Insights Into Heterogeneous Shear Zone Evolution

Ductile Shear Zones

Ductile Shear Zones From micro‐ to macro‐scales

Edited by Soumyajit Mukherjee Department of Earth Sciences, Indian Institute of Technology Bombay, Powai, Mumbai 400076, Maharashtra, India Kieran F. Mulchrone Department of Applied Mathematics, University College, Cork, Ireland This edition first published 2016 © 2016 by John Wiley & Sons, Ltd

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Library of Congress Cataloging‐in‐Publication Data Ductile shear zones: from micro- to macro-scales / edited by Soumyajit Mukherjee and Kieran F. Mulchrone. pages cm Includes bibliographical references and index. ISBN 978-1-118-84496-0 (cloth) 1. Shear zones (Geology) 2. Geology, Structural. I. mukherjee, Soumyajit, editor. II. mulchrone, Kieran F., editor. QE606.D82 2016 551.8′72–dc23 2015024896 A catalogue record for this book is available from the British Library.

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Cover image: A sigmoid-shaped muscovite fish with top-to-right ductile shear sense. Photo length: 5 mm. Under cross polarized light. Location: Karakoram range. Reproduced from fig. 3b of Mukherjee (2011). Ref: Mukherjee S. (2011) Mineral fish: their morphological classification, usefulness as shear sense indicators and genesis. International Journal of Earth Sciences 100, 1303–1314.

Set in 9.5/11.5 pt Melior by SPi Global, Pondicherry, India

1 2016 Contents

Contributors vii 8 Brittle‐ductile shear zones along inversion‐related Acknowledgments ix frontal and oblique thrust ramps: Insights from Introduction x the Central–Northern Apennines curved thrust system (Italy) 111 Paolo Pace, Fernando Calamita, Part I: Theoretical Advances and New Methods and Enrico Tavarnelli

1 From finite to incremental strain: Insights 9 Microstructural variations in quartzofeldspathic into heterogeneous shear zone evolution 3 mylonites and the problem of vorticity analysis Stefano Vitale and Stefano Mazzoli using rotating porphyroclasts in the Phulad Shear Zone, Rajasthan, India 128 2 How far does a ductile shear zone permit Sudipta Sengupta and Sadhana transpression? 14 M. Chatterjee Sujoy Dasgupta, Nibir Mandal, and Santanu Bose 10 Mineralogical, textural, and chemical reconstitution of granitic rock in ductile 3 2D model for development of steady‐state and shear zones: A study from a part of the South oblique foliations in simple shear and more Purulia Shear Zone, West Bengal, India 141 general deformations 30 Nandini Chattopadhyay, Sayan Ray, Kieran F. Mulchrone, Patrick A. Meere, Sanjoy Sanyal, and Pulak Sengupta and Dave J. McCarthy 11 Reworking of a basement–cover interface 4 Ductile deformation of single inclusions during Terrane Boundary shearing: in simple shear with a finite‐strain An example from the Khariar basin, hyperelastoviscoplastic rheology 46 Bastar craton, India 164 Christoph Eckart Schrank, Ali Karrech, Subhadip Bhadra and Saibal Gupta David Alexandre Boutelier, and Klaus Regenauer‐Lieb 12 Intrafolial folds: Review and examples from the western Indian Higher Himalaya 182 5 Biviscous horizontal simple shear zones of Soumyajit Mukherjee, Jahnavi Narayan concentric arcs (Taylor–Couette flow) with Punekar, Tanushree Mahadani, and incompressible Newtonian rheology 59 Rupsa Mukherjee Soumyajit Mukherjee and Rakesh Biswas 13 Structure and Variscan evolution of Malpica–Lamego ductile shear zone Part II: Examples from Regional Aspects (NW of Iberian Peninsula) 206 Jorge Pamplona, Benedito C. Rodrigues, 6 Quartz‐strain‐rate‐metry (QSR), an efficient Sergio Llana‐Fúnez, Pedro Pimenta tool to quantify strain localization in the Simões, Narciso Ferreira, Carlos Coke, continental crust 65 Eurico Pereira, Paulo Castro, and Emmanuelle Boutonnet and José Rodrigues Phillipe‐Hervé Leloup 14 Microstructural development in ductile 7 Thermal structure of shear zones from deformed metapelitic–metapsamitic rocks: Ti‐in‐quartz thermometry of mylonites: A case study from the greenschist to granulite Methods and example from the basal shear facies megashear zone of the Pringles zone, northern Scandinavian Caledonides 93 Metamorphic Complex, Argentina 224 Andrea M. Wolfowicz, Matthew J. Kohn, Sergio Delpino, Marina Rueda, Ivana Urraza, and Clyde J. Northrup and Bernhard Grasemann

v vi Contents

15 Strike–slip ductile shear zones in Thailand 250 17 Flanking structures as shear sense indicators Pitsanupong Kanjanapayont in the Higher Himalayan gneisses near Tato, West Siang District, Arunachal Pradesh, India 293 16 Geotectonic evolution of the Nihonkoku Tapos Kumar Goswami and Sukumar Baruah Mylonite Zone of north central Japan based on geology, geochemistry, and radiometric ages of the Nihonkoku Mylonites: Index 302 Implications for Cretaceous to Paleogene tectonics of the Japanese Islands 270 Yutaka Takahashi Contributors

Sukumar Baruah Sergio Delpino Department of Applied Geology, Dibrugarh University, INGEOSUR (CONICET‐UNS), Dibrugarh 786004, Assam, India Departamento de Geología (UNS), San Juan 670 (B8000ICN), Bahía Blanca, Argentina Subhadip Bhadra Department of Earth Sciences, Pondicherry University, Departamento de Geología, (Universidad Nacional del Sur), R.V. Nagar, Kalapet, Puducherry 605014, India Bahía Blanca, Argentina Rakesh Biswas Narciso Ferreira Geodata Processing and Interpretation Centre, Oil and Laboratório Nacional de Energia e Geologia, Rua da Natural Gas Corporation Limited, Dehradun, India Amieira, Apartado 1089, 4466 901 S. Mamede de Santanu Bose Infesta, Portugal Department of Geology, University of Calcutta, Kolkata, Tapos Kumar Goswami 700019, India Department of Applied Geology, Dibrugarh University, David Alexandre Boutelier Dibrugarh 786004, Assam, India The University of Newcastle, School of Environmental Bernhard Grasemann and Life Sciences, University Drive, Callaghan, NSW, Department of Geodynamics and Sedimentology, 2308, Australia Structural Processes Group, University of Vienna, Emmanuelle Boutonnet Austria Institute of Geosciences, Johannes Gutenberg University Saibal Gupta Mainz, J.‐J.‐Becher‐Weg 21, D‐55128 Mainz, Germany Department of Geology and Geophysics, Indian Laboratoire de Géologie de Lyon – Terre, Planètes, Institute of Technology Kharagpur, Kharagpur 721302, Environnement UMR CNRS 5276, UCB Lyon1 – ENS Lyon, West Midnapore, West Bengal, India 2 rue Raphael Dubois, 69622 Villeurbanne, France Pitsanupong Kanjanapayont Fernando Calamita Department of Geology, Faculty of Science, Dipartimento di Ingegneria e Geologia, Università degli Chulalongkorn University, Bangkok 10330, Thailand Studi “G. D’Annunzio” di Chieti‐Pescara,Via dei Vestini 31, 66013, Chieti Scalo (CH), Italy Ali Karrech The University of Western Australia, School of Civil, Paulo Castro Environmental and Mining Engineering, 35 Stirling Laboratório Nacional de Energia e Geologia, Rua da Highway, Crawley, 6009, WA, Australia Amieira, Apartado 1089, 4466 901 S. Mamede de Infesta, Portugal Matthew J. Kohn Department of Geosciences, Boise State University, 1910 Sadhana M. Chatterjee University Drive, Boise, ID 83725, USA Department of Geological Sciences, Jadavpur University, Kolkata 700032, India Phillipe‐Hervé Leloup Laboratoire de Géologie de Lyon – Terre, Planètes, Nandini Chattopadhyay Environnement UMR CNRS 5276, UCB Lyon1 – ENS Lyon, Department of Geological Sciences, Jadavpur University, 2 rue Raphael Dubois, 69622 Villeurbanne, France Kolkata 700032, India Carlos Coke Sergio Llana‐Fúnez Departamento de Geologia, Universidade de Trás‐os‐ Departamento de Geología, Universidad de Oviedo, Montes e Alto Douro, Apartado 1013, 5001‐801 Arias de Velasco s/n, 33005 Oviedo, Spain Vila Real, Portugal Tanushree Mahadani Sujoy Dasgupta Department of Earth Sciences, Indian Institute of Department of Geological Sciences, Jadavpur University, Technology Bombay, Powai, Mumbai 400076, Kolkata, 700032, India Maharashtra, India

vii viii Contributors

Nibir Mandal Benedito C. Rodrigues Department of Geological Sciences, Jadavpur University, Institute of Earth Sciences (ICT)/University of Minho Kolkata, 700032, India Pole, Universidade do Minho, Campus de Gualtar, Stefano Mazzoli 4710-057 Braga, Portugal Dipartimento di Scienze della Terra, dell’Ambiente e José Rodrigues delle Risorse (DiSTAR), Università degli studi di Napoli Laboratório Nacional de Energia e Geologia, Rua da ‘Federico II’, Largo San Marcellino 10, 80138 Napoli, Italy Amieira, Apartado 1089, 4466 901 S. Mamede de Dave J. McCarthy Infesta, Portugal Department of Geology, University College, Cork, Marina Rueda Ireland Departamento de Geología, (Universidad Nacional Patrick A. Meere del Sur), Bahía Blanca, Argentina Department of Geology, University College, Cork, Sanjoy Sanyal Ireland Department of Geological Sciences, Jadavpur University, Rupsa Mukherjee Kolkata 700032, India Department of Earth Sciences, Indian Institute of Christoph Eckart Schrank Technology Bombay, Powai, Mumbai 400076, Queensland University of Technology, School of Earth, Maharashtra, India Environmental and Biological Sciences, Brisbane, 4001, Soumyajit Mukherjee QLD, Australia Department of Earth Sciences, Indian Institute of The University of Western Australia, School of Earth Technology Bombay, Powai, Mumbai 400076, and Environment, 35 Stirling Highway, Crawley, 6009, Maharashtra, India WA, Australia Kieran F. Mulchrone Pulak Sengupta Department of Applied Mathematics, University Department of Geological Sciences, Jadavpur University, College, Cork, Ireland Kolkata 700032, India Clyde J. Northrup Sudipta Sengupta Department of Geosciences, Boise State University, 1910 Department of Geological Sciences, Jadavpur University, University Drive, Boise, ID 83725, USA Kolkata 700032, India Paolo Pace Pedro Pimenta Simões Dipartimento di Ingegneria e Geologia, Università degli Institute of Earth Sciences (ICT)/University of Minho Studi “G. D’Annunzio” di Chieti‐Pescara,Via dei Vestini Pole, Universidade do Minho, Campus de Gualtar, 31, 66013, Chieti Scalo (CH), Italy 4710-057 Braga, Portugal Jorge Pamplona Yutaka Takahashi Institute of Earth Sciences (ICT)/University of Minho Geological Survey of Japan, AIST, 1‐1‐1 Higashi, Pole, Universidade do Minho, Campus de Gualtar, Tsukuba, Ibaraki 305‐8567, Japan 4710-057 Braga, Portugal Enrico Tavarnelli Eurico Pereira Dipartimento di Scienze Fisiche, della Terra e Laboratório Nacional de Energia e Geologia, Rua da dell’Ambiente, Università degli Studi di Siena, Amieira, Apartado 1089, 4466 901 S. Mamede de Via Laterina 8, 53100, Siena, Italy Infesta, Portugal Jahnavi Narayan Punekar Ivana Urraza Department of Geosciences, Princeton University, Departamento de Geología, (Universidad Nacional Princeton, NJ, USA del Sur), Bahía Blanca, Argentina Sayan Ray Stefano Vitale Department of Geological Sciences, Jadavpur University, Dipartimento di Scienze della Terra, dell’Ambiente e Kolkata 700032, India delle Risorse (DiSTAR), Università degli studi di Napoli ‘Federico II’, Largo San Marcellino 10, 80138 Napoli, Italy Klaus Regenauer‐Lieb The University of Western Australia, School of Earth Andrea M. Wolfowicz and Environment, 35 Stirling Highway, Crawley, Department of Geosciences, Boise State University, 1910 6009, WA, Australia University Drive, Boise, ID 83725, USA The University of New South Wales, School of Petroleum Shell International Exploration and Production, Shell Engineering, Tyree Energy Technologies Building, Woodcreek Complex, 200 N Dairy Ashford Rd, Houston, H6 Anzac Parade, Sydney, NSW, 2052, Australia TX 77079, USA Acknowledgments

Thanks to Ian Francis, Delia Sandford, and Kelvin Thanks to Beth Dufour for looking at permission issues Matthews (Wiley Blackwell) for handling this edited and to Alison Woodhouse for assistance in copyediting, volume. Comments by the three anonymous reviewers on and Kavitha Chandrasekar, Sukanya Shalisha Sam and the book proposal helped us to remain cautious in editing. Janyne Ste Mary for numerous help for all the chapters in We thank all the authors and reviewers for participation. this book.

ix Introduction

Kinematics of ductile shear zones is a fundamental Chattopadhyay et al. (2016) describe how ductile shear aspect of structural geology (e.g. Ramsay 1980; Regenauer‐ altered the mineralogy, chemistry and texture of rocks from Lieb and Yuen 2003; Mandal et al. 2004; Carreras et al. the South Purulia Shear Zone (India). Using phase dia- 2005; Passchier and Trouw 2005; Mukherjee 2011, 2012, grams, they also constrain the temperature of metasoma- 2013, 2014a; Koyi et al. 2013; Mukherjee and Mulchrone tism. In a study of ductile shear zones in the Khariar 2013; Mukherjee and Biswas 2014; and many others). basin (India), Bhadra and Gupta (2016) decipher two This edited volume compiles a total of 17 research papers movement phases along the Terrane Boundary Shear related to various aspects of ductile shear zones. Zone. Mukherjee et al. (2016) review morphology and In the first section “Theoretical Advances and New genesis of intrafolial folds and deduce their Class 1C and Methods”, Vitale and Mazzoli (2016) describe an inverse Class 2 morphologies from Zanskar Shear Zone from method to deduce the incremental strain path in heteroge- Kashmir Himalaya. Pamplona et al. (2016) classify the neous ductile shear zones, and have applied the method in Malpica Lamego Ductile Shear Zone into sectors of dif- a wrench zone hosted in pre‐Alpine batholiths. Field stud- ferent deformation patterns, such as sinistral or dextral ies, analog and numerical modeling presented by Dasgupta shear and flattening. Pseudosection studies by Delpino et et al. (2016) strongly indicate that volume reduction aug- al. (2016) for ductile shear zone in the Pringles ments transpression in ductile shear zones. In addition, Metamorphic Complex (Argentina) yield thermal curves. two parameters that control shortening perpendicular to Kanjanapayont (2016) reviews ductile shear zones in shear zones are defined. Mulchrone et al. (2016) analyti- Thailand, presents structural details, and constrains and cally model steady state and oblique foliation develop- correlates when they were active. Takahashi (2016) stud- ment in shear zones and present the possibility of ies the Nihonkoku Mylonite Zone (Japan) and found that estimating: (i) the relative strength of foliation destroying its mylonitization during 55–60 Ma correlates with processes, (ii) the relative competency of the grains, and deformation in the Tanagura Tectonic Line. Flanking (iii) the kinematic vorticity number. Schrank et al. (2016) structures (Passchier 2001; Mukherjee and Koyi 2009; analytically model the deformation of inclusions with a Mukherjee 2014b, etc.) has recently been of great interest hyperelastoviscoplastic rheology under ductile litho- in the context of ductile shear zones. Goswami et al. sphere conditions, and predict the evolution of the shape (2016) describe the geometry of flanking structures from of the inclusion. Mukherjee and Biswas (2016) presented Arunachal Pradesh, Higher Himalaya, India and use con- kinematics of layered curved simple shear zones. tractional flanking structures to deduce shear sense. Considering Newtonian viscous rheology of the litho‐layers, they explain how aspect ratios of inactive initially cir- Soumyajit Mukherjee cular markers keep changing. Kieran F. Mulchrone In the second section “Examples from Regional Aspects”, Boutonnet and Leloup (2016) discuss Quartz strain‐rate‐metry from shear zones at Ailao Shan–Red References River (China) and Karakoram (India) and strain rate variation within these zones. They decipher high slip rates of Bhadra S, Gupta S. 2016. Reworking of a basement–cover interface the order of cm per year from both these zones. Applying during Terrane Boundary shearing: An example from the Khariar basin, Bastar craton, India. In Ductile Shear Zones: From Micro- Titanium‐in‐quartz thermobarometry on Scandinavian to Macro-scales, edited by S. Mukherjee and K.F. Mulchrone, Caledonides, Wolfowicz et al. (2016) deduce a geother- John Wiley & Sons, Chichester. mal gradient and support a critical taper mechanism of Boutonnet E, Leloup P-H. 2016. Quartz-strain-rate-metry (QSR), an deformation. Pace et al. (2016) study brittle‐ductile shear efficient tool to quantify strain localization in the continental zones from the Central–Northern Apennines related to crust. In Ductile Shear Zones: From Micro- to Macro-scales, edited by S. Mukherjee and K.F. Mulchrone, John Wiley & Sons, frontal and oblique ramps and deduced structural inher- Chichester. itance of extensional faults. Sengupta and Chatterjee Carreras J, Druguet E, Griera A. 2005. Shear zone‐related folds. (2016) deduce lower amphibolites facies metamorphism Journal of Structural Geology 27, 1229–1251. in the Phulad Shear Zone (India). Antithetically oriented Chattopadhyay N. et al. 2016. Mineralogical, textural, and chemical clasts indicate a general shear deformation; however, the reconstitution of granitic rock in ductile shear zones: A study from a part of the South Purulia Shear Zone, West Bengal, India. method of vorticity analysis applied was found unsuita- In Ductile Shear Zones: From Micro- to Macro-scales, edited ble since the deformation was heterogeneous and the by S. Mukherjee and K.F. Mulchrone, John Wiley & Sons, shear zone contains a number of phases of folds. Chichester. x Introduction xi

Dasgupta S, Mandal N, Bose S. 2016. How far does a ductile shear Zones: From Micro- to Macro-scales, edited by S. Mukherjee and zone permit transpression?. In Ductile Shear Zones: From Micro- K.F. Mulchrone, John Wiley & Sons, Chichester. to Macro-scales, edited by S. Mukherjee and K.F. Mulchrone, Mulchrone KF, Meere PA, McCarthy DJ. 2016. 2D model for devel- John Wiley & Sons, Chichester. opment of steady‐state and oblique foliations in simple shear Delpino S. et al. 2016. Microstructural development in ductile and more general deformations. In Ductile Shear Zones: deformed metapelitic–metapsamitic rocks: A case study from From Micro- to Macro-scales, edited by S. Mukherjee and K.F. the Greenschist to Granulite facies megashear zone of the Mulchrone, John Wiley & Sons, Chichester. Pringles Metamorphic Complex, Argentina. In Ductile Shear Pace P, Calamita F, Tavarnelli E. 2016 Brittle-ductile shear zones Zones: From Micro- to Macro-scales, edited by S. Mukherjee and along inversion-related frontal and oblique thrust ramps: K.F. Mulchrone, John Wiley & Sons, Chichester. Insights from the Central–Northern Apennines curved thrust Goswami TK, Baruah S. 2016. Flanking structures as shear sense system (Italy). In Ductile Shear Zones: From Micro- to Macro- indicators in the higher Himalayan gneisses near Tato, West scales, edited by S. Mukherjee and K.F. Mulchrone, John Wiley Siang District, Arunachal Pradesh, India. In Ductile Shear & Sons, Chichester. Zones: From Micro- to Macro-scales, edited by S. Mukherjee and Passchier C. 2001. Flanking structures, Journal of Structural K.F. Mulchrone, John Wiley & Sons, Chichester. Geology 23, 951–962. Kanjanapayont P. 2016. Strike–slip ductile shear zones in Thailand. Passchier CW, Trouw RAJ. 2005. Microtectonics, second edition. In Ductile Shear Zones: From Micro- to Macro-scales, edited by Springer, Berlin. S. Mukherjee and K.F. Mulchrone, John Wiley & Sons, Chichester. Pamplona J. et al. 2016. Structure and Variscan evolution of Koyi H, Schmeling H, Burchardt S, Talbot C, Mukherjee S, Sjöström Malpica–Lamego ductile shear zone (NW of Iberian Peninsula). H, Chemia Z. 2013. Shear zones between rock units with no rela- In Ductile Shear Zones: From Micro- to Macro-scales, edited by tive movement. Journal of Structural Geology 50, 82–90. S. Mukherjee and K.F. Mulchrone, John Wiley & Sons, Chichester. Mandal N, Samanta SK, Chakraborty C. 2004. Problem of folding in Ramsay JG. 1980. Shear zone geometry: a review. Journal of ductile shear zones: a theoretical and experimental investiga- Structural Geology 2, 83–99. tion. Journal of Structural Geology 26, 475–489. Regenauer‐Lieb K, Yuen DA. 2003. Modeling shear zones in geologi- Mukherjee S. 2011. Mineral fish: their morphological classification, cal and planetary sciences: solid‐and fluid‐thermal‐mechanical usefulness as shear sense indicators and genesis. International approaches. Earth Science Reviews 63, 295–349. Journal of Earth Sciences 100, 1303–1314. Schrank, CE. et al. 2016. Ductile deformation of single inclusions in Mukherjee S. 2012. Simple shear is not so simple! Kinematics simple shear with a finite‐strain hyperelastoviscoplastic rheol- and shear senses in Newtonian viscous simple shear zones. ogy. In Ductile Shear Zones: From Micro- to Macro-scales, edited Geological Magazine 149, 819–826. by S. Mukherjee and K.F. Mulchrone, John Wiley & Sons, Mukherjee S. 2013. Deformation Microstructures in Rocks. Springer, Chichester. Berlin. Sengupta S, Chatterjee SM. 2016. Microstructural variations in Mukherjee S. 2014a. Atlas of shear zone structures in meso‐scale. quartzofeldspathic mylonites and the problem of vorticity analy- Springer, Berlin. sis using rotating porphyroclasts in the Phulad Shear Zone, Mukherjee S. 2014b. Review of flanking structures in meso‐and Rajasthan, India. In Ductile Shear Zones: From Micro- to Macro- micro‐scales. Geological Magazine, 151, 957–974. scales, edited by S. Mukherjee and K.F. Mulchrone, John Wiley & Mukherjee S, Biswas R. 2014. Kinematics of horizontal simple Sons, Chichester. shear zones of concentric arcs (Taylor–Couette flow) with Takahashi Y. 2016. Geotectonic evolution of the Nihonkoku Mylonite incompressible Newtonian rheology. International Journal of Zone of north central Japan based on geology, geochemistry, and Earth Sciences 103, 597–602. radiometric ages of the Nihonkoku Mylonites: Implications for Mukherjee S, Biswas R. 2016. Biviscous horizontal simple shear Cretaceous to Paleogene tectonics of the Japanese Islands. In zones of concentric arcs (Taylor–Couette Flow) with incom- Ductile Shear Zones: From Micro- to Macro-scales, edited by pressible Newtonian rheology. In Ductile Shear Zones: From S. Mukherjee and K.F. Mulchrone, John Wiley & Sons, Chichester. Micro- to Macro-scales, edited by S. Mukherjee and K.F. Vitale S, Mazzoli S. 2016. From finite to incremental strain: Insights Mulchrone, John Wiley & Sons, Chichester. into heterogeneous shear zone evolution. In Ductile Shear Mukherjee S, Koyi HA. 2009. Flanking microstructures. Geological Zones: From Micro- to Macro-scales, edited by S. Mukherjee and Magazine 146, 517–526. K.F. Mulchrone, John Wiley & Sons, Chichester. Mukherjee S, Mulchrone KF. 2013. Viscous dissipation pattern in Wolfowicz AM, Kohn MJ, Northrup CJ. 2016. Thermal structure of incompressible Newtonian simple shear zones: an analytical shear zones from Ti-in-quartz thermometry of mylonites: model. International Journal of Earth Sciences 102, Methods and example from the basal shear zone, northern 1165–1170. Scandinavian Caledonides. In Ductile Shear Zones: From Micro- Mukherjee S. et al. 2016. Intrafolial Folds: Review and examples to Macro-scales, edited by S. Mukherjee and K.F. Mulchrone, from the Western Indian Higher Himalaya. In Ductile Shear John Wiley & Sons, Chichester.

PART I Theoretical Advances and New Methods

Chapter 1 From finite to incremental strain: Insights into heterogeneous shear zone evolution

Stefano Vitale and Stefano Mazzoli Dipartimento di Scienze della Terra, dell’Ambiente e delle Risorse (DiSTAR), Università degli studi di Napoli ‘Federico II’, Largo San Marcellino 10, 80138, Napoli, Italy

1.1 Introduction by different authors, such as Hull (1988), Mitra (1991) and Means (1995). The latter author envisaged strain softening/ Heterogeneous ductile shear zones are very common in hardening as the main rheological control on shear zone the Earth’s lithosphere and are particularly well exposed evolution: shear zones characterized by a thickness in mountain belts (e.g. Iannace and Vitale 2004; Yonkee decreasing with time (Type II) result from strain soften 2005; Vitale et al. 2007a,b; Okudaira and Beppu 2008; ing, whereas shear zones characterized by increasing Alsleben et al. 2008; Sarkarinejad et al. 2010; Kuiper et al. thickness (Type I) are produced by strain hardening 2011; Dasgupta et al. 2012; Zhang et al. 2013; Samani (Means 1995). Based on this view, each part of a heteroge 2013; Mukherjee 2013, 2014; also see Chapter 9), where neous ductile shear zone is the result of a different strain they provide useful tools for a better understanding of evolution, and taken all together, the various shear zone the processes and parameters controlling strain locali sectors may be able to record the whole strain history. zation, type of deformation, and rock rheology. The During the last few years, several papers dealt with occurrence of strain markers such as fossils, ooids and the possibility of calculating the incremental strain ellipsoidal clasts in sedimentary rocks, or equant minerals, knowing the temporal and spatial evolution of the defor deflected veins and dykes in igneous rocks, allows one to mation. Provost et al. (2004) reconstruct the deformation quantify the finite strain by means of various methods history by means of the n times iteration of the trans (e.g. Dunnet 1969; Fry 1979; Lisle 1985; Erslev 1988; forming equation characterizing the incremental strain, Vitale and Mazzoli 2005, 2010). where n is the number of deformation stages. Horsman Finite strains are all quantities, directly measured or and Tikoff (2007) focus the opportunity of separating, derived, related to the final state of deformation. These by previous method, the strain related to the shear finite quantities, such as strain ratio, effective shear zone margins, where according to Ramsay (1980) the strain (sensu Fossen and Tikoff 1993), and angle θ’ deformation is weak, and that associated with the more between the shear plane and oblique foliation in hetero deformed shear zone sectors. The authors consider geneous ductile shear zones, cannot furnish unequivocal heterogeneous shear zones as consisting of sub‐zones, information about the temporal strain evolution (i.e. each characterized by a roughly homogeneous deforma strain path; Flinn 1962). This is because there are several tion. Based on their temporal and spatial evolution, combinations of deformation types such as simple shear, shear zones are then classified into three main groups: pure shear and volume change, that can act synchro (i) constant‐volume deformation, (ii) localizing, and nously or at different times, leading to the same final (iii) delocalizing deformation. In the first case, the shear strain configuration (Tikoff and Fossen 1993; Fossen and zone boundaries remain fixed (Type III shear zone of Tikoff 1993; Vitale and Mazzoli 2008, 2009; Davis and Hull (1988); Mitra (1991); Means (1995)), whereas for the Titus 2011). Appropriate constraints are needed to latter two groups the shear zone boundaries migrate obtain a unique solution – or at least reduce the under‐ with time, leading to decreasing (group ii) or increasing determination. This also implies introducing some (group iii) thickness of the actively deforming zone assumptions in the definition of the strain model. The (respectively Type II and Type I shear zones of Hull strain path may be envisaged as a temporal accumulation (1988); Mitra (1991); Means (1995). of small strain increments, and the final strain arrange Following Means (1995), Vitale and Mazzoli (2008) ment as the total addition (Ramsay 1967). A possible provide a mathematical forward model of strain accumu relationship between final strain configuration and tem lation within an ideal heterogeneous shear zone by subdi poral evolution (i.e. incremental strains) was suggested viding it into n homogenously deformed layers, each one

3 4 S. Vitale and S. Mazzoli bound by shear planes (C‐planes: Passchier and Trouw characterized by no stretches along the shear direction 2005) and characterized by a specific evolution, this and no volume change. being related to that of adjacent layers within the frame work of a defined temporal succession. In the case of strain hardening, the strain evolution starts with a homo 1.2 Incremental strain geneous deformation affecting originally a specific volume of rock (being represented by a single layer in the To obtain a mathematical relationship between incre model). As the original “single layer” is able to accumu mental and finite strain, consider the general case of late only a specific amount of strain (due to strain hard deformation being localized within a heterogeneous duc ening), further shearing involves new material located tile shear zone with synchronous deformation in the host along the shear zone margins (Mazzoli and Di Bucci rock. The shear zone is composed of n deformed layers, 2003; Mazzoli et al. 2004), thereby increasing the active each characterized by homogeneous strain. The strain shear zone volume (delocalizing zone of Horsman and evolution is illustrated in Fig. 1.1 when strain softens Tikoff 2007). On the contrary, in the strain softening case, (localizing shear zone) and hardens (delocalizing shear zone), where matrices B and Cfin represent finite strain the deformation – originally homogeneous and affecting i an ideal “multilayer” – progressively abandons the layers within the shear zone and in the host rock in the last configuration, respectively, whereas matrices A and C located at the shear zone margins due to easier strain i accumulation in the central sector (localizing zone of are related to incremental strain. Horsman and Tikoff 2007). The difference between the In the case of a localizing shear zone, indicating with B the finite strain matrix of the i‐th layer in the last con approach of Horsman and Tikoff (2007) and that of Vitale i and Mazzoli (2008) is that the latter authors relate the figuration (n), the finite strain matrix is related to the temporal and spatial evolution of the shear zone to strain incremental matrices by the following relationships softening/hardening, whereas the former authors avoid (with i ranging between 2 to n – 1): any genetic implication. nn1 1 1 nn1 1 1 Building on the results obtained by Vitale and Mazzoli BC1 AC1 BC1 CA1 (2008), and following the mathematical approach of n 1 1 AC11B , Provost et al. (2004) and Horsman and Tikoff (2007), 1 n 2 nn2 1 (1) a technique is proposed in this paper, which is able to BC2 AA21 BC2 AC2 B1 nn2 1 1 1 provide information on the incremental strain path AC2 BB21C , based on measured finite strains. The incremental strain n i 1 1 ni1 analysis is then applied to a heterogeneous wrench zone ACi BBii1 C .

y (a) 4 (b) 4 3 3 2 2 4 fin 1 C4 Cfin 1 C C n C3 n C3 2 2 C C C C 3 3 A 1 B 3 A C B C2A C 1 C 1 1 CA 1 2 1 C C A1 1 1 2 2 A CA A A 2 1 B A C 2 1 C 2 2 A C2 A2 1 B A A C 1 2 2 A1 2 1 2 C A 1 C A 2 B A 1 A A A 3 3 A A C A 2 3 2 1 CA C A1C 2 1 A 3 B3 3 A1 A2A1 3

A 1 A1 A A 2 4 A A3A2A1 A A2 4 1 A2A1 A A A A 3 1 A2A1 A4 3 B4 3 2 1 A 4 B4

Layers 3 Layers 3 A A A A A 1 C A1C A A C A C 1 A2A1 3 2 1 A 2 2 1 A2 1 CA 3 B3 A3 B3 2 2 C A1 A A 2 2 2 2 1 CA A 2 A 1 C A1C 2 1 A 2 Finite strain configuration A2A1C C B B Finite strain configuration 1 2 1 2 A1 C 2 2 C CA1 C A1 3 3 3 A 1 C A C C B 1 B1 C 1 C C2 C2 C3 C3 C4 Cfin C4 Cfin

Active A = Incremental strain matrix of the i-th layer of the active shear zone Shear zone : 1 Inactive C=Incremental strain matrix of the inactive shear zone and host rock

Bi = Finite strain matrix of the i-th layer of the shear zone in the last configuration Host rock Cfin = Finite strain matrix of the host rock in the last configuration

Fig. 1.1. Examples of strain evolution along the xy plane of the coordinate reference frame for heterogeneous shear zones consisting of seven homogeneously deformed layers and characterized by transtension in the active shear zone and synchronous pure shear elsewhere. (a) Localizing shear zone. (b) Delocalizing shear zone. From finite to incremental strain 5

In the case of a delocalizing shear zone the relation and ship is: fin k fin fin incr i 1 i 1 ni 1 ni1 1 1 i . (8) ABCCBBCB . (2) i fin fin fin i i ii1 i 1 k kk 2 i 1 1 i 1 2 i 1

1.2.1 special case of no deformation in the host rock In the case of a transpressional/transtensional wrench zone with k = 1 and k k = 1, equation (8) becomes: In the case of C = 1 (identity matrix), i.e. no deformation 1 2 3 in the host rock, Equations (1) and (2) are always substi fin fin tuted by the equation: incr i i 1 fin fin k ffin . (9) i kkfin fin i i 13i 1 2 i 1 2 i 1 1 ABiiBi 1 . (3) Note that, for a deformation characterized by simple

In this circumstance, the relationships between shear only (k1 = k2 = k3 = 1), the incremental shear strain incremental and finite strain quantities (stretches and corresponds to the finite shear strain increment. effective shear strains) may be directly obtained by In the case of no synchronous pure shear deformation rewriting Equation 3 in an explicit form. Consider a in the host rock (i.e. C = 1), the final strain configurations wrench zone in which each i‐th layer is characterized of localizing and delocalizing shear zones (Fig. 1.1) are by finite strain represented by the matrix (Tikoff and indistinguishable. However, according to Means (1995), Fossen 1993): useful information may be obtained by the analysis of the shear strain across the shear zone. In the case of strain k fin fin 0 softening, which is assumed to control the development 1 i i of localizing shear zones, the finite shear strain profile B 00k fin , (4) displays a peaked shape. On the contrary, in the case of i 2 i strain hardening (i.e. in the case of delocalizing shear 00k fin 3 i zones) the profile is flat‐shaped. Therefore an accurate study of the shear strain gradient across the shear zone where may effectively unravel the type of rheological behaviour (strain hardening/softening) characterizing the analysed fin fin structure. kk12 fin fin i i i i fin (5) k1 ln i k fin 1.3 Finite strain 2 i It is generally very difficult to obtain all four parameters is the i‐th finite effective shear strain. of the finite matrix (Equation 4) by analyzing naturally Applying Equation 3 this yields: deformed shear zones. However, in some cases, it is pos sible to determine all derived strain parameters starting fin fin fin fin k1 k1 from measured ones. Among these, the case of a shear i i i i 1 0 kkfin fin k fin k fin zone characterized by no volume variation and nor 1 i 1 2 i 1 1 i 1 2 i 1 stretch along the x direction (k1 = 1). fin k2 Consider a wrench zone (Fig. 1.2) where each i‐th layer ABB 1 00i , iii 1 fin is characterized by synchronous simple and pure shear k2 i 1 represented by the finite strain matrix (in order to sim fin k3 plify the formulae, the label i is omitted and all quanti 00 i k fiin ties have to be considered as finite values): 3 i 1

(6) 10

B 00k2 . (10) where A is the incremental matrix referred to the i‐th i 00k3 step. The relationships between incremental and finite Generally one can directly measure only the (R, θ’) quantities are obtained: and/or (Γ, θ’) values, where R is the aspect ratio of the finite strain ellipse (e.g. Ramsay and Huber 1983) and fin fin fin θ’ is the angle between the finite strain ellipsoid XY plane k1 k2 k3 k incr i ;;k incr i k incr i (7) and the shear plane xy (e.g. Vitale and Mazzoli 2008, 1 i k fin 2 i k fin 3 i k fin 1 i 1 2 i 1 3 i 1 2010). R and Γ can be obtained using the Rf /ϕ method 6 S. Vitale and S. Mazzoli

(a) the foliation) from the first equation of the system z (Equation 11) and choosing the appropriate value of λ*, the angle θ’ is obtained as follows:

1 2 * z tan . (14) y k3 x

x X (c) The X‐axis of the strain ellipsoid (the maximum (b) stretching) can lie in the xz plane (Fig. 1.2b) or be paral Y lel to the y‐axis (Fig. 1.2c) of the reference coordinate X system. In both cases the value of λ* in the Equation 14 is Y Z Z 1 * kk22124 kk22 2224 2 1 ; (15) 2 3 3 3 3 Fig. 1.2. (a) Cartoon showing a homogeneous wrench zone. (b) Finite strain ellipsoid geometry in case the x‐axis lies in the xy plane of the coordinate reference frame. (c) Finite strain ellipsoid geometry in case substituting the value of λ* of Equation 15 in the formula the x‐axis is parallel to the z‐axis of the coordinate reference frame. (Equation 14), the resulting equation is

2 tan k3 1 (Dunnet 1969) and the cotangent rule (Ramsay and Huber 1 22 4 22 24 2 1983; Vitale and Mazzoli 2010), respectively. Starting kk3 123 kk3 223 10, 2 from the values of R and θ’, let us try to find other strain parameters such as shear strain and stretches. To obtain which simplifies to a relationship between k and Γ, let us calculate the math ematical expression of the principal strain ratios RXZ, RYZ 2 2 2 tantkk3 an 113 tan 0. (16) and RXY starting from the magnitudes of the strain ellip soid axes (λ1,2,3), corresponding to the eigenvalues of the T T matrix BB (where B is the transposed matrix of B): Solving for k3 yields

2 1 xk3z x 2 2 4 2 2 2 2 TT 2 tantan 24tantan BB Ie BB I y ky 0, k3 2 2tan z kx kz2 (17) 3 3 and (11)

tant2 2 an 4 242 tant2 2 an 2 where e is the eigenvector and I is the identity matrix. k3 . The solution is: 2tan (18)

2 k2 The solution for k3 in Equation 18 provides negative

1 values (k3 must be 0), and hence has to be eliminated. kk22124 kk22 2224 2 1 . 12,,3 2 3 3 3 3 In order to find a suitable equation to join with Equation 17 in the variables k3 and Γ, let us consider the 1 22 4 22 24 2 k3 1 kkk3 223 k3 21 strain ratio relationship 2 (12)

22 4 22 24 2 Indicating with , and the maximum, intermedi kk3 123 kk3 223 1 λ1 λ2 λ3 R 0. (19) ate and minimum value, respectively (i.e. > > ), the 22 4 22 224 2 λ1 λ2 λ3 kk3 123 kk3 2 3 21 strain ratios of the principal finite strain ellipses are: If the direction of the maximum lengthening (x‐axis of 1 2 1 RRXZ ;;YZ RXY . (13) the strain ellipsoid) lies in the xy plane of the reference 3 3 2 coordinate system (Fig. 1.2a) than the second value of λ

in the Equation 12 is the maximum one and R = RXZ, In order to find the angle θ’ between the xz plane of the else if the X‐axis is parallel to the z‐axis (Fig. 1.2b), the reference coordinate system (parallel to the shear plane) second value of λ is the intermediate one and R = RYZ. and the XY plane of the finite strain ellipsoid (parallel to Solving for k3 yields From finite to incremental strain 7

11RR22RR424 2 low‐strain domain of an elsewhere extensively deformed (20) k3 and mylonitized pre‐Alpine intrusive granitoid body 2R included within the amphibolite facies Zentralgneiss (Penninic units exposed within the Tauern tectonic In order to obtain real solutions the argument of the window, Eastern Alps; Fig. 1.3c; Mancktelow and square root must be zero or positive, hence Pennacchioni 2005; Pennacchioni and Mancktelow 2007). Shear zone nucleation was controlled by the pres 1 RR2440R22 , ence of precursor joints, and occurred by a widespread with R 1 and 0. These inequalities hold only when reactivation process that characterizes solid‐state defor R 2 1. Under this condition, the solutions that mation of granitoid plutons also elsewhere (e.g. furnish positive values are Pennacchioni 2005; Mazzoli et al. 2009). Wrench zones are characterized by a well‐developed foliation and 22422 deformed quartz veins that are intersected by the shear 11RRRR4 k3 . (21) zone themselves (Fig. 1.3a). Wrench zones are sub‐ 2R vertical and characterized by sub‐horizontal slip vectors, and sinistral and dextral sense of shear. Geochemical Combining Equations 21 and 17 yields analyses of major and trace elements of deformed and undeformed rocks (Pennacchioni 2005), indicate no geo tant22an 4224tant22 an 2 chemical changes occurred during deformation and 2tan (22) hence suggesting that the deformation involved no vol 11RR22R4 4R22 . ume variation (Grant 1986). 2R

Solving for Γ gives the only positive and real solution 1.4.1 Finite strain The analyzed wrench zone is characterized by localized R2 1 tan synchronous simple shear and pure shear. The main 2 . (23) R 1 tan finite strain parameters of the shear zone were evaluated by analyzing deformed planar markers (Vitale and To find k we can substitute the formula (Equation 23) 3 Mazzoli 2010). In this case, the shear zone was divided into Equation 17. Furthermore k = k –1 and for the oth 2 3 into layers characterized by a roughly homogeneous ers strain quantities, such as shear strain and kinematic internal deformation (Fig. 1.3b). For each layer, finite vorticity number, we can use the following equations, quantities of θ’ and Γ were measured and plotted in a respectively: scatter diagram (Fig. 1.4). The latter also includes a k2–γ grid that was constructed considering the known condi log k3 (24) tions of no volume change (Δ = 0) and assuming k1 = 1 1 k2 (i.e. transpressional/transtensional deformation sensu

Sanderson and Marchini 1984) by varying the stretch k2 and and the shear strain γ in the equations:

1 k2 Wk . 2 2 2 2 (25) (26) 2 loglkkog 2 4logk log k 2 3 3 3 and Summarizing, in the special case of k1 = k2k3 = 1, starting from the strain ratio (R if the strain ellipsoid X‐axis lies in XZ 2 1 1 max the xz plane, or RYZ if the strain ellipsoid x‐axis is parallel tan (27) to the y‐axis) and the angle θ’ that the foliation forms with k2 the shear plane, it is possible to obtain the values of k3 (and k2), γ and Wk by means of Equations 16, 23, 24, and 25. The obtained data plot along a general path involving increasing shear strain γ and decreasing values of the

stretch k2 moving from the margin toward the shear zone 1.4 Practical application of centre. Using Equations 24 and 27 one can obtain the –1 incremental and finite strain exact value of the stretch k3 (and hence k2 = k3 ) and of analyses the shear strain γ. The finite values of the strain ratios

RXZ, RYZ and RXY and the kinematic vorticity number Wk The technique proposed in this study is applied to a het are obtained by applying Equations 19 and 25. erogeneous ductile wrench zone (Fig. 1.3a), previously In order to smooth out the data in the incremental analyzed by Vitale and Mazzoli (2010), exposed in a strain analysis that will be carried out in the following (a) 5 cm

(d)

R=1

(b) (c) Innsbruck 12°E

Vein Host rock Groβvenediger

Dreiherm Spitze Olperer 47°N Shear zone

Brunico Australpine

Jura

0 24km Southern Alps Milan Dinarides Foliation Penninic Po Basin Penninic Units Austroalpine Units Helvetic Host rock Zentralgneise Appennines Schieferhulle

Fig. 1.3. (a) Outcrop view of the analyzed heterogeneous dextral wrench zone deforming quartz vein. (b) Subdivision into homogeneously deformed layers. (c) Geological sketch map of part of the Eastern Alps, showing site of the structural analysis (star) (modified after Pennacchioni and Mancktelow 2007). (d) Normalized Fry plot showing finite strain measured in the host rock.

90 5.00 ∆ =0, k =1 1.1 1 80

70 0.10 1.01 Transtension γ 60

1.00 k2 >1 50 ’

θ 1.00 40 k2 <1

30 0.99

20 0.9 5

10 Transpression

0.1 0 Fig. 1.4. Γ− θ’ scatter diagram. The k –γ grid was con 10–2 10–1 100 101 2 structed for a transpressional/transtensional deformation Effective shear strain Г (Δ = 0 and k1 = 1). From finite to incremental strain 9

(a) (b) 16 14 14 12 12 Г = 31,724θ’–0,815 10 γ = 60,117θ’–1,066 10 R2 = 0,8501 R2 = 0,9547 8 γ Г 8 6 6 4 4 2 2 0 0 0° 20° 40° 60° 80° 0° 20°40° 60° 80° θ’ θ’ (c) (d) 200 3.5 180 3 160 2.5 140 –1,354 RXZ = 599,66θ’ 120 R2 = 0,9191 2 2 XZ 100 k R 80 1.5 60 1 0,4803 40 k2 = 0,2915θ’ 20 0.5 R2 = 0,7417 0 0 0° 20° 40° 60° 80°0°20° 40°60° 80° θ’ θ’ (e) 1.2

1 Wk = –0,0171θ’+ 1,4338 R2 = 0,9806 0.8

k 0.6 W Wk = –0,0004θ’+ 0,9967 2 0.4 R = 0,0505

0.2

0 0° 10° 20°30° 40° 50° 60°70° θ’

Fig. 1.5. Scatter diagrams of (a) finite effective shear strain Γ, (b) finite shear strain γ, (c) finite strain ratio RXZ, (d) finite elongation k2, and

(e) finite kinematic vorticity number Wk versus finite angle θ’. Best‐fit curves are also shown with associated equation and coedfficient of determination R2.

section, best‐fit power‐law curves are determined for the unity) for angles between about 30° and the minimum finite values of effective shear strain Γ (Fig. 1.5a), shear observed θ’ values (<5°; Fig. 1.5e). Note that if the increase strain γ (Fig. 1.5b), strain ratio RXZ (Fig. 1.5c), and stretch in effective shear strain, shear strain and strain ratio with k2 (Fig. 1.5d) as a function of the angle θ’. A power‐law decreasing θ’ are somewhat expected, much less obvious curve is used to fit the scatter data because it provides is the decrease in elongation k2. To evaluate finite strain in the best values of the coefficient of determination R2 the host rock, the normalized‐Fry method (Fry 1979; (which is a measure of how well the data fit the adopted Erslev 1988) was applied to the rock areas surrounding statistical model). the structure. The obtained values of ellipticity on the XZ host The finite kinematic vorticity number Wk increases lin plane (RXZ ) are of about 1, indicating no strain (Fig. 1.3d). early for θ’, ranging from the maximum observed value Summarizing, the ductile wrench zone is character (about 70°) to about 30°, becoming constant (and close to ized by: (i) non‐constant finite values of the stretches 10 S. Vitale and S. Mazzoli

(a)(b) 10 14 Finite Incremental 12 8 10

6 8 γ Г 4 6 4 2 2

0 0 010 20 010 20 nn (c) (d) 90 2.5 80 70 2 60 1.5 50 2 XZ k R 40 1 30 20 0.5 10 0 0 010 20 010 20 n n (e) 1.2

0.8

k 0.6 W

0.4

0.2 Fig. 1.6. Profiles of finite and incremental values of: 0 (a) effective shear strain Γ, (b) shear strain γ, (c) strain 0510 15 20 ratio R , (d) stretch k , and (e) kinematic vorticity num n XZ 2 ber Wk versus layer number n.

k2 and k3, with k2 values mostly larger than unity (having step, discrete values of k2 and Γ were obtained from the assumed k1 = 1); (ii) localized deformation occurring best‐fit equations (Fig. 1.5). Equation 3 has been used to within the shear zone only (i.e. undeformed host rock); calculate the incremental strain because this shear zone and (iii) no volume variation. These features point out displays no deformation outside of it (Fig. 1.3a, d). the occurrence of material flow along the z‐axis of the Figure 1.6 displays the profiles of finite and incremen reference frame (i.e. in the vertical direction). This effect tal values for effective shear strain Γ, shear strain γ, is dominant in the low‐strain parts of the shear zone (i.e. stretch k2, strain ratio RXZ and kinematic vorticity number for high values of the angle θ’) characterized by k2 values Wk versus number of steps, whereas in Fig. 1.7(a,b) finite above unity (transtensional deformation), becoming and incremental strain paths are plotted on: (i) Γ− θ’ and

negligible for the simple shear‐dominated (Wk ≈ 1) cen (ii) logarithmic Flinn diagrams (Flinn 1962; Ramsay tral sector of localized high strain. 1967), respectively. It must be stressed that the first incre mental strain step corresponds to the first step of finite strain (transtension); on the contrary, the subsequent 1.4.2 Incremental strain incremental strain values (from 2 to 20) indicate a The incremental strain analysis of the studied shear zone transpressional deformation, although the finite strain is was carried out considering a total number of n = 20 of dominantly transtensional type. For example, the first steps forthe application of the inverse method. For each incremental value of k2 is 2.23 (transtension), whereas From finite to incremental strain 11

(a) (b) 90 5.00 ∆ = 0, k =1 1.1 1 80 Transtension prolateness 0.10 1 1 20 70 1.01 10 Transtension γ 60 Finite strain 5 k >1 1.00 Finite strain 50 2

’ 20

1.00 XY θ R 40 10 k2 <1 15

30 15 1 5 10 0.99 Transpression 10 1 15 oblateness 20 5 0.9 Incremental 5 2 strain Incremental 10 20 Transpression 20 strain 0.1 0 1 15 2 10–2 10–1 100 101 1 101

Effective shear strain Г RYZ

Fig. 1.7. (a) Γ− θ’ and (b) logarithmic Flinn diagrams showing incremental and finite strain paths.

the following incremental k2 path (from 2 to 20 steps, the temporal evolution of the shear zone. However, the Fig. 1.7a) is generally characterized by values lower than 1, suggested strain evolution is more consistent with a decreasing toward the center of the shear zone. localizing shear zone (Fig. 1.1a, with C = 1) characterized Finite and incremental profiles of effective shear strain Γ, by: (i) an early homogeneous transtensional deformation shear strain γ and strain ratio RXZ show similar peaked affecting the whole shear zone; and (ii) a following local shapes, pointing out a non‐linear increase during shear ization of the transpressional strain in the central part, zone evolution (Fig. 1.6a–c). The peaked shape of the probably driven by strain softening processes, with curve confirms the interpretation, already suggested, respect to a delocalizing shear zone (Fig. 1.1b, with C = 1) based on finite strain analysis, that shear zone rheology where an initial transtension affects the central part and was characterized by strain softening, involving both subsequently migrates outward, with synchronous simple shear and the pure shear components of the defor transpression affecting the inner sectors. mation. However, both finite and incremental kinematic vorticity numbers increase, up to unity, for increasing deformation (Fig. 1.6e). Therefore, the partitioning 1.5 Conclusions between simple shear and pure shear changed during shear zone evolution from prevailing pure shear (Wk ≈ 0.4) According to the Means hypothesis (Means 1975) and as to dominant simple shear, eventually reaching condi suggested by Provost et al. (2004) and Horsman and tions of simple shear alone (Wk ≈ 1) for the latest stages of Tikoff (2007), information on the incremental strain his highly localized deformation in the softened central sec tory may be obtained from the analysis of the final strain tor of the shear zone. configuration in a heterogeneous shear zone. In particu The incremental strain paths plotted on the Γ− θ’ lar, in case the structural evolution was characterized by diagram (Fig. 1.7a) and in the logarithmic Flinn diagram strain softening or hardening – which are assumed to (Fig. 1.7b) confirm that the incremental strain from steps control the development of localizing and delocalizing 2 to 20 consistently lies in the transpressional oblate shear zones, respectively – one can unravel the relation field. Also, note that none of the incremental strain ship between finite strain across the shear zone and parameters holds a constant value during the temporal incremental strains. Based on this assumption, an inverse evolution; therefore the incremental deformation evolu method was derived which is able to evaluate the incre tion is non‐steady state. mental strain matrices starting from measured finite As previously mentioned, the first increment points strain quantities in a heterogeneous ductile shear zone. out a transtensional deformation whereas the subsequent The proposed technique uses the finite values of the strain increments are of transpressional type. In the case effective shear strain Γ and the finite angle θ’ (angle of no synchronous deformation in the host rock, the final between the foliation, i.e. the xy plane of the finite strain strain configuration does not provide information about ellipsoid, and the shear plane) obtained for n layers, in 12 S. Vitale and S. Mazzoli which a shear zone may be subdivided according to Iannace A, Vitale S. 2004. Ductile shear zones on carbonates: the homogeneity criteria. Shear zone deformation may then calcaires plaquettés of Northern Calabria (Italy). Comptes Rendues Geosciences 336, 227–234. be described in terms of n finite strain matrices, each rep Kuiper YD, Lin S, Jiang D. 2011. Deformation partitioning in resenting homogeneous deformation of the related layer. transpressional shear zones with an along‐strike stretch compo Starting from these matrices, it is possible to derive the nent: An example from the Superior Boundary Zone, Manitoba, incremental strain matrices. For simple cases, the pro Canada. Journal of Structural Geology 33, 192–202. posed method furnishes symbolic formulae relating Lisle RJ. 1985. Geological Strain Analysis: A Manual for the Rf/ϕ finite and incremental values of the main strain parame Method. Pergamon Press, Oxford. Mancktelow NS, Pennacchioni G. 2005. The control of precursor ters, such as shear strain and stretches. The inverse brittle fracture and fluid‐rock interaction on the development of method requires knowing the strain parameters k1, k2, k3, single and paired ductile shear zones. Journal of Structural and Γ. In particular instances such as that analyzed in Geology 27, 645–661. this paper, it is possible to derive all of the required Mazzoli S, Di Bucci D. 2003. Critical displacement for normal fault strain parameters from simple formulae. For the ana nucleation from en‐échelon vein arrays in limestones: a case study from the southern Apennines (Italy). Journal of Structural lyzed wrench zone, characterized by no stretches along Geology 25, 1011–1020. the x direction and no volume change, the incremental Mazzoli S, Invernizzi C, Marchegiani L, Mattioni L, Cello G. 2004. strain path suggests a localizing shear zone evolution Brittle‐ductile shear zone evolution and fault initiation in lime characterized by an initial homogeneous transtensional stones, Monte Cugnone (Lucania), southern Apennines, Italy. In deformation in the whole shear zone and a subsequent Transport and Flow Processes in Shear Zones, edited by I. Alsop, and R.E. Holdsworth, Geological Society, London, Special incremental transpression driven by strain softening pro Publications, 224, pp. 353–373. cesses affecting progressively inner sectors. Mazzoli S, Vitale S, Delmonaco G, Guerriero V, Margottini C, Spizzichino D, 2009. “Diffuse faulting” in the Machu Picchu granitoid pluton, Eastern Cordillera, Peru. Journal of Structural Acknowledgments Geology 31, 1395–1408. 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Vitale S, Mazzoli S. 2005. Influence of object concentration on finite northern Calabria, southern Italy. In Deformation of the strain and effective viscosity contrast: Insights from naturally Continental Crust: The Legacy of Mike Coward, edited by A.C. deformed packstones. Journal of Structural Geology 27, Ries, R.W.H. Butler, and R.H. Graham, Geological Society, 2135–2149. London, Special Publications 272, pp. 145–156. Vitale S, Mazzoli S. 2008. Heterogeneous shear zone evolution: the Vitale S, White JC, Iannace A, Mazzoli S. 2007b. Ductile strain par role of shear strain hardening/softening. Journal of Structural titioning in micritic limestones, Calabria, Italy: the roles and Geology 30, 1363–1395. mechanisms of intracrystalline and intercrystalline deforma Vitale S, Mazzoli S. 2009. Finite strain analysis of a natural ductile tion. Canadian Journal of Earth Sciences 44, 1587–1602. shear zone in limestones: insights into 3‐D coaxial vs. non‐ Yonkee A. 2005. Strain patterns within part of the Willard thrust coaxial deformation partitioning. Journal of Structural Geology sheet, Idaho–Utah–Wyoming thrust belt. Journal of Structural 31, 104–113. Geology 27, 1315–1343. Vitale S, Mazzoli S. 2010. Strain analysis of heterogeneous ductile Zhang Q, Giorgis S, Teyssier C. 2013. Finite strain analysis of the shear zones based on the attitude of planar markers. Journal of Zhangbaling metamorphic belt, SE China e Crustal thinning in Structural Geology 32, 321–329. transpression. Journal of Structural Geology 49, 13–22. Vitale S, Iannace A, Mazzoli S. 2007a. Strain variations within a major carbonate thrust sheet of the Apennine collisional belt, Chapter 2 How far does a ductile shear zone permit transpression?

Sujoy Dasgupta1, Nibir Mandal1, and Santanu Bose2 1 Department of Geological Sciences, Jadavpur University, Kolkata, 700032, India 2 Department of Geology, University of Calcutta, Kolkata, 700019, India

2.1 Introduction of pure and simple shear kinematics in ductile shear zones. Similarly, a parallel line of studies has dealt with Understanding the shear zone kinematics has enormous structural (e.g. stylolites; Tondi et al. 2006) and chemical implications in interpreting a wide variety of geological criteria (e.g. enrichment of immobile elements; O’Hara processes, ranging from the exhumation of deep crustal and Blackburn 1989; Mohanty and Ramsay 1994; rocks to the formation of sedimentary basins. Kine Srivastava et al. 1995; Fagereng 2013) to determine the matically, ductile shear zones are defined as regions volume loss in shear zones. marked by localization of intense non‐coaxial deforma In many tectonic settings shear zones developed under tions. Considering a homogeneous strain model, Ramberg general non‐coaxial deformation show components of (1975) first provided a theoretical analysis of the general shear and shortening parallel and orthogonal to the shear non‐coaxial deformations by combining pure shear and zone boundaries, respectively. From a kinematic point of simple shear flows. Based on the kinematic vorticity view, these shear zones have been described as transpres W number, expressed as: W (Truesdell sion zones, a term first coined by Harland (1971) to k 1 describe the zone of oblique convergence between two 2 2 2 2 2 1 2 3 crustal blocks. Sanderson and Marchini (1984) modeled

1954), where i is the principal longitudinal strain rate a vertical transpression zone sandwiched between two and W is the magnitude of the vorticity vector, Ramberg laterally moving rigid blocks, which gave rise to a strike– (1975) has shown characteristic flow patterns in ductile slip motion coupled with shortening across the zone. shear zones. His analysis derives Wk as a function of the Their model imposes a slip boundary condition to allow ratio (Sr) of pure and simple shear rates, and the orienta the material extrusion in the vertical direction, that is, tion of the principal axes of pure shear with respect to perpendicular to the shear direction. It was pointed out the simple shear frame. For Wk = 1, shear zone deforma later that a slip boundary condition had a mechanical tions are characterized by shear‐parallel flow paths, limitation to produce shearing motion in a transpression implying simple shear kinematics. On the other end, zone (Robin and Cruden 1994; Dutton 1997). To meet non‐coaxial deformations in shear zones with Wk < 1 this shortcoming, they advanced the transpression model develop open hyperbolic particle paths, which trans with a non‐slip boundary condition, and explained the form into closed paths as Wk > 1. However, deformations structural variations in terms of the heterogeneous flow with Wk > 1 described as a pulsating type, have been developed in their non‐slip model. A series of kinematic rarely reported from natural shear zones. Ramsay and models have been proposed afterwards; all of them, in his co‐workers included volume strain in the kinematic principle, pivot on the same theoretical formulation of analysis of ductile shear zones (Ramsay and Graham Ramberg (1975) that combines the homogeneous simple 1970; Ramsay 1980; Ramsay and Huber 1987). A range shear and pure shear fields. As a consequence, the of natural structures (at both micro‐ and mesoscopic transpression can show either a monoclinic or a triclinic scales), for example, anastomose mylonitic fabrics kinematic symmetry, depending upon the orientation of (Gapais et al. 1987), porphyroclast tail patterns (Ghosh pure shear axes with respect to the simple shear (Dewey and Ramberg 1976; Simpson and De Paor 1997; Passchier et al. 1998; Jones and Holdsworth 1998; Ghosh 2001; and Simpson 1986; Mandal et al. 2000; Kurz and Fernández and Díaz‐Azpiroz 2009). Northrup 2008), and instantaneous strain axis (ISA) Despite an enormous volume of research work over (Passchier and Urai 1988; Tikoff and Fossen 1993; the last several decades, there have been so far few Xypolias 2010, and references therein) have been used attempts to analyze the mechanics and to estimate the to explain these structures and to demonstrate the effects degree of transpression physically possible in a ductile

14 How far does a ductile shear zone permit transpression? 15 shear zone. Flow modeling for a viscous layer sand convergence, giving rise to an overall E–W structural wiched between two rigid walls (Mandal et al. 2001) trend (Fig. 2.1). The CGGC in the study area recorded four show that the viscous extrusion is much more energeti major ductile deformation episodes (Mahmoud, 2008). In cally expensive, as compared to the gliding motion of the the course of these ongoing events, the terrain has experi rigid blocks. According to Mandal et al. (2001), this con enced regionally a brittle–ductile transition, producing trasting energetics thus leads to dominantly simple shear vertical shear zones on centimeter to meter scales. In the kinematics even when the bulk compression is at a high western part of Purulia district the gneissic rocks display angle to the shear zone. This theoretical prediction is in excellent outcrops of such shear zones, broadly in two good agreement with the dominantly simple shear kine sets, trending NNE–SSW and NE–SW, showing both dex matics of deep‐crustal ductile shear zones reported from tral and sinistral strike–slip motion, as revealed from the high‐grade metamorphic terrains (Puelles et al. 2005). deflection of dominant gneissic foliations or markers, like Furthermore, our own field observations of centimeter quartz veins. to meter scale shear zones from the Chotanagpur Granite The deflection patterns of mylonitic foliation pro Gneiss Complex point to limited flattening. In contrast, duced by the motion of the shear zones were used to many field studies have documented a range of struc undertake a qualitative analysis of the shear zone kine tural evidences in support of the transpressional kine matics. We assumed that the distortion pattern of trans matics (Ghosh and Sengupta 1987; Sengupta and Ghosh verse markers is a function of the ratio (Sr) between pure 2004; Žák et al. 2005; Massey and Moecher 2013). A and simple shear rates (Mandal et al. 2001; Puelles et al. revisit to the problem of transpressional movement in 2005). The distortion of a passive marker at an instant ductile shear zones is needed to address such apparently can be reconstructed from the following velocity equa contradictory field observations. Using analog experi tions (after Jaeger 1969) in a Cartesian space (x, y): ments the present study aims to physically evaluate how much flattening is possible in a coherent ductile shear 1 y 2 ux3 x (1) zone hosted in an undeformable medium. Our experi bb2 t mental results confirm earlier theoretical predictions that shear zones with large aspect ratios are unlikely to 2 undergo significant flattening. We also demonstrate from 1 y v  y 3 , (2) the laboratory experiments that appreciable flattening b 2 t can occur under specific geometrical conditions. Finite element model simulations were performed to substanti Where, b and b are the bulk flattening and shear rates, ate these findings. u and v are the components of velocity along the x and y Section 2.2 presents a set of field examples of small directions, respectively and t is the instantaneous shear scale shear zones along with a qualitative evaluation of zone thickness. Using Equations 1 and 2, it can be dem their flattening. Section 2.3 deals with analog modeling, onstrated that a line parallel to the y‐axis will be dis giving a quantitative estimation of flattening as a func torted with outward convexity, the symmetry of which tion of shear zone geometry. In Section 2.4, we discuss depends on the ratio of pure and simple shear rates simulated ductile shear zones in finite element (FE)  S b and the initial orientation of markers with the models, considering physical properties approximated r b to the crustal rheology. In Section 2.5 we discuss the shear direction. To investigate the distortion pattern, we experimental findings in the context of actual field obser chose a set of lines across the shear zone (Fig. 2.2) vations, and propose syn‐shearing volume changes as a described by the following equation: mechanically potential mechanism for transpression in ductile shear zones. Section 2.6 concludes the principal y mx C (3) outcomes of this work. where, m = tanθ; θ and C are the initial angles of lines with respect to the shear direction and their distance 2.2 Field observations: geometric from the shear zone center along the shear direction, analysis respectively (Fig. 2.2). The lines were deformed by incre mental displacements by using the velocity function in We investigated outcrop‐scale ductile shear zones in the Equations 1 and 2. All the parameters, such as shear zone Chotanagpur Granite Gneiss Complex (CGGC) terrain, thickness t were modified at each step of the iterations. lying north of the Singhbhum Proterozoic mobile belt Using this theoretical approach we obtained the dis (Fig. 2.1). The dominant mineral constituents of the CGGC tortion patterns of a set of parallel passive markers as rocks are quartz, feldspars, micas and garnet with second a function of Sr and θ, and compared them with those ary phases, such as tourmaline and amphibole. Petrological observed in natural shear zones. For Sr = 0, the markers studies suggest that the terrain has undergone a peak show angular deflections without any distortion, irre metamorphism (P ~ 6 kbar, T ~ 850°C) in granulite facies spective of their initial orientation (θ). The degree of (Maji et al. 2008), and regional deformations under N–S outward convexity decreases with decreasing values of 16 S. Dasgupta, N. Mandal, and S. Bose

(a) (b)

72° 80° 88° 28° 20 km CGGC Begunkudor Singhbhum NSMB Manbazar 20°

DV 12°

SSZ

ASC

(c)

S 0 F1 S1 F2 S2 F S3 3

Upright antiform 23°30′

Pleistocene sediments

Gondwana sediments 23°15′ Intrusive granite

Basalt Dalma group Metabasalt

Phyllite/Schist (Singhbhum group) Gabbro & Anorthosite

Granite gneiss & migmatite CGGC Calc granulite/calc schist

Mica schist 23°0′ Amphibolite & 86°0′ 86°15′ 86°30′ 86°45′ 87°0′ Hornblende schist

Fig. 2.1. A generalized geological map of Singhbhum Craton, modified after Saha (1994). (a) Position of the Singhbhum region. (b) Simplified geological map showing the distribution of lithological units in Singhbhum craton (after Saha 1994). Abbreviated units: CGGC: Chhotanagpur Granite Gneiss Complex; ASC: Archean Singhbhum craton; NSMB: North Singhbhum mobile belt; SSZ: Singhbhum shear zone, DV: Dalmaviolcanics. (c) Geological map of Purulia district (modified after map published by Geological Survey of India, 2001), West Bengal within the eastern part of CGGC. Black dashed box is the study area. Symbols in the legend indicate lithology and structural fabrics and fold axis.

both Sr and θ (Fig. 2.2). The graphical plots indicate that an angle of about 70°. A close inspection of the distorted markers oriented initially normal to the shear zone pattern of foliation markers within the shear zone reveals boundaries (θ = 90°) do not show any appreciable out that they maintain their planar geometry along the entire ward convexity for Sr values less than 0.05. length of the shear zone. Comparing the distortion pat Figure 2.3(a) shows an isolated shear zone at a right terns with the corresponding theoretical one (Fig. 2.2), the angle to the foliation, with an aspect ratio of 10.8. The shear zone is predicted to have undergone little flattening, foliation marker has been deflected in a sinistral sense by and evolved dominantly by simple shear (i.e. Sr ~ 0).