The geometry and kinematics of flow perturbation folds

Minor folds formed synchronous with ductile deformation in high strain zones can preserve a record of the scale and kinematics of heterogeneous flow. Using structures associated with WNW-directed Caledonian thrusting in N Scotland, we show that localised perturbations in flow resulted in the generation of predominantly cylindrical minor folds with hinges lying at low angles to the transport direction. These define a series of larger-scale fold culminations (reflecting ‘surging flow’) or depressions (reflecting ‘slackening flow’) that are bisected by transport-parallel culmination and depression surfaces. The fold patterns suggest a dominance of layer-normal differential shearing due to gradients in shear strain normal to transport. Culmination surfaces are marked by along-strike reversals in the polarity of structural facing and vergence of minor folds which, contrary to classic fold patterns, define reverse asymmetric relationships. Culmination surfaces separate folding in to clockwise (Z folds) and anticlockwise (S folds) domains relative to the transport lineation. The dip of fold axial planes systematically increases as their strike becomes sub-parallel to transport resulting in a 3D statistical fanning arrangement centred about the transport direction. Thus, mean S- and Z-fold axial planes intersect precisely parallel to the transport lineation and potentially provide a means of determining transport directions in cases where lineations are poorly preserved. Culminations display convergent fold patterns with fold hinges becoming sub-parallel to transport towards the culmination surface and underlying detachment, whilst axial planes define overall concave up listric geometries which are bisected by the culmination surface. Thus, around culminations and depressions there are ordered, scale-independent relationships between transport direction, shear sense, fold facing, vergence and hinge/axial plane orientations. The techniques described here can be applied and used predictively within any kinematically coherent system of ductile flow.     

The sheath folds in the Tananao Group between Tienshiang and Tailuko, east-west cross-island highway, Taiwan

Sheath folds or “eye” folds on decimetric to metric scales are well-developed in the metachert-marble-green rock interlayers of the Changchun Formation and in the marble lens of the Tienhsiang Formation, within the Tananao Group between Tienhsiang and Tailuko, along E-W cross-island highway of Taiwan. Closely associated with the sheath folds are the tight to isoclinal folds with rectilinear axes which are parallel to the hinge line of the “eyes”, and the directions of these folds range from N-S to N30°E with gentle plunges to the north or south.The sheath folds are believed to have been formed during the second phase of deformation in this region. The traces of the earlier folding can generally be found at the hinges or limbs of these sheath folds.The explanation presented here is that the sheath fold might be generated episodically during the F₂ deformational phase throughout the entire history of progressive shearing as a result of episodic instability of the flow with successive refolding of metamorphic fabric, during Plio-Pleistocene deformation of Taiwan.     

Planar, non-planar and refolded sheath folds in the Phulad Shear Zone, Rajasthan, India

Progressive ductile shearing in the Phulad Shear Zone of Rajasthan, India has produced a complex history of folding, with development of planar, non-planar and refolded sheath folds. There are three generations of reclined folds, F₁, F₂ and F₃, with a striping lineation (L₁) parallel to the hinge lines of F₁. The planar sheath folds of F₁ have long subparallel hinge lines at the flanks joining up in hairpin curves at relatively small apices. L₁ swerves harmoniously with the curving of F₁ hinge line. There is a strong down-dip mineral lineation parallel to the striping lineation in most places, but intersecting it at apices of first generation sheath folds. Both the striping and the mineral lineation are deformed in U-patterns over the hinges of reclined F₂ and F₃. Folding of axial surfaces and hinge lines of earlier reclined folds by later folds was accompanied by very large stretching and led to the development of non-planar sheaths. The reclined folds of all the three generations were deformed by a group of subhorizontal folds. Each generation of fold initially grew with the hinge line at a very low angle with the Y-axis of bulk non-coaxial strain and was subsequently rotated towards the down-dip direction of maximum stretching. The patterns of deformed lineations indicate that the stretching along the X-direction was extremely large, much in excess of 6000 percent.     

Sheath fold development in monoclinic shear zones

We use numerical simulations to investigate the evolution of sheath folds around slip surfaces in simple‐shear‐dominated monoclinic shear zones. A variety of sheath fold shapes develops under general shear, including tubular folds with low aspect ratio eye patterns and tongue‐like structures showing bivergent flanking structures in sections normal to the sheath elongation, which may potentially lead to confusing shear sense interpretations. Not all investigated monoclinic flow end‐members lead to the development of sheath folds sensu stricto (folds with apical angle <90°). The aspect ratio of the eye patterns, R_yz, correlates with the ratio between the principal strain in the Y‐direction and the smaller of the principal strains in the X–Z plane, and thus it could be used in strain analysis.     

Side-stepping of axial surface traces in superposed folding

During the refolding of an early non-isoclinal fold (say,F ₁) we may find an offset or side-stepping of the axial surfaces of the later folds (say,F ₂). The offsets can be seen in both type 2 and type 3 interference patterns. An analysis of the shear fold model shows that there is a maximum limit for the magnitude of side-stepping. The side-stepping is larger for larger interlimb angles ofF ₁. It decreases with progressive tightening ofF ₂. By recognizing such side-stepping we can predict on which side the F₁ hinge should lie even if the hinge is unexposed or lies outside the domain of observation. The general rule for the sense of side-stepping is the same for shear folds, flexural slip folds and buckling folds. However, the side-stepping in buckling folds should be used with caution, sinceF ₂ folds on buckled single-layers may show an offset whose sense is opposite to that predicted by the general rule.     

Finite-element folds of similar geometry

Model folds of similar geometry have been produced by using the finite-element method and the constitutive relations of a layer of wet quartzite embedded in a marble matrix with an initially sinusoidal configuration and a 10° limb dip. The power law for steady-state flow of Yule Marble (Heard and Raleigh, 1972) is used for the matrix and our new law for Canyon Creek quartzite deformed in the presence of water is used for the layer. The equiv- alent viscosity of the wet quartzite is highly temperature-sensitive, giving rise to a strong temperature dependence of the quartzite: marble viscosity ratio which, at a strain rate of 10⁻¹⁴/sec, drops from 543 at 200° to 0.13 at 800°C. At 375°C (η_q/η_m = 10), concentric folds develop at all strains to 80% natural shortening and stress, finite strain and viscosity distributions are somewhat similar to those found previously. Raising the temperature to 550° C (η_q/η_m = 1), at any stage of prior amplification, causes the folds to flatten with increasing strain, accompanied by attenuation of limbs and thickening of hinges, leading to folds with similar geometries and isoclinal folds at extreme strains. The effects are more pronounced at higher temperatures and at 700° C (η_q/η_m = 0.3) limb attenuation is so severe as to give rise to unrealistic geometries. At temperatures below about 600° C (η_q/η_m = 2), similar folds do not form. It thus appears as if a viscosity contrast near unity is required to produce similar folds in rocks, under the conditions simulated and different temperature dependencies of viscosities of materials in layered sequences is one important means of reducing viscosity contrasts.     

Structural geometry of the early Precambrian terrane south of Coimbatore in the “Palghat Gap”, southern India

The ENE-plunging macroscopic folds, traced by calc gneiss interbanded with marble and sillimanite schist within the Peninsular Gneiss around Suganapuram in the ‘Palghat gap’ in southern India, represent structures of the second generation (D₂). They have folded the axial planes of a set of D₁ isoclinal folds on stratification coaxially, so that the mesoscopic D₁ folds range from reclined in the hinge zones, through inclined to upright in the limb zones of the D₂ folds. Orthogonal relation between stratification and axial planar cleavage, and ‘M’ shaped folds on layering locate the hinge zones of the D₁ folds, whereas folds on axial planar cleavage with ‘M’ shaped folds are the sites of the D₂ fold hinges. Extreme variation in the shapes of the isoclinal D₁ folds from class 1B through class 1C to nearly class 2 of Ramsay is a consequence of buckling followed by flattening on layers of widely varying viscosity contrast. The large ENE-trending structures in this supracrustal belt within the Peninsular Gneiss in the ‘Palghat gap’ could not have evolved by reorientation of NS-trending structures of the Dharwar tectonic province to the north by movement along the Moyar-Bhavani shear zone which marks the boundary between the two provinces. This is because the Moyar and Bhavani faults are steep dipping reverse faults with dominant dip-slip component. Deceased     

Progressive deformation and the rotation of contemporary fold axes in the Ballybofey Nappe,north-west Ireland

Internal regions of orogenic belts may be characterized by an alignment of fold axes with mineral elongation lineations. This relationship is commonly interpreted as representing progressive tightening and rotation towards the shear direction of early buckle folds, the hinges of which were initiated orthogonal to this direction. Detailed structural analysis of lower amphibolite facies Dalradian metasediments of the Ballybofey (fold) Nappe, north-west Ireland, shows that an intense S₃ schistosity is developed axial planar to mesoscopic and minor F₃ folds. In areas of low D₃ strain, F₃ fold axes plunge gently towards the north-east, whereas in regions of greater strain plunges are towards the south-east subparallel to the constant mineral lineation. Minor folds which initiated at angles of 70–80° from the mineral lineation subsequently rotated towards the shear direction in a consistent clockwise sense. Progressive and variable non-coaxial deformation oblique to the original mean F₃ orientation has resulted in a unimodal distribution pattern of fold axes. Analysis of the angular rotation of fold axes enables estimates of the bulk shear strain to be evaluated and models of progressive deformation to be assessed.     

Layer shortening and fold-shape development in the buckling of single layers

The progressive development of folds by buckling in single isolated viscous layers compressed parallel to the layering and embedded in a less viscous host is examined in several ways; by use of experiments, an analogue model to simulate simultaneous buckling and flattening and by an application of finite-element analysis.The appearance of folds with a characteristic wavelength in an initially flat layer occurs in the experiments for viscosity ratios (μ_layer/μ_host = μ₁/μ₂) of between 11 and 100; progressive fold development after the initial folds have appeared is similar in the experiments and in the finite-element models. Except for the finite-element model for μ₁/μ₂ = 1,000 layer-parallel shortening occurs in the early stages of folding and a stage is reached where little further changes in arc length occur. The amount of layer-parallel shortening increases with decreasing viscosity contrast, and becomes relatively unimportant after the folds have attained limb dips of about 15°–25°.Thickness variations with dip are only significant here for the finite-element model with μ₁/μ₂ = 10, and in experiments for μ₁/μ₂ = 5 where the layer is initially in the form of a moderate-amplitude sine wave. The variations range from a parallel to a near-similar fold geometry, and in general depend on the viscosity contrast, the degree of shortening and the initial wavelength/thickness ratio. They are very similar to the variations predicted by the analogue model of combined buckling and flattening. The difference between the thickness/dip variations in a fold produced by buckling at low viscosity contrast and one produced by flattening a parallel fold is marked at high limb dips and very slight at low limb dips.Many natural folds in isolated rock layers or veins show thickness/dip relationships expected for a flattened parallel fold, and some show relationships expected for buckling at low viscosity contrasts. Studies of the wavelength/thickness ratios in natural folds have suggested that competence contrast is often low. Many folds in isolated rock layers or veins whose geometry may vary between parallel and almost similar, and may be indistinguishable from those of flattened parallel folds, have probably developed by a process of buckling at low viscosity contrasts.     

构造置换及其控矿规律——以吉林板石沟铁矿为例

 强烈的塑性变形使华北地台东北部太古宙鞍山群中的吉林板石沟铁矿发生强烈的构造置换;造成原始仅有二三层的铁矿褶皱重复,在X(包络线)、Y(枢纽线)方向均被拉断,形成透镜状的复式褶皱勾状体。现有的19个矿组均为这种复式褶皱的转折端,并多呈"Z"型不对称形式。根据以上控矿规律本文提出两个找矿方向,一是包络线方向,另一是枢纽线方向,对1、3矿组具体地做了勘探设计。目前本文的勘探设计已得到勘探验证,新增铁矿储量数千万吨。     

Non-axial planar cleavage and Caledonian sinistral transpression in eastern Ireland

Transected F₁ fold structures in eastern Ireland are associated with subhorizontal stretching in the S₁, cleavage whereas axial planar cleavage contains a vertical elongation direction. This suggests that the non-axial planar cleavage was influenced by a distributed strike-slip ductile shear. A major NE-SW trending F₁ syncline is described in which the minor F₁ folds show systematic variations in cleavage transection parameters. On the steep limb of the major syncline the cleavage transects the minor F₁ folds in a consistently clockwise sense, whereas on the normal limb anticlockwise transected folds are seen. Axial planar cleavage occurs at the core of the major syncline. Fold profile analysis indicates that the buckling of the layers began before the initiation of the cleavage. Open, parallel folds at the major synclinal hinge zone are progressively ‘flattened’ on the steep limb towards a major D₁ sinistral transcurrent fault. The angular transection, A, attains a maximum of 15° clockwise which diminishes to <5° at higher strains adjacent to the major fault. Incremental fibre growth in pressure shadows show a two-stage tectonic strain superposition of vertical pure shear followed by sinistral transcurrent simple shear during the development of the clockwise transecting cleavage. Anticlockwise transected folds were influenced by local dextral strike-slip on the southern margins of a rigid terrane. As a regional feature, the clockwise transection is explained by a sinistral transpressive deformation of end-Silurian age.     

Structural and P-T Evolution of a Major Cross Fold in the Central Zone of the Limpopo High-Grade Terrain, South Africa

The Central Zone (CZ) of the Limpopo Complex of southern Africais characterized by a complex deformational pattern dominatedby two types of fold geometries: large sheath folds and crossfolds. The sheath folds are steeply SSW-plunging closed structureswhereas the cross folds are north–south-oriented withnear-horizontal fold axes. In the area south of Messina thiscomplexly folded terrain grades continuously towards the southinto a crustal-scale ENE–WSW-trending ductile shear zonewith moderate dip towards the WSW. All sheath folds documentconsistent top-to-the-NE thrust movement of high-grade material.The timing of this shear deformational event (D₂) and thus ofthe gneissic fabric (S₂) is constrained (at     

A mathematical model for orientation data from macroscopic cylindrical folds

An asymptotic form of Bingham's distribution on the sphere is applied to orientation data from cylindrical folds. Data from cylindrical folds typically form two clusters, one cluster for each fold limb. A bimodal distribution is obtained by fitting a unimodal distribution to each cluster. One parameter of the distribution gives the fold axis, another parameter is directly related to the curvature of the fold limb. Certain tests of hypotheses based on this distribution are the same as tests based on the Dimroth—Watson (symmetric girdle)distribution. One such is the test of whether two folds have the same fold axis.     

Strain and vorticity analysis using small-scale faults and associated drag folds

Small-scale faults with associated drag folds in brittle-ductile rocks can retain detailed information on the kinematics and amount of deformation the host rock experienced. Measured fault orientation (α), drag angle (β) and the ratio of the thickness of deflected layers at the fault (L) and further away (T) can be compared with α, β and L/T values that are calculated with a simple analytical model. Using graphs or a numerical best-fit routine, one can then determine the kinematic vorticity number and initial fault orientation that best fits the data. The proposed method was successfully tested on both analogue experiments and numerical simulations with BASIL. Using this method, a kinematic vorticity number of one (dextral simple shear) and a minimum finite strain of 2.5–3.8 was obtained for a population of antithetic faults with associated drag folds in a case study area at Mas Rabassers de Dalt on Cap de Creus in the Variscan of the easternmost Pyrenees, Spain.     

Sheath fold morphology in simple shear

Sheath folds are highly non-cylindrical structures often associated with shear zones. We investigate the formation of sheath folds around a weak inclusion acting as a slip surface in simple shear by means of an analytical model. We present results for different slip surface orientations and shapes. Cross-sections perpendicular to the shear direction through the sheath fold display closed contours, so called eye-structures. The aspect ratio of the outermost closed contour is strongly dependent on the initial slip surface configuration. The center of the eye-structure is subject to change in height with respect to the upper edge of the outermost closed contour for different cross-sections perpendicular to the shear direction. This results in a large variability in layer thickness across the sheath fold length, questioning the usefulness of eye-structures as shear sense indicators. The location of the center of the eye structure is largely invariant to the initial configurations of the slip surface as well as to strain. The values of the aspect ratios of the closed contours within the eye-pattern are dependent on the strain and the cross-section location. The ratio (R′) of the aspect ratios of the outermost closed contour (R_yz) and the innermost closed contour (R_y′z′) shows values above and below 1. R′ shows dependence on the slip surface shape and orientation but not on the number of involved contours. Using R′ measurements to deduce the bulk strain type may be erroneous.     

Strain analysis of a Northern Apennine shear zone using deformed marble breccias

The Alpi Apuane region of the Northern Apennines appears to have been deformed within a large-scale, low-angle shear zone with an overthrust sense of movement. The presence of mineral stretching lineations, folds progressively rotated into the X strain direction, and schistosities which intersect the nappe boundaries at small angles suggest that a component of shear strain occurred during the deformation. The strain ratios and orientations on two-dimensional sections have been determined from deformed marble breccias, reduction spots, and oncalites. Data from three or more non-perpendicular, non-principal sections have been combined to determine the finite strain ellipsoids at 33 sites within the shear zone.The finite strains have been separated into components of simple shear (γ), longitudinal strain (λ), and volume change (Δ). Algebraic expressions have been derived and graphs constructed which enable components of γ, γ and Δ, and γ and λ to be determined directly from a knowledge of strain ratio (R) within the shear zone and the angle (θ) between the principal strain direction and the shear zone boundary. The Alpi Apuane data indicate that neither simple shear alone, nor simple shear with volume change can satisfactorily explain the observed strains. Consideration of simple shear plus longitudinal strain leads to a general relationship in which the value of shear increases, and the values of longitudinal strain change along a SW-NE profile across the zone. Integration of the resulting shear strain-distance curves gives a minimum displacement of 4 km within the shear zone. Combination of the finite strains with the total time of deformation known from K/Ar studies leads to average strain rates from 1.4 to 9.6 × 10⁻¹⁵ sec⁻¹.A characteristic flat-ramp-flat geometry initially formed the boundaries of what was later to develop into the overthrust shear zone, and deformation of the underlying crystalline basement is believed to have occurred by ductile shearing. Estimates of 21% crustal shortening for the region suggest that the crustal thickness prior to deformation was approximately 20 km in this part of the Northern Apennines.     

A simple theory for the dispersion of real and apparent finite-strain lineations

In some metamorphic terrains, lineations in folded surfaces are coaxial to the folds at their hinges, but show a systematic dispersion on the limbs. A simple theoretical model is presented, based on two assumptions: (1) the layering is folded according to two idealised models, “ideal compression folding” and “ideal shear folding”, which assume that the rock material is homogeneous and the layering passive; (2) the lineation is a manifestation of the total product of the pre-folding and folding strains. In an ideal compression fold, only apparent lineations can be dispersed away from the fold-axial trend; in an ideal shear fold, however, both real and apparent lineations are dispersed in a similar way, the degree of similarity depending on the X/Y ratio of the pre-fold strain. The lineation loci of the two models are sufficiently distinct for them to be used, together with other features of the fabric, to distinguish between folds produced by dominantly vertical movements, and those produced by dominantly horizontal movements.     

Towards a volcanic–structural balance: relative importance of volcanism, folding, and remobilisation of nickel sulphides at the Perseverance Ni–Cu–(PGE) deposit, Western Australia

Perseverance is a world-class, komatiite-hosted nickel sulphide deposit situated in the well-endowed Leinster nickel camp of the Agnew–Wiluna greenstone belt, Western Australia. The mine stratigraphy at Perseverance trends north-northwest (NNW), dips steeply to the west, and is overturned. Stratigraphic footwall units lie along the western margin of the Perseverance Ultramafic Complex (PUC). The PUC comprises a basal nickel sulphide-bearing orthocumulate- to mesocumulate-textured komatiite that is overlain by a thicker, nickel sulphide-poor, dunite lens. Hanging wall rocks include rhyodacite that is texturally and compositionally similar to footwall volcanic rocks. These rocks separate the PUC from a second sequence of nickeliferous, E-facing, spinifex-textured komatiite units (i.e. the East Perseverance komatiite). Past workers argue for a conformable stratigraphic contact between the PUC and the East Perseverance komatiite and conclude that the PUC is extrusive. This study, however, clearly demonstrates that these komatiite sequences are discordant, implying that the PUC may have intruded rhyodacite country rock as a sill with subsequent structural juxtaposition against the East Perseverance komatiite. Early N–S shortening associated with the regional D_I deformation event (corresponding to the local D_P1 to D_P3 events at Perseverance) resulted in the heterogeneous partitioning of strain along the margins of the competent dunite. A mylonite developed in the more ductile footwall rocks along the footwall margin of the PUC, while isoclinal F₃ folds, such as the Hanging wall limb and Felsic Nose folds, formed in low-mean stress domains along the fringes of the elongated dunite lens. Strata-bound massive and disseminated nickel sulphides were passively fold thickened in hinge areas of isoclinal folds, whereas basal massive sulphides lubricated fold limbs and promoted thrust movement along shallowly dipping lithological contacts. Massive sulphides were physically remobilised up to 20 m from their primary footwall position into deposit-scale fold hinges to form the 1A and Felsic Nose orebodies. First-order controls on the geometry of the Perseverance deposit include the thermomechanical erosion of footwall rocks and the channelling of the mineralised komatiitic magma. Second- or third-order controls are several postvolcanic deformation events, which resulted in the progressive folding and shearing of the footwall contact, as well as the passive fold thickening of massive and disseminated sulphide orebodies. Massive sulphides were physically remobilised into multiple generations of fold hinges and shear zones. Important implications for near-mine exploration in the Leinster camp include identifying nickeliferous komatiite units, defining their three-dimensional geometry, and targeting fold hinge areas. Fold plunge directions and stretching lineations are indicators of potential plunge directions of massive sulphide orebodies.     

Synmetamorphic structural evolution of the Seward Peninsula blueschist terrane,Alaska

Blueschist-facies rocks of the central Seward Peninsula cropout over 8000 km². Protoliths were Lower Paleozoic-Precambrian(?) shallow-water miogeoclinal sediments that were metamorphosed during the Middle Jurassic. Thermobarometric estimates yield ‘peak’ metamorphic conditions of 10–12 kbar at 460 ± 30°C. Crystallization of blueschist-facies minerals was synkinematic with development of a transposition foliation. This foliation is parallel to lithologic contacts and is axial planar to recumbent mesoscopic isoclinal folds. These folds are refolded by larger scale recumbent tight to isoclinal folds. Both fold sets have hinges parallel to a well-developed N—S stretching lineation. Sheath folds are also present. The long axes of the sheath folds also parallel the stretching lineation. This deformation was non-coaxial as indicated by microstructures and quartz c-axis fabrics. Folds nucleated, then rotated into parallelism with the stretching direction. Kinematic indicators show unequivocal top-to-the-north shear sense, compatible with blueschist formation during mid-Jurassic collision between the Brooks Range continental margin and a N-facing island arc (Yukon-Koyukuk). Convergence of these two plates is believed to have been nearly N—S (in present co-ordinates).