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Strain distribution of the different strain patterns on fold profiles. a) Pure tangential longitudinal strain; b) pure flexural flow (g is shear strain); c) homogeneous deformation before buckling (initial layer shortening); and d) homogeneous deformation after buckling (flattening). In c) and d) the buckling stage is produce by tangential longitudinal strain.
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Analysis of symmetrical folds developed in competent layers yields a kinematic folding model based on the study of the geometric characteristics of the folded layer, finite strain measurements and c-axis preferred orientation of detrital quartz. The meter-scale folds that we studied were formed during the first phase of Variscan deformation in the...
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... models of tangential lon- gitudinal strain (TLS), flexural flow (FF) and homogeneous deformation (HD). According to this author, for TLS the axes of the finite strain ellipses are arranged tangentially and per- pendicularly to the layering. The layer is divided in two zones by a surface, known as the neutral surface, with no longitudinal strain (Fig. 1a). Strain magnitude increases with curvature and distance from the neutral surface. In this paper, we will use the term ''neutral line'', since the study has been made based on fold profiles (2D). FF is a layer-parallel simple shear, in which shear magnitude increases with greater layer dip change (Fig. 1b). HD, geometrically, represents ...
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... surface, with no longitudinal strain (Fig. 1a). Strain magnitude increases with curvature and distance from the neutral surface. In this paper, we will use the term ''neutral line'', since the study has been made based on fold profiles (2D). FF is a layer-parallel simple shear, in which shear magnitude increases with greater layer dip change (Fig. 1b). HD, geometrically, represents an affine transforma- tion of the layer points. It is called layer shortening if it occurs at the beginning of the folding, and flattening if it operates at the end (Fig. 1c,d). The geometrical effects on the folded layer are different in both cases. Ramsay and Huber (1987, pp. Hudleston and Holst, ...
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... been made based on fold profiles (2D). FF is a layer-parallel simple shear, in which shear magnitude increases with greater layer dip change (Fig. 1b). HD, geometrically, represents an affine transforma- tion of the layer points. It is called layer shortening if it occurs at the beginning of the folding, and flattening if it operates at the end (Fig. 1c,d). The geometrical effects on the folded layer are different in both cases. Ramsay and Huber (1987, pp. Hudleston and Holst, 1984;Gutiérrez-Alonso and Gross, 1999;Ormand and Hudleston, 2003), an approximation to the strain patterns involved in the folding process has been ob- tained. Aspects such as the area decrease or the migration of ...
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... order to understand the 3D strain and the deformation re- gime within the folded layer, we measured the R values of sec- tions A and B in fold 155 (Figs. 10 and 11), and we observed that the relationships between the axes of finite strain in the two sections were very similar. The ellipsoid in every point sampled was plotted in a Flinn diagram (Fig. 12). All the points lie within the field of flattening ellipsoids in the case ...
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... order to understand the 3D strain and the deformation re- gime within the folded layer, we measured the R values of sec- tions A and B in fold 155 (Figs. 10 and 11), and we observed that the relationships between the axes of finite strain in the two sections were very similar. The ellipsoid in every point sampled was plotted in a Flinn diagram (Fig. 12). All the points lie within the field of flattening ellipsoids in the case ...
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... fabrics along the fold shows a c-axis pattern charac- terized by a symmetric cross girdle normal to b with a large half opening angle (Fig. 10). This corresponds to a constrictive regime (e.g., Lister and Hobbs, 1980) and shows stretching parallel to the fold axis. It is difficult to explain the inconsis- tence between the ellipsoid obtained using strain data and the one using c-axis. The study of the thin sections of the samples did not provide any evidence that indicated ...
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... R values stated in this paper must reflect quite accurate the real bulk strain that the rocks underwent, since using different methods we have reached approximately the same re- sults. However, under several conditions these methods can underestimate the strain. Fig. 12 might represent an indication in this regard, because all the values obtained are lower than the results reached by other authors. In the DTNNM, underes- timation of strain may happen when the original grain distribu- tion is not anticluster and random, while in R f -f method it occurs when all the strain does not result in a change of ...
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Citations
... From these studies, it is clear that the assumption of mechanical isotropy within single layers is an oversimplification, often with important influence of anisotropy both along and across competent single-layers, or in an aggregate response. In addition, we know that the internal fabric of folded single-layers in nature, in particular that of veins, shows significant complexity (Zhang et al., 1993;Hippertt and Tohver, 2002;Kocher et al., 2006;Toimil and Fernández, 2007;Toimil and Griera, 2007). It is, though, to date still poorly understood how exactly the internal fabric influences folding. ...
Flexural flow is thought unlikely to occur in naturally deformed, competent isotropic single-layers. In this study we discuss a particular case of folded bedding-parallel fibrous dolomite veins in shale, in which the internal strain pattern and microstructural deformation features provide new insights in the mechanisms enabling flexural flow folding. Strain in the pre-folding veins is accommodated by two main mechanisms: intracrystalline deformation by bending and intergranular deformation with bookshelf rotation of dolomite fibres. The initially orthogonal dolomite fibres allowed a reconstruction of the strain distribution across the folded veins. This analysis shows that the planar mechanical anisotropy created by the fibres causes the veins to approximate flexural flow. During folding, synkinematic veins overgrow the pre-folding fibrous dolomite veins. Microstructures and dolomite growth morphologies reflect growth during progressive fold evolution, with evidence for flexural slip at fold lock-up. Homogeneous flattening, as evidenced by disjunctive axial-planar cleavage, subsequently modified these folds from class 1B to 1C folds. Our study shows that the internal vein fabric has a first-order influence on folding kinematics. Moreover, the fibrous dolomite veins show high viscosity contrasts with the shale matrix, essential in creating transient permeability for subsequent mineralising stages in the later synkinematic veins during progressive folding.
... The study of the different strain patterns provides insight into the kinematic evolution of the folds from their initiation stage to their final stages of formation (e.g. Toimil and Fernández, 2007). The mechanisms that operated during deformation are reflected in the microtextures and fabrics produced by deformation and are controlled by the strain histories. ...
3D finite strain analyses and kinematic vorticity measurements were carried out on the Loghon Anticline within the HP-LT Sanandaj–Sirjan metamorphic belt (Neyriz area, SW Iran). Rƒ/φ and Fry methods were used on the strain markers (e.g. deformed fossils) to interpret geometric relationships between the fold axis, strain ellipsoid axes and shear zone boundaries. The results indicate the predominance of prolate strain in the anticline. Quantitative kinematic analyses show that the Wk parameter is 0. 67 ± 0. 06 (i.e. pure-shear dominated non-coaxial flow). This study quantitatively supports the establishment of a dextral transpressive system, which is responsible for the development of the large-scale right-lateral shear zones that strike sub-parallel to the major folds. Flexural shear combined with regional dextral-shear is suggested to be the most common mechanism of folding in this area. Copyright © 2011 John Wiley & Sons, Ltd.
... For a more complete kinematical fold analysis, other strain patterns, such as flexural flow or homogeneous pure-shear strain, are usually applied on top of TLS (Bastida et al., 2003;Bobillo-Ares et al., 2004). TLS is also referred to as orthogonal flexure (Twiss and Moores, 2007) and neutral line folding (Lisle et al., 2009) and has been applied, for example, to the kinematical analysis of symmetrical folds (Hudleston and Holst, 1984;Toimil and Fernandez, 2007), asymmetrical folds (Aller et al., 2010) and chevron folds (Bastida et al., 2007). ...
... Common to all different versions of TLS for the kinematical fold analysis (Bobillo-Ares et al., 2000, 2004, 2006Bastida et al., 2003;Toimil and Fernandez, 2007;Lisle et al., 2009;Aller et al., 2010) is the assumption of a neutral line that is continuous along the fold. However, the presented FE simulations show that in a mechanical model of buckle folds none of the two neutral lines is continuous along the fold. ...
... This is the case with papers on the large recumbent folds that appear in most of the orogens, such as those in the Alps (Ramsay, 1981;Ramsay et al., 1983;Dietrich and Casey, 1989;Butler, 1992;Rowan and Kligfield, 1992) and the Iberian Variscan belt . The detailed studies made by Hudleston (1973a) on folds of Loch Monar (Scotland), Sanderson (1979) and Rattey and Sanderson (1982) on folds from the Variscan fold belt of Southwest England and Toimil and Fernández (2007) on folds from the Iberian Variscan belt are also noteworthy. In some of these studies, the role of simple shear or sub-simple shear (combination of simple shear and pure shear; De Paor, 1983;Simpson and De Paor, 1993) has been recognized as an essential bulk strain regime in the development of folds. ...
... All measurements made from microstructural analyses (Fry or R f /f methods) give strain ratio (R) values much lower than those deduced from numerical modelling by 'FoldModeler' for the corresponding folds. This difference was detected in minor F 1 folds from the Navia-Alto Sil unit and the Courel recumbent syncline (Toimil and Fernández, 2007;Fernández et al., 2007). The very low R values obtained from samples collected in different parts of very tight folds are surprising in the latter case. ...
Folding during the Variscan deformation in NW Iberia has been analysed from the foreland to the hinterland of the orogen using several geometrical techniques complemented by the numerical simulation of kinematical folding mechanisms with the aid of a computer program (‘FoldModeler’). In the foreland, folds are related to thrusts; in the inner zones, folds can be attributed to three deformation phases. D1 and D2 involved deformation with horizontal foreland-directed displacements. D1 gave rise to closed or tight folds (F1) and cleavage (S1); development of large recumbent F1 folds in the hinterland required a simple shear regime and a final coaxial strain component with sub-vertical maximum shortening. Strain incompatibilities at deeper levels, together with high temperatures, favoured the concentration of ductile deformation in shear zones and development of mylonites during D2. Local flow instabilities generated F2 folds that were passively amplified by a combination of simple shear, coaxial strain and area change. D3 involved a change to a regime with dominant coaxial deformation and a sub-horizontal maximum shortening; it gave rise to upright or steeply inclined folds (F3). Development of D3 structures was heterogeneous and depended on the previous dip of the bedding and S1, the presence or emplacement of granitoids, the stacking of thrust sheets or the previous development of large faults bringing into contact rocks with different competence. D3 structures are mainly concentrated in metapelitic areas and appear distributed in bands on several scales. On a small scale, tectonic banding appears associated with small folds as a result of pressure-solution processes. In areas with sub-vertical S1, later sub-horizontal kink bands were formed by a vertical compression. Copyright © 2010 John Wiley & Sons, Ltd.
... They concluded that it is unlikely that competent layers would be sufficiently anisotropic as to develop a significant component of flexural fold during folding. Toimil and Fernández (2007), analysing by computer the kinematics of symmetric natural folds in competent layers, conclude that FF is much less important than TLS and it can occur after the latter as a small component due to geometrical incompatibilities generated during TLS. Bastida et al. (2007) mathematically modelled the kinematics of chevron folds and concluded that, in general, FF is necessary at the last stage of buckling, although the increment of folding due to this mechanism can be very small. ...
Mathematical 2D modelling of asymmetric folds is carried out by applying a combination of different kinematic folding mechanisms: tangential longitudinal strain, flexural flow and homogeneous deformation. The main source of fold asymmetry is discovered to be due to the superimposition of a general homogeneous deformation on buckle folds that typically produces a migration of the hinge point. Forward modelling is performed mathematically using the software ‘FoldModeler’, by the superimposition of simple shear or a combination of simple shear and irrotational strain on initial buckle folds. The resulting folds are Ramsay class 1C folds, comparable to those formed by symmetric flattening, but with different length of limbs and layer thickness asymmetry. Inverse modelling is made by fitting the natural fold to a computer-simulated fold. A problem of this modelling is the search for the most appropriate homogeneous deformation to be superimposed on the initial fold. A comparative analysis of the irrotational and rotational deformations is made in order to find the deformation which best simulates the shapes and attitudes of natural folds.
... Good fits can be also obtained if the application order of the two mechanisms is reversed, but the relative intensity of the flexural flow episode must be increased. Tangential longitudinal strain preceding flexural flow is suggested by the analysis of other folds in the area (Toimil and Ferná ndez, 2007). Layer B: Guideline eccentricity ¼ 0.6 (ellipse arc) and a single folding episode of flexural flow (h ¼ 1 in the right limb). ...
Two-dimensional analysis of folded surfaces oblique to the mechanical layering can shed light on the
kinematic mechanisms that operated during the development of folds. A new version of the program
‘FoldModeler’, developed in the MATHEMATICA� environment, is used to obtain the deformed configuration
of an initial pattern of oblique surfaces deformed by any combination of the most common kinematic
folding mechanisms: flexural flow, tangential longitudinal strain, with or without area change and
heterogeneous simple shear. The layer can also undergo any form of homogeneous strain at any moment
of the folding process. The outputs of the program provide complete information about the strain
distribution in the folded layer that includes graphs of the angle between the oblique surfaces as
a function of the inclination of the layering through the fold. These graphs can be very useful to
discriminate between the mechanisms that operate in the development of natural folds, and they have
been obtained and discussed for the most common combinations of strain patterns. The program is
applied to obtain theoretical folds that give a good fit of some natural examples of folded oblique
surfaces.
... The study of the different strain patterns provides insight into the kinematic evolution of the folds from their initiation stage to their final stages of formation (e.g. Toimil and Fernández, 2007). The mechanisms that operated during deformation are reflected in the microtextures and fabrics produced by deformation and are controlled by the strain histories. ...
The study of fold mechanisms in non-coaxial deformation regimes has been the subject of increasing interest of structural geologists throughout the world in recent years. These types of mechanisms are reflected in the rock fabrics which are controlled by the strain history. Using 3D finite strain analysis and kinematic vorticity measurements which carried out on the Loghon anticline. This anticline allows us to suggest fold mechanism along the HP-LT Sanandaj-Sirjan metamorphic belt, southwestern, Iran. The study of different patterns provides insight into the kinematic of folds. Several strain measurement methods were used by different strain markers (e.g. deformed conglomerates) to interpret geometric signatures of the deformation zones within the anticline. Quantitative kinematic analysis (e.g. Wk, kinematic vorticity number) of the strain markers within this anticline have shown that the pure-shear dominated with high-proportion of simple shear components flow, which support the establishment of a dextral transpression system. The transpressional flow is responsible for the development of the large-scale dextral shear zones which is sub-parallel the major folding. The finite strain within folded layers result from the accumulation of deformations affecting the layers. Finally it is suggested that flexural shear combined with regional dextral shear seem to be the most common mechanisms of folding in the HP-LT Sanandaj-Sirjan metamorphic belt along the Zagros orogenic belt.
... A characteristic of the constant area TLS model is the high strain ratios produced as a result of folding, especially in folds with large amplitude relative to the layer thickness. Toimil and Fernandez (2007) describe folds from Asturias, northern Spain, that show the geometrical characteristics of TLS folds. However, strain analyses using the Fry method on sandstone samples from these folds yield strain estimates that are significantly lower than those expected from the TLS method. The parallel TLS (areachange ) model (Bobillo-Ares et al., ...
Abstract Neutral surface folding is a significant contributor to fold development. This mechanism produces contrasting strains in the inner and outer arcs of the folded layer that arise from principal stress orientations that are approximately parallel and perpendicular to the layer. We demonstrate that such stress patterns imply significant gradients of mean stress across the folding layer, being more tensional on the outer arc and more compressive in the inner arc. This could pump fluids towards the outer arc during folding and result in heterogeneous volume changes. We conclude that the neutral surface folding model should be adapted to accommodate volumetric strains, in order to explain dilatational structures (e.g. open fractures, veining) on the extrados and volume-loss structures (e.g. pressure solution seams, stylolitic cleavages) on the intrados. This dilatation has economic implications as it allows prediction of sites of mineralization and zones of secondary permeability in fold-related hydrocarbon traps. Terra Nova, 21, 14–20, 2009
Folds with different values of viscosity contrast and anisotropy have been simulated using the finite-difference code FLAC™. The kinematical analysis of these folds has enabled conclusions to be reached about strain accommodation mechanisms. The sequence of strain patterns in all the folds analysed only differs in the intensities of the different mechanisms involved, which depend on the mechanical properties of the folds. The order of the different strain patterns in the sequence is the same, regardless of the anisotropy and viscosity contrast. Strain accommodation in folds follows the patterns of tangential longitudinal strain, flexural flow and layer shortening. Nevertheless, no combination of these strain patterns can explain the shape of the folded layer at the inflection point and the high strain intensity values in the inner arc. These problems can only be solved by considering a variant of longitudinal tangential strain that is less intense than has classically been thought and combined with a heterogeneous distribution of flexural flow and layer shortening across the layer. The dependence of the different folding mechanisms on the mechanical properties has been used to devise a graphical method for estimating viscosity contrast and anisotropy from the intensities of the strain patterns in the sequence.
