zone widens and is everywhere active. Shear strain profiles, thickness-evolution, and thickness of active part of shear zone through time are shown for each case.

446 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

(1979) map, shows how similarly oriented neighboring shear zones that a c d b formed during the same deformation phase and P-T conditions in the same rock show very different thicknesses and different amounts of strain localization. It is difficult to tell what caused these differences, and more research is required to obtain a better understanding of shear zone behavior during growth. 1 m N 5.5. Shear zone arrays

Fig. 20. Foliation patterns in granite in the Maggia Nappe, Swiss Alps, revealing meter- As stated above, shear zones typically form arrays or networks. scale shear zones that show marked differences in width and strain localization. The There are two fundamentally different ways for shear zone to organize examples are selected from Plate I in Ramsay and Allison (1979). themselves into arrays. One is the kind of network consisting of anastomosing high-strain zones that together form a wider zone of shear ~50 km displacement, and localizes most of its strain to a ~1 m thick (Fig. 21a–b). The other is conjugate or polymodal shear zones that de- layer of calc-mylonite (the Lochseitenkalk) derived from a Jurassic fine volumes (lozenges) of less deformed or undeformed rocks limestone layer (Schmid, 1975). (Fig. 21d), as a parallel to conjugate sets of shear fractures or de- The Glarus thrust example displays another interesting aspect that formation bands in the brittle regime (Fig. 21c). concerns the evolution of major shear zones, namely that of changing The first category is the case where non-planar shear zones together temperature conditions. This is an important consideration for major form an anastomosing pattern of interconnected shear zone elements shear zones that develop over long geologic time periods, during which with a consistent sense of shear, hence reflecting bulk non-coaxial de- a prograde, and/or retrograde evolution may occur. Changes in tem- formation. Such shear zones form by linkage of individual shear zone perature cause changes in deformation mechanisms, which can affect elements (see above), by the formation of internally oblique shear zones the evolution of shear zone thickness. In the case of the Glarus thrust, a or shear bands, similar to smaller-scale S-C structures (e.g., Lister and reduction in temperature over time caused reworking of early high-T Snoke, 1984), and by deflection of shear around more rigid objects that fabrics by low-T shearing in the central part of the shear zone (Ebert can vary in size from porphyroclasts to large magmatic bodies. et al., 2007). A marked reduction in steady-state grain size was noted The more symmetric conjugate arrays are kinematically different from the outer high-T mylonite to the central low-T core, altogether from anastomosing shear zones in that the different sets show different suggesting that the shear zone narrowed during cooling. Eventually sense of shear, and together relate to a bulk coaxial or close to coaxial cataclasite and gouge developed along thin bands during late brittle deformation (Fig. 21b–c). Symmetric arrays are described from both shearing. This evolution is clearly consistent with Type 2 evolution magmatic and metamorphic complexes, notably from the Aar Massif of (Fig. 19), with softening possibly being related to grain-size reduction. the Alps (Choukroune and Gapais, 1983; Lamouroux et al., 1991; Returning to Fig. 18, all of the above mentioned factors contribute Wehrens et al., 2017), and large-scale symmetric networks have been to the large variation in the thickness-displacement relation exhibited postulated for the lower crust based on reflection seismic data (Reston, in this graph. They are also difficult to address because many of the 1988; Blundell, 1990; Odinsen et al., 2000; Clerc et al., 2015). weakening and hardening mechanisms can change through the de- The deformation in networks is by nature partitioned, primarily formation history or even be transient (Steffen et al., 2001; Rutter et al., between non-parallel sets of shear zones and less deformed lozenges 2001). Moreover, Fig. 18 reveals that many shear zones that appear to between these shear zones (Carreras et al., 2013). Several authors have have initiated on fractures (triangles in Fig. 18) have higher displace- claimed that the three-dimensional geometry of shear zone networks ment/thickness (D/T) ratios then the rest of the data, which is to be reflect bulk strain symmetry, in the sense that orthorhombic networks expected since they localize on thin and already weak fractures. On the reflect bulk coaxial strain while networks formed during non-coaxial contrary, vein-forming brittle-ductile shear zones (Fig. 8a) (circles in deformation develop with lower symmetry (Fig. 22)(Choukroune and Fig. 18) show low D/T ratios, because veins propagate relatively rapidly Gapais, 1983; Gapais et al., 1987; Tikoff et al., 2013). In this context, into the shear zone walls. These two groups, both of which involve a elongated lenses of undeformed rock characterize bulk constriction, brittle component of deformation, thus define the upper and lower while disk-shaped lenses reflect general flattening. However, care must boundaries of the D/T range for outcrop-scale shear zones. The re- be taken where shear zone networks form by exploitation of preexisting maining D/T data include shear zones with no evidence of associated weak heterogeneities such as fractures and dikes, in which case the brittle structures. They still show a large variation in D/T, as ex- shear zone architecture could be an inherited one. emplified by Fig. 20. This figure, extracted from Ramsay and Allison's Whereas volumes between conjugate sets of brittle shear features

(a) Non-coaxial (c) Coaxial network Fig. 21. Schematic view of a fault zone (a), composite shear zone with internal anastomosing pattern (b), con- zone jugate fault network (c) and conjugate shear zone network (d). a–b show non-coaxial strain and asymmetric struc- Brittle tures, while c–d show symmetrically arranged structures reﬂecting coaxial strain. <90° Inspired by Choukroune et al. (1987).

(b) (d)

Plastic

>90°

447 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

(a) Fig. 22. a) Interpretation of shear zone array geometry in terms R -1 of bulk strain, as illustrated in the context of the Flinn diagram. k= XY b–c) Kinematics around a lens of less deformed rock extracted R =X/Y from a conjugate (b) and anastomosing (c) shear zone array. XY RYZ-1

k=1

RYZ=Y/Z (b) (c)

Conjugate Anastomosing

(slip surfaces, deformation bands, faults) tend to be undeformed, vo- internal deformation and rotation of lozenges. The way that flow is lumes bound by sets of shear zones more easily deform internally, partitioned within shear zone network and the associated variations in which causes the angular relations between the shear zones to change Wk, strain geometry and strain magnitude is complicated and variable, (Mancktelow, 2002). In particular, the angle between sets facing the and deserves further attention. Hudleston (1999) approached this si- shortening direction may increase with progressive deformation (Mitra, tuation by constructing a simple pseudo-3D model (Fig. 23) of two sets 1979; Ramsay and Huber, 1983; Carreras et al., 2010). Hence, while the of interlinked shear zones in a volume deforming by bulk simple shear, maximum finite strain axis always bisects the acute angle between with shear along the horizontal x coordinate axis on the horizontal yx- conjugate sets in the brittle field, it bisects the obtuse angle in most plane. The prismatic lozenges between the shear zone elements remain shear zone networks. This feature is also influenced by the fact that unstrained in this model, and the resulting deformation in the shear initial conjugate shear zone sets make ~45° to the main principal stress network varies from local transpression via simple shear to transtension direction (Mancktelow, 2002) while this angle is smaller, typically (Fig. 23). Adding a distributed strain, such as pure shear to form closer to 30°, for brittle shear structures (Fig. 21). Again, however, care transpression, would add to these complications (Hudleston, 1999). should be taken that shear zone orientations may be influenced by Hudleston's simple example demonstrates how even very simple and preexisting heterogeneities (e.g., Pennacchioni and Zucchi, 2013). idealized shear zone networks generate large spatial variations in strain In general, the total strain within a heterogeneously deformed rock geometry, strain magnitude and vorticity, and that local observations volume is partitioned between the different shear zone sets and by the within shear zone network are unlikely to be representative of the bulk

Fig. 23. a) Simple shear zone network in a bulk simple shear (a) (b) framework (shearing along the coordinate x-axis with no bulk strain in the y-z plane and no internal strain in the lozenges). Con- The strain varies within the shear zone network (yellow) be- striction tween constriction, k = 1 and flattening, reflecting deviations from simple shear. b) Flinn diagram showing qualitatively dif- TT k = 1 ferent strain paths. TT = transtension, TP = transpression, X/Y TP SS SS = simple shear. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of TT SS this article.) TP Modified from Hudleston (1999).

Flattening Y/Z z x y

448 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455 deformation of the system. Natural networks would have non-planar 6.3. Veins and dikes shear zone elements defining more complex and irregular geometries, with correspondingly less predictable variations in strain and coaxi- Veins and dikes with different orientations shorten (buckle) or ality. Both field observations from well-exposed shear zone arrays lengthen (boudinage) according to Wk and strain, and thus represent (Ramsay and Allison, 1979; Choukroune and Gapais, 1983; Carreras, another source of information about vorticity, provided that they can be 2001; Fusseis et al., 2006; Carreras et al., 2010; Pennacchioni, 2005) treated as passive markers (calcite veins in carbonate rock, quartz veins and numerical modeling (Mancktelow, 2002) are called for to further in quartzite, granitic dikes in granite, etc.; Talbot, 1970; Hutton, 1982; explore the distribution of strain and variations in vorticity in shear Passchier, 1986). Line directions showing finite extension (e), con- zone arrays for different bulk strain conditions. traction (c), and contraction followed by extension (c,e) are then plotted in order to constrain the respective sectors (Fig. 24) (note that

6. Estimating the kinematic vorticity number (Wk) from sheared extension followed by contraction (e,c) is not possible during steady- rocks state deformation, and indicates non-steady-state flow or polyphase deformation). Regardless of the type of deformation, the c,e sectors The non-coaxiality of shear zones is expressed by the kinematic increase in size with increasing strain as the boundary between the c,e fi vorticity number Wk (Means et al., 1980) and can, given some as- and e elds rotate during extension (Fig. 25). For pure shear, there are sumptions and simplifications, be estimated from naturally deformed two c,e sectors of identical range, while there is only one for simple rocks in several ways (Xypolias, 2010). Vorticity analysis is based on shear (Fig. 25). For subsimple shear the two c,e sectors are of different information about progressive deformation or flow parameters, i.e. sizes, but proportionally constant as they grow during strain accumu- fl incremental strain, instantaneous stretching axes (ISA), and flow apo- lation. This proportion re ects Wk, which can be found by means of the physis, and in this context the rotation patterns defined by line and Mohr construction for strain, as outlined in Passchier (1990) and em- plane structures during deformation (Fig. 24). Clearly these are para- ployed by several authors (e.g., Passchier and Urai, 1988; Wallis, 1992; meters that may be challenging to extract from naturally deformed Short and Johnson, 2006). The method requires dikes or veins with a rocks. The most common assumption is that of subsimple shear, i.e. wide range of orientations to work. plane strain. The other is that of steady-state deformation, or that the estimated Wk value represents an average Wk over the deformation 6.4. Porphyroclast systems interval during which the applied structure or fabric formed. In addition, constant volume is commonly assumed, which will, for simplicity, Many studies of vorticity involve porphyroclasts and porphyroblasts also be assumed in the following. and their rotation patterns. These methods assume perfect coupling (no slip) between clast and matrix, no clast interference, 2D clast shapes

6.1. Foliation (RXY-θ method) Subsimple shear

The simplest approach is to use the orientation of the foliation that Pure shear Wk=0.81 Simple shear traces the X-Y plane of the strain ellipsoid. The initiation angle θ of this foliation with the shear zone is 45° for simple shear (foliation visible at ISA slightly lower angles), but for shear that involves thinning across the 1 ISA shear zone, the angle is lower (Fig. 7). Similarly, thickening shear zones c c 1 c θ ISA e 27.2° e have higher values (Fig. 7). The relationship between and Wk is e e 1 e shown graphically in Fig. 8, and for plane strain the relation is: e c c c Wk =−cos(90 2θ) (17) c,e c,e c,e c,e 6.2. Vein tips c c c c,e e e e e The relationship shown in Eq. (17) can also be used for the orientation of synkinematic veins or vein tips in vein systems (brittle- ductile shear zones). Veins initiate at 45° (θ = 45°) to the shear zone boundary in simple shear zones, and incipient vein or vein tip or- θ ientation can be used to constrain and therefore Wk, as shown in c,e c c,e c c,e c c,e Fig. 8. c,e e e e e

Strain ellipse

c (contracted) c,e c c,e c c,e c,e c c,e e c,e e e e

c,e

e (extended) e Fig. 25. The evolution of fields containing passive line structures that experienced con- Fig. 24. Orientation of deformed veins that show contraction (field c), contraction, then traction and then extension (field c,e). As strain accumulates, the two fields evolve in a extension (e.g., boudinaged folds; field c,e), and only extension (field e). The combined symmetric way for pure shear, in an asymmetric way for subsimple shear, and for simple size of the c,e-fields relates to strain, while the asymmetry or relative difference in size of shear one of the field is completely collapsed. The asymmetry indicates Wk, as the ratio fi the c,e-fields characterizes Wk. For pure shear, the two c,e-fields would be equal, while for between the two elds is constant for steady-state deformations. ISA1 is the fastest in- simple shear there would be only one. Data from Wallis (1992), who estimated stantaneous stretching direction, which is 0° for pure shear, 45° for simple shear and ~27°

0.51 < Wk < 0.70. The ﬁnite strain was estimated to RXZ = 1:3.5. for the chosen subsimple shear (Wk = 0.81).

449 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

and constant Wk (i.e., steady-state) deformation (Xypolias, 2010), plane forward) depending on Wk and their shape (R) implies that the shape of strain, and that the plane of observation is the X-Z plane, i.e. perpen- their tails/wings can be used to constrain the type of flow regime. This dicular to the foliation and parallel to the stretching lineation. For is utilized in the method known as the porphyroclast hyperbolic dis- simple shear, particles will rotate permanently (round the clock) for all tribution (PHD) method, which considers tailed porphyroclasts and their realistic porphyroclast shapes, but for subsimple shear (0 < Wk < 1), aspect ratio (R), inclination (orientation), sense of rotation and por- particles with an aspect ratio above a critical aspect value (Rc) will phyroclast type. The diagram used (Fig. 27) is based on a hyperbolic net rotate into a stable position and then stay fixed (Jeffery, 1922). This (Simpson and De Paor, 1993) where the porphyroclasts are plotted with critical aspect ratio Rc relates to Wk through the relationship: respect to orientation and aspect ratio (R), the latter represented by the radius. Furthermore, each clast is indexed with respect to the type of W =−(R2 1) (R2 + 1) k c c (18) porphyroclast (σ or δ) and sense of rotation. A hyperbola is drawn so (Passchier, 1987). that one limb is asymptotic to the shear zone, while the other separates forward- and backward-rotating porphyroclasts. The hyperbola should To find Rc we plot the porphyroclast aspect ratio (R) against the fi σ– angle between the clasts long axis and the foliation as observed in the t the positions of type mantled clasts with the highest aspect ratios XZ plane (Fig. 27). This method is commonly referred to as the por- to the hyperbolic curve (Passchier and Trouw, 2005). The two limbs of fl phyroclast aspect ratio (PAR) method, and is applied in a number of re- the hyperbola are assumed to represent the two ow apophyses α cent studies (e.g., Law et al., 2004; Xypolias and Kokkalas, 2006; Forte (Fig. 27), in which case the cosine of the angle between them gives ff and Bailey, 2007; Zhang and Teyssier, 2013; Ring et al., 2015; Faleiros Wk (Eq. (10)) (strictly valid for plane strain deformations only; Tiko et al., 2016). The rotational behavior of porphyroclasts with different and Fossen, 1995). shapes also has consequences for mantled porphyroclast systems; δ- clasts are favored by rapid rotation relative to the recrystallization rate 6.5. Crystallographic fabrics and are therefore more likely to form at aspect values < Rc, whereas σ- type porphyroclasts would be better represented for clasts with Crystallographic preferred orientation (CPO) patterns of quartz can,

R>Rc, i.e. the right-hand part of Fig. 26. together with strain (RXZ), be used to constrain vorticity (Wallis, 1992, The fact that porphyroclasts rotate diﬀerently (backward or 1995; Law et al., 2013). Most methods rely on the presence of a Type 1

Fig. 26. a) Porphyroclast aspect ratio (R) plotted against their or-

ientation with respect to the macroscopic mylonitic foliation. Rc is the cutoﬀ angle that separates continuously rotating clasts from non-ro-

tating clasts, and is used to estimate Wk. Note that R is not related to strain, but to the short/long axis of the porphyroclast. Modiﬁed from Law et al. (2004). b) Illustration of aspect ratio R. c) Rotation during simple shear (consistent rotation direction). d) Rotation during subsimple shear, where some clasts rotate backwards toward the shear plane.

450 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

Wk ==sin 2θ sin 2(β + δ) (20)

R This method is referred to as the oblique grain-shape and quartz c-axis fabric method (Wallis, 1995), or simply the δ/β method (e.g., Xypolias, Forward 2010). AP 2 Experiments (Herwegh and Handy, 1996) indicate that the angle δ

in Fig. 28 is related to the flow vorticity and to the finite strain RXZ at Forward the end of the deformation. Again, assuming that this angle approx- fi Back- ward rotation imates the angle between ISA1 and the X-Y plane of the nite strain rotation ellipsoid, Wk can then be calculated from the equation (Xypolias, 2009): R c R1XZ + AP Wk = sin(2δ) 1 R1XZ − (21)

α and the method is known as the RXY/δ method in much of the current literature. R=2

3 6.7. General results and challenges

4 If we consider the growing number of Wk estimates that have been 5 extracted from deformed rocks based on the above mentioned methods, the majority of estimates range from 0.6–1, with a peak close to Fig. 27. Hyperbolic plot of porphyroclasts, where apophysis (AP1 and AP2) separate clasts Wk = 0.7. Qualitatively this makes the case that most shear zones in- of opposite rotation sense. The gray circle in the middle has radius Rc and within that volve a component of pure shear. Quantitatively we should be aware circle everything rotates constantly with the ﬂow (clockwise). Wk is the cosine to the angle between AP1 and AP2. For simple shear, there is no ﬁeld of back-rotation, α =0 that the methods mentioned above involve several assumptions and and AP2 =AP1. uncertainties, and it has been demonstrated that some methods con-

sistently give different results. For example, Wk estimates based on (Lister, 1977) cross-girdle quartz c-axis fabric, whose normal is as- quartz c-axis microfabrics tend to yield higher Wk estimates (commonly sumed to represent the shear (or flow) plane, i.e. the plane defined by close to 0.9) than the commonly used porphyroclast methods (e.g., Law the shear zone walls. Hence, the orientation of the shear plane is found et al., 2004; Sullivan, 2008; Johnson et al., 2009; Xypolias, 2009, 2010; by constructing a line perpendicular to the central segment of the fabric Stahr and Law, 2011). This could mean that some of the assumptions girdle, as shown in Fig. 28. For the RXZ/β method, the angle β between are incorrect, but could also mean that they record different portions of this plane and the foliation is utilized in a similar way to the RXY-θ the deformation history, which would suggest non-steady flow. Even if method above. Accordingly, Wk can be found from the formula Wk estimates may be quantitatively imprecise, it is interesting to note that they have been used to map variations in Wk within shear zones, 2 ⎡ −1 ⎛ 1Rtanβ− XZ ⎞⎤ for examples in Caledonian thrusts in Scotland, where quartz micro- Wk = cos tan ⎜⎟ ⎢ 1Rtanβ− ⎥ ⎣ ⎝ XZ ⎠⎦ (19) fabrics indicate an increase in non-coaxiality (Wk number) toward structurally higher levels of the Moine Thrust Zone and overlying Moine (Xypolias, 2009) by means of the Mohr circle for strain (Wallis, 1992), Nappe (Thigpen et al., 2010a,b; also see Xypolias, 2010). The fact that β θ or by using Fig. 7 by substituting for . The main challenge with this many of these spatial variations in W estimates are gradual suggests fi β k method is de ning the angle , since the central segment of c-axis that they are real, at least qualitatively. Such variations are also ex- girdles rarely are perfectly straight. pected to exist in different locations within shear zone networks, with

shear zone intersections representing anomalous areas of strain and Wk

6.6. Oblique grain-shape fabric (δ/β and RXY/δ methods) values (see Hudleston, 1999). Hence, future research on Wk should include mapping of Wk in shear zone networks at various scales. Mylonites commonly show dynamically recrystallized quartz aggregates or domains with a grain-shape fabric at an angle δ to the main 7. Discussion foliation (Fig. 28b). The quartz grain shape fabric (Si) forming the maximum angle δ with the mylonitic foliation may be taken to closely 7.1. Strain and strain variations parallel ISA1, based on the assumption that the grain has only experienced a small portion of the ﬁnite strain and therefore a negligible The role of shear zones in the crust is hard to overestimate, and even amount of rotation (Wallis, 1995). These angular relations can then be though our knowledge of such zones has advanced a lot over the last used to estimate Wk (Fig. 7): 50 years, there is a strong need to better understand the properties and

Fig. 28. a) Quartz c-axis fabric diagram, where the shear plane (a) (b) is perpendicular to the straight central girdle fragment. b) ~0.1-1 mm Angular relationships between the shear plane (horizontal), ISAmax mylonitic foliation at angle θ′ to the shear plane, and a late internal preferred orientation deﬁning a weak and late Si fabric at an angle δ to S. The shear plane in b) can be found from a). Shear plane Si ψ Foliation δ S β L S θ θ ' Shear θ≈θ'+δ≈β+δ plane

451 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

development of shear zones, from the microscale to the scale of the zone softened in its central part. Hence, it is possible that different Wk lithosphere. Simplifying the complexity of natural shear zones is ne- from different methods reflect changes in vorticity during deformation cessary, and the development from exploring shear zones in terms of (non-steady flow), simply because each method captures different simple shear, then as subsimple shear and finally non-coaxial 3D strain portions or parts of the deformation history. At the same time it should (notably transpression and transtension) has been logical and neces- be emphasized that each method is based on one or more simplifying sary. Plane strain is still widely assumed, and when considering the fact assumptions, such as plane strain, no slip along porphyroclasts, no that many or most shear zones show evidence of non-plane strain (e.g., partitioning of strain within the field of observation, correct observa- Baird and Hudleston, 2007), this assumption may clearly lead to in- tion of the shear plane orientation, etc., and it is not always easy to accurate estimates of shear strain variations, offset and Wk. Deviation justify that these conditions are fulfilled. Nevertheless, variations in Wk from plane strain is reflected by both prolate and oblate strain ellipsoid are to be expected due to changing external or internal conditions geometries, and are particularly common in shear zone networks and during shear zone evolution, for instance related to linkage of shear thrust zones. Volume loss may contribute to flattening strain (e.g., zone elements or the geometric effect of protolithic lozenges, variations

Mohanty and Ramsay, 1994), but significant volume change is not in- in rate of volume loss, etc. Fossen and Tikoff (1997) showed how Wk volved in all shear zones, and even when it is, it can be a mere addition will vary from near simple shear to gradually become more pure-shear to a general non-coaxial 3D strain (Bhattacharyya and Hudleston, dominated if the amount of strain is minimized with respect to offset 2001). Furthermore, constrictional strain formed by steady-state flow (producing a given offset with a minimum amount of strain). Other cannot be explained by plane strain and volume change unless the cases may be envisioned, but in general, perfect steady-state deforma- volume change happens parallel to the shear zone and perpendicular to tion seems unlikely, and only serves as a useful model when informa- the shear direction – a rather unlikely situation for most shear zones. tion about the deformation history is lacking. Again, detailed field- However, the possibility that non-plane strain is the result of flow based observations combined with techniques for dating local de- perturbations during progressive deformation (Holst and Fossen, 1987) formation and numerical modeling are needed to predict how and to or the superposition of deformations (Ratschbacher, 1986) should al- what extent Wk varies for different tectonic situations. ways be considered. 3D deformation creates flow of material within shear zones in all 8. Concluding remarks directions, and it is interesting, in this context, that strain geometry within shear zones and thrust zones tends to vary across the shear or Shear zones contain valuable information that can be extracted by transport direction (Strine and Wojtal, 2004), sometimes from strongly analysis of small-scale structures and with implications for larger-scale flattening to almost purely constrictional over relatively short dis- tectonics. Most of the methods available to extract this information rely tances, (e.g., Hossack, 1968; Kligfield et al., 1981; Lisle, 1984; Gapais on assumptions such as simple or subsimple shear (plane strain). et al., 1987; Holst and Fossen, 1987). An interesting question is whether Estimations of Wk (kinematic vorticity number) typically sample rela- the resulting variations in strain geometry add up to a simple total tively small portions of shear zones, sometimes on the microscopic deformation such as simple shear or simple transpression. Local thin- scale, and should therefore be used with care, as Wk may vary across ning and extrusion may be balanced by local thickening, but it is and along shear zones. However, the most challenging question to be usually difficult to obtain enough strain data from natural shear zone addressed is that of flow steadiness, i.e. to what extent deformation and networks to evaluate their total deformation. Similarly, vorticity esti- Wk change during the course of shear zone evolution. Related to this mates, which have become increasingly popular over the last two question is a need to better understand incremental strain fabrics and decades, also vary due to strain variations and partitioning, and a few rheological aspects of sheared rocks, i.e. how to read deformation his- estimates of Wk on the microscale should not automatically be con- tory out of shear zone structures and fabrics. For practical purposes we sidered representative for the shear zone as a whole. Hence, strain and need to make simplifying assumptions and models, such as subsimple

Wk are scale dependent, similar to concepts such as pure and simple shear (plane strain), but use finite strain indicators and other evidence shear. It seems clear that numerical modeling is needed to explore how to justify our assumptions. It is useful to be able to describe relative such variations may realistically occur in various tectonic settings and variations in strain and flow parameters across and between shear under different kinematic boundary conditions. zones, even if inaccurate in terms of absolute values. At the same time, numerical modeling of shear zones should be carried out to explore 7.2. Steady state or not? more complex and realistic situations, notably shear zone networks and the consequence of geometric irregularities in shear zones. One of the As always in structural geology, field-based observations are limited most important aspects of such modeling should be the relationship to the finite state of strain, and the deformation history can only be between local and bulk strain and vorticity of shear zone arrays, which assessed indirectly. Hence the question regarding steady-state de- has implications for the understanding of the larger-scale tectonic pic- formation, where the flow parameters are the same at any instant of ture. Field-based studies are still fundamentally important when ex- deformation, is both an important and a challenging one, and requires ploring shear zone evolution, but need to involve detailed micro- information about the deformation history of the shear zone. structural work and high-resolution techniques for constraining Extracting history from shear zone requires knowledge of the shear temperature, pressure, chronology and deformation mechanisms. zone evolution through time (Means, 1995) so that structures representing different increments of deformation can be identified. For Acknowledgments example, if there is evidence for shear zone thickening, then the margins will record the last part of the history. In cases where the active The authors are grateful for very helpful review comments by part of the shear zone narrows, the margins record early deformation. Giorgio Pennacchioni and an unknown reviewer. Special thanks to Furthermore, in a shear zone system, older shear zones cut by younger Katherine Cavalcante Fossen for joining our team. This work was made ones may provide information about the first part of the deformation possible by support from FAPESP projects 2015/23572-5, 2013/19061- history. Quartz microfabrics (Fig. 28) may for example only record the 0 and 2014/10146-5, and from L. Meltzers Høyskolefond. last increment, while deformed pre-existing markers (Fig. 24) record an average of the entire deformation history. Furthermore, porphyroclast References orientation will be strongly affected by the last portion of the deformation history, while the orientation of the weak initial foliation Austrheim, H., 1987. Eclogitization of lower crust granulites by fluid migration through along a shear zone margin may reflect early-stage vorticity if the shear shear zones. Earth Planet. Sci. Lett. 81, 221–232.

452 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

Austrheim, H., Boundy, T.M., 1994. Pseudotachylytes generated during seismic faulting Ebert, A., Herwegh, M., Pfiffner, A., 2007. Cooling induced strain localization in carbo- and eclogitization of the deep crust. Science 265, 82–83. http://dx.doi.org/10.1126/ nate mylonites within a large-scale shear zone (Glarus thrust, Switzerland). J. Struct. science.265.5168.82. Geol. 29, 1164–1184. Bailey, C.M., Simpson, C., De Paor, D.G., 1994. Volume loss and tectonic flattening strain Faleiros, F.M., Campanha, G.A.C., Pavan, M., Almeida, V.V., Rodrigues, S.W.O., Araújo, in granitic mylonites from the Blue Ridge province, central Appalachians. J. Struct. B.P., 2016. Short-lived polyphase deformation during crustal thickening and ex- Geol. 16, 1403–1416. humation of a collisional orogen (Ribeira Belt, Brazil). J. Struct. Geol. 93, 106–130. Baird, G.B., Hudleston, P., 2007. Modeling the influence of tectonic extrusion and volume http://dx.doi.org/10.1016/j.jsg.2016.10.006. loss on the geometry, displacement, vorticity, and strain compatibility of ductile Finch, M.A., Weinberg, R.F., Hunter, N.J.R., 2016. Water loss and the origin of thick shear zones. J. Struct. Geol. 29, 1665–1678. http://dx.doi.org/10.1016/j.jsg.2007. ultramylonites. Geology 44, 599–602. http://dx.doi.org/10.1130/G37972.1. 06.012. Flinn, D., 1962. On folding during three-dimensional progressive deformation. Q. J. Geol. Bercovici, D., Ricard, Y., 2012. Mechanisms for the generation of plate tectonics by two- Soc. Lond. 118, 385–433. phase grain damage and pinning. Phys. Earth Planet. Inter. 202–203, 27–55. http:// Flinn, D., 1979. The deformation matrix and the deformation ellipsoid. J. Struct. Geol. 1, dx.doi.org/10.1016/j.pepi.2012.05.003. 299–307. Berthé, D., Choukroune, P., Jegouzo, P., 1979. Orthogneiss, mylonite and non-coaxial Forte, A.M., Bailey, C.M., 2007. Testing the utility of the porphyroclast hyperbolic dis- deformation of granites: the example of the South Amorican Shear Zone. J. Struct. tribution method of kinematic vorticity analysis. J. Struct. Geol. 29, 983–1001. Geol. 1, 31–42. Fossen, H., 2010. Extensional tectonics in the North Atlantic Caledonides: a regional view. Bertrand, M.A., 1884. Rapports de structure des Alpes de Glarus et du bassin houiller du In: Law, R.D., Butler, R.W.H., Krabbendam, M., Strachan, R.A. (Eds.), Continental nord. Bull. Soc. Géol. Fr. 12, 318–330. Tectonics and Mountain Building: The Legacy of Peach and Horne. Geological Society Bestmann, M., Prior, D.J., 2003. Intragranular dynamic recrystallization in naturally Special Publications 335. pp. 767–793. http://dx.doi.org/10.1144/SP335.31. deformed calcite marble: diffusion accommodated grain boundary sliding as a result Fossen, H., 2016. Structural Geology, second ed. Cambridge University Press, Cambridge of subgrain rotation recrystallization. J. Struct. Geol. 25, 1597–1613. http://dx.doi. (ISBN 978-1-107-05764-7). org/10.1016/S0191-8141(03)00006-3. Fossen, H., Rotevatn, A., 2016. Fault linkage and relay structures in extensional set- Bhattacharyya, P., 2000. Shear Zones of Northern Swedish Caledonides. (Ph.D. thesis) tings—a review. Earth Sci. Rev. 154, 14–28. http://dx.doi.org/10.1016/j.earscirev. University of Minnesota. 2015.11.014. Bhattacharyya, P., Hudleston, P., 2001. Strain in ductile shear zones in the Caledonides of Fossen, H., Rykkelid, E., 1990. Shear zone structures in the Øygarden area, western northern Sweden: a three-dimensional puzzle. J. Struct. Geol. 23, 1549–1565. Norway. Tectonophysics 174, 385–397. Bird, P.C., Cartwright, J.A., Davies, T.L., 2015. Basement reactivation in the development Fossen, H., Tikoff, B., 1993. The deformation matrix for simultaneous simple shearing, of rift basins: an example of reactivated Caledonide structures in the West Orkney pure shearing, and volume change, and its application to transpression/transtension Basin. J. Geol. Soc. 172, 77–85. tectonics. J. Struct. Geol. 15, 413–422. Blundell, D., 1990. Seismic images of continental lithosphere. J. Geol. Soc. 147, 895–913. Fossen, H., Tikoff, B., 1997. Forward modeling of non-steady-state deformations and the Brun, J.P., Cobbold, P.R., 1980. Strain heating and thermal softening in continental shear “minimum strain path”. J. Struct. Geol. 19, 987–996. zones: a review. J. Struct. Geol. 2, 149–158. Fossen, H., Tikoff, B., 1998. Extended models of transpression/transtension and appli- Butler, R.W.H., Bond, C.E., Shipton, Z.K., Jones, R.R., Casey, M., 2008. Fabric anisotropy cation to tectonic settings. Geol. Soc. Spec. Publ. 135, 15–33. controls faulting in the continental crust. J. Geol. Soc. 165, 449–452. Fusseis, F., Handy, M.R., 2008. Micromechanisms of shear zone propagation at the brit- Byerlee, J.D., 1968. Brittle-ductile transition in rocks. J. Geophys. Res. 73, 4741–4750. tle–viscous transition. J. Struct. Geol. 30, 1242–1253. http://dx.doi.org/10.1016/j. Campanha, G.A.C., Sadowski, G.R., 2002. Determinações da deformação finita em rochas jsg.2008.06.005. metassedimentares da faixa Ribeira na região de Iporanga e Apiaí, SP. Rev. Bras. Fusseis, F., Handy, M.R., Schrank, C., 2006. Networking of shear zones at the brittle-to- Geosci. 32, 107–118. viscous transition (Cap de Creus, NE Spain). J. Struct. Geol. 28, 1228–1243. http:// Carreras, J., 2001. Zooming on Northern Cap de Creus shear zones. J. Struct. Geol. 23, dx.doi.org/10.1016/j.jsg.2006.03.022. 1457–1486. Fusseis, F., Regenauer-Lieb, K., Liu, J., Hough, R.M., De Carlo, F., 2009. Creep cavitation Carreras, J., Czeck, D.M., Druguet, E., Hudleston, P.J., 2010. Structure and development can establish a dynamic granular fluid pump in ductile shear zones. Nature 459, of an anastomosing network of ductile shear zones. J. Struct. Geol. 32 (5), 656–666. 974–977. http://dx.doi.org/10.1016/j.jsg.2010.03.013. Ganade de Araujo, C.E., Weinberg, R., Cordani, U., 2013. Extruding the Borborema Carreras, J., Cosgrove, J.W., Druguet, E., 2013. Strain partitioning in banded and/or Province (NE-Brazil): a two-stage Neoproterozoic collision process. Terra Nova 26, anisotropic rocks: implications for inferring tectonic regimes. J. Struct. Geol. 50, 157–168. http://dx.doi.org/10.1111/ter.12084. 7–21. http://dx.doi.org/10.1016/j.jsg.2012.12.003. Gapais, D., Bale, P., Choukroune, P., Cobbold, P.R., Mahjoub, Y., Marquer, D., 1987. Bulk Cavalcante, G.C.G., Viegas, G., Archanjo, C.J., da Silva, M.E., 2016. The influence of kinematics from shear zone patterns: some field examples. J. Struct. Geol. 9, partial melting and melt migration on the rheology of the continental crust. J. 635–646. Geodyn. 101, 186–199. http://dx.doi.org/10.1016/j.jog.2016.06.002. Geike, A., 1884. The crystalline schists of the Scottish Highlands. Nature 31, 29–31. Chen, I.W., Argon, A.S., 1979. Grain boundary and interphase boundary sliding in power Gleason, G.C., DeSisto, 2008. A natural example of crystal-plastic deformation enhancing law creep. Acta Metall. 27, 749–754. http://dx.doi.org/10.1016/0001-6160(79) the incorporation of water into quartz. Tectonophysics 446, 16–30. http://dx.doi. 90108-1. org/10.1016/j.tecto.2007.09.006. Childs, C., Manzocchi, T., Walsh, J.J., Bonson, C.G., Nicol, A., Schöpfer, M.P.J., 2009. A Godin, L., Grujic, D., Law, R.D., Searle, M.P., 2006. Channel flow, ductile extrusion and geometric model of fault zone and fault rock thickness variations. J. Struct. Geol. 31, exhumation in continental collision zones: an introduction. Geol. Soc. Spec. Publ. 117–127. http://dx.doi.org/10.1016/j.jsg.2008.08.009. 268, 1–23. http://dx.doi.org/10.1144/GSL.SP.2006.268.01.01. Choukroune, P., Gapais, D., 1983. Strain pattern in the Aar Granite (Central Alps): or- Goncalves, P., Poilvet, J.-C., Oliot, E., Trap, P., Marquer, D., 2016. How does shear zone thogneiss developed by bulk inhomogeneous flattening. J. Struct. Geol. 5, 411–418. nucleate? An example from the Suretta nappe (Swiss Eastern Alps). J. Struct. Geol. Choukroune, P., Gapais, D., Merle, O., 1987. Shear criteria and structural symmetry. J. 86, 166–180. http://dx.doi.org/10.1016/j.jsg.2016.02.015. Struc. Geol. 9, 525–530. Guermani, A., Pennacchioni, G., 1998. Brittle precursors of plastic deformation in a Christiansen, P.P., Pollard, D.D., 1997. Nucleation, growth and structural development of granite: an example from the Mont Blanc massif (Helvetic, western Alps). J. Struct. mylonitic shear zones in granitic rock. J. Struct. Geol. 19, 1159–1172. Geol. 20, 135–148. Clerc, C., Jolivet, L., Ringenbach, J.-C., 2015. Ductile extensional shear zones in the lower Gueydan, F., Leroy, Y.M., Jolivet, L., Agard, P., 2003. Analysis of continental midcrustal crust of a passive margin. Earth Planet. Sci. Lett. 431, 1–7. http://dx.doi.org/10. strain localization induced by reactionsoftening and microfracturing. J. Geophys. 1016/j.epsl.2015.08.038. Res. 108, 2064. http://dx.doi.org/10.1029/2001JB000611. Cobbold, P.R., 1977a. Description and origin of banded deformation structures. I. Hageskov, B., 1985. Constrictional deformation of the Koster dyke swarm in a ductile Regional strain, local perturbations and deformation bands. Can. J. Earth Sci. 14, sinistral shear zone, Koster islands, SW Sweden. Bull. Geol. Soc. Den. 34, 151–197. 1721–1731. Handy, M.R., Mulch, A., Rosenau, M., Rosenberg, C.L., 2001. The role of fault zones and Cobbold, P.R., 1977b. Description and origin of banded deformation structures. II. melts as agents of weakening, hardening and differentiation of the continental crust: Rheology and the growth of banded perturbations. Can. J. Earth Sci. 14, 2510–2523. a synthesis. Geol. Soc. Lond. Spec. Publ. 186, 305–332. Cobbold, P.R., Quinquis, H., 1980. Development of sheath folds in shear regions. J. Struct. Harker, A., 1885. The cause of slaty cleavage: compression v. shearing. Geol. Mag. 2, Geol. 2, 119–126. 15–17. Cottle, J.M., Larson, K.P., Kellett, D.A., 2015. How does the mid-crust accommodate Herwegh, M., Handy, M.R., 1996. The evolution of high-temperature mylonitic micro- deformation in large, hot collisional orogens? A review of recent research in the fabrics: evidence from simple shearing of a quartz analogue (norcamphor). J. Struct. Himalayan orogen. J. Struct. Geol. 78, 119–133. Geol. 18, 689–710. Coward, M.P., 1976. Strain within ductile shear zones. Tectonophysics 34, 181–197. Hippertt, J., Rocha, A., Lana, C., Egydio-Silva, M., Takeshita, T., 2001. Quartz plastic Coward, M.P., Kim, J.H., 1981. Strain within thrust sheets. Geol. Soc. Spec. Publ. 9, segregation and ribbon development in high-grade striped gneisses. J. Struct. Geol. 275–292. 23, 67–80. Davidson, D.M.J., 1983. Strain analysis of deformed granitic rocks (Helikian), Muskoka Hirth, G., Tullis, J., 1992. Dislocation creep regimes in quartz aggregates. J. Struct. Geol. District, Ontario. J. Struct. Geol. 5, 181–195. 14, 145–159. Dawers, N.H., Anders, M.H., 1995. Displacement-length scaling and fault linkage. J. Hobbs, B.E., Mülhaus, H.B., Ord, A., 1990. Instability, softening and localization of de- Struct. Geol. 17, 607–614. formation. Geol. Soc. Spec. Publ. 54, 143–165. De Bresser, J., Ter Heege, J., Spiers, C., 2001. Grain size reduction by dynamic re- Holcombe, R.J., Little, T.A., 2001. A sensitive vorticity gauge using rotated porphyro- crystallization: can it result in major rheological weakening? Int. J. Earth Sci. 90, blasts, and its application to rocks adjacent to the Alpine Fault, New Zealand. J. 28–45. Struct. Geol. 23, 979–989. Dennis, A.J., Secor, D.T., 1990. On resolving shear direction in foliated rocks deformed by Holst, T.B., Fossen, H., 1987. Strain distribution in a fold in the West Norwegian simple shear. Geol. Soc. Am. Bull. 102, 1257–1267. Caledonides. J. Struct. Geol. 9, 915–924.

453 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

Homberg, C., Schnyder, J., Roche, V., Leonardi, V., Benzaggagh, M., 2017. The brittle and Mech. 9, 95–144. ductile components of displacement along fault zones. Geol. Soc. Lond., Spec. Publ. Marrett, R., Allmendinger, R.W., 1991. Estimates of strain due to brittle faulting: sam- 439. http://dx.doi.org/10.1144/SP439.21. pling fault populations. J. Struct. Geol. 13, 735–738. Hossack, J., 1968. Pebble deformation and thrusting in the Bygdin area (Southern Marsh, J.H., Gerbi, C.C., Culshaw, N.G., Potter, J., Longstaffe, F.J., Johnson, S.E., 2011. Norway). Tectonophysics 5, 315–339. Initiation and development of the Twelve Mile Bay shear zone: the low viscosity sole Hudleston, P., 1999. Strain compatibility and shear zones: is there a problem? J. Struct. of a granulite nappe. J. Metamorph. Geol. 29, 167–191. http://dx.doi.org/10.1111/j. Geol. 21, 923–932. 1525-1314.2010.00913.x. Hull, J., 1988. Thickness-displacement relationships for deformation zones. J. Struct. Means, W.D., 1984. Shear zones of types I and II and their significance for reconstruction Geol. 4, 431–435. of rock history. Geol. Soc. Am. Abstr. 16, 50. Hutton, D.H.W., 1982. A tectonic model for the emplacement of the Main Donegal Means, W.D., 1989. Stretching faults. Geology 17, 893–896. Granite, NW Ireland. J. Geol. Soc. Lond. 139, 615–631. Means, W.D., 1990. One-dimensional kinematics of stretching faults. J. Struct. Geol. 12, Ingles, J., Lamouroux, C., Soula, J.-C., Debat, N.P., 1999. Nucleation of ductile shear 267–272. zones in a granodiorite under greenschist facies conditions, Néouvielle massif, Means, W.D., 1995. Shear zones and rock history. Tectonophysics 247, 157–160. Pyrenees, France. J. Struct. Geol. 21, 555–576. Means, W.D., Hobbs, B.E., Lister, B.E., Williams, P.F., 1980. Vorticity and non-coaxiality James, P.R., MacDonald, P., Parker, M., 1989. Strain and displacement in the Harts Range in progressive deformations. J. Struct. Geol. 2, 371–378. Detachment Zone: a structural study of the Bruna Gneiss from the western margin of Merle, O., 1989. Strain models within spreading nappes. Tectonophysics 165, 57–71. the Entia Dome, central Australia. Tectonophysics 158, 23–48. Misra, S., Mandal, N., 2007. Localization of plastic zones in rocks around rigid inclusions: Jeffery, G.B., 1922. The motion of ellipsoidal particles immersed in a viscous fluid. Proc. insights from experimental and theoretical models. J. Geophys. Res. 112, 15. R. Soc. Lond. A 102, 161–179. Mitra, G., 1979. Ductile deformation zones in Blue Ridge basement rocks and estimation Ji, S., Jiang, Z., Rybacki, E., Wirth, R., Prior, D., Xia, B., 2004. Strain softening and mi- of finite strains. Geol. Soc. Am. Bull. 90, 935–951. crostructural evolution of anorthite aggregates and quartz–anorthite layered com- Mittempergher, S., Dallai, L., Pennacchioni, G., Renard, F., Di Toro, G., 2014. Origin of posites deformed in torsion. Earth Planet. Sci. Lett. 222, 377–390. http://dx.doi.org/ hydrous fluids at seismogenic depth: constraints from natural and experimental fault 10.1016/j.epsl.2004.03.021. rocks. Earth Planet. Sci. Lett. 385, 97–109. http://dx.doi.org/10.1016/j.epsl.2013. Jiang, Z., Prior, D.J., Wheeler, J., 2000. Albite crystallographic preferred orientation and 10.027. grain misorientation distribution in a low-grade mylonite: implications for granular Mohanty, S., Ramsay, J.G., 1994. Strain partitioning in ductile shear zones: an example flow. J. Struct. Geol. 22, 1663–1674. from a Lower Pennine nappe of Switzerland. J. Struct. Geol. 16, 663–676. Johnson, S.E., Lenferink, H.J., Price, N.A., Marsh, J.H., Koons, P.O., West, D.P., Beane, R., Montesi, L., 2013. Fabric development as the key for forming ductile shear zones and 2009. Clast-based kinematic vorticity gauges: the effects of slip at matrix/clast in- enabling plate tectonics. J. Struct. Geol. 50, 254–266. http://dx.doi.org/10.1016/j. terfaces. J. Struct. Geol. 31, 1322–1339. http://dx.doi.org/10.1130/G30227A.1. jsg.2012.12.011. Jones, R.R., Holdsworth, R.E., 1998. Oblique simple shear in transpression zones. Geol. Nicol, A., Walsh, J.J., Berryman, K., Nodder, S., 2005. Growth of a normal fault by the Soc. Spec. Publ. 135, 35–40. accumulation of slip over millions of years. J. Struct. Geol. 27, 327–342. Jones, R.R., Tanner, P.W.G., 1995. Strain partitioning in transpression zones. J. Struct. Northrup, C.J., 1996. Structural expressions and tectonic implications of general non- Geol. 17, 793–802. coaxial flow in the midcrust of a collisional orogen: the northern Scandinavian Jones, R.R., Holdsworth, R.E., Clegg, P., McCaffrey, K., Travarnelli, E., 2004. Inclined Caledonides. Tectonics 15, 490–505. transpression. J. Struct. Geol. 26, 1531–1548. http://dx.doi.org/10.1016/j.jsg.2004. Odinsen, T., Christiansson, P., Gabrielsen, R.H., Faleide, J.I., Berge, A., 2000. The geo- 01.004. metries and deep structure of the northern North Sea. Geol. Soc. Spec. Publ. 167, Kilian, R., Heilbronner, R., Stunitz, H., 2011. Quartz grain size reduction in a granitoid 41–57. rock and the transition from dislocation to diffusion creep. J. Struct. Geol. 33 Oliot, E., Goncalves, P., Marquer, D., 2010. Role of plagioclase and reaction softening in a (1265–1284), 2011. http://dx.doi.org/10.1016/j.jsg.2011.08.005. metagranite shear zone at mid-crustal conditions (Gotthard Massif, Swiss Central Klepeis, K.A., Daczko, N.R., Clarke, G.L., 1999. Kinematic vorticity and tectonic sig- Alps). J. Metamorph. Geol. 28, 849–871. http://dx.doi.org/10.1111/j.1525-1314. nificance of superposed mylonites in a major lower crustal shear zone, northern 2010.00897.x. Fiordland, New Zealand. J. Struct. Geol. 21, 1385–1405. Park, P.J., 1997. Foundations of structural geology, third ed. Chapman and Hall978- Kligfield, R., Carmignani, L., Owens, W.H., 1981. Strain analysis of a Northern Apennine 0748758029. shear zone using deformed marble breccias. J. Struct. Geol. 3, 431–436. Passchier, C.W., 1986. Flow in natural shear zones - the consequences of spinning flow Kronenberg, A.K., 1994. Hydrogen speciation and chemical weakening of quartz. In: regimes. Earth Planet. Sci. Lett. 77, 70–80. Heaney, P.J., Prewitt, C.T., Heaney, P.J., Prewitt, C.T. (Eds.), Silica: Physical Passchier, C.W., 1987. Stable positions of rigid objects in non-coaxial flow - a study in Behavior, Geochemistry and Materials Applications. 29. Mineralogical Society of vorticity analysis. J. Struct. Geol. 9, 679–690. America, Reviews of Mineralogy, pp. 123–176. Passchier, C.W., 1990. Reconstruction of deformation and flow parameters from de- Kronenberg, A., Tullis, J., 1984. Flow strengths of quartz aggregates: grain size and formed vein sets. Tectonophysics 180, 185–199. pressure effects due to hydrolytic weakening. J. Geophys. Res. 89 (B6), 4281–4297. Passchier, C.W., 1992. Pseudotachylyte and the development of ultramylonite bands in Lamouroux, C., Ingles, J., Debat, P., 1991. Conjugate ductile shear zones. Tectonophysics the Saint-Barthélemy Massif, French Pyrenees. J. Struct. Geol. 4, 69–79. 185, 309–323. Passchier, C.W., Trouw, R.A.J., 2005. Microtectonics, second ed. Springer, Berlin. Law, R.D., Searle, M.P., Simpson, R.L., 2004. Strain, deformation temperatures and Passchier, C.W., Urai, J.L., 1988. Vorticity and strain analysis using Mohr diagrams. J. vorticity of flow at the top of the Greater Himalayan Slab, Everest Massif, Tibet. J. Struct. Geol. 10, 755–763. Geol. Soc. 161, 305–320. Paterson, M.S., Wong, T.-F., 2005. Experimental Rock Deformation - The Brittle Field, Law, R.D., 2010. Moine thrust zone mylonites at the stack of glencoul: II–results of vor- second ed. Spinger-Verlag, New York. ticity analyses and their tectonic significance. In: Law, R.D., Butler, R.W.H., Peach, B.N., Horne, J., Gunn, W., Clough, C.T., Hinxman, L.W., Teall, J.J.H., 1907. The Holdsworth, R.E., Krabbendam, M., Strachan, R.A. (Eds.), Continental tectonics and geological structure of the NW Highlands of Scotland. Geol. Surv. Great Brit. Mem mountain building: the legacy of peach and horne. Geol. Soc. Spec. Pub. 335. pp. (668 pp.). 579–602. http://dx.doi.org/10.1144/SP335.23. Peacock, D.C.P., Sanderson, D.J., 1991. Displacements, segment linkage and relay ramps Law, R.D., Stahr, D.W., Francsis, M.K., Ashley, K.T., Grasemann, B., Ahmad, T., 2013. in normal fault zones. J. Struct. Geol. 13, 721–733. Deformation temperatures and flow vorticities near the base of the Greater Pennacchioni, G., 2005. Control of the geometry of precursor brittle structures on the type Himalayan Series, Sutlej Valley and Shimla Klippe, NW India. J. Struct. Geol. 54, of ductile shear zone in the Adamello tonalites, Southern Alps (Italy). J. Struct. Geol. 21–53. 27, 627–644. http://dx.doi.org/10.1016/j.jsg.2004.11.008. Lisle, J., 1984. Strain discontinuities within the Seve-Köli Nappe Complex, Scandinavian Pennacchioni, G., Cesare, B., 1997. Ductile-brittle transition in pre-Alpine amphibolite Caledonides. J. Struct. Geol. 6, 101–110. facies mylonites during evolution from water-present to water-deficient conditions Lister, G.S., 1977. Discussion: cross-girdle c-axis fabrics in quartzites plastically deformed (Mont Mary nappe, Italian Western Alps). J. Metamorph. Geol. 15, 777–791. by plane strain and progressive simple shear. Tectonophysics 39, 51–54. Pennacchioni, G., Mancktelow, N.S., 2007. Nucleation and initial growth of a shear zone Lister, G.S., Snoke, A.W., 1984. S-C mylonites. J. Struct. Geol. 6, 617–638. network within compositionally and structurally heterogeneous granitoids under Lister, G.S., Williams, P.F., 1979. Fabric development in shear zones: theoretical controls amphibolite facies conditions. J. Struct. Geol. 29, 1757–1780. http://dx.doi.org/10. and observed phenomena. J. Struct. Geol. 1, 283–297. 1016/j.jsg.2007.06.002. Malvern, L., 1969. Introduction to the Mechanics of a Continuous Medium. Prentice-Hall, Pennacchioni, G., Zucchi, E., 2013. High temperature fracturing and ductile deformation Englewood Cliffs, N.J. during cooling of a pluton: the Lake Edison granodiorite (Sierra Nevada batholith, Mancktelow, N.S., 2002. Finite-element modelling of shear zone development in vis- California). J. Struct. Geol. 50, 54–81. http://dx.doi.org/10.1016/j.jsg.2012.06.001. coelastic materials and its implications for localisation of partial melting. J. Struct. Phillips, T.B., Jackson, C.A.L., Bell, R.E., Duffy, O.B., Fossen, H., 2016. Reactivation of Geol. 24, 1045–1053. intrabasement structures during rifting: a case study from offshore southern Norway. Mancktelow, N., Pennacchioni, G., 2004. The influence of grain boundary fluids on the J. Struct. Geol. 91, 54–73. http://dx.doi.org/10.1016/j.jsg.2016.08.008. microstructure of quartz-feldspar mylonites. J. Struct. Geol. 26, 47–69. http://dx.doi. Pittarello, L., Pennacchioni, G., Di Toro, G., 2013. Amphibolite-facies pseudotachylytes in org/10.1016/S0191-8141(03)00081-6. Premosello metagabbro and felsic mylonites (Ivrea Zone, Italy). Tectonophysics 580, Mancktelow, N.S., Pennacchioni, G., 2005. The control of precursor brittle fracture and 43–57. http://dx.doi.org/10.1016/j.tecto.2012.08.001. fluid–rock interaction on the development of single and paired ductile shear zones. J. Platt, J.P., 1983. Progressive refolding in ductile shear zones. J. Struct. Geol. 5, 619–622. Struct. Geol. 27, 645–661. http://dx.doi.org/10.1016/j.jsg.2004.12.001. Platt, J.P., 2015. Influence of shear heating on microstructurally defined plate boundary Mandal, N., Misra, S., Samanta, S.K., 2004. Role of weak flaws in nucleation of shear shear zones. J. Struct. Geol. 79, 80–89. http://dx.doi.org/10.1016/j.jsg.2015.07.009. zones: an experimental and theoretical study. J. Struct. Geol. 26, 1391–1400. http:// van der Pluijm, B., Marshak, S., 2004. Earth Structure. An Introduction to Structural dx.doi.org/10.1016/j.jsg.2004.01.001. Geology and Tectonics, second ed. WW Norton & Company. Mandl, G., DeJong, L.N.J., Maltha, A., 1977. Shear zones in granular material. Rock Poirier, J.P., 1980. Shear localization and shear instability in materials in the ductile field.

454 H. Fossen, G.C.G. Cavalcante Earth-Science Reviews 171 (2017) 434–455

J. Struct. Geol. 2, 135–142. Scotland: implications for the kinematic and structural evolution of the northernmost Powell, D., Glendinning, N.R.W., 1990. Late Caledonian extensional reactivation of a Moine Thrust zone. Geol. Soc. Lond., Spec. Publ. 335, 623–662. http://dx.doi.org/10. ductile thrust in NW Scotland. J. Geol. Soc. Lond. 147, 979–987. 1016/j.jsg.2010.05.001. Ramberg, H., 1975a. Particle paths, displacement and progressive strain applicable to Thigpen, J.R., Law, R.D., Lloyd, G.E., Brown, S.J., 2010b. Deformation temperatures, rocks. Tectonophysics 28, 1–37. vorticity of flow, and strain in the Moine thrust zone and Moine nappe: reassessing Ramberg, H., 1975b. Superposition of homogeneous strain and progressive deformation the tectonic evolution of the Scandian foreland–hinterland transition zone. J. Struct. in rocks. Bull. Geol. Inst. Univ. Uppsala 6, 35–67. Geol. 32, 920–940. http://dx.doi.org/10.1016/j.jsg.2010.05.001. Ramsay, J.G., 1967. Folding and Fracturing of Rocks. McGraw-Hill, New York. Tikoff, B., Fossen, H., 1993. Simultaneous pure and simple shear: the unified deformation Ramsay, J.G., 1980. Shear zone geometry: a review. J. Struct. Geol. 2, 83–99. matrix. Tectonophysics 217, 267–283. Ramsay, J.G., Allison, I., 1979. Structural analysis of shear zones in an alpinised Tikoff, B., Fossen, H., 1995. The limitations of three-dimensional kinematic vorticity Hercynian granite. Schweiz. Mineral. Petrogr. Mitt. 59, 251–279. analysis. J. Struct. Geol. 17, 1771–1784. Ramsay, J.G., Graham, R.H., 1970. Strain variation in shear belts. Can. J. Earth Sci. 7, Tikoff, B., Teyssier, C.T., 1994. Strain modeling of displacement-field partitioning in 786–813. transpressional orogens. J. Struct. Geol. 16, 1575–1588. Ramsay, J.G., Huber, M.I., 1983. The Techniques of Modern Structural Geology: Strain Tikoff, B., Blenkinsop, T.G., Kruckenberg, S.C., Morgan, S., Newman, J., Wojtal, S.F., Analysis. 1 Academic Press, London (307 pp.). 2013. A perspective on the emergence of modern structural geology: celebrating the Ramsay, J.G., Woods, D.S., 1973. The geometric effects of volume change during de- feedbacks between historical-based and process-based approaches. Geol. Soc. Am. formation processes. Tectonophysics 16, 263–277. Spec. Pap. 500, 65–119. http://dx.doi.org/10.1130/2013.2500(03). Ratschbacher, L., 1986. Kinematics of Austro-Alpine cover nappes: changing translation Törnebohm, A.E., 1888. Om Fjallproblemet. Geol. Fören. Stockh. Förh. 10, 328–336. path due to transpression. Tectonophysics 125, 335–356. Trudgill, B., Cartwright, J., 1994. Relay-ramp forms and normal-fault linkages, Reston, T.J., 1988. Evidence for shear zones in the lower crust offshore Britain. Tectonics Canyonlands National Park, Utah. Geol. Soc. Am. Bull. 106, 1143–1157. 7, 929–945. Tullis, J., Snoke, A.W., Todd, V.R., 1982. Significance and petrogenesis of mylonitic rocks. Reusch, H., 1888. Bømmeløen og Karmøen med omgivelser. Kristiania (Oslo). Geology 10, 227–230. Ring, U., Bernet, M., Tulloch, A., 2015. Kinematic, finite strain and vorticity analysis of Twiss, R.J., Moores, E.M., 2007. Structural Geology. H.W. Freeman and Company the Sisters Shear Zone, Stewart Island, New Zealand. J. Struct. Geol. 73, 114–129. (736 pp.). http://dx.doi.org/10.1016/j.jsg.2015.02.004. Vauchez, A., Egydio-Silva, M., Babinski, M., Tommasi, A., Uhlein, A., Liu, D., 2007. Robin, P.-Y.F., Cruden, A.R., 1994. Strain and vorticity patterns in ideally ductile trans- Deformation of a pervasively molten middle crust: insights from the Neoproterozoic pression zones. J. Struct. Geol. 16, 447–466. Ribeira-Araçuai orogen (SE Brazil). Terra Nova 19, 278–286. http://dx.doi.org/10. Rutter, E.H., 1986. On the nomenclature of mode of failure transitions in rocks. 1111/j.1365-3121.2007.00747.x. Tectonophysics 122, 381–387. Vauchez, A., Tommasi, A., Mainprice, D., 2012. Faults (shear zones) in the Earth's mantle. Rutter, E.H., Holdsworth, R.E., Knipe, R., 2001. The nature and tectonic significance of Tectonophysics 558–1559, –27. http://dx.doi.org/10.1016/j.tecto.2012.06.006. fault-zone weakening: an introduction. Geol. Soc. Lond. Spec. Publ. 186, 1–11. Viegas, G., Menegon, L., Archanjo, C., 2016. Brittle grain-size reduction of feldspar, phase Rykkelid, E., Fossen, H., 1992. Composite fabrics in mid-crustal gneisses: observations mixing and strain localization in granitoids at mid-crustal conditions (Pernambuco from the Øygarden Complex, West Norway Caledonides. J. Struct. Geol. 14, 1–9. shear zone, NE Brazil). Solid Earth 7, 1–22. http://dx.doi.org/10.5194/se-7-1-2016. Sanderson, D., Marchini, R.D., 1984. Transpression. J. Struct. Geol. 6, 449–458. Vitale, S., Mazzoli, S., 2008. Heterogeneous shear zone evolution: the role of shear strain Schmid, D.W., 1975. The Glarus overthrust: field evidence and mechanical model. Geol. hardening/softening. J. Struct. Geol. 30 (11), 1383–1395. http://dx.doi.org/10. Helv. 68, 247–280. 1016/j.jsg.2008.07.006. Scholz, C.H., 1988. The brittle-plastic transition and the depth of seismic faulting. Geol. Vitale, S., Mazzoli, S., 2009. Finite strain analysis of a natural ductile shear zone in Rundsch. 77, 319–328. limestones: insights into 3-D coaxial vs. non-coaxial deformation partitioning. J. Schultz, R.A., Fossen, H., 2002. Displacement-length scaling in three dimensions: the Struct. Geol. 31 (1), 104–113. http://dx.doi.org/10.1016/j.jsg.2014.09.010. importance of aspect ratio and application to deformation bands. J. Struct. Geol. 24, Vitale, S., Mazzoli, S., 2010. Strain analysis of heterogeneous ductile shear zones based on 1389–1411. the attitudes of planar markers. J. Struct. Geol. 32, 321–329. http://dx.doi.org/10. Segall, P., Simpson, C., 1986. Nucleation of ductile shear zones on dilatant fractures. 1016/j.jsg.2010.01.002. Geology 14, 56–59. Vollmer, F.W., 1988. A computer model of sheath-nappes formed during crustal shear in Shimizu, I., 2008. Theories and applicability of grain size piezometers: the role of dy- the Western Gneiss Region, central Norwegian Caledonides. J. Struct. Geol. 10, namic recrystallization mechanisms. J. Struct. Geol. 30, 899–917. http://dx.doi.org/ 735–745. 10.1016/j.jsg.2008.03.004. Wallis, S.R., 1992. Vorticity analysis in a metachert from the Sanbagawa Belt, SW Japan. Short, H.A., Johnson, S.E., 2006. Estimation of vorticity from fibrous calcite veins, central J. Struct. Geol. 12, 271–280. Maine, USA. J. Struct. Geol. 28, 1167–1182. http://dx.doi.org/10.1016/j.jsg.2006. Wallis, S., 1995. Vorticity analysis and recognition of ductile extension in the Sanbagawa 03.024. belt, SW Japan. J. Struct. Geol. 17, 1077–1093. Sibson, R.H., 1977. Fault rocks and fault mechanisms. J. Geol. Soc. Lond. 133, 191–213. Walsh, J.J., Watterson, J., 1988. Analysis of the relationship between displacements and Simpson, C., 1981. Ductile Shear Zones: A Mechanism of Rock Deformation in the dimensions of faults. J. Struct. Geol. 10, 239–247. Orthogneisses of the Maggia Nappe, Ticino. (Ph.D. thesis) ETH Zurich. Walsh, J.J., Nicol, A., Childs, C., 2002. An alternative model for the growth of faults. J. Simpson, C., De Paor, D.G., 1993. Strain and kinematic analysis in general shear zones. J. Struct. Geol. 24, 1669–1675. Struct. Geol. 15, 1–20. Walsh, J.J., Bailey, W.R., Childs, C., Nicol, A., Bonson, C.G., 2003. Formation of seg- Snyder, D.B., Kjarsgaard, B.A., 2013. Mantle roots of major Precambrian shear zones mented normal faults: a 3-D perspective. J. Struct. Geol. 25, 1251–1262. inferred from structure of the Great Slave Lake shear zone, northwest Canada. Warren, J., Hirth, G., 2006. Grain size sensitive deformation mechanisms in naturally Lithosphere 5, 539–546. http://dx.doi.org/10.1130/L299.1. deformed peridotites. Earth Planet. Sci. Lett. 248, 438–450. Soliva, R., Benedicto, A., 2004. A linkage criterion for segmented normal faults. J. Struct. Watterson, J., Childs, C., Walsh, J.J., 1998. Widening of fault zones by erosion of aspe- Geol. 26, 2251–2267. http://dx.doi.org/10.1016/j.jsg.2004.06.008. rities formed by bed-parallel slip. Geology 26, 71–74. Soliva, R., Benedicto, A., Maerten, L., 2006. Spacing and linkage of confined normal Wehrens, P., Baumberger, R., Berger, A., Herwegh, M., 2017. How is strain localized in a faults: importance of mechanical thickness. J. Geophys. Res. 111 (B1). http://dx.doi. meta-granitoid, mid-crustal basement section? Spatial distribution of deformation in org/10.1029/2004JB003507. the central Aar massif (Switzerland). J. Struct. Geol. 94, 47–67. Stahr, D.W., Law, R.D., 2011. Effect of finite strain on clast-based vorticity gauges. J. Wells, M.L., 2001. Rheological control on the initial geometry of the Raft River detach- Struct. Geol. 33, 1178–1192. http://dx.doi.org/10.1016/j.jsg.2011.05.002. ment fault and shear zone, western United States. Tectonics 20, 435–457. Steffen, K., Selverstone, J., Brearley, A., 2001. Episodic weakening and strengthening Wernicke, B., 1985. Uniform-sense normal simple shear of the continental lithosphere. during synmetamorphic deformation in a deep-crustal shear zone in the Alps. Geol. Can. J. Earth Sci. 22, 108–125. Soc. Lond. Spec. Publ. 186, 141–156. Wibberley, C.A.J., Yielding, G., Di Toro, G., 2008. Recent advances in the understanding Stipp, M., Kunze, K., 2007. Dynamic recrystallization near the brittle-plastic transition in of fault zone internal structure: a review. Geol. Soc. Spec. Publ. 299, 5–33. http://dx. naturally and experimentally deformed quartz aggregates. Tectonophysics 448, doi.org/10.1144/SP299.2. 77–97. http://dx.doi.org/10.1016/j.tecto.2007.11.041. Wong, T.-f., Baud, P., 2012. The brittle-ductile transition in porous rock: a review. J. Stipp, M., Stünitz, H., Heilbron, M., Schmid, D.W., 2002. The eastern Tonale fault zone: a Struct. Geol. 44, 25–53. http://dx.doi.org/10.1016/j.jsg.2012.07.010. natural laboratory for crystal plastic deformation of quartz over a temperature range Woodcock, N.H., Fisher, M., 1986. Strike-slip duplexes. J. Struct. Geol. 7, 725–735. from 250 to 700 °C. J. Struct. Geol. 24, 1861–1884. Xypolias, P., 2009. Some new aspects of kinematic vorticity analysis in naturally de- Strine, M., Wojtal, S.F., 2004. Evidence for non-plane strain flattening along the Moine formed quartzites. J. Struct. Geol. 31, 3–10. http://dx.doi.org/10.1016/j.jsg.2008.09. thrust, Loch Srath nan Aisinnin, North-West Scotland. J. Struct. Geol. 26, 1755–1772. 009. http://dx.doi.org/10.1016/j.jsg.2004.02.011. Xypolias, P., 2010. Vorticity analysis in shear zones: a review of methods and applica- Sullivan, W.A., 2008. Significance of transport-parallel strain variations in part of the Raft tions. J. Struct. Geol. 32, 2072–2092. http://dx.doi.org/10.1016/j.jsg.2010.08.009. River shear zone, Raft River Mountains, Utah, USA. J. Struct. Geol. 30, 138–158. Xypolias, P., Kokkalas, S., 2006. Heterogeneous ductile deformation along a mid-crustal http://dx.doi.org/10.1016/j.jsg.2007.11.007. extruding shear zone: an example from the External Hellenides (Greece). Geol. Soc. Talbot, C.J., 1970. The minimum strain ellipsoid using deformed quartz veins. Spec. Publ. 268, 497–516. Tectonophysics 9, 47–76. Zhang, Q., Teyssier, C., 2013. Flow vorticity in Zhangbaling transpressional attachment Thigpen, J.R., Law, R.D., Lloyd, G.E., Brown, S.J., Cook, B., 2010a. Deformation tem- zone, SE China. J. Struct. Geol. 48, 72–84. http://dx.doi.org/10.1016/j.jsg.2012.12. peratures, vorticity of flow and strain symmetry in the Loch Eriboll mylonites, NW 006.

455