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Kinematics of Ductile Shear Zones with Deformable Or Mobile Walls

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Kinematics of Ductile Shear Zones with Deformable Or Mobile Walls J. Earth Syst. Sci. (2019) 128 218 Ó Indian Academy of Sciences https://doi.org/10.1007/s12040-019-1238-y (0123456789().,-volV)(0123456789().,-volV) Kinematics of ductile shear zones with deformable or mobile walls 1, 2 KIERAN FMULCHRONE * and SOUMYAJIT MUKHERJEE 1 Department of Applied Mathematics, School of Mathematical Sciences, University College, Cork, Ireland. 2 Department of Earth Sciences, Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra 400 076, India. *Corresponding author. e-mail: [email protected] MS received 22 May 2018; revised 21 February 2019; accepted 16 May 2019 Shear zones are important phenomena in the Earth’s middle and lower crust and are of great interest to structural geologists. Models involving rigid boundaries moving parallel to themselves are extended here to include the case where (i) walls are deformable and (ii) mobile rigid walls approach each other. These models are combined with Couette and Poiseuille flow to define a broad range of kinematic possibilities. Deformable wall models lead to smooth transitions from deformed to undeformed materials as well as with the zone transitions to gentler and more spread out deformation. Mobile walls, on the other hand, lead to shear zones where shear sense can change along a shear zone boundary. Keywords. Shear zone kinematics; rheology; structural geology; deformation mechanism; Couette flow; fluid mechanics. 1. Introduction context); (iv) Poiseuille flow: the boundaries of the shear zone remain static and an along zone pres- Ductile shear zones at different scales of observa- sure difference causes flow along the shear zone tion are intensely studied by structural geologists (figure 1d; Beaumont et al. 2001); and (v) com- because, in addition to theoretical reasons (Fossen bined simple shear and Poiseuille flow: the and Cavalcante 2017), these zones define major boundaries shear past each other along with a plate boundaries and are the loci of seismicity pressure gradient-induced fluid flow inside the zone (Regenauer-Lieb and Yuen 2003). Taking the (figure 1e; Mukherjee and Koyi 2010). Recently, simplest case of a shear zone with parallel rigid these different ductile shear mechanisms have been boundaries, several kinds of ductile shear have discussed and debated vigorously in the context of been recognised: (i) simple shear/Couette flow: extrusion of portions of large, hot orogens, such as where one or both the boundaries move parallel to the Greater Himalayan Crystallines (Appendix of themselves (figure 1a; Ramsay 1980); (ii) pure Mukherjee 2013a). At a much smaller scale, flow of shear/cream-cake model: the boundaries move partially molten material through brittle planes perpendicular to themselves (figure 1b; Mukherjee can follow a Poiseuille flow mechanism during the submitted), (iii) general shear/sub-simple shear: ductile shear process. Assuming an incompressible the boundaries move in a way that have both Newtonian rheology for material inside the shear simple- and pure shear components (figure 1c; zone, velocity profiles for simple shear through a Vannay and Grasemann (2001) in a tectonic horizontal shear zone are linear, and for all other 218 Page 2 of 11 J. Earth Syst. Sci. (2019) 128 218 Figure 1. Ductile shear kinematics. Parallel boundary cases: (a) Simple shear; (b) Pure shear; (c) General shear, (d) Poiseuille flow of a Newtonian fluid; (e) Combined simple shear and Poiseuille flow; (f) Poiseuille flow of a non-Newtonian fluid. Non- parallel boundary cases: (g) Slipping boundary; (h) Simple shear with tapering boundaries; (i) Jeffery Hamel flow of Newtonian fluid. (j) Simple shear within a circular zone. Refer to section 1: Introduction. ductile shear types referred above they look The possibility of shear zones with deformable or parabolic. For non-Newtonian rheology, Couette mobile boundaries has been recognised for some flow profile is non-specific (Hobbs 1972), and for a time (Bailey et al. 2004 and references therein) but purely Poiseuille flow bell-shaped (figure 1f; Tur- their kinematic details are not well known. For cotte and Schubert 2014). example, Lisle (2014) analysed the kinematics of Besides, these common ductile shear patterns, ductile deformation assuming the rigid boundaries. Mandal et al. (2002) analogue modelled flow kine- Flattening/pure shear of a zone with deformable matics for tapering ductile shear zones with rigid walls was analysed only by Mandal et al. (2001). walls (figure 1h). Mukherjee et al. (2012) mechan- Their kinematic analysis involves a parameter that ically modelled ductile extrusion through a shear defines the competency contrast between the shear zone that converges at depth (figure 1i). Mukherjee zone rock and its wall rock. Ductile sheared mig- and Biswas (2014, 2015) analytically modelled matites can be characterised by leucosome layers simple shear flow profile through circular horizon- defining the primary shear planes near which tal shear zones (figure 1j). Mulchrone and alternate layers of leucosomes and melanosomes Mukherjee (2016) investigated the simple shear swerve defining S-fabrics (Mukherjee 2010). The with or without Poiseuille flow for slipping occurrence of leucosome layers along C-planes boundary cases (figure 1g). indicates the syntectonic/syn-shear migmatisation J. Earth Syst. Sci. (2019) 128 218 Page 3 of 11 218 (Marchildon and Brown 2003). While undergoing (Mukherjee 2013b). In phyllites, the ratio of migmatisation, the leucosome was in a fluid stage. viscosity between mica-poor and mica-rich layers We, therefore, interpret the common observations ranges 1–2 (Bayly 1970). Except for a single esti- that such C-planes are not perfectly planar mate of viscosity (1021–1022 Pa s) for a feldspar-rich (figure 2a, b), as an indication of internal ductile rock at high temperatures (Rybacki et al. 2002), deformation of the soft fluid layer. Lloyd et al. viscosity magnitudes of ductile deforming micas, (1992) reported the deformed shear zone margins at quartz and feldspar are largely unknown. In the the grain scale from mylonites in Scotland. Zhang ductile regime, below 8–15 km depth, there is no et al. (2012) document the deformed footwall of a guarantee that the shear zone material deforms in a shear zone from Yiwulushan (China), both having ductile manner while simultaneously the surround- similar kinematic indicators. Roy Choudhury et al. ing rocks behave rigidly. (2016) documented the deformation in the footwall Mica-rich layers defining narrow shear zones of a mylonitised shear zone (Rajasthan, India). inside a quartzofeldspathic matrix are common in It will be important not to compare the present many rock types (e.g., Mukherjee 2013b), where model with cases where the shear zone boundary the shear zone boundaries are defined by preferred deformed after the ductile deformation e.g., a alignment of micas that are recognised also as C- or brittle deformed margin in a metamorphic core primary shear planes (Passchier and Trouw 2005). complex (Davis 1983). We presently neither have viscosity magnitudes Shear zone boundaries act rigidly when the ratio nor ratios of such micas and quartzofeldspathic of viscosity between the shear zone and the sur- minerals to compare whether theoretically such rounding rocks is 10-7 (Mancktelow 2008). How- mica layers can act rigidly during the shear. A ever, inside such rigid ‘‘ÁÁÁboundaries, the softer common observation, however, is that such mica rock would produce primary shear planes parallel to layers are not always perfectly straight in meso- the boundaries of the shear zones’’ (Passchier and (figure 2a–d) and micro-scales (figure 3a–d), pos- Trouw 2005). Note that we do not mean those C- sibly indicating that mica layers acted as deform- planes to act as shear zone boundaries in this paper. able boundaries of such shear zones. A similar Such C-planes to are locally found to be warped conclusion can be drawn from ductile shear zones recognised on mega-scales using the remote sensing images (Pour and Hashim 2016). C-planes are readily recognised based on sharp termination/ swerving of S-fabrics and are clearly curving in exposures and therefore must also be curvi-planar in 3D. Note that at smaller scales step-overs (of mica fish trails denoting the mylonitic foliation/C-plane: Lister and Snoke 1984) and possibly intrafolial folded C-planes indicate ductile shear of the C- plane themselves. Thus, there is a need to extend the kinematic theory of ductile shear zones to include the case of deformable and mobile bound- aries in structural geology. Figure 2. Ductile shear zones in meso-scale, with non-planar All analogue and most numerical models of shear C-plane. Reproduced from figures 1.4, 1.5, 1.49 and 2.7, zones in structural geology and tectonics tend to respectively, of Mukherjee and Biswas (2014). Blue full arrow: consider the rigid boundaries. Curviplanar margins curved C-plane. (a, b) S-fabric defined by thicker leucosome of shear zones were implicitly presumed to be pre- and thinner and close-spaced melanosome layers C-plane traces white line. Top-to-S (top-to-right) shear. Greater deformational. Curved primary ductile shear Himalayan Crystallines, Sutlej river section, Himachal Pra- planes in meso-scales (Coward 1976) and in hand desh state, India. (c) A delta structure of quartz clast. Top-to- specimens (Gapais et al. 1987) are well known. S (top-to-left up) sheared. Bhagirathi section of Greater Hyperbolic- and linear flow paths for pure and Himalayan Crystallines, India. (d) A train of intrafolial fold simple shear zones (Schlichting 1960) have also (Mukherjee and Biswas 2015) bound by C-planes. Top-to-NE down (top-to-left down) sheared. Near Karcham, Himachal been well established. However, the velocity pro- Pradesh, Sutlej river section, Greater Himalayan Crystallines, les for shear zones with deformable boundaries India. have not been explored. 218 Page 4 of 11 J. Earth Syst. Sci. (2019) 128 218 Figure 3. Ductile shear zone within mylonitized gneiss in micro-scale, with non-planar C-plane, all photomicrographs lengths are 0.24 mm.
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