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Spatial variations of ductile strain in fold-and-thrust belts: From model to nature
Journal Pre-proof Spatial variations of ductile strain in fold-and-thrust belts: From model to nature Sreetama Roy, Santanu Bose, Puspendu Saha PII:
S0191-8141(19)30339-6
DOI:
https://doi.org/10.1016/j.jsg.2020.104012
Reference:
SG 104012
To appear in:
Journal of Structural Geology
Received Date: 16 August 2019 Revised Date:
4 February 2020
Accepted Date: 9 February 2020
Please cite this article as: Roy, S., Bose, S., Saha, P., Spatial variations of ductile strain in fold-andthrust belts: From model to nature, Journal of Structural Geology (2020), doi: https://doi.org/10.1016/ j.jsg.2020.104012. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.
Credit Author Statement S.B., S.R. and P.S. designed the research; S.R. and P.S. did the experiments. S.B. and S.R. contributed equally to the analysis of experimental results and writing the manuscript.
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Spatial variations of ductile strain in fold-and-thrust belts:
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from model to nature
3
Sreetama Roya, Santanu Bosea,b*, Puspendu Sahac
4 5 6 7
Department of Geology, University of Calcutta, Kolkata – 700019 Department of Geology, Presidency University, Kolkata – 700073 c Department of Geological Sciences, Jadavpur University, Kolkata – 700032
a
b
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*Corresponding author: [email protected]
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Abstract:
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Fold and thrust belts (FTBs) accommodate tectonic convergence through folding
11
and faulting of crustal rocks during a collisional event between two continental plates.
12
Although evidence of distributed deformation is common in FTBs that usually leads to
13
continuous foliations and regionally occurring ductile structures of multiple orders, it has
14
rarely been given much attention assuming the zones of localized deformation, like shear
15
zones and brittle faults, as potential locales for accommodating the amount of convergence.
16
This study presents 3D laboratory-scale models, using viscous thin sheet as crustal layers, to
17
understand the evolution of ductile strain in a tectonic wedge. We varied the degree of
18
mechanical coupling at the basal decollement (i.e., weak versus strong) to investigate this
19
issue at constant convergence velocity in all experiments to avoid the influence of rate-
20
dependence on viscous rheology. Our results reveal that the strength of basal decollement
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controls the mode of wedge growth and hence, the strain pattern particularly towards the
22
hinterland. The weak decollement models yield a zone of constriction towards the central part
23
of hinterland, explaining the occurrence of isolated patches of L-tectonites and cross-folds in
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FTBs; while the strong decollement condition allows gravity driven flow to be active in the
25
hinterland, leading to orogen-parallel recumbent folds. In contrast, both weak and strong
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decollement models produce deformation that characterises the commonness of pervasive, 1
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hinterland dipping ductile fabrics towards the mountain front. We correlate our findings to
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show that spatio-temporal variations in basal coupling are responsible for varying occurrence
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of ductile structures in FTBs.
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Key words: Fold-and-thrust belts, Viscous rheology, Ductile structures, Constrictional
32
deformation, L- tectonites, Weak and strong decollement
33 34
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1. Introduction: A fold-and-thrust belt is a long zone of deformed crustal rocks, formed by the
36
collision between two continental plates. A series of theoretical and experimental studies have
37
been carried out in the past three decades to understand the structural evolution of this
38
deformed crustal section (Tapponnier et al., 1982; Platt, 1986; Le Pichon et al., 1992;
39
Houseman and England, 1993; Lallemand et al., 1994; Willett, 1999b; Beaumont et al., 1999;
40
Mandal et al., 2009; Vanderhaeghe, 2012; Ruh et al., 2012; Jamieson and Beaumont, 2013).
41
These studies have considered varying rheology of crustal rocks from frictional-plastic
42
(Chapple, 1978; Davis et al., 1983; Dahlen et al., 1984; Malavieille, 1984, 2010; Mulugeta,
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1988; Liu et al., 1992; Storti et al., 2000; Persson, 2001; Graveleau et al., 2012; Bose et al.,
44
2014b, 2015) to viscous (England and McKenzie, 1982; Emerman and Turcotte, 1983;
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England et al., 1985; Houseman and England, 1986; Cohen and Morgan, 1986; Buck and
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Sokoutis,1994; Ellis et al., 1995; Royden, 1996; Willett, 1999a; Rossetti et al., 2000;
47
Chattopadhyay and Mandal, 2002; Vanderhaeghe et al., 2003) and visco-elasto-plastic (Erdős
48
et al., 2015; Jaquet et al., 2018). The mechanical behaviour of crustal rocks is commonly
49
modelled by frictional plastic rheology that involves friction laws (Byerlee, 1978). Using the
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theory of brittle failure, the laboratory models validated the concept of critically tapered
2
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wedge model to explain the wedge-shaped geometry of mountain belts and the process of
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sequential thrusting from hinterland to foreland (Davis et al., 1983; Dahlen et al., 1984).
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According to this model, dynamic equilibrium within the wedges maintains a critical balance
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between overlying gravitational load on the basal decollement and the tangential shear stress
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along it. Using scaled laboratory experiments, a large number of workers have subsequently
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shown that a number of parameters, like thickness of homogeneous sand layers (Liu et al.,
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1992; Marshak and Wilkerson, 1992; Mandal et al., 1997), basal decollement slope
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(Mulugeta, 1988; Saha et al., 2013; Bose et al., 2014b), and geometry of the indenter (Byrne
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et al., 1988, 1993; Ratschbacher et al., 1991; Lu and Malavieille, 1994; Gutscher et al., 1996,
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1998; Bonini et al., 1999; Dominguez et al., 2000; Persson, 2001; Persson and Sokoutis,
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2002; Koyi and Vendeville, 2003) play a vital role in regulating the geometric evolution of a
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tectonic wedge. All these models have shown that the frontal propagation of a wedge is
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indeed punctuated by a series of sequential thrusts, splaying from the basal decollement.
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Introduction of kinematic factors, like frictional resistance at the basal decollement
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(Mulugeta, 1988; Liu et al., 1992; Lallemand et al., 1992; Gutscher et al., 1996, 1998; Mandal
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et al., 1997; Konstantinovskaia and Malavieille, 2005; Saha et al., 2016), the rate of
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convergence (Ratschbacher et al., 1991) and surface processes (Koons, 1989, 1990; Storti and
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McClay, 1995; Storti et al.,2000; Konstantinovskaia and Malavieille, 2005; Hoth et al., 2006,
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2008; Malavieille, 2010) have refined our understanding in predicting the spacing between
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successive imbricate thrusts with horizontal shortening and influence of surface erosion on
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wedge development. However, these models for crustal deformation using brittle theories
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cannot explain the regional occurrence of penetrative ductile fabrics and associated folds and
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boudinage structures in orogenic belts (Grasemann et al., 1999; Ring and Brandon, 1999;
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Kassem and Ring, 2004; Law et al., 2004; Jessup et al., 2006; Xypolias and Kokkalas, 2006;
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Larson and Godin, 2009; Law, 2010; Thigpen et al., 2010a, 2010b; Xypolias, 2010; Xypolias
3
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et al., 2010; Cottle et al., 2015; Bauville and Schmalholz, 2015; von Tscharner et al., 2016;
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Butler et al., 2019). The occurrence of penetrative ductile structures in FTBs thus implies a
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significant role of an alternative mechanism, such as distributed ductile deformation during
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the evolution of fold-and-thrust belts. The association of brittle and ductile structures
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throughout the entire mountain belts indicates the crustal rocks to deform over varying time
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scales, where fracturing and brittle faults develop mostly over short time scale (Sibson, 1982)
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and large scale ductile deformation in the crustal rock takes place by creeping in long time
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scale (Hauck et al., 1998; Schmid et al., 1996). Moreover, field investigations reveal that
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geometry of ductile structures varies significantly from hinterland to foreland (Coleman,
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1996; Carosi and Palmeri, 2002; Jessup et al., 2008; Xu et al., 2013). The frontal part of all
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mountain belts is usually characterised by pervasive development of along-strike ductile
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foliations, associated with upright to inclined folds, whereas the hinterland region is
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dominated by complexly deformed fold structures that include interfering of fold types
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(Murphy, 1987; Godin, 2003; Williams and Jiang, 2005; Culshaw et al., 2006; Williams et al.,
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2006; Denèle et al., 2009; Kellett and Godin, 2009; Godin et al., 2011). A number of
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theoretical and experimental studies have used viscous models for explaining the
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development of such ductile structures in mountain belts (Buck and Sokoutis, 1994;
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Medvedev, 2002; Chattopadhyay and Mandal, 2002; Lujan et al., 2010). Earlier studies have
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even shown the crustal deformation to occur often in association with diffusion creep in
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sediments at low temperature similar to viscous fluid rheology at large scale (Rutter, 1983;
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Emerman and Turcotte, 1983; Wheeler, 1992).
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In recent times, a number of mechanical models have been proposed to show the
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contribution of ductile deformation in mountain building processes. For example, Bose et al.,
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2014a showed that the influence of ductile deformation is crucial in the development of a
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series of terrane-scale transverse structural domes in the eastern Himalayas. Their 4
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interpretation on the development of complex fold patterns in the Rangit window of
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Darjeeling-Sikkim Himalaya (DSH) is consistent with the mechanism of superposed buckling
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of ductile folds (Ghosh et al., 1992). Moreover, Butler et al., 2019 have emphasized the
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importance of buckle folding in predicting the geometry of subsurface structures in fold-and-
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thrust belts. Besides widespread occurrence of common ductile structures, many FTBs also
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exhibit patchy occurrences of L-tectonites or L>S tectonites towards the hinterland (Flinn,
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1956, 1958, 1959; Hossack, 1968; Chapman et al., 1979; Holst and Fossen, 1987; Sylvester
108
and Janecky, 1988; Passchier et al., 1997; Braathen et al., 2000; Poli and Oliver, 2001;
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Piazolo et al., 2004; Sullivan, 2006, 2013). L-tectonites are generally considered as an
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expression of pure constrictional strain field (Treagus and Treagus, 1981, Ramsay and Huber,
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1983; Ghosh et al., 1995). However, it is not clear how the constrictional strain field evolves
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in fold-and-thrust belts in the framework of collisional setting under unidirectional stress
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field. In addition, reports of cross folds and transverse ductile fabrics from many FTBs (Glen
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and Walsche, 1999; Bell et al., 2004; Little, 2004) further substantiate the relevance of the
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development of contractional strain field orthogonal to the bulk shortening direction in a
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collisional belt.
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Using laboratory experiments, this study reinvestigates the significance of the viscous
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wedge model for explaining the occurrences of varying ductile structures in fold-and-thrust
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belts. Our models demonstrate that constrictional strain field can locally develop towards the
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hinterland of a growing FTB over weak basal decollement, leading to L tectonites and cross
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folds. Strong decollement condition, in contrast, allows gravity driven flow to occur in the
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hinterland, giving rise to the localization of orogen-parallel recumbent folds. Our experiments
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suggest that both weak and strong decollement produce pervasive, hinterland dipping ductile
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fabrics towards the frontal part of fold-and-thrust belts. Based on our laboratory experiments,
5
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we conclude that distributed ductile strain has a strong control on the structural evolution of
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fold-and-thrust belts.
127
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2. Experimental Approach:
129
2.1
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Material and Model Set up: We used a conventional sandbox-like deformation box (e.g., squeeze box under
131
normal gravity) as shown in Mulugeta (1988). The box was made of transparent acrylic.
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Linearly viscous polydimethyl-siloxane (PDMS, manufactured by Dow Corning under the
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trade name SGM36; see Weijermars, 1986 for PDMS properties) was chosen as a modelling
134
material to explore crustal flow trajectory in response to continuous horizontal shortening.
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While the linear viscous PDMS used in our experiments greatly simplifies the modelling of
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flow behaviour in heterogeneous crustal rocks, it provides considerable insights on internal
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deformation within a viscous wedge. The viscosity of PDMS (5 × 104 Pas) is also suitable for
138
understanding the interaction of gravity flow in a collisional setting.
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A rectangular PDMS slab of dimension (40 cm length, 25.3 cm width and 2.0cm
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thickness) was prepared separately to simulate the undeformed crustal rocks in fold-and-thrust
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belts. Four side walls and the basal plate of the deformation box were carefully washed, dried
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and. then the lateral walls were coated with a weak lubricant before placing the PDMS slab
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within the deformation box (Fig. 1). The weak lubricant was used to minimise the frictional
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resistance along the interface between the PDMS slab and the inner walls of the deformation
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box. The interface between the basal acrylic plate and the PDMS slab is considered as the
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basal decollement surface. We performed two sets of experiments by varying the decollement
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strength (weak or strong). The weak decollement was simulated by lubricating the basal plate
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uniformly with a low viscosity (~ 4068 m Pas) fluid (See Supplementary Fig. S1) and strong
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decollement was simulated with no lubrication on the basal plate. The viscosity of the fluid 6
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was measured using a Cone-and-plate (CP-40, conical plate of diameter 40 mm and an angle
151
of 1°) measuring system in an Anton Paar MCR 92 Rheometer under laboratory room
152
temperature of 25°C. In all experiments we kept the piston speed (~ 1.97 × 10-4 ms-1)
153
constant to nullify the effects of rate dependence on viscous models. The model was
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deformed by moving the vertical side wall (backstop), guided by a rigid piston connected to a
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computer-controlled step-up motor, over the basal plate (Fig. 1). In our experiments, we
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ensured the condition of constant volume of wedge material during the entire experimental
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run and care has been taken so that no material can leak through the 1mm slit between the
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rigid backstop and basal plate.
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We analysed our model results in a three-dimensional Cartesian coordinate system
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(Fig. 1). During experimental run, the model was allowed to grow vertically along the X-axis.
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The model-width (along the Y-axis) was kept constant in order to obtain the condition of no
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rotation on the YZ and XY planes of bulk strain (Pfiffner and Ramsay, 1982). Hence, our
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experiments were performed under bulk plane strain condition. In order to continuously
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monitor the evolution of 3D strain pattern during the wedge growth, we stamped dry carbon
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powder as circular passive markers on two surfaces (top surface and front lateral surface) of
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the initial model corresponding to YZ and XZ planes. However, we could not monitor the
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progressive change in strain pattern along the XY plane. In our model setup, the XY plane
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(~backstop wall) is attached to the moving piston. The calculation of strain variations on the
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XY plane were obtained from the strain ratios on YZ plane. It is possible because we ran our
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experiments under bulk plane strain condition at constant volume (Bajolet et al., 2013). Two
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digital cameras were positioned at a fixed distance to record progressive stages of
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deformation for top-view and sectional-view (Fig.1) at regular preset time intervals during the
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experimental runs. We then measured the displacement of passive markers by tracking the
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successive change in positions of the material points using the ImageJ software. Using SSPX
7
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software, strain maps for both XZ and YZ planes were computed from the displacement data
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using the Grid Distance Weighted (GDW) method (Cardozo and Allmendinger, 2009). It is to
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note that computed strain maps do not reveal the topographic outline observed on the XZ
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section of the model because the GDW method uses a uniform grid spacing consisting of
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square cells to calculate strain distribution in the deformed state (Cardozo and Allmendinger,
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2009). Strain is calculated at the centre of each square cell using all the stations (i.e. using the
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total number of passive marker points in our model). The individual stations are weighted on
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the basis of their distance from the centre of the square cells by a specific weighting factor.
183
Moreover, it is essential to note that the GDW method of strain computation involves
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calculation of strain on a surface that is either flat (slice) or on a surface that follows the
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topography of the data. In our calculation, we computed strain at all stations (centre of
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circular markers) in the deformed stage to obtain a first order strain magnitude for the entire
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model length. Strain magnitudes are calculated based on the finite displacement between
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neighbouring points, leading to either extension (positive) or contraction (negative).
189
190
2.2 Scaling of the model: The selection of analogue materials and modelling approach took into account the
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necessity of ensuring proper scaling of our experiments with nature (Table -1). The ratio
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between model length and thickness of 20:1 scales to nature in the order of 106. This implies
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that an initial model length of 40 cm (
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while the initial slab thickness (ℎ ) of 2 cm and width of 25.3 cm of our model correspond to
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a crustal thickness (ℎ ) of ~ 20 km and a lateral extent of ~ 253 km respectively. The
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rheological behaviour of analogue materials (PDMS) is governed by constitutive equations of
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viscous flow, implying the importance of time for appropriate scaling of a viscous model to
198
its natural prototype. The convergence velocity (V ) of 1.97 × 10-4 ms-1 in our experiments
199
corresponding to the plate velocity (V ) of 3.1 cm/yr (De Mets et al., 2010; Argus et al.,
) represents a stretch of ~ 400 km in nature (
8
)
200
2011), leads to a strain rate ratio ( ) ~ 4.5 × 10-12, between nature and model and a time ratio
201
(
202
hour corresponds to ~23Ma in a natural system and an experimental strain rate (
203
4 -1
204
are scaled with natural prototype by considering a balance between the ratio of viscous force
205
and gravitational force as follows:
) ~ 2 × 1011. A time ratio (
) of 2 × 1011 in our experiment means that model run of one
s in our models approximately simulates the natural strain rate ( ) of 10-15 s-1. Our models
=
206 207
where,
,
,
,
and
---------------------eq.1
are the viscosity, strain rate, density, acceleration due to
208
gravity and length ratios between nature and model respectively.
209
As the ratio of gravitational acceleration (
210
( ) is an inverse of the time ratio ( =
211
) is 1 with negligible error and the strain rate ratio
), equation 1 given above is thus simplified as follows:
-----------------------------eq.2
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From equation 2, the viscosity ratio (
213
of crustal rocks (
214
the order of 104 Pas.
215
) of 2 × 10-
) is computed to be 5.6 × 1017, such that the viscosity
) is in the order of 5.6 × 1021 Pas for a viscosity of model material (
) in
We also calculated the Argand number, Ar, as a ratio between gravitational stress (
216
and horizontal compressional viscous stress (
) from our deformed model width (w),
217
following Medvedev (2002) (Table -1). From our models of weak decollement (Fig. 2a), the
218
gravitational stress [
219
compressive viscous flow stress [
220
the wedge is ~ 56.285Pa respectively, leading to Ar of ~6.82. In case of models with strong
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decollement, the value of Ar becomes ~ 8.42 corresponding to the gravitational stress [
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965 kgm-3 × 9.8ms-2 × 8.78×10-2m] of ~ 830.324Pa and normal compressive viscous flow
223
stress, [
= 965 kgm-3 × 9.8ms-2 × 4.06×10-2m] is ~ 383.954Pa and normal = (5×104 Pas × 1.97×10-4 ms-1) / (17.5×10-2 m)] within
= (5×104 Pas × 1.97×10-4 ms-1) / (10×10-2 m)] of ~ 98.5 Pa respectively. Such 9
=
)
224
values of Argand number are considered to be relevant for describing force balance in
225
evolving orogenic wedges (England and McKenzie, 1982; Dewey et al., 1986; Cruden et al.,
226
2006).
227 228
3. Experimental results:
229
3.1 Weak Decollement
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Rectangular PDMS slab of 2.0 cm thickness produced a crude wedge-shaped geometry
231
adjacent to the hinterland buttress after the model was shortened by ~ 3.3% (Fig. 2a). During
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this stage of shortening (initial stage), wedge grew mostly vertically and thereby,
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continuously increased the wedge elevation near the hinterland buttress. With continued
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shortening for about 10.5%, the wedge elevation reached to 2.98 cm. At this stage, the width
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of the deformed wedge became 8.3 cm with a surface slope (α) of the wedge around 10.15°
236
(Figs. 2a, 3a). However, further shortening of 5.9 cm (i.e., total model shortening = 10.08 cm)
237
increased the surface slope (α) by 2.65°, indicating decrease in the rate of vertical growth as
238
shown in Fig.3a. We designate this declining stage of vertical growth rate as intermediate
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stage of wedge evolution. However, the decrease in vertical growth rate allowed the wedge to
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propagate horizontally in the frontal direction during the intermediate stage (Fig. 2a). This
241
reflects a distinct shift in the mode of wedge evolution from initial vertical growth to
242
widening of the deformation wedge in the intermediate stage. However, it is interesting to
243
note that the maximum elevation of the growing wedge varied along the Y-axis of the model
244
near the hinterland buttress during the intermediate stage. The highest elevation of the wedge
245
was attained adjacent to both lateral walls (front wall and back wall), developing a trough like
246
geometry in the central part of the model (Fig. 4a, Supplementary Fig.S2). We anticipated the
247
cause of such variable wedge elevation to be the narrow dimension of the deformation box
248
along Y-axis of bulk strain. We then performed a second set of experiments with large model
10
249
width (35 cm), keeping the thickness of the initial model constant (2.0 cm). However, this set
250
of experiments also revealed similar topographic variations towards the hinterland (See
251
Supplementary Fig. S3), suggesting little or no effects of confinement on our first set of
252
model results (Souloumiac et al., 2012). We discuss the cause and implication of such
253
localized topographic highs near the lateral walls in section 4.2. Further shortening of the
254
model, in contrast, started to lower the wedge slope (α) (Figs. 2a, 3a). Our experiments show
255
that the entire amount of horizontal shortening was then used to increase the width of the
256
deforming wedge by complete cessation of the vertical growth. We mark this stage of wedge
257
growth as final stage of wedge evolution. The preceding discussion reveals that the horizontal
258
shortening of the model facilitates the wedge to grow continuously in the frontal direction
259
though the vertical growth of the wedge ceases after a threshold elevation near the hinterland
260
buttress. This observation from our experimental results is consistent with the occurrence of
261
low surface slope in natural fold-and-thrust belts (e.g., α has been estimated to be around 4°
262
for the entire Himalayan wedge, Avouac (2007), though our models had a horizontal
263
decollement in contrast to dipping basal decollement (Main Himalayan Thrust) below the
264
Himalayan wedge. Moreover, our experimental results also do not account for syntectonic
265
surface erosion, which would also be likely to lower the surface slope of a tectonic wedge.
266
Passive circular markers stamped on the XZ section immediately deformed into
267
ellipses near the hinterland buttress with the onset of model deformation. The long axes of
268
strain ellipses at the initial stage were oriented approximately normal to the basal plate i.e
269
along the X-axis of bulk strain. However, the orientation of their long axes underwent
270
anticlockwise rotation in the rear part of the model with progressive shortening, giving rise to
271
a zone of steeply inclined (>70°) strain ellipses (Fig. 2a). At this stage, aspect ratios of
272
ellipses also increased substantially. Strain maps from the XZ section distinctly reveal this
273
change in the magnitude of longitudinal strain from 2.05% to 29.7% in the hinterland with
11
274
progressive shortening (Fig. 2b). Strain maps in successive stages also show progressive
275
change in the orientation of extensional axis, corresponding to the major axis of strain
276
ellipses. The deformation of passive markers towards the frontal direction evolved by varying
277
inclinations of strain ellipses with depth. The amount of inclination decreased with depth,
278
developing an asymptotic trace of the long axes of strain ellipses (Fig. 2a). Such a depth-wise
279
variation in the inclination of strain ellipses towards the foreland can be compared with
280
previous theoretical studies on the evolution of viscous wedge (Pollard and Fletcher, 2005).
281
Passive markers on the YZ section (top surface), also deformed to ellipses near the
282
hinterland with the initiation of bulk shortening, where long axis of ellipses were oriented
283
along the Y-axis of bulk strain (Fig. 4a). The aspect ratio of strain ellipses varied between 1.1
284
and 4.9 during the initial stage of wedge growth (Fig. 4a). The increased rate of frontal ward
285
propagation of deformation during the intermediate stage of wedge growth is marked by
286
continuous increase in the aspect ratios of passive markers towards frontal direction.
287
However, at this stage (~26% shortening) the aspect ratio of strain ellipses near the hinterland
288
buttress stopped increasing (Fig. 4a). Instead, the aspect ratios started to decrease by
289
decreasing the length of the major axis of strain ellipses. This phenomenon of contraction of
290
the major axes became prominent when the model was shortened by at least ~38% (Fig. 4a).
291
With further shortening, a large number of strain ellipses transformed to almost circular shape
292
in the central part of the hinterland, indicating the development of a local compressional strain
293
field close to the hinterland buttress, along Y-axis of bulk strain (Fig. 4a). Interestingly, the
294
length of diameters of the new deformed circles decreased by 16% of the diameter of
295
undeformed passive markers in the initial model. Models with large dimension (40cm × 35cm
296
× 2cm) also yielded similar results (See Supplementary Fig.S3). However, the aspect ratios of
297
strain ellipses continued to increase towards the frontal direction with progressive shortening
298
for both sets of experiments (Figs. 4a, Supplementary Fig. S3). Strain maps from YZ sections
12
299
of this model distinctly demarcate a zone of overall compression (marked by dashed white
300
line in Fig. 4c) near the hinterland buttress, leading to the localization of overall
301
compressional strain field. Analysis of our model results thus suggests the relevance of
302
viscous wedge models for explaining the prevalence of patchy occurrences of L-tectonites and
303
cross folds in fold-and-thrust belts (Sylvester and Janecky, 1988; Passchier et al., 1997;
304
Braathen et al., 2000; Piazolo et al., 2004; Sullivan, 2006, 2013; Das et al., 2016), which
305
demand the existence of along-strike shortening during orogenic wedge growth. Our model
306
results show that the occurrence of orogen-parallel ductile fabrics towards the frontal part of
307
fold-and-thrust belts is consistent with the orientation of strain pattern revealed from our
308
experiments (Fig. 4c).
309
310
311
3.2 Strong decollement Strongly coupled decollement experiments developed a steep surface slope (α=31.61°)
312
during the initial stage of wedge growth when the model was shortened by ~ 10.76% (Fig.
313
5a). With increasing the amount of shortening (~34.9% i.e., ~14 cm of shortening), the
314
surface slope steepened further to ~37.84° over a relatively narrow wedge (~7.0 cm) (Fig. 5a),
315
However, the wedge height near the hinterland stopped increasing after reaching a threshold
316
elevation (8.36 cm) and further shortening (>35%) eventually lowered the wedge slope (Figs.
317
3b, 5a). However, the mechanism of lowering the wedge slope over strong decollement is
318
drastically different from that of the weak decollement experiments discussed in section 3.1,
319
where it was controlled by increasing the frontal propagation rate of the deforming wedge. In
320
contrast, the lowering of topographic slope for strong decollement is associated with lateral
321
flow of wedge material from the hinterland towards the foreland along the topographic slope.
322
It also hints that the frontal propagation of the wedge was not significant over strong
323
decollement. We also envisage the initiation of such lateral flow of wedge material as a 13
324
consequence of large elevation difference (~ 6 cm) between the hinterland and foreland over a
325
narrow (~ 7 cm) deformation wedge (Fig. 5a). The activation of material flow along the
326
wedge slope is distinct from the progressive rotation of passive markers on the XZ section,
327
where the dip of the long axis of strain ellipses near the hinterland continuously decreased to
328
become approximately sub-horizontal till the model was shortened by ~43% (Fig. 5a). The
329
development of a narrow wedge indicates that the amount of horizontal shortening was
330
largely accommodated by increasing the wedge elevation during the entire wedge growth. It is
331
to note that the maximum value of wedge height attained over strong decollement was
332
substantially larger than that developed over weak decollement experiments for an equivalent
333
amount of shortening (Fig. 3). Interestingly, the wedge height remained constant along the Y-
334
axis of bulk strain near the hinterland buttress in contrast to the varying wedge elevation over
335
weak decollement. This finding not only signifies a strong influence of decollement strength
336
on the mode of viscous wedge evolution, but also validates our model results with little or no
337
effects of lateral confinement in our experiments. Towards the frontal part of the wedge, the
338
passive markers on the XZ section were uniformly inclined towards the hinterland and
339
thereby, separated the hinterland segment from the foreland of a deforming wedge by a sharp
340
contrast in the orientation of strain ellipses (Fig. 5a). Based on our model results, we infer that
341
the presence of regional occurrence of low foliation dips towards the hinterland might be an
342
expression of a strong basal decollement beneath the fold-and-thrust belts. Additionally, our
343
experiments show that the orientation of strain ellipses in the upper part of the model wedge
344
started to rotate backward towards the hinterland after a significant amount of shortening
345
(>10%, Fig. 5a). According to our experiments, the mechanism of the back-rotation of the
346
strain ellipses is consistent with the occurrence of north-verging back folds reported from
347
orogenic hinterland of the Nepal Himalaya (Godin et al., 2011). Although our laboratory
348
experiments provide new insights on the evolution of ductile structures in fold-and-thrust
14
349
belts, scaling of topography in our models shows significant exaggeration compared to natural
350
prototype. We attribute this dichotomy to the absence of isostatic compensation in our
351
experiments, where models were deformed over a rigid basal plate for understanding the
352
mechanics of crustal deformation in orogenic belts. In addition, absence of surface erosion in
353
our experiments might have also played a role to increase the wedge elevation.
354
The strain maps computed from the displacement of passive markers on the XZ
355
section (Fig. 5b) revealed the progressive change in the magnitude and orientation of
356
extensional strain from hinterland to foreland with continuous shortening. The amount of
357
longitudinal strain increased from 22.7% (initial stage) to 135% (intermediate stage) in the
358
hinterland with progressive shortening. Further shortening, however, did not reveal much
359
changes in the magnitude of strain, but exhibited significant variations in the orientations of
360
extensional axis, particularly towards the hinterland. Interestingly, this change in the
361
orientation of strain ellipses is accompanied by lowering of wedge slope in our models (Figs.
362
3b, 5a). We attribute the combination of rotation of strain ellipses on the XZ section and
363
decrease in wedge slope to the activation of gravity flow in the hinterland. Finally, the
364
extensional axes near the hinterland became almost horizontal in consistence with the
365
orientation of strain ellipses after a large amount of shortening (Figs. 5a, 5b).
366
On the YZ section (i.e. top surface, Fig. 6a), deformation of passive markers showed
367
distinct differences in their orientation from that of the weak decollement (Fig. 4a). At the
368
initial stage, the long axes of strain ellipses (aspect ratio ~ 1.5) were oriented parallel to the Y
369
axis of bulk strain near the hinterland buttress (Fig. 6a). However, after a horizontal
370
shortening of 9.5% in the model, the former short axes of the ellipses in the initial stage
371
started to lengthen and eventually, transformed to major axis of the strain ellipses with
372
progressive shortening. Such a switch from minor to major axis of the finite strain ellipse
373
became evident when the amount of shortening was fairly large (32%). The computed strain 15
374
maps also revealed consistent orientation of extensional axes towards the hinterland with
375
increasing deformation (Fig.6c). In the finite model, the orientation of deformed passive
376
markers also developed two distinct zones of contrasting orientation of strain ellipses
377
corresponding to hinterland and foreland segments on the YZ- plane: (i) parallel to the Z- axis
378
of bulk shortening towards the hinterland, and (ii) parallel to the Y- axis of bulk strain
379
towards the foreland. Analysis of our model results from YZ sections thus led us to conclude
380
that the change in the direction of the long axis of strain ellipses must have resulted due to the
381
activation of the lateral flow of wedge material from hinterland to foreland (Figs. 6a, 6c). The
382
zone separating the two segments of contrasting orientation of strain ellipses on YZ section
383
fairly coincides with the intensely stretched zone of strain ellipses of very high aspect ratio on
384
the XZ section (Fig. 5a). Interestingly, this zone also marks the region of topographic slope
385
break on the XZ section. Based on above discussion regarding the distribution of strain
386
patterns on the XZ and YZ planes over strong decollement, we infer that localization of large
387
strain near the topographic slope break on the XZ section can be a potential site for large scale
388
thrusting event in orogenic belts.
389
4. Discussion:
390
4.1 Wedge topography
391
Our experiments described above show that the degree of coupling at the basal
392
decollement is an important parameter that regulates the first-order topographic evolution of
393
mountain belts. The ratio of vertical growth to horizontal propagation of a tectonic wedge
394
increases with increasing the degree of basal coupling. Our model results suggest that weak
395
decollement promotes a tectonic wedge to grow horizontally for a large extent, forming a
396
gentle surface slope (Figs. 2a, 3a). On the other hand, strongly coupled decollement leads to a
397
narrow wedge with steep surface slope (Figs. 3b, 5a). This variation in the development of
16
398
viscous wedge geometry at different decollement strengths corresponds well with previous
399
studies for varying Ramberg number, Rm (Medvedev, 2002). Higher value of Rm develops
400
wedges similar to weak decollement experiments, whereas lowering the value of Rm gives rise
401
to a narrow wedge with steep surface slope similar to our models over strong decollement.
402
Lowering the rate of frontal propagation over strong decollement allowed the wedge to grow
403
vertically at a faster rate towards the hinterland, resulting in variations in internal gravitational
404
potential due to a large elevation difference from hinterland to foreland. This lateral variation
405
in elevation eventually resulted in the initiation of gravity driven flow towards the frontal
406
direction. The onset of gravity flow has been clearly recognized by continuously tracking the
407
successive positions of passive markers on the XZ section (Fig.5b). The displacement vectors
408
showed a large vertical component in the initial stage of wedge growth, which in turn reduced
409
greatly with the onset of gravity flow. The reduction of vertical component was also evident
410
from progressive narrowing of spacing between successive flow vectors (Fig. 5b). The
411
influence of gravity driven flow in the formation of wedge geometry in our experiments is
412
consistent with earlier theoretical models (Copley, 2012). Furthermore, tracing the terminal
413
points of deformed passive markers, which were initially aligned horizontally in the
414
undeformed model, gave rise to a recumbent fold like geometry on the XZ plane with a
415
convex upward topographic profile (Figs. 5a, 5b). Knowing fully well that our experiments
416
are much simpler than that of natural deformation in FTBs, it provides an alternative
417
explanation for the development of orogen-parallel recumbent folds that are reported from
418
many fold-and-thrust belts. The development of convex-upward topographic profile similar to
419
our models is also not uncommon in nature, rather it shows strong consistence to explain the
420
bathymetric profiles across the Kurile, Ryukyu and Aleutian accretionary wedges (Emerman
421
and Turcotte, 1983). This study also revealed the crustal rocks to behave as a Newtonian fluid
422
similar to our experiments.
17
423
The geometry of viscous wedges discussed above over weak and strong decollement
424
show close resemblance to the geometry of brittle wedges at varying frictional resistance on
425
the basal decollement (Davis et al., 1983; Gutscher et al., 1996; Schott and Koyi, 2001; Bose
426
et al., 2009). This implies that the magnitude of shear stress on the basal decollement
427
essentially guides the development of first-order mountain topography, irrespective of crustal
428
rock rheology. The viscous wedge models, however, have provided much insights on the
429
distribution of ductile strain during the evolution of a tectonic wedge.
430
4.2 Analysis of internal strain in a viscous wedge
431
Our experiments on viscous wedge distinctly reveal the cause of spatially varying
432
ductile structures in fold-and-thrust belts. Although the formation of a viscous wedge is
433
phenomenologically similar for both strong and weak decollements described in many earlier
434
studies (Emerman and Turcotte, 1983; Rossetti et al., 2000; Chattopadhyay and Mandal,
435
2002), strain pattern within the wedge varies drastically with changing decollement rheology.
436
Our experiments under plane strain condition, show that uniformly weak basal decollement
437
condition may lead to along-strike variations in ductile structures towards the orogenic
438
hinterland. We discuss below how the kinematic condition at the basal decollement can
439
influence the evolution of ductile structures in fold-and-thrust belts.
440
The weak decollement experiments developed a self-regulating convergent flow in the
441
central part of the hinterland on the YZ section, resulting in continuous decrease in the aspect
442
ratio of strain ellipses during the intermediate stage of the wedge growth. The decrease in
443
aspect ratio transformed some strain ellipses even to circular shape (Fig. 4a). However, the
444
surface area of the deformed circular markers has been reduced significantly (~by 30%) from
445
that of the undeformed stage, suggesting the wedge material to stretch vertically along X-axis
446
in order to conserve the volume under plane strain. We correlate the significance of this
447
vertical stretching interpreted from our models as a probable mechanism for the development 18
448
of patchy L-tectonites in FTBs. Strain maps computed from the model results at successive
449
steps distinctly define a zone of overall compressional regime on the YZ section
450
corresponding to the occurrence of circular strain markers (Fig. 4c). Based on our
451
experimental results, we attribute this compressional zone as responsible for the development
452
of cross folds, L-tectonites and dome-basin structures documented from many fold-and-thrust
453
belts (Sylvester and Janecky, 1988; Passchier et al., 1997; Glen and Walsche, 1999; Braathen
454
et al., 2000; Piazolo et al., 2004; Bell et al., 2004; Little, 2004; Sullivan, 2006, 2013; Das et
455
al., 2016). Our experimental results thus seemingly contend the interpretation of orogen-
456
parallel ductile stretching in the Greater Himalayan sequence of the Annapurna-Dhaulagiri
457
Himalaya (Parsons et al., 2016). However, their analyses suggest that the orogen-parallel
458
crustal stretching in the Annapurna Dhaulagiri Himalaya must have resulted in a flattening
459
(oblate/sub-oblate) strain regime. The difference between our model results and natural
460
observations suggest that bulk plane strain condition might play a crucial role for localizing
461
the compressional regime towards the hinterland, leading to the formation of L-tectonites and
462
orogen-transverse ductile fabrics in FTBs. However, factors causing the plane strain
463
deformation condition in natural situation have still remained unclear, albeit the assumption
464
of plane strain condition has been widely used for understanding the evolution of FTBs at
465
large scale (Willett, 1992; Beaumont et al., 1992; Fullsack, 1995). Integrating our model
466
results and structural imprints in FTBs we envisage that along-strike rheological variations
467
(Jamieson et al., 2007) might constrain the deformation to occur under plane strain condition
468
in orogenic belts. In such situations, the laterally occurring relatively stronger crustal rocks
469
can act as lateral walls similar to our laboratory experiments. In addition, we also show that
470
laterally varying rheology of basal decollement can also lead to along-strike compressional
471
regime towards the hinterland above weak decollement segment (Supplementary Fig. S4),
472
giving rise to orogen-transverse ductile structures in fold-and-thrust belts.
19
473
In order to reveal better insights on the progressive evolution of three dimensional
474
strain state over weak decollement, we plotted strain ratio data of 495 passive markers in a
475
Flinn diagram to evaluate the progressive growth of tectonic wedges. Analysis of Flinn plots
476
at successive stages reveal that tectonic wedges evolve through spatial and temporal
477
variations in deformation. For example, at the initial stage, flattening strain governs the
478
development of ductile structures in the entire wedge (Fig.7a). However, with increasing
479
shortening, strain pattern changes remarkably from hinterland to foreland. The flattening
480
strain, however, continued to control the deformation in the frontal part of the wedge (Fig.
481
7c), whereas the hinterland part of the wedge shows the development of localized
482
constrictional strain field (Fig. 7b). Based on our model results over weak decollement, we
483
provide a generalised 3D structure of wedge geometry to show the characteristic strain pattern
484
variations from hinterland to foreland in figure 8.
485
We also investigated the incremental evolution of strain pattern from our model results
486
(Fig. 9) by adopting the protocol described by previous workers (Fischer and Keating, 2005;
487
Cardozo and Allmendinger, 2009). After a significant amount of shortening (>30%), the
488
strain maps at successive incremental steps show marked differences in the strain pattern in
489
the central zone of compression, compared to the strain maps computed from finite strain
490
(Figs. 4c, 9). For example, Fig. 9d clearly reveals that the compressional zone partly
491
transformed to extensional regime, close to the hinterland buttress. Further increments of bulk
492
shortening converted the entire zone of compression as in Fig. 9c to a zone of extension (Fig.
493
9e). Interestingly, the orientations of extension axes within the transformed zone are found to
494
orient along the direction of bulk shortening, i.e. parallel to Z-axis. This observation further
495
validates the localization of convergent flow along the Y-axis of bulk strain in our models.
496
Based on our model results, we attribute the dissimilarity between the finite and incremental
497
strain maps to the mode of convergence in fold-and-thrust belts. The strain maps computed
20
498
from finite strain (Fig. 4c) represent a collisional setting of continuous convergence,
499
developing the strong compressional regime towards the hinterland, whereas incremental
500
strain maps indicate the evidence of intermittent breaks during the convergence between two
501
continental plates. The above discussion thus suggests that segmented episodes of
502
convergence in collisional belts may play a crucial role in the localization of cross folds and
503
orogen-transverse ductile fabrics in FTBs (Glen and Walsche, 1999; Bell et al., 2004; Little,
504
2004). The gradual change of compressional strain field to extensional regime further builds a
505
coherent reasoning to explain why L-tectonites are rare in fold-and-thrust belts.
506
For strongly coupled basal decollement, the attainment of steep wedge slope (~
507
32.48°) set the wedge to deform internally under the action of gravity and thereby, rotated the
508
earlier steeply dipping strain ellipses to become almost sub-horizontal on the XZ-plane
509
towards the hinterland (Figs. 5a, 5b). The evidence of gravity flow is also distinct from the
510
orientation of strain ellipses (parallel to the direction of bulk shortening) in the hinterland
511
zone of YZ- section (Fig. 6a). However, alignments of strain ellipses towards the foreland on
512
both XZ and YZ sections indicates relatively weak or no influence of gravity driven flow
513
(Figs. 5a, 6a). Based on our experiments, we infer that the phenomenon of episodic
514
gravitational collapse and spreading of overlying crustal rocks in the Nepal Himalaya
515
described by previous workers (Bell and Sapkota, 2012) is likely to have occurred when the
516
rheology of the MHT (basal decollement) below the Nepal Himalaya was relatively strong.
517
The deformation of strain markers on the XZ section in experiments over strong decollement
518
(Fig. 5b) suggest that the gravity driven flow can be responsible for the development of
519
orogen-parallel recumbent folds in fold-and-thrust belts (Valdiya, 1981; Coward et al., 1982,
520
1988; Brun et al., 1985; Searle and Rex, 1989; Jain and Manickavasagam, 1993; Godin, 2003;
521
Banerjee et al., 2015). Moreover, based on our analogue models over strong decollement we
522
predict that occurrence of recumbent fold zone in fold-and-thrust belts can be considered as a
21
523
separator between the foreland and hinterland. Earlier studies also ascribed the influence of
524
gravity driven flow in building the architecture of orogenic belts (Copley, 2012). Flinn plots
525
from the deformed models show that deformation of tectonic wedge over strongly coupled
526
decollement is entirely governed by flattening type of deformation (Fig. 10).
527
4.3 Implications on Himalayan fold-and-thrust belts
528
This study has significant implications in interpreting the development of ductile
529
structures and first-order topographic evolution of fold-and-thrust belts. Geological records
530
suggest that fold-and-thrust belts are characterised by penetrative ductile foliations and
531
associated buckle folds of multiple orders. In Himalayan tectonics, multi-ordered folds have
532
recently been reported from the Darjeeling-Sikkim section of the eastern Himalaya (Bose et
533
al., 2014a). Their studies have advocated the concept of superposed buckling as responsible
534
for the development of multi-ordered dome-basin structures. In a recent study, Das et al.,
535
2016 reported the presence of L-tectonites in the hanging wall rocks (e.g., Lingtse granite) of
536
Main Central Thrust (MCT) from the Darjeeling-Sikkim Himalaya (DSH). Strain analysis
537
from our weak decollement experiments relate the development of these L-tectonites towards
538
the extreme hinterland of the Darjeeling-Sikkim Himalayan wedge during the intermediate
539
stage of the wedge growth in response to Indo-Asia collisional event and subsequently
540
transported southward to the present location during the MCT thrusting. Combining our
541
experimental findings and field structures described from DSH it appears that the Main
542
Himalayan Thrust (basal decollement) beneath the Darjeeling-Sikkim Himalayan wedge was
543
relatively weak, resulting in the development of cross folds, L-tectonites and dome-basin
544
structures. Although L-tectonites are rare in the Himalayan belts, there are reports of patchy
545
occurrences of L-tectonites from NW Himalaya (Singh and Thakur, 2001; Dipietro and
546
Pogue, 2004). Recently, we also recorded isolated patch of L-tectonites in the high grade
547
rocks of Arunachal Himalaya (N 28° 23.485', E 095° 55.363'). The spatially varying 22
548
occurrence of Himalayan L-tectonites is consistent with the localization of patchy
549
constrictional strain field in our experimental models over weak decollement (Fig. 4).
550
Darjeeling-Sikkim Himalaya also witnessed the development of multi-ordered
551
recumbent folds (Banerjee et al., 2015). According to our experimental results, gravity driven
552
flow over strong decollement plays a role in developing recumbent folds in tectonic wedges.
553
However, co-existence of dome-basin structure (Bose et al., 2014a), L-tectonites (Das et al.,
554
2016) and orogen-parallel recumbent folds (Bose et al., 2014a, Banerjee et al., 2015) in the
555
DSH reflects temporal variations in the MHT rheology (decollement strength) beneath the
556
Darjeeling-Sikkim Himalaya during the evolution of Himalayan fold-and-thrust belts. On the
557
west of DSH, the evidences of north-verging folds at shallow crustal level (Godin et al., 2011)
558
and gravitational collapse towards the hinterland of the Central Nepal (Bell and Sapkota,
559
2012) indicate the Himalayan wedge to grow over relatively stronger MHT. These findings
560
not only reconcile our experimental studies with laterally varying ductile structures of
561
Himalayan belts, but also provide a strong basis for understanding the cause of along-strike
562
variations of topography and seismic activities in the Himalayan wedge (Singer et al., 2017;
563
Bai et al., 2019).
564
5. Conclusion:
565
This study provides an analysis of three-dimensional strain pattern for explaining the
566
cause of spatially varying ductile structures in fold-and-thrust belts. The recognition of
567
systematic variations in ductile structures across the orogenic belts is useful for gaining first-
568
order understanding on the rheology of basal decollement during the growth of mountain
569
belts. Development of isolated patches of L-tectonites and cross-folds in orogenic hinterland
570
signify either laterally varying crustal rheology or decollement strength in fold-and-thrust
571
belts. Our models over strong decollement show that localization of gravity driven flow in the
23
572
hinterland may lead to orogen-parallel recumbent folds in fold-and-thrust belts. The
573
development of pervasive, hinterland dipping ductile fabric in the frontal part of fold-and-
574
thrust belts indicates overall flattening type of deformation for both weak and strong basal
575
decollements.
576
577
578
Acknowledgements We thank two anonymous reviewers for their constructive suggestions and Joao Hippertt
579
for editorial handling. SB acknowledge financial supports from the project funded by SERB,
580
Government of India, (Project No. EMR/2015/000910). SR received the Inspire fellowship
581
(No. DST/INSPIRE Fellowship/2016/IF160071) for doctoral research and PS acknowledge
582
the postdoctoral research project (No. F.4-2/2006(BSR)/ES/17-18/0035), funded by UGC.
583
584
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Structural Geology, 27(8), 1486-1504.
972
Williams, P. F., Jiang, D., Lin, S. (2006). Interpretation of deformation fabrics of
973
infrastructure zone rocks in the context of channel flow and other tectonic
974
models. Geological Society, London, Special Publications, 268(1), 221-235.
975
Xu, Z., Wang, Q., Pêcher, A., Liang, F., Qi, X., Cai, Z., Cao, H. (2013). Orogen‐parallel
976
ductile extension and extrusion of the Greater Himalaya in the late Oligocene and
977
Miocene. Tectonics, 32(2), 191-215.
978 979
980
Xypolias, P. (2010). Vorticity analysis in shear zones: a review of methods and applications. Journal of Structural Geology, 32(12), 2072-2092. Xypolias, P., Kokkalas, S. (2006). Heterogeneous ductile deformation along a mid-crustal
981
extruding shear zone: an example from the External Hellenides (Greece). Geological
982
Society, London, Special Publications, 268(1), 497-516.
983
Xypolias, P., Spanos, D., Chatzaras, V., Kokkalas, S., Koukouvelas, I. (2010). Vorticity of
984
flow in ductile thrust zones: examples from the Attico-Cycladic Massif (Internal
985
Hellenides, Greece). Geological Society, London, Special Publications, 335(1), 687-
986
714.
987
988
Figure captions:
41
989
Fig.1 Schematic diagram of experimental setup. Inset showing initial model geometry with
990
reference to Cartesian coordinate system. Vertical and horizontal scale bars shown in diagram
991
are in cm.
992
Fig.2 (a) Cross-sectional view (XZ section) of successive stages of wedge evolution over a
993
weak decollement. Note that wedge slope gradually increased until the deformation of the
994
wedge reached the final stage of wedge growth. The final stage is marked by the onset of
995
decreasing the wedge slope (α) with continuous shortening. Corresponding line drawings for
996
successive stages are shown below. Dashed lines represent the traces of long axes of
997
deformed ellipses. The light shaded portion of the model marks the width of the deformed
998
wedge (also demarcated by a double sided arrow); while the dark shaded portion represents
999
the undeformed segment of the model. Vertical and horizontal scale bars are shown in cm.
1000
(b) Progressive evolution of particle flow trajectory (using the software Image J) and strain
1001
pattern (computed with SSPX software, using the Grid Distance Weighted method). Here
1002
each set of flow vector diagram (top) and strain distribution map (bottom) corresponds to
1003
successive stages of progressive shortening shown on the left in (a). Coloured vertical scale
1004
shows the magnitude of strain. Tm and Tn represent time in model and nature respectively.
1005
Fig.3 Graphical plots show evolution of wedge geometry (wedge angle and wedge height) as
1006
a function of horizontal shortening in experimental model over weak (a) and strong (b)
1007
decollements respectively. Schematic representative three-dimensional wedge models (not to
1008
scale) are shown for each stage of wedge evolution.
1009
Fig.4 (a) Top view (YZ section) of successive stages of deformation in experimental model
1010
over a weak decollement. Note that the distance between the strain markers along Y-axis
1011
decreased continuously adjacent to the hinterland buttress, giving rise to a zone of
1012
compression (marked by a white dashed line) and deformed circular markers are shown using
42
1013
red solid arrows. Using Grid Distance Weighted method in SSPX software, evolution of
1014
particle flow trajectory (b) and strain maps (c) are shown corresponding to the stages of
1015
deformation in (a). Note that compressional zone is also shown in strain map (c) by white
1016
dashed line. Coloured vertical scale shows the magnitude of strain. Tm and Tn represent time
1017
in model and nature respectively.
1018
Fig.5 (a) Cross-sectional view (XZ section) of successive stages of deformation in
1019
experimental model over a strong decollement. Note that wedge slope increased until the
1020
deformation of the wedge reached the final stage. The final stage is marked by the beginning
1021
of reduction in wedge slope with continuous shortening. Schematic line drawings of wedge
1022
evolution with progressive shortening are shown below corresponding to each stage. Dashed
1023
lines represent the traces of long axes of deformed ellipses. The light shaded portion of the
1024
model marks the width of the deformed wedge (also demarcated by a double sided arrow);
1025
while the dark shaded portion represents the undeformed segment in the front. Vertical and
1026
horizontal scale bars shown in cm. The two red dashed lines in the final stage mark the zone
1027
of high strain localization, indicating a possible location for large-scale thrusting. (b)
1028
Progressive evolution of particle flow trajectory and strain pattern (computed with SSPX
1029
software, using the Grid Distance Weighted method) are shown corresponding to deformation
1030
stages in (a). Note that the trace of the final position of the initial horizontally aligned dots
1031
produce recumbent fold geometry (marked by red dashed line in the final model) with
1032
increasing shortening. Chaotic alignment of extension axes in strain maps represent the
1033
undeformed parts of the model at different stages as indicated by negligible particle
1034
displacement in the frontal part of the model in each corresponding flow vector diagram.
1035
Coloured vertical scale shows the magnitude of strain. Tm and Tn represent time in model and
1036
nature respectively.
43
1037
Fig.6 (a) Top view (YZ section) of successive stages of deformation in experimental model
1038
over a strong decollement. Using Grid Distance Weighted method in SSPX software,
1039
evolution of particle flow trajectory (b) and strain maps (c) are shown corresponding to the
1040
stages of deformation in (a). Chaotic alignment of extension axes in strain maps represent the
1041
undeformed parts of the model at different stages as indicated by negligible particle
1042
displacement, as shown in (b), in the frontal part of the model. Coloured vertical scale shows
1043
the magnitude of strain. Tm and Tn represent time in model and nature respectively.
1044
Fig.7 Flinn plots for weak decollement: strain ratios correspond to the entire model (a),
1045
hinterland (b) and foreland (c) respectively. Separate plots in (b) and (c) estimate the nature
1046
and amount of strain partitioning within the hinterland and foreland at different stages of
1047
wedge growth. Initial flattening type of deformation in the hinterland region is transformed to
1048
constrictional type with progressive shortening in (b). The intensity of flattening increases
1049
with shortening towards the foreland (c).
1050
Fig. 8 Three-dimensional representation of deformed viscous wedge developed over a weak
1051
basal decollement. The deformed wedge is characterised by a low surface slope as revealed
1052
from XZ section of finite model. The XY section is characterised by undulating topography
1053
near the hinterland buttress (oblique view of three dimensional wedge model in
1054
Supplementary Fig. S2 distinctly shows the topographic variations). Note the region of
1055
topographic low between two lateral topographic highs adjacent to lateral walls (front wall
1056
and back wall), responsible for generating convergent flow along Y-axis of bulk strain
1057
(shaded area in the central part of the hinterland and marked by black arrows). Schematic
1058
representation of strain ellipsoids indicates the manifestation of spatially varying three-
1059
dimensional strain pattern from foreland to hinterland: flattening type of strain characterises
1060
the foreland and constrictional deformation localizes preferentially towards the rear part of the
1061
hinterland. Undeformed cube at the extreme foreland represents region of no deformation. 44
1062
Fig.9 Strain maps (using Grid Distance Weighted method in SSPX software) for successive
1063
incremental steps of top-view (YZ section) in model with weak decollement. (a) Development
1064
of compressional zone (marked by white dashed line) near the hinterland buttress in the initial
1065
stage of wedge growth, indicating the development of constrictional strain field. (b) and (c)
1066
Constrictional strain field (marked by white dashed line) persists during the intermediate stage
1067
of wedge growth. Note that extensional strain axes (black line) always run parallel to the Y-
1068
axis of bulk strain during the initial and intermediate stages of wedge growth. (d) Incremental
1069
strain map, showing reduction in surface area of compressional zone and development of
1070
extensional zone near the hinterland buttress. Note that extensional axes are now aligned
1071
parallel to Z- axis of bulk strain in the zone of extension (e) Incremental step showing the
1072
increase in surface area of extensional zone, (f) Complete obliteration of compression zone by
1073
extensional zone near the hinterland buttress. Change from compressional zone to local
1074
extensional zone near the hinterland buttress indicates increase in the intensity of convergent
1075
flow along Y-axis of bulk strain. Coloured vertical scale shows the magnitude of strain.
1076
Fig.10 Flinn plots for strong decollement: strain ratios correspond to the entire model (a),
1077
hinterland (b) and foreland (c). Note that, both hinterland (b) and foreland (c) are
1078
characterised by flattening type of deformation with increasing progressive shortening, in
1079
contrast to strain pattern over weak decollement discussed in Fig. 7.
45
Parameter
Units
Length of viscous slab ( ) Thickness of viscous slab (h) Convergence velocity (V)
metre (m)
In nature
In model
= 400 km = 4 x 105 m
Scale Factor= (Nature/Model)
= 40 cm = 4 x 10-3 m
= 106 (after Rossetti et al., 2001)
4
metre (m)
ℎ
metre per second (ms-1)
V = 3.1 cm/year (after De Mets et al., 2010; Argus et al.,
= 20 km =2 x 10 m
2011) = 9.83× 10
-10
Pascal second (Pas)
Density of slab material ( )
kilogram per metre cube (kgm3 )
= 2700 kgm-3
Strain rate ( )
per second (s-1)
= 10-15 s-1
ℎ
= 2 cm= 2 x 10 m
V
= 1.97 × 10-4 ms-1
-----------V = 4.9898×10
-6
ms-1
= 5.6 × 1021 Pas
Viscosity of slab material ( )
-2
(calculated)
= 104 Pas (Weijermars, 1986)
= 965 kgm-3 (Weijermars,
= 5.6 × 1017 (calculated from eq.2 in text)
=2.7979 ≈ 2.8
1986)
= 2 × 10-4 s-1 (calculated)
= 4.5 × 10-12 (calculated from the values of and V respectively)
Time (t)
second (s)
= 6.8493 Ma (calculated)
=1080 s (measured experimental run time)
Gravitational stress (
)=
Pascal (Pa)
--------------
ℎ
Weak decollement [ = 965 kgm-3 × 9.8ms-2 × 4.06×10 2 m] = 383.954 Pa
= 2 × 1011 (derived from the inverse of )
------------
(calculated)
Strong decollement [ = 965 kgm-3 × 9.8ms-2 × 8.78×10-2m] = 830.324Pa (calculated)
Compressive normal viscous stress ( ) = V w
Pascal (Pa)
--------------
Weak decollement [ = (5×104 Pas × 1.97×10-4 ms-1) / (17.5×10-2 m)] = 56.285Pa
------------
(calculated)
Strong decollement [ = (5×104 Pas × 1.97×10-4 ms-1) / (10×10-2 m)] = 98.5 Pa (calculated)
Argand Number (Ar) =
Dimensionless
---------------
Weak decollement = 6.82 (calculated)
Strong decollement = 8.42 (calculated)
-----------
Table. 1 Scaling of experimental parameters.
X-axis
Camera 2
Z-axis Y-axis
d
e Fix
ll a w
Bac
kw
all
Pas
sive
Fro
nt w
all
2
ma
ll a rs e w p) l b ea ksto v Mo (Bac
rke
0
40 25.3
Camera 1
Motor driven piston 0
Strain in entire model
Strain at 3.8 cm (9.5% shortening)
Field of constrictional strain
Strain in foreland
Strain in hinterland in
tra
f
a pl
o ne
Field of constrictional strain
in
Field of constrictional strain
s ne
tra
s ne
in
tra
a
Li
ne
l fp
s ne
o
Li
Axially symmetric Field of flattening strain stretching
la fp Field of flattening strain
o ne
Li
Field of flattening strain
Axially symmetric flattening
in
Strain at 8.4 cm (21.0% shortening)
Field of constrictional strain
Field of constrictional strain
tra
s ne
a
f eo
pl
Axially symmetric stretching
Axially symmetric flattening
Field of constrictional strain
n
Strain at 12.8 cm (32.0% shortening)
e in
n
Li
Field of flattening strain
n
Field of constrictional strain
an
an
pl
f eo
tr es
of
pl
n
p of
Li
ai
Field of constrictional strain
ai
tr es
tr es
la
ne
ne Li Field of flattening strain
Field of flattening strain
n
ai
Field of constrictional strain
n
la
p of
n
Li
n
ai
tr es
n
ai
tr es
an
f eo
L Field of flattening strain
pl
n Li Field of flattening strain
Field of flattening strain
Strain at 14.5 cm (36.2% shortening)
in
n
ai
Field of constrictional strain
n
la
ne
Li
p of
tr es
Field of constrictional strain
in
ne
a str
ne
Li
p of
Li Field of flattening strain
Field of flattening strain
Axially symmetric flattening
(a)
(b)
s ne
la
fp
o ne
la
Field of flattening strain
tra
Field of constrictional strain
(c)
3.3 % shortening
8.76°
4
35
40
30
25
20
15
10
(in cm) 0 510.5 % shortening
Tm=196 s, Tn= 1.25 Ma
4
10.15°
ETL
2
35
40
0
5
30
25
20
15
10
Initial stage
2
0
5 2
30
25
20
15
10 5 Deformed wedge
12.80°
25.2 % shortening
Tm=334 s, Tn=2.13 Ma
0
Intermediate stage
35
40
4 2
35
40
30
25
20
10
15
5
0
10
5
0
10
5
0
2
35
30
25
(in cm) 0 532.3 % shortening
15 20 Deformed wedge 7.35°
ETL
4 2
35
40
Tm=602 s, Tn= 3.84 Ma
30
25
20
15
4
Magnitude of strain
2
35
40
30
25
(in cm) 43.0 % shortening
20
Deformed wedge 6.11°
15
10
5
Tm=860 s, Tn=5.49 Ma
0
2
40
35
30
25
20
15 4
10
5
0
7.58 e-02 2.05 e-02
Tm=990 s, Tn=6.32 Ma (a)
35
30
25 Deformed wedge
20
15
2.42 e-01
1.31e-01
2
40
2.97 e-01
1.86 e-01
4
ETL
Final stage
40
10
5
0
(b)
Initial stage
Intermediate stage
Final stage
Initial stage
Intermediate stage
Final stage
x
x
z
z x
y
y x
z x
z
y y x
z
z
y
(a)
y
Wedge angle Wedge height
Wedge angle Wedge height
(b)
Initial stage 10 (in cm) 0 ETL
6.0 cm (15.00% shortening)
10 (in cm) 0 ETL
10.4 cm (26.00% shortening)
10 (in cm) 0 ETL
15.2 cm (38.00% shortening)
10 (in cm) 0 ETL
18.3 cm (45.75% shortening)
Tm =105s,Tn =0.67 Ma
Tm =271s,Tn =1.73 Ma
Tm =474s,Tn =3.02 Ma
Tm =715s,Tn =4.56 Ma
Tm =858 s,Tn =5.48 Ma
Deformed circular marker
10 (in cm) 0 ETL
(a)
21.0 cm (52.50% shortening)
Intermediate stage
2.5 cm (6.25% shortening)
Final stage
10 (in cm) 0 ETL
Tm =1001 s,Tn =6.39 Ma
(b)
(c)
Magnitude of strain
Tm = 264s, Tn = 1.68 Ma
Initial stage Intermediate stage
Tm = 68s, Tn = 0.43 Ma
Tm = 688s, Tn = 4.39 Ma Magnitude of strain
Final stage
1.35 e+00 1.07 e+00 7.88 e-01 5.07 e-01 2.27 e-01
Tm = 872s, Tn = 5.57 Ma (b)
0
-5.43 e-02
Initial stage 0
2.4 cm (6.0% shortening)
0
3.8 cm (9.5% shortening)
0
8.4 cm (21.0% shortening)
0
12.8 cm (32.0% shortening)
ETL
10
(in cm) ETL
10
(in cm) ETL
10
(in cm) ETL
Tm=282 s, Tn=1.80Ma
Tm=690 s,Tn =4.40Ma
Tm=900 s,Tn=5.75Ma
Tm=1080 s, Tn=6.90 Ma
Magnitude of strain
1.48 e-01 1.18 e-01 8.71 e-02 5.66 e-02 2.62 e-02 0 -4.28 e-03
10
(in cm) ETL
(a)
0
Intermediate stage
(in cm)
14.5 cm (36.2% shortening)
Tm=1188 s, Tn=7.59Ma
(b)
(c)
Final stage
10
n ne la
fp eo Li n
Field of constrictional strain
in tra pl
of ne Li
Li
Li
ne
ne
of
of
pl
pl
an
an
es
tra
in
Field of flattening strain
es
in tra es an
Strain at 10.4 cm (26.0% shortening)
Axially symmetric stretching
ai
n ai str la
fp eo Field of constrictional strain
Field of flattening strain
Field of flattening strain
Field of constrictional strain
Field of constrictional strain
Li n
la eo
fp
Axially symmetric flattening
Li n
Axially symmetric stretching
Strain in foreland
ne
str
ai
n
Field of constrictional strain
ne
Strain at 6 cm (15.0% shortening)
Field of constrictional strain
Strain in hinterland
str
Strain in entire model
Field of flattening strain
Field of flattening strain
Field of flattening strain
Axially symmetric flattening
in tra
in tra es
an of
of
ne
ne
Li
Li
Li
ne
Axially symmetric flattening
pl
pl
of
an
pl
an
Field of constrictional strain
es
in tra
Field of constrictional strain
es
Strain at 15.2 cm (38.0% shortening)
Field of constrictional strain
Field of flattening strain
Field of flattening strain
tra in ne s
Li
Li ne
ne
of
of
Axially symmetric flattening
pl an
pl a
of ne Li
Axially symmetric stretching
Field of constrictional strain
Field of flattening strain
Field of flattening strain
Field of flattening strain
(a)
(b)
es tra
ne s
Field of constrictional strain
pl a
Strain at 21cm (52.5% shortening)
Field of constrictional strain
in
tra in
Field of flattening strain
(c)
Orogen transverse trend
x x y
Foreland
Hinterland
z
d
l
r
e all
og r O
e
a np
n tre
2.5-6 cm displacement (15.00% shortening)
(c)
6-10.4 cm displacement (26.00% shortening)
(d)
10.4-15.2 cm displacement (38.00% shortening)
Initial stage
(b)
Intermediate stage
2.5 cm displacement (6.25% shortening)
Final stage
(a)
Magnitude of strain 1.27 e-01 9.46 e-02
(e)
15.2-18.3 cm displacement (45.75% shortening)
6.22 e-02 2.97 e-02 0
(f)
18.3-21 cm displacement (52.50% shortening)
-2.68 e-03 -3.51 e-02
Research Highlights • • • •
Development of ductile structures in fold-and-thrust belts is sensitive to decollement strength L-tectonites and cross folds preferentially localize in a tectonic wedge over weak decollement Strong decollement leads to recumbent fold in convergent setting Hinterland-dipping ductile fabrics in the foreland correspond to flattening type of deformation
Conflict of interest
There is no conflict of interest.
S0191-8141(19)30339-6
DOI:
https://doi.org/10.1016/j.jsg.2020.104012
Reference:
SG 104012
To appear in:
Journal of Structural Geology
Received Date: 16 August 2019 Revised Date:
4 February 2020
Accepted Date: 9 February 2020
Please cite this article as: Roy, S., Bose, S., Saha, P., Spatial variations of ductile strain in fold-andthrust belts: From model to nature, Journal of Structural Geology (2020), doi: https://doi.org/10.1016/ j.jsg.2020.104012. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.
Credit Author Statement S.B., S.R. and P.S. designed the research; S.R. and P.S. did the experiments. S.B. and S.R. contributed equally to the analysis of experimental results and writing the manuscript.
1
Spatial variations of ductile strain in fold-and-thrust belts:
2
from model to nature
3
Sreetama Roya, Santanu Bosea,b*, Puspendu Sahac
4 5 6 7
Department of Geology, University of Calcutta, Kolkata – 700019 Department of Geology, Presidency University, Kolkata – 700073 c Department of Geological Sciences, Jadavpur University, Kolkata – 700032
a
b
8
*Corresponding author: [email protected]
9
Abstract:
10
Fold and thrust belts (FTBs) accommodate tectonic convergence through folding
11
and faulting of crustal rocks during a collisional event between two continental plates.
12
Although evidence of distributed deformation is common in FTBs that usually leads to
13
continuous foliations and regionally occurring ductile structures of multiple orders, it has
14
rarely been given much attention assuming the zones of localized deformation, like shear
15
zones and brittle faults, as potential locales for accommodating the amount of convergence.
16
This study presents 3D laboratory-scale models, using viscous thin sheet as crustal layers, to
17
understand the evolution of ductile strain in a tectonic wedge. We varied the degree of
18
mechanical coupling at the basal decollement (i.e., weak versus strong) to investigate this
19
issue at constant convergence velocity in all experiments to avoid the influence of rate-
20
dependence on viscous rheology. Our results reveal that the strength of basal decollement
21
controls the mode of wedge growth and hence, the strain pattern particularly towards the
22
hinterland. The weak decollement models yield a zone of constriction towards the central part
23
of hinterland, explaining the occurrence of isolated patches of L-tectonites and cross-folds in
24
FTBs; while the strong decollement condition allows gravity driven flow to be active in the
25
hinterland, leading to orogen-parallel recumbent folds. In contrast, both weak and strong
26
decollement models produce deformation that characterises the commonness of pervasive, 1
27
hinterland dipping ductile fabrics towards the mountain front. We correlate our findings to
28
show that spatio-temporal variations in basal coupling are responsible for varying occurrence
29
of ductile structures in FTBs.
30
31
Key words: Fold-and-thrust belts, Viscous rheology, Ductile structures, Constrictional
32
deformation, L- tectonites, Weak and strong decollement
33 34
35
1. Introduction: A fold-and-thrust belt is a long zone of deformed crustal rocks, formed by the
36
collision between two continental plates. A series of theoretical and experimental studies have
37
been carried out in the past three decades to understand the structural evolution of this
38
deformed crustal section (Tapponnier et al., 1982; Platt, 1986; Le Pichon et al., 1992;
39
Houseman and England, 1993; Lallemand et al., 1994; Willett, 1999b; Beaumont et al., 1999;
40
Mandal et al., 2009; Vanderhaeghe, 2012; Ruh et al., 2012; Jamieson and Beaumont, 2013).
41
These studies have considered varying rheology of crustal rocks from frictional-plastic
42
(Chapple, 1978; Davis et al., 1983; Dahlen et al., 1984; Malavieille, 1984, 2010; Mulugeta,
43
1988; Liu et al., 1992; Storti et al., 2000; Persson, 2001; Graveleau et al., 2012; Bose et al.,
44
2014b, 2015) to viscous (England and McKenzie, 1982; Emerman and Turcotte, 1983;
45
England et al., 1985; Houseman and England, 1986; Cohen and Morgan, 1986; Buck and
46
Sokoutis,1994; Ellis et al., 1995; Royden, 1996; Willett, 1999a; Rossetti et al., 2000;
47
Chattopadhyay and Mandal, 2002; Vanderhaeghe et al., 2003) and visco-elasto-plastic (Erdős
48
et al., 2015; Jaquet et al., 2018). The mechanical behaviour of crustal rocks is commonly
49
modelled by frictional plastic rheology that involves friction laws (Byerlee, 1978). Using the
50
theory of brittle failure, the laboratory models validated the concept of critically tapered
2
51
wedge model to explain the wedge-shaped geometry of mountain belts and the process of
52
sequential thrusting from hinterland to foreland (Davis et al., 1983; Dahlen et al., 1984).
53
According to this model, dynamic equilibrium within the wedges maintains a critical balance
54
between overlying gravitational load on the basal decollement and the tangential shear stress
55
along it. Using scaled laboratory experiments, a large number of workers have subsequently
56
shown that a number of parameters, like thickness of homogeneous sand layers (Liu et al.,
57
1992; Marshak and Wilkerson, 1992; Mandal et al., 1997), basal decollement slope
58
(Mulugeta, 1988; Saha et al., 2013; Bose et al., 2014b), and geometry of the indenter (Byrne
59
et al., 1988, 1993; Ratschbacher et al., 1991; Lu and Malavieille, 1994; Gutscher et al., 1996,
60
1998; Bonini et al., 1999; Dominguez et al., 2000; Persson, 2001; Persson and Sokoutis,
61
2002; Koyi and Vendeville, 2003) play a vital role in regulating the geometric evolution of a
62
tectonic wedge. All these models have shown that the frontal propagation of a wedge is
63
indeed punctuated by a series of sequential thrusts, splaying from the basal decollement.
64
Introduction of kinematic factors, like frictional resistance at the basal decollement
65
(Mulugeta, 1988; Liu et al., 1992; Lallemand et al., 1992; Gutscher et al., 1996, 1998; Mandal
66
et al., 1997; Konstantinovskaia and Malavieille, 2005; Saha et al., 2016), the rate of
67
convergence (Ratschbacher et al., 1991) and surface processes (Koons, 1989, 1990; Storti and
68
McClay, 1995; Storti et al.,2000; Konstantinovskaia and Malavieille, 2005; Hoth et al., 2006,
69
2008; Malavieille, 2010) have refined our understanding in predicting the spacing between
70
successive imbricate thrusts with horizontal shortening and influence of surface erosion on
71
wedge development. However, these models for crustal deformation using brittle theories
72
cannot explain the regional occurrence of penetrative ductile fabrics and associated folds and
73
boudinage structures in orogenic belts (Grasemann et al., 1999; Ring and Brandon, 1999;
74
Kassem and Ring, 2004; Law et al., 2004; Jessup et al., 2006; Xypolias and Kokkalas, 2006;
75
Larson and Godin, 2009; Law, 2010; Thigpen et al., 2010a, 2010b; Xypolias, 2010; Xypolias
3
76
et al., 2010; Cottle et al., 2015; Bauville and Schmalholz, 2015; von Tscharner et al., 2016;
77
Butler et al., 2019). The occurrence of penetrative ductile structures in FTBs thus implies a
78
significant role of an alternative mechanism, such as distributed ductile deformation during
79
the evolution of fold-and-thrust belts. The association of brittle and ductile structures
80
throughout the entire mountain belts indicates the crustal rocks to deform over varying time
81
scales, where fracturing and brittle faults develop mostly over short time scale (Sibson, 1982)
82
and large scale ductile deformation in the crustal rock takes place by creeping in long time
83
scale (Hauck et al., 1998; Schmid et al., 1996). Moreover, field investigations reveal that
84
geometry of ductile structures varies significantly from hinterland to foreland (Coleman,
85
1996; Carosi and Palmeri, 2002; Jessup et al., 2008; Xu et al., 2013). The frontal part of all
86
mountain belts is usually characterised by pervasive development of along-strike ductile
87
foliations, associated with upright to inclined folds, whereas the hinterland region is
88
dominated by complexly deformed fold structures that include interfering of fold types
89
(Murphy, 1987; Godin, 2003; Williams and Jiang, 2005; Culshaw et al., 2006; Williams et al.,
90
2006; Denèle et al., 2009; Kellett and Godin, 2009; Godin et al., 2011). A number of
91
theoretical and experimental studies have used viscous models for explaining the
92
development of such ductile structures in mountain belts (Buck and Sokoutis, 1994;
93
Medvedev, 2002; Chattopadhyay and Mandal, 2002; Lujan et al., 2010). Earlier studies have
94
even shown the crustal deformation to occur often in association with diffusion creep in
95
sediments at low temperature similar to viscous fluid rheology at large scale (Rutter, 1983;
96
Emerman and Turcotte, 1983; Wheeler, 1992).
97
In recent times, a number of mechanical models have been proposed to show the
98
contribution of ductile deformation in mountain building processes. For example, Bose et al.,
99
2014a showed that the influence of ductile deformation is crucial in the development of a
100
series of terrane-scale transverse structural domes in the eastern Himalayas. Their 4
101
interpretation on the development of complex fold patterns in the Rangit window of
102
Darjeeling-Sikkim Himalaya (DSH) is consistent with the mechanism of superposed buckling
103
of ductile folds (Ghosh et al., 1992). Moreover, Butler et al., 2019 have emphasized the
104
importance of buckle folding in predicting the geometry of subsurface structures in fold-and-
105
thrust belts. Besides widespread occurrence of common ductile structures, many FTBs also
106
exhibit patchy occurrences of L-tectonites or L>S tectonites towards the hinterland (Flinn,
107
1956, 1958, 1959; Hossack, 1968; Chapman et al., 1979; Holst and Fossen, 1987; Sylvester
108
and Janecky, 1988; Passchier et al., 1997; Braathen et al., 2000; Poli and Oliver, 2001;
109
Piazolo et al., 2004; Sullivan, 2006, 2013). L-tectonites are generally considered as an
110
expression of pure constrictional strain field (Treagus and Treagus, 1981, Ramsay and Huber,
111
1983; Ghosh et al., 1995). However, it is not clear how the constrictional strain field evolves
112
in fold-and-thrust belts in the framework of collisional setting under unidirectional stress
113
field. In addition, reports of cross folds and transverse ductile fabrics from many FTBs (Glen
114
and Walsche, 1999; Bell et al., 2004; Little, 2004) further substantiate the relevance of the
115
development of contractional strain field orthogonal to the bulk shortening direction in a
116
collisional belt.
117
Using laboratory experiments, this study reinvestigates the significance of the viscous
118
wedge model for explaining the occurrences of varying ductile structures in fold-and-thrust
119
belts. Our models demonstrate that constrictional strain field can locally develop towards the
120
hinterland of a growing FTB over weak basal decollement, leading to L tectonites and cross
121
folds. Strong decollement condition, in contrast, allows gravity driven flow to occur in the
122
hinterland, giving rise to the localization of orogen-parallel recumbent folds. Our experiments
123
suggest that both weak and strong decollement produce pervasive, hinterland dipping ductile
124
fabrics towards the frontal part of fold-and-thrust belts. Based on our laboratory experiments,
5
125
we conclude that distributed ductile strain has a strong control on the structural evolution of
126
fold-and-thrust belts.
127
128
2. Experimental Approach:
129
2.1
130
Material and Model Set up: We used a conventional sandbox-like deformation box (e.g., squeeze box under
131
normal gravity) as shown in Mulugeta (1988). The box was made of transparent acrylic.
132
Linearly viscous polydimethyl-siloxane (PDMS, manufactured by Dow Corning under the
133
trade name SGM36; see Weijermars, 1986 for PDMS properties) was chosen as a modelling
134
material to explore crustal flow trajectory in response to continuous horizontal shortening.
135
While the linear viscous PDMS used in our experiments greatly simplifies the modelling of
136
flow behaviour in heterogeneous crustal rocks, it provides considerable insights on internal
137
deformation within a viscous wedge. The viscosity of PDMS (5 × 104 Pas) is also suitable for
138
understanding the interaction of gravity flow in a collisional setting.
139
A rectangular PDMS slab of dimension (40 cm length, 25.3 cm width and 2.0cm
140
thickness) was prepared separately to simulate the undeformed crustal rocks in fold-and-thrust
141
belts. Four side walls and the basal plate of the deformation box were carefully washed, dried
142
and. then the lateral walls were coated with a weak lubricant before placing the PDMS slab
143
within the deformation box (Fig. 1). The weak lubricant was used to minimise the frictional
144
resistance along the interface between the PDMS slab and the inner walls of the deformation
145
box. The interface between the basal acrylic plate and the PDMS slab is considered as the
146
basal decollement surface. We performed two sets of experiments by varying the decollement
147
strength (weak or strong). The weak decollement was simulated by lubricating the basal plate
148
uniformly with a low viscosity (~ 4068 m Pas) fluid (See Supplementary Fig. S1) and strong
149
decollement was simulated with no lubrication on the basal plate. The viscosity of the fluid 6
150
was measured using a Cone-and-plate (CP-40, conical plate of diameter 40 mm and an angle
151
of 1°) measuring system in an Anton Paar MCR 92 Rheometer under laboratory room
152
temperature of 25°C. In all experiments we kept the piston speed (~ 1.97 × 10-4 ms-1)
153
constant to nullify the effects of rate dependence on viscous models. The model was
154
deformed by moving the vertical side wall (backstop), guided by a rigid piston connected to a
155
computer-controlled step-up motor, over the basal plate (Fig. 1). In our experiments, we
156
ensured the condition of constant volume of wedge material during the entire experimental
157
run and care has been taken so that no material can leak through the 1mm slit between the
158
rigid backstop and basal plate.
159
We analysed our model results in a three-dimensional Cartesian coordinate system
160
(Fig. 1). During experimental run, the model was allowed to grow vertically along the X-axis.
161
The model-width (along the Y-axis) was kept constant in order to obtain the condition of no
162
rotation on the YZ and XY planes of bulk strain (Pfiffner and Ramsay, 1982). Hence, our
163
experiments were performed under bulk plane strain condition. In order to continuously
164
monitor the evolution of 3D strain pattern during the wedge growth, we stamped dry carbon
165
powder as circular passive markers on two surfaces (top surface and front lateral surface) of
166
the initial model corresponding to YZ and XZ planes. However, we could not monitor the
167
progressive change in strain pattern along the XY plane. In our model setup, the XY plane
168
(~backstop wall) is attached to the moving piston. The calculation of strain variations on the
169
XY plane were obtained from the strain ratios on YZ plane. It is possible because we ran our
170
experiments under bulk plane strain condition at constant volume (Bajolet et al., 2013). Two
171
digital cameras were positioned at a fixed distance to record progressive stages of
172
deformation for top-view and sectional-view (Fig.1) at regular preset time intervals during the
173
experimental runs. We then measured the displacement of passive markers by tracking the
174
successive change in positions of the material points using the ImageJ software. Using SSPX
7
175
software, strain maps for both XZ and YZ planes were computed from the displacement data
176
using the Grid Distance Weighted (GDW) method (Cardozo and Allmendinger, 2009). It is to
177
note that computed strain maps do not reveal the topographic outline observed on the XZ
178
section of the model because the GDW method uses a uniform grid spacing consisting of
179
square cells to calculate strain distribution in the deformed state (Cardozo and Allmendinger,
180
2009). Strain is calculated at the centre of each square cell using all the stations (i.e. using the
181
total number of passive marker points in our model). The individual stations are weighted on
182
the basis of their distance from the centre of the square cells by a specific weighting factor.
183
Moreover, it is essential to note that the GDW method of strain computation involves
184
calculation of strain on a surface that is either flat (slice) or on a surface that follows the
185
topography of the data. In our calculation, we computed strain at all stations (centre of
186
circular markers) in the deformed stage to obtain a first order strain magnitude for the entire
187
model length. Strain magnitudes are calculated based on the finite displacement between
188
neighbouring points, leading to either extension (positive) or contraction (negative).
189
190
2.2 Scaling of the model: The selection of analogue materials and modelling approach took into account the
191
necessity of ensuring proper scaling of our experiments with nature (Table -1). The ratio
192
between model length and thickness of 20:1 scales to nature in the order of 106. This implies
193
that an initial model length of 40 cm (
194
while the initial slab thickness (ℎ ) of 2 cm and width of 25.3 cm of our model correspond to
195
a crustal thickness (ℎ ) of ~ 20 km and a lateral extent of ~ 253 km respectively. The
196
rheological behaviour of analogue materials (PDMS) is governed by constitutive equations of
197
viscous flow, implying the importance of time for appropriate scaling of a viscous model to
198
its natural prototype. The convergence velocity (V ) of 1.97 × 10-4 ms-1 in our experiments
199
corresponding to the plate velocity (V ) of 3.1 cm/yr (De Mets et al., 2010; Argus et al.,
) represents a stretch of ~ 400 km in nature (
8
)
200
2011), leads to a strain rate ratio ( ) ~ 4.5 × 10-12, between nature and model and a time ratio
201
(
202
hour corresponds to ~23Ma in a natural system and an experimental strain rate (
203
4 -1
204
are scaled with natural prototype by considering a balance between the ratio of viscous force
205
and gravitational force as follows:
) ~ 2 × 1011. A time ratio (
) of 2 × 1011 in our experiment means that model run of one
s in our models approximately simulates the natural strain rate ( ) of 10-15 s-1. Our models
=
206 207
where,
,
,
,
and
---------------------eq.1
are the viscosity, strain rate, density, acceleration due to
208
gravity and length ratios between nature and model respectively.
209
As the ratio of gravitational acceleration (
210
( ) is an inverse of the time ratio ( =
211
) is 1 with negligible error and the strain rate ratio
), equation 1 given above is thus simplified as follows:
-----------------------------eq.2
212
From equation 2, the viscosity ratio (
213
of crustal rocks (
214
the order of 104 Pas.
215
) of 2 × 10-
) is computed to be 5.6 × 1017, such that the viscosity
) is in the order of 5.6 × 1021 Pas for a viscosity of model material (
) in
We also calculated the Argand number, Ar, as a ratio between gravitational stress (
216
and horizontal compressional viscous stress (
) from our deformed model width (w),
217
following Medvedev (2002) (Table -1). From our models of weak decollement (Fig. 2a), the
218
gravitational stress [
219
compressive viscous flow stress [
220
the wedge is ~ 56.285Pa respectively, leading to Ar of ~6.82. In case of models with strong
221
decollement, the value of Ar becomes ~ 8.42 corresponding to the gravitational stress [
222
965 kgm-3 × 9.8ms-2 × 8.78×10-2m] of ~ 830.324Pa and normal compressive viscous flow
223
stress, [
= 965 kgm-3 × 9.8ms-2 × 4.06×10-2m] is ~ 383.954Pa and normal = (5×104 Pas × 1.97×10-4 ms-1) / (17.5×10-2 m)] within
= (5×104 Pas × 1.97×10-4 ms-1) / (10×10-2 m)] of ~ 98.5 Pa respectively. Such 9
=
)
224
values of Argand number are considered to be relevant for describing force balance in
225
evolving orogenic wedges (England and McKenzie, 1982; Dewey et al., 1986; Cruden et al.,
226
2006).
227 228
3. Experimental results:
229
3.1 Weak Decollement
230
Rectangular PDMS slab of 2.0 cm thickness produced a crude wedge-shaped geometry
231
adjacent to the hinterland buttress after the model was shortened by ~ 3.3% (Fig. 2a). During
232
this stage of shortening (initial stage), wedge grew mostly vertically and thereby,
233
continuously increased the wedge elevation near the hinterland buttress. With continued
234
shortening for about 10.5%, the wedge elevation reached to 2.98 cm. At this stage, the width
235
of the deformed wedge became 8.3 cm with a surface slope (α) of the wedge around 10.15°
236
(Figs. 2a, 3a). However, further shortening of 5.9 cm (i.e., total model shortening = 10.08 cm)
237
increased the surface slope (α) by 2.65°, indicating decrease in the rate of vertical growth as
238
shown in Fig.3a. We designate this declining stage of vertical growth rate as intermediate
239
stage of wedge evolution. However, the decrease in vertical growth rate allowed the wedge to
240
propagate horizontally in the frontal direction during the intermediate stage (Fig. 2a). This
241
reflects a distinct shift in the mode of wedge evolution from initial vertical growth to
242
widening of the deformation wedge in the intermediate stage. However, it is interesting to
243
note that the maximum elevation of the growing wedge varied along the Y-axis of the model
244
near the hinterland buttress during the intermediate stage. The highest elevation of the wedge
245
was attained adjacent to both lateral walls (front wall and back wall), developing a trough like
246
geometry in the central part of the model (Fig. 4a, Supplementary Fig.S2). We anticipated the
247
cause of such variable wedge elevation to be the narrow dimension of the deformation box
248
along Y-axis of bulk strain. We then performed a second set of experiments with large model
10
249
width (35 cm), keeping the thickness of the initial model constant (2.0 cm). However, this set
250
of experiments also revealed similar topographic variations towards the hinterland (See
251
Supplementary Fig. S3), suggesting little or no effects of confinement on our first set of
252
model results (Souloumiac et al., 2012). We discuss the cause and implication of such
253
localized topographic highs near the lateral walls in section 4.2. Further shortening of the
254
model, in contrast, started to lower the wedge slope (α) (Figs. 2a, 3a). Our experiments show
255
that the entire amount of horizontal shortening was then used to increase the width of the
256
deforming wedge by complete cessation of the vertical growth. We mark this stage of wedge
257
growth as final stage of wedge evolution. The preceding discussion reveals that the horizontal
258
shortening of the model facilitates the wedge to grow continuously in the frontal direction
259
though the vertical growth of the wedge ceases after a threshold elevation near the hinterland
260
buttress. This observation from our experimental results is consistent with the occurrence of
261
low surface slope in natural fold-and-thrust belts (e.g., α has been estimated to be around 4°
262
for the entire Himalayan wedge, Avouac (2007), though our models had a horizontal
263
decollement in contrast to dipping basal decollement (Main Himalayan Thrust) below the
264
Himalayan wedge. Moreover, our experimental results also do not account for syntectonic
265
surface erosion, which would also be likely to lower the surface slope of a tectonic wedge.
266
Passive circular markers stamped on the XZ section immediately deformed into
267
ellipses near the hinterland buttress with the onset of model deformation. The long axes of
268
strain ellipses at the initial stage were oriented approximately normal to the basal plate i.e
269
along the X-axis of bulk strain. However, the orientation of their long axes underwent
270
anticlockwise rotation in the rear part of the model with progressive shortening, giving rise to
271
a zone of steeply inclined (>70°) strain ellipses (Fig. 2a). At this stage, aspect ratios of
272
ellipses also increased substantially. Strain maps from the XZ section distinctly reveal this
273
change in the magnitude of longitudinal strain from 2.05% to 29.7% in the hinterland with
11
274
progressive shortening (Fig. 2b). Strain maps in successive stages also show progressive
275
change in the orientation of extensional axis, corresponding to the major axis of strain
276
ellipses. The deformation of passive markers towards the frontal direction evolved by varying
277
inclinations of strain ellipses with depth. The amount of inclination decreased with depth,
278
developing an asymptotic trace of the long axes of strain ellipses (Fig. 2a). Such a depth-wise
279
variation in the inclination of strain ellipses towards the foreland can be compared with
280
previous theoretical studies on the evolution of viscous wedge (Pollard and Fletcher, 2005).
281
Passive markers on the YZ section (top surface), also deformed to ellipses near the
282
hinterland with the initiation of bulk shortening, where long axis of ellipses were oriented
283
along the Y-axis of bulk strain (Fig. 4a). The aspect ratio of strain ellipses varied between 1.1
284
and 4.9 during the initial stage of wedge growth (Fig. 4a). The increased rate of frontal ward
285
propagation of deformation during the intermediate stage of wedge growth is marked by
286
continuous increase in the aspect ratios of passive markers towards frontal direction.
287
However, at this stage (~26% shortening) the aspect ratio of strain ellipses near the hinterland
288
buttress stopped increasing (Fig. 4a). Instead, the aspect ratios started to decrease by
289
decreasing the length of the major axis of strain ellipses. This phenomenon of contraction of
290
the major axes became prominent when the model was shortened by at least ~38% (Fig. 4a).
291
With further shortening, a large number of strain ellipses transformed to almost circular shape
292
in the central part of the hinterland, indicating the development of a local compressional strain
293
field close to the hinterland buttress, along Y-axis of bulk strain (Fig. 4a). Interestingly, the
294
length of diameters of the new deformed circles decreased by 16% of the diameter of
295
undeformed passive markers in the initial model. Models with large dimension (40cm × 35cm
296
× 2cm) also yielded similar results (See Supplementary Fig.S3). However, the aspect ratios of
297
strain ellipses continued to increase towards the frontal direction with progressive shortening
298
for both sets of experiments (Figs. 4a, Supplementary Fig. S3). Strain maps from YZ sections
12
299
of this model distinctly demarcate a zone of overall compression (marked by dashed white
300
line in Fig. 4c) near the hinterland buttress, leading to the localization of overall
301
compressional strain field. Analysis of our model results thus suggests the relevance of
302
viscous wedge models for explaining the prevalence of patchy occurrences of L-tectonites and
303
cross folds in fold-and-thrust belts (Sylvester and Janecky, 1988; Passchier et al., 1997;
304
Braathen et al., 2000; Piazolo et al., 2004; Sullivan, 2006, 2013; Das et al., 2016), which
305
demand the existence of along-strike shortening during orogenic wedge growth. Our model
306
results show that the occurrence of orogen-parallel ductile fabrics towards the frontal part of
307
fold-and-thrust belts is consistent with the orientation of strain pattern revealed from our
308
experiments (Fig. 4c).
309
310
311
3.2 Strong decollement Strongly coupled decollement experiments developed a steep surface slope (α=31.61°)
312
during the initial stage of wedge growth when the model was shortened by ~ 10.76% (Fig.
313
5a). With increasing the amount of shortening (~34.9% i.e., ~14 cm of shortening), the
314
surface slope steepened further to ~37.84° over a relatively narrow wedge (~7.0 cm) (Fig. 5a),
315
However, the wedge height near the hinterland stopped increasing after reaching a threshold
316
elevation (8.36 cm) and further shortening (>35%) eventually lowered the wedge slope (Figs.
317
3b, 5a). However, the mechanism of lowering the wedge slope over strong decollement is
318
drastically different from that of the weak decollement experiments discussed in section 3.1,
319
where it was controlled by increasing the frontal propagation rate of the deforming wedge. In
320
contrast, the lowering of topographic slope for strong decollement is associated with lateral
321
flow of wedge material from the hinterland towards the foreland along the topographic slope.
322
It also hints that the frontal propagation of the wedge was not significant over strong
323
decollement. We also envisage the initiation of such lateral flow of wedge material as a 13
324
consequence of large elevation difference (~ 6 cm) between the hinterland and foreland over a
325
narrow (~ 7 cm) deformation wedge (Fig. 5a). The activation of material flow along the
326
wedge slope is distinct from the progressive rotation of passive markers on the XZ section,
327
where the dip of the long axis of strain ellipses near the hinterland continuously decreased to
328
become approximately sub-horizontal till the model was shortened by ~43% (Fig. 5a). The
329
development of a narrow wedge indicates that the amount of horizontal shortening was
330
largely accommodated by increasing the wedge elevation during the entire wedge growth. It is
331
to note that the maximum value of wedge height attained over strong decollement was
332
substantially larger than that developed over weak decollement experiments for an equivalent
333
amount of shortening (Fig. 3). Interestingly, the wedge height remained constant along the Y-
334
axis of bulk strain near the hinterland buttress in contrast to the varying wedge elevation over
335
weak decollement. This finding not only signifies a strong influence of decollement strength
336
on the mode of viscous wedge evolution, but also validates our model results with little or no
337
effects of lateral confinement in our experiments. Towards the frontal part of the wedge, the
338
passive markers on the XZ section were uniformly inclined towards the hinterland and
339
thereby, separated the hinterland segment from the foreland of a deforming wedge by a sharp
340
contrast in the orientation of strain ellipses (Fig. 5a). Based on our model results, we infer that
341
the presence of regional occurrence of low foliation dips towards the hinterland might be an
342
expression of a strong basal decollement beneath the fold-and-thrust belts. Additionally, our
343
experiments show that the orientation of strain ellipses in the upper part of the model wedge
344
started to rotate backward towards the hinterland after a significant amount of shortening
345
(>10%, Fig. 5a). According to our experiments, the mechanism of the back-rotation of the
346
strain ellipses is consistent with the occurrence of north-verging back folds reported from
347
orogenic hinterland of the Nepal Himalaya (Godin et al., 2011). Although our laboratory
348
experiments provide new insights on the evolution of ductile structures in fold-and-thrust
14
349
belts, scaling of topography in our models shows significant exaggeration compared to natural
350
prototype. We attribute this dichotomy to the absence of isostatic compensation in our
351
experiments, where models were deformed over a rigid basal plate for understanding the
352
mechanics of crustal deformation in orogenic belts. In addition, absence of surface erosion in
353
our experiments might have also played a role to increase the wedge elevation.
354
The strain maps computed from the displacement of passive markers on the XZ
355
section (Fig. 5b) revealed the progressive change in the magnitude and orientation of
356
extensional strain from hinterland to foreland with continuous shortening. The amount of
357
longitudinal strain increased from 22.7% (initial stage) to 135% (intermediate stage) in the
358
hinterland with progressive shortening. Further shortening, however, did not reveal much
359
changes in the magnitude of strain, but exhibited significant variations in the orientations of
360
extensional axis, particularly towards the hinterland. Interestingly, this change in the
361
orientation of strain ellipses is accompanied by lowering of wedge slope in our models (Figs.
362
3b, 5a). We attribute the combination of rotation of strain ellipses on the XZ section and
363
decrease in wedge slope to the activation of gravity flow in the hinterland. Finally, the
364
extensional axes near the hinterland became almost horizontal in consistence with the
365
orientation of strain ellipses after a large amount of shortening (Figs. 5a, 5b).
366
On the YZ section (i.e. top surface, Fig. 6a), deformation of passive markers showed
367
distinct differences in their orientation from that of the weak decollement (Fig. 4a). At the
368
initial stage, the long axes of strain ellipses (aspect ratio ~ 1.5) were oriented parallel to the Y
369
axis of bulk strain near the hinterland buttress (Fig. 6a). However, after a horizontal
370
shortening of 9.5% in the model, the former short axes of the ellipses in the initial stage
371
started to lengthen and eventually, transformed to major axis of the strain ellipses with
372
progressive shortening. Such a switch from minor to major axis of the finite strain ellipse
373
became evident when the amount of shortening was fairly large (32%). The computed strain 15
374
maps also revealed consistent orientation of extensional axes towards the hinterland with
375
increasing deformation (Fig.6c). In the finite model, the orientation of deformed passive
376
markers also developed two distinct zones of contrasting orientation of strain ellipses
377
corresponding to hinterland and foreland segments on the YZ- plane: (i) parallel to the Z- axis
378
of bulk shortening towards the hinterland, and (ii) parallel to the Y- axis of bulk strain
379
towards the foreland. Analysis of our model results from YZ sections thus led us to conclude
380
that the change in the direction of the long axis of strain ellipses must have resulted due to the
381
activation of the lateral flow of wedge material from hinterland to foreland (Figs. 6a, 6c). The
382
zone separating the two segments of contrasting orientation of strain ellipses on YZ section
383
fairly coincides with the intensely stretched zone of strain ellipses of very high aspect ratio on
384
the XZ section (Fig. 5a). Interestingly, this zone also marks the region of topographic slope
385
break on the XZ section. Based on above discussion regarding the distribution of strain
386
patterns on the XZ and YZ planes over strong decollement, we infer that localization of large
387
strain near the topographic slope break on the XZ section can be a potential site for large scale
388
thrusting event in orogenic belts.
389
4. Discussion:
390
4.1 Wedge topography
391
Our experiments described above show that the degree of coupling at the basal
392
decollement is an important parameter that regulates the first-order topographic evolution of
393
mountain belts. The ratio of vertical growth to horizontal propagation of a tectonic wedge
394
increases with increasing the degree of basal coupling. Our model results suggest that weak
395
decollement promotes a tectonic wedge to grow horizontally for a large extent, forming a
396
gentle surface slope (Figs. 2a, 3a). On the other hand, strongly coupled decollement leads to a
397
narrow wedge with steep surface slope (Figs. 3b, 5a). This variation in the development of
16
398
viscous wedge geometry at different decollement strengths corresponds well with previous
399
studies for varying Ramberg number, Rm (Medvedev, 2002). Higher value of Rm develops
400
wedges similar to weak decollement experiments, whereas lowering the value of Rm gives rise
401
to a narrow wedge with steep surface slope similar to our models over strong decollement.
402
Lowering the rate of frontal propagation over strong decollement allowed the wedge to grow
403
vertically at a faster rate towards the hinterland, resulting in variations in internal gravitational
404
potential due to a large elevation difference from hinterland to foreland. This lateral variation
405
in elevation eventually resulted in the initiation of gravity driven flow towards the frontal
406
direction. The onset of gravity flow has been clearly recognized by continuously tracking the
407
successive positions of passive markers on the XZ section (Fig.5b). The displacement vectors
408
showed a large vertical component in the initial stage of wedge growth, which in turn reduced
409
greatly with the onset of gravity flow. The reduction of vertical component was also evident
410
from progressive narrowing of spacing between successive flow vectors (Fig. 5b). The
411
influence of gravity driven flow in the formation of wedge geometry in our experiments is
412
consistent with earlier theoretical models (Copley, 2012). Furthermore, tracing the terminal
413
points of deformed passive markers, which were initially aligned horizontally in the
414
undeformed model, gave rise to a recumbent fold like geometry on the XZ plane with a
415
convex upward topographic profile (Figs. 5a, 5b). Knowing fully well that our experiments
416
are much simpler than that of natural deformation in FTBs, it provides an alternative
417
explanation for the development of orogen-parallel recumbent folds that are reported from
418
many fold-and-thrust belts. The development of convex-upward topographic profile similar to
419
our models is also not uncommon in nature, rather it shows strong consistence to explain the
420
bathymetric profiles across the Kurile, Ryukyu and Aleutian accretionary wedges (Emerman
421
and Turcotte, 1983). This study also revealed the crustal rocks to behave as a Newtonian fluid
422
similar to our experiments.
17
423
The geometry of viscous wedges discussed above over weak and strong decollement
424
show close resemblance to the geometry of brittle wedges at varying frictional resistance on
425
the basal decollement (Davis et al., 1983; Gutscher et al., 1996; Schott and Koyi, 2001; Bose
426
et al., 2009). This implies that the magnitude of shear stress on the basal decollement
427
essentially guides the development of first-order mountain topography, irrespective of crustal
428
rock rheology. The viscous wedge models, however, have provided much insights on the
429
distribution of ductile strain during the evolution of a tectonic wedge.
430
4.2 Analysis of internal strain in a viscous wedge
431
Our experiments on viscous wedge distinctly reveal the cause of spatially varying
432
ductile structures in fold-and-thrust belts. Although the formation of a viscous wedge is
433
phenomenologically similar for both strong and weak decollements described in many earlier
434
studies (Emerman and Turcotte, 1983; Rossetti et al., 2000; Chattopadhyay and Mandal,
435
2002), strain pattern within the wedge varies drastically with changing decollement rheology.
436
Our experiments under plane strain condition, show that uniformly weak basal decollement
437
condition may lead to along-strike variations in ductile structures towards the orogenic
438
hinterland. We discuss below how the kinematic condition at the basal decollement can
439
influence the evolution of ductile structures in fold-and-thrust belts.
440
The weak decollement experiments developed a self-regulating convergent flow in the
441
central part of the hinterland on the YZ section, resulting in continuous decrease in the aspect
442
ratio of strain ellipses during the intermediate stage of the wedge growth. The decrease in
443
aspect ratio transformed some strain ellipses even to circular shape (Fig. 4a). However, the
444
surface area of the deformed circular markers has been reduced significantly (~by 30%) from
445
that of the undeformed stage, suggesting the wedge material to stretch vertically along X-axis
446
in order to conserve the volume under plane strain. We correlate the significance of this
447
vertical stretching interpreted from our models as a probable mechanism for the development 18
448
of patchy L-tectonites in FTBs. Strain maps computed from the model results at successive
449
steps distinctly define a zone of overall compressional regime on the YZ section
450
corresponding to the occurrence of circular strain markers (Fig. 4c). Based on our
451
experimental results, we attribute this compressional zone as responsible for the development
452
of cross folds, L-tectonites and dome-basin structures documented from many fold-and-thrust
453
belts (Sylvester and Janecky, 1988; Passchier et al., 1997; Glen and Walsche, 1999; Braathen
454
et al., 2000; Piazolo et al., 2004; Bell et al., 2004; Little, 2004; Sullivan, 2006, 2013; Das et
455
al., 2016). Our experimental results thus seemingly contend the interpretation of orogen-
456
parallel ductile stretching in the Greater Himalayan sequence of the Annapurna-Dhaulagiri
457
Himalaya (Parsons et al., 2016). However, their analyses suggest that the orogen-parallel
458
crustal stretching in the Annapurna Dhaulagiri Himalaya must have resulted in a flattening
459
(oblate/sub-oblate) strain regime. The difference between our model results and natural
460
observations suggest that bulk plane strain condition might play a crucial role for localizing
461
the compressional regime towards the hinterland, leading to the formation of L-tectonites and
462
orogen-transverse ductile fabrics in FTBs. However, factors causing the plane strain
463
deformation condition in natural situation have still remained unclear, albeit the assumption
464
of plane strain condition has been widely used for understanding the evolution of FTBs at
465
large scale (Willett, 1992; Beaumont et al., 1992; Fullsack, 1995). Integrating our model
466
results and structural imprints in FTBs we envisage that along-strike rheological variations
467
(Jamieson et al., 2007) might constrain the deformation to occur under plane strain condition
468
in orogenic belts. In such situations, the laterally occurring relatively stronger crustal rocks
469
can act as lateral walls similar to our laboratory experiments. In addition, we also show that
470
laterally varying rheology of basal decollement can also lead to along-strike compressional
471
regime towards the hinterland above weak decollement segment (Supplementary Fig. S4),
472
giving rise to orogen-transverse ductile structures in fold-and-thrust belts.
19
473
In order to reveal better insights on the progressive evolution of three dimensional
474
strain state over weak decollement, we plotted strain ratio data of 495 passive markers in a
475
Flinn diagram to evaluate the progressive growth of tectonic wedges. Analysis of Flinn plots
476
at successive stages reveal that tectonic wedges evolve through spatial and temporal
477
variations in deformation. For example, at the initial stage, flattening strain governs the
478
development of ductile structures in the entire wedge (Fig.7a). However, with increasing
479
shortening, strain pattern changes remarkably from hinterland to foreland. The flattening
480
strain, however, continued to control the deformation in the frontal part of the wedge (Fig.
481
7c), whereas the hinterland part of the wedge shows the development of localized
482
constrictional strain field (Fig. 7b). Based on our model results over weak decollement, we
483
provide a generalised 3D structure of wedge geometry to show the characteristic strain pattern
484
variations from hinterland to foreland in figure 8.
485
We also investigated the incremental evolution of strain pattern from our model results
486
(Fig. 9) by adopting the protocol described by previous workers (Fischer and Keating, 2005;
487
Cardozo and Allmendinger, 2009). After a significant amount of shortening (>30%), the
488
strain maps at successive incremental steps show marked differences in the strain pattern in
489
the central zone of compression, compared to the strain maps computed from finite strain
490
(Figs. 4c, 9). For example, Fig. 9d clearly reveals that the compressional zone partly
491
transformed to extensional regime, close to the hinterland buttress. Further increments of bulk
492
shortening converted the entire zone of compression as in Fig. 9c to a zone of extension (Fig.
493
9e). Interestingly, the orientations of extension axes within the transformed zone are found to
494
orient along the direction of bulk shortening, i.e. parallel to Z-axis. This observation further
495
validates the localization of convergent flow along the Y-axis of bulk strain in our models.
496
Based on our model results, we attribute the dissimilarity between the finite and incremental
497
strain maps to the mode of convergence in fold-and-thrust belts. The strain maps computed
20
498
from finite strain (Fig. 4c) represent a collisional setting of continuous convergence,
499
developing the strong compressional regime towards the hinterland, whereas incremental
500
strain maps indicate the evidence of intermittent breaks during the convergence between two
501
continental plates. The above discussion thus suggests that segmented episodes of
502
convergence in collisional belts may play a crucial role in the localization of cross folds and
503
orogen-transverse ductile fabrics in FTBs (Glen and Walsche, 1999; Bell et al., 2004; Little,
504
2004). The gradual change of compressional strain field to extensional regime further builds a
505
coherent reasoning to explain why L-tectonites are rare in fold-and-thrust belts.
506
For strongly coupled basal decollement, the attainment of steep wedge slope (~
507
32.48°) set the wedge to deform internally under the action of gravity and thereby, rotated the
508
earlier steeply dipping strain ellipses to become almost sub-horizontal on the XZ-plane
509
towards the hinterland (Figs. 5a, 5b). The evidence of gravity flow is also distinct from the
510
orientation of strain ellipses (parallel to the direction of bulk shortening) in the hinterland
511
zone of YZ- section (Fig. 6a). However, alignments of strain ellipses towards the foreland on
512
both XZ and YZ sections indicates relatively weak or no influence of gravity driven flow
513
(Figs. 5a, 6a). Based on our experiments, we infer that the phenomenon of episodic
514
gravitational collapse and spreading of overlying crustal rocks in the Nepal Himalaya
515
described by previous workers (Bell and Sapkota, 2012) is likely to have occurred when the
516
rheology of the MHT (basal decollement) below the Nepal Himalaya was relatively strong.
517
The deformation of strain markers on the XZ section in experiments over strong decollement
518
(Fig. 5b) suggest that the gravity driven flow can be responsible for the development of
519
orogen-parallel recumbent folds in fold-and-thrust belts (Valdiya, 1981; Coward et al., 1982,
520
1988; Brun et al., 1985; Searle and Rex, 1989; Jain and Manickavasagam, 1993; Godin, 2003;
521
Banerjee et al., 2015). Moreover, based on our analogue models over strong decollement we
522
predict that occurrence of recumbent fold zone in fold-and-thrust belts can be considered as a
21
523
separator between the foreland and hinterland. Earlier studies also ascribed the influence of
524
gravity driven flow in building the architecture of orogenic belts (Copley, 2012). Flinn plots
525
from the deformed models show that deformation of tectonic wedge over strongly coupled
526
decollement is entirely governed by flattening type of deformation (Fig. 10).
527
4.3 Implications on Himalayan fold-and-thrust belts
528
This study has significant implications in interpreting the development of ductile
529
structures and first-order topographic evolution of fold-and-thrust belts. Geological records
530
suggest that fold-and-thrust belts are characterised by penetrative ductile foliations and
531
associated buckle folds of multiple orders. In Himalayan tectonics, multi-ordered folds have
532
recently been reported from the Darjeeling-Sikkim section of the eastern Himalaya (Bose et
533
al., 2014a). Their studies have advocated the concept of superposed buckling as responsible
534
for the development of multi-ordered dome-basin structures. In a recent study, Das et al.,
535
2016 reported the presence of L-tectonites in the hanging wall rocks (e.g., Lingtse granite) of
536
Main Central Thrust (MCT) from the Darjeeling-Sikkim Himalaya (DSH). Strain analysis
537
from our weak decollement experiments relate the development of these L-tectonites towards
538
the extreme hinterland of the Darjeeling-Sikkim Himalayan wedge during the intermediate
539
stage of the wedge growth in response to Indo-Asia collisional event and subsequently
540
transported southward to the present location during the MCT thrusting. Combining our
541
experimental findings and field structures described from DSH it appears that the Main
542
Himalayan Thrust (basal decollement) beneath the Darjeeling-Sikkim Himalayan wedge was
543
relatively weak, resulting in the development of cross folds, L-tectonites and dome-basin
544
structures. Although L-tectonites are rare in the Himalayan belts, there are reports of patchy
545
occurrences of L-tectonites from NW Himalaya (Singh and Thakur, 2001; Dipietro and
546
Pogue, 2004). Recently, we also recorded isolated patch of L-tectonites in the high grade
547
rocks of Arunachal Himalaya (N 28° 23.485', E 095° 55.363'). The spatially varying 22
548
occurrence of Himalayan L-tectonites is consistent with the localization of patchy
549
constrictional strain field in our experimental models over weak decollement (Fig. 4).
550
Darjeeling-Sikkim Himalaya also witnessed the development of multi-ordered
551
recumbent folds (Banerjee et al., 2015). According to our experimental results, gravity driven
552
flow over strong decollement plays a role in developing recumbent folds in tectonic wedges.
553
However, co-existence of dome-basin structure (Bose et al., 2014a), L-tectonites (Das et al.,
554
2016) and orogen-parallel recumbent folds (Bose et al., 2014a, Banerjee et al., 2015) in the
555
DSH reflects temporal variations in the MHT rheology (decollement strength) beneath the
556
Darjeeling-Sikkim Himalaya during the evolution of Himalayan fold-and-thrust belts. On the
557
west of DSH, the evidences of north-verging folds at shallow crustal level (Godin et al., 2011)
558
and gravitational collapse towards the hinterland of the Central Nepal (Bell and Sapkota,
559
2012) indicate the Himalayan wedge to grow over relatively stronger MHT. These findings
560
not only reconcile our experimental studies with laterally varying ductile structures of
561
Himalayan belts, but also provide a strong basis for understanding the cause of along-strike
562
variations of topography and seismic activities in the Himalayan wedge (Singer et al., 2017;
563
Bai et al., 2019).
564
5. Conclusion:
565
This study provides an analysis of three-dimensional strain pattern for explaining the
566
cause of spatially varying ductile structures in fold-and-thrust belts. The recognition of
567
systematic variations in ductile structures across the orogenic belts is useful for gaining first-
568
order understanding on the rheology of basal decollement during the growth of mountain
569
belts. Development of isolated patches of L-tectonites and cross-folds in orogenic hinterland
570
signify either laterally varying crustal rheology or decollement strength in fold-and-thrust
571
belts. Our models over strong decollement show that localization of gravity driven flow in the
23
572
hinterland may lead to orogen-parallel recumbent folds in fold-and-thrust belts. The
573
development of pervasive, hinterland dipping ductile fabric in the frontal part of fold-and-
574
thrust belts indicates overall flattening type of deformation for both weak and strong basal
575
decollements.
576
577
578
Acknowledgements We thank two anonymous reviewers for their constructive suggestions and Joao Hippertt
579
for editorial handling. SB acknowledge financial supports from the project funded by SERB,
580
Government of India, (Project No. EMR/2015/000910). SR received the Inspire fellowship
581
(No. DST/INSPIRE Fellowship/2016/IF160071) for doctoral research and PS acknowledge
582
the postdoctoral research project (No. F.4-2/2006(BSR)/ES/17-18/0035), funded by UGC.
583
584
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714.
987
988
Figure captions:
41
989
Fig.1 Schematic diagram of experimental setup. Inset showing initial model geometry with
990
reference to Cartesian coordinate system. Vertical and horizontal scale bars shown in diagram
991
are in cm.
992
Fig.2 (a) Cross-sectional view (XZ section) of successive stages of wedge evolution over a
993
weak decollement. Note that wedge slope gradually increased until the deformation of the
994
wedge reached the final stage of wedge growth. The final stage is marked by the onset of
995
decreasing the wedge slope (α) with continuous shortening. Corresponding line drawings for
996
successive stages are shown below. Dashed lines represent the traces of long axes of
997
deformed ellipses. The light shaded portion of the model marks the width of the deformed
998
wedge (also demarcated by a double sided arrow); while the dark shaded portion represents
999
the undeformed segment of the model. Vertical and horizontal scale bars are shown in cm.
1000
(b) Progressive evolution of particle flow trajectory (using the software Image J) and strain
1001
pattern (computed with SSPX software, using the Grid Distance Weighted method). Here
1002
each set of flow vector diagram (top) and strain distribution map (bottom) corresponds to
1003
successive stages of progressive shortening shown on the left in (a). Coloured vertical scale
1004
shows the magnitude of strain. Tm and Tn represent time in model and nature respectively.
1005
Fig.3 Graphical plots show evolution of wedge geometry (wedge angle and wedge height) as
1006
a function of horizontal shortening in experimental model over weak (a) and strong (b)
1007
decollements respectively. Schematic representative three-dimensional wedge models (not to
1008
scale) are shown for each stage of wedge evolution.
1009
Fig.4 (a) Top view (YZ section) of successive stages of deformation in experimental model
1010
over a weak decollement. Note that the distance between the strain markers along Y-axis
1011
decreased continuously adjacent to the hinterland buttress, giving rise to a zone of
1012
compression (marked by a white dashed line) and deformed circular markers are shown using
42
1013
red solid arrows. Using Grid Distance Weighted method in SSPX software, evolution of
1014
particle flow trajectory (b) and strain maps (c) are shown corresponding to the stages of
1015
deformation in (a). Note that compressional zone is also shown in strain map (c) by white
1016
dashed line. Coloured vertical scale shows the magnitude of strain. Tm and Tn represent time
1017
in model and nature respectively.
1018
Fig.5 (a) Cross-sectional view (XZ section) of successive stages of deformation in
1019
experimental model over a strong decollement. Note that wedge slope increased until the
1020
deformation of the wedge reached the final stage. The final stage is marked by the beginning
1021
of reduction in wedge slope with continuous shortening. Schematic line drawings of wedge
1022
evolution with progressive shortening are shown below corresponding to each stage. Dashed
1023
lines represent the traces of long axes of deformed ellipses. The light shaded portion of the
1024
model marks the width of the deformed wedge (also demarcated by a double sided arrow);
1025
while the dark shaded portion represents the undeformed segment in the front. Vertical and
1026
horizontal scale bars shown in cm. The two red dashed lines in the final stage mark the zone
1027
of high strain localization, indicating a possible location for large-scale thrusting. (b)
1028
Progressive evolution of particle flow trajectory and strain pattern (computed with SSPX
1029
software, using the Grid Distance Weighted method) are shown corresponding to deformation
1030
stages in (a). Note that the trace of the final position of the initial horizontally aligned dots
1031
produce recumbent fold geometry (marked by red dashed line in the final model) with
1032
increasing shortening. Chaotic alignment of extension axes in strain maps represent the
1033
undeformed parts of the model at different stages as indicated by negligible particle
1034
displacement in the frontal part of the model in each corresponding flow vector diagram.
1035
Coloured vertical scale shows the magnitude of strain. Tm and Tn represent time in model and
1036
nature respectively.
43
1037
Fig.6 (a) Top view (YZ section) of successive stages of deformation in experimental model
1038
over a strong decollement. Using Grid Distance Weighted method in SSPX software,
1039
evolution of particle flow trajectory (b) and strain maps (c) are shown corresponding to the
1040
stages of deformation in (a). Chaotic alignment of extension axes in strain maps represent the
1041
undeformed parts of the model at different stages as indicated by negligible particle
1042
displacement, as shown in (b), in the frontal part of the model. Coloured vertical scale shows
1043
the magnitude of strain. Tm and Tn represent time in model and nature respectively.
1044
Fig.7 Flinn plots for weak decollement: strain ratios correspond to the entire model (a),
1045
hinterland (b) and foreland (c) respectively. Separate plots in (b) and (c) estimate the nature
1046
and amount of strain partitioning within the hinterland and foreland at different stages of
1047
wedge growth. Initial flattening type of deformation in the hinterland region is transformed to
1048
constrictional type with progressive shortening in (b). The intensity of flattening increases
1049
with shortening towards the foreland (c).
1050
Fig. 8 Three-dimensional representation of deformed viscous wedge developed over a weak
1051
basal decollement. The deformed wedge is characterised by a low surface slope as revealed
1052
from XZ section of finite model. The XY section is characterised by undulating topography
1053
near the hinterland buttress (oblique view of three dimensional wedge model in
1054
Supplementary Fig. S2 distinctly shows the topographic variations). Note the region of
1055
topographic low between two lateral topographic highs adjacent to lateral walls (front wall
1056
and back wall), responsible for generating convergent flow along Y-axis of bulk strain
1057
(shaded area in the central part of the hinterland and marked by black arrows). Schematic
1058
representation of strain ellipsoids indicates the manifestation of spatially varying three-
1059
dimensional strain pattern from foreland to hinterland: flattening type of strain characterises
1060
the foreland and constrictional deformation localizes preferentially towards the rear part of the
1061
hinterland. Undeformed cube at the extreme foreland represents region of no deformation. 44
1062
Fig.9 Strain maps (using Grid Distance Weighted method in SSPX software) for successive
1063
incremental steps of top-view (YZ section) in model with weak decollement. (a) Development
1064
of compressional zone (marked by white dashed line) near the hinterland buttress in the initial
1065
stage of wedge growth, indicating the development of constrictional strain field. (b) and (c)
1066
Constrictional strain field (marked by white dashed line) persists during the intermediate stage
1067
of wedge growth. Note that extensional strain axes (black line) always run parallel to the Y-
1068
axis of bulk strain during the initial and intermediate stages of wedge growth. (d) Incremental
1069
strain map, showing reduction in surface area of compressional zone and development of
1070
extensional zone near the hinterland buttress. Note that extensional axes are now aligned
1071
parallel to Z- axis of bulk strain in the zone of extension (e) Incremental step showing the
1072
increase in surface area of extensional zone, (f) Complete obliteration of compression zone by
1073
extensional zone near the hinterland buttress. Change from compressional zone to local
1074
extensional zone near the hinterland buttress indicates increase in the intensity of convergent
1075
flow along Y-axis of bulk strain. Coloured vertical scale shows the magnitude of strain.
1076
Fig.10 Flinn plots for strong decollement: strain ratios correspond to the entire model (a),
1077
hinterland (b) and foreland (c). Note that, both hinterland (b) and foreland (c) are
1078
characterised by flattening type of deformation with increasing progressive shortening, in
1079
contrast to strain pattern over weak decollement discussed in Fig. 7.
45
Parameter
Units
Length of viscous slab ( ) Thickness of viscous slab (h) Convergence velocity (V)
metre (m)
In nature
In model
= 400 km = 4 x 105 m
Scale Factor= (Nature/Model)
= 40 cm = 4 x 10-3 m
= 106 (after Rossetti et al., 2001)
4
metre (m)
ℎ
metre per second (ms-1)
V = 3.1 cm/year (after De Mets et al., 2010; Argus et al.,
= 20 km =2 x 10 m
2011) = 9.83× 10
-10
Pascal second (Pas)
Density of slab material ( )
kilogram per metre cube (kgm3 )
= 2700 kgm-3
Strain rate ( )
per second (s-1)
= 10-15 s-1
ℎ
= 2 cm= 2 x 10 m
V
= 1.97 × 10-4 ms-1
-----------V = 4.9898×10
-6
ms-1
= 5.6 × 1021 Pas
Viscosity of slab material ( )
-2
(calculated)
= 104 Pas (Weijermars, 1986)
= 965 kgm-3 (Weijermars,
= 5.6 × 1017 (calculated from eq.2 in text)
=2.7979 ≈ 2.8
1986)
= 2 × 10-4 s-1 (calculated)
= 4.5 × 10-12 (calculated from the values of and V respectively)
Time (t)
second (s)
= 6.8493 Ma (calculated)
=1080 s (measured experimental run time)
Gravitational stress (
)=
Pascal (Pa)
--------------
ℎ
Weak decollement [ = 965 kgm-3 × 9.8ms-2 × 4.06×10 2 m] = 383.954 Pa
= 2 × 1011 (derived from the inverse of )
------------
(calculated)
Strong decollement [ = 965 kgm-3 × 9.8ms-2 × 8.78×10-2m] = 830.324Pa (calculated)
Compressive normal viscous stress ( ) = V w
Pascal (Pa)
--------------
Weak decollement [ = (5×104 Pas × 1.97×10-4 ms-1) / (17.5×10-2 m)] = 56.285Pa
------------
(calculated)
Strong decollement [ = (5×104 Pas × 1.97×10-4 ms-1) / (10×10-2 m)] = 98.5 Pa (calculated)
Argand Number (Ar) =
Dimensionless
---------------
Weak decollement = 6.82 (calculated)
Strong decollement = 8.42 (calculated)
-----------
Table. 1 Scaling of experimental parameters.
X-axis
Camera 2
Z-axis Y-axis
d
e Fix
ll a w
Bac
kw
all
Pas
sive
Fro
nt w
all
2
ma
ll a rs e w p) l b ea ksto v Mo (Bac
rke
0
40 25.3
Camera 1
Motor driven piston 0
Strain in entire model
Strain at 3.8 cm (9.5% shortening)
Field of constrictional strain
Strain in foreland
Strain in hinterland in
tra
f
a pl
o ne
Field of constrictional strain
in
Field of constrictional strain
s ne
tra
s ne
in
tra
a
Li
ne
l fp
s ne
o
Li
Axially symmetric Field of flattening strain stretching
la fp Field of flattening strain
o ne
Li
Field of flattening strain
Axially symmetric flattening
in
Strain at 8.4 cm (21.0% shortening)
Field of constrictional strain
Field of constrictional strain
tra
s ne
a
f eo
pl
Axially symmetric stretching
Axially symmetric flattening
Field of constrictional strain
n
Strain at 12.8 cm (32.0% shortening)
e in
n
Li
Field of flattening strain
n
Field of constrictional strain
an
an
pl
f eo
tr es
of
pl
n
p of
Li
ai
Field of constrictional strain
ai
tr es
tr es
la
ne
ne Li Field of flattening strain
Field of flattening strain
n
ai
Field of constrictional strain
n
la
p of
n
Li
n
ai
tr es
n
ai
tr es
an
f eo
L Field of flattening strain
pl
n Li Field of flattening strain
Field of flattening strain
Strain at 14.5 cm (36.2% shortening)
in
n
ai
Field of constrictional strain
n
la
ne
Li
p of
tr es
Field of constrictional strain
in
ne
a str
ne
Li
p of
Li Field of flattening strain
Field of flattening strain
Axially symmetric flattening
(a)
(b)
s ne
la
fp
o ne
la
Field of flattening strain
tra
Field of constrictional strain
(c)
3.3 % shortening
8.76°
4
35
40
30
25
20
15
10
(in cm) 0 510.5 % shortening
Tm=196 s, Tn= 1.25 Ma
4
10.15°
ETL
2
35
40
0
5
30
25
20
15
10
Initial stage
2
0
5 2
30
25
20
15
10 5 Deformed wedge
12.80°
25.2 % shortening
Tm=334 s, Tn=2.13 Ma
0
Intermediate stage
35
40
4 2
35
40
30
25
20
10
15
5
0
10
5
0
10
5
0
2
35
30
25
(in cm) 0 532.3 % shortening
15 20 Deformed wedge 7.35°
ETL
4 2
35
40
Tm=602 s, Tn= 3.84 Ma
30
25
20
15
4
Magnitude of strain
2
35
40
30
25
(in cm) 43.0 % shortening
20
Deformed wedge 6.11°
15
10
5
Tm=860 s, Tn=5.49 Ma
0
2
40
35
30
25
20
15 4
10
5
0
7.58 e-02 2.05 e-02
Tm=990 s, Tn=6.32 Ma (a)
35
30
25 Deformed wedge
20
15
2.42 e-01
1.31e-01
2
40
2.97 e-01
1.86 e-01
4
ETL
Final stage
40
10
5
0
(b)
Initial stage
Intermediate stage
Final stage
Initial stage
Intermediate stage
Final stage
x
x
z
z x
y
y x
z x
z
y y x
z
z
y
(a)
y
Wedge angle Wedge height
Wedge angle Wedge height
(b)
Initial stage 10 (in cm) 0 ETL
6.0 cm (15.00% shortening)
10 (in cm) 0 ETL
10.4 cm (26.00% shortening)
10 (in cm) 0 ETL
15.2 cm (38.00% shortening)
10 (in cm) 0 ETL
18.3 cm (45.75% shortening)
Tm =105s,Tn =0.67 Ma
Tm =271s,Tn =1.73 Ma
Tm =474s,Tn =3.02 Ma
Tm =715s,Tn =4.56 Ma
Tm =858 s,Tn =5.48 Ma
Deformed circular marker
10 (in cm) 0 ETL
(a)
21.0 cm (52.50% shortening)
Intermediate stage
2.5 cm (6.25% shortening)
Final stage
10 (in cm) 0 ETL
Tm =1001 s,Tn =6.39 Ma
(b)
(c)
Magnitude of strain
Tm = 264s, Tn = 1.68 Ma
Initial stage Intermediate stage
Tm = 68s, Tn = 0.43 Ma
Tm = 688s, Tn = 4.39 Ma Magnitude of strain
Final stage
1.35 e+00 1.07 e+00 7.88 e-01 5.07 e-01 2.27 e-01
Tm = 872s, Tn = 5.57 Ma (b)
0
-5.43 e-02
Initial stage 0
2.4 cm (6.0% shortening)
0
3.8 cm (9.5% shortening)
0
8.4 cm (21.0% shortening)
0
12.8 cm (32.0% shortening)
ETL
10
(in cm) ETL
10
(in cm) ETL
10
(in cm) ETL
Tm=282 s, Tn=1.80Ma
Tm=690 s,Tn =4.40Ma
Tm=900 s,Tn=5.75Ma
Tm=1080 s, Tn=6.90 Ma
Magnitude of strain
1.48 e-01 1.18 e-01 8.71 e-02 5.66 e-02 2.62 e-02 0 -4.28 e-03
10
(in cm) ETL
(a)
0
Intermediate stage
(in cm)
14.5 cm (36.2% shortening)
Tm=1188 s, Tn=7.59Ma
(b)
(c)
Final stage
10
n ne la
fp eo Li n
Field of constrictional strain
in tra pl
of ne Li
Li
Li
ne
ne
of
of
pl
pl
an
an
es
tra
in
Field of flattening strain
es
in tra es an
Strain at 10.4 cm (26.0% shortening)
Axially symmetric stretching
ai
n ai str la
fp eo Field of constrictional strain
Field of flattening strain
Field of flattening strain
Field of constrictional strain
Field of constrictional strain
Li n
la eo
fp
Axially symmetric flattening
Li n
Axially symmetric stretching
Strain in foreland
ne
str
ai
n
Field of constrictional strain
ne
Strain at 6 cm (15.0% shortening)
Field of constrictional strain
Strain in hinterland
str
Strain in entire model
Field of flattening strain
Field of flattening strain
Field of flattening strain
Axially symmetric flattening
in tra
in tra es
an of
of
ne
ne
Li
Li
Li
ne
Axially symmetric flattening
pl
pl
of
an
pl
an
Field of constrictional strain
es
in tra
Field of constrictional strain
es
Strain at 15.2 cm (38.0% shortening)
Field of constrictional strain
Field of flattening strain
Field of flattening strain
tra in ne s
Li
Li ne
ne
of
of
Axially symmetric flattening
pl an
pl a
of ne Li
Axially symmetric stretching
Field of constrictional strain
Field of flattening strain
Field of flattening strain
Field of flattening strain
(a)
(b)
es tra
ne s
Field of constrictional strain
pl a
Strain at 21cm (52.5% shortening)
Field of constrictional strain
in
tra in
Field of flattening strain
(c)
Orogen transverse trend
x x y
Foreland
Hinterland
z
d
l
r
e all
og r O
e
a np
n tre
2.5-6 cm displacement (15.00% shortening)
(c)
6-10.4 cm displacement (26.00% shortening)
(d)
10.4-15.2 cm displacement (38.00% shortening)
Initial stage
(b)
Intermediate stage
2.5 cm displacement (6.25% shortening)
Final stage
(a)
Magnitude of strain 1.27 e-01 9.46 e-02
(e)
15.2-18.3 cm displacement (45.75% shortening)
6.22 e-02 2.97 e-02 0
(f)
18.3-21 cm displacement (52.50% shortening)
-2.68 e-03 -3.51 e-02
Research Highlights • • • •
Development of ductile structures in fold-and-thrust belts is sensitive to decollement strength L-tectonites and cross folds preferentially localize in a tectonic wedge over weak decollement Strong decollement leads to recumbent fold in convergent setting Hinterland-dipping ductile fabrics in the foreland correspond to flattening type of deformation
Conflict of interest
There is no conflict of interest.