Strain and rotation in a multilayered fold

Strain was estimated in a fold of Cambrian interlayered siltstones and pelites by determining the preferred orientation of chlorite grains with an X-ray goniometer. Strains so obtained and the postulate that continuity be preserved allowed unfolding of the fold and the determination of rigid body rotations that accompanied the strain. Petrologic investigation showed no sign of major differential volume changes in the siltstones, and this in conjunction with measured strains led to the conclusion that one of the silty layers making up the fold was not, originally, a bed of uniform thickness but a lenticular body, probably representing a single ripple on a ripple-marked tidal flat.Unfolding by piecemeal fitting of unstrained domains shows that none of the principal axes of strain lie consistently parallel to or at right angles to the fold axis. Rock material was displaced with components orthogonal to the profile plane as well as parallel to it. Strain due to compaction during an early history of increasing sediment overburden cannot be separated from strain during tectonic deformation. Its influence is most clearly seen in differential volume change between siltstones and pelites. Additional differential volume changes within pelite beds could have occurred at any time of the deformational history.A comparison of the orientation of strain and rotation axes in the two limbs of the fold, and also comparison of the same orientations in Eulerian coordinates (Cartesian coordinates in the observed fold) and in Lagrangean coordinates (Cartesian in the unfolded fold) make it probable that episodes of relatively uniform strain both preceded and followed the buckling episode that produced the sharp hinge in the competent silt-stone. The siltstone may have been less indurated and thus no more competent than the pelite during early deformation.     

Folds in multilayered rocks of Proterozoic age,Rajasthan, India

First phase folds F₁ developed in polydeformed Ajabgarh Group rocks of Proterozoic age are studied using various geometrical methods of analysis for compatibility of homogeneous strain in both class 1–3 pairs by correlatingt′ _ga/α plots with existing curves for competent layers and matchingt _ga/α plots with the flattening curves for the incompetent layers. F¹ folds were initiated by the process of buckling but underwent [(λ₂/λ₁) = 0.2 to 0.7] for competent layers andR- values of 1.1 to 5 for incompetent layers. The varying flattening is also revealed by the geometry of folds. The apparent buckle shortening of folds which ranges between 49 and 67 per cent with a majority of the folds having shortening values between 50% and 55% (exclusive of layer parallel strain) and inverse thickness method strain up to 50%. Besides flattening, the fold geometry was also modified by the pressure solution. This is borne by the presence of dark seams rich in phyllosilicates and disseminated carbonaceous material offsetting limbs of buckled quartz veins in slates     

Strain and competence contrast estimation from fold shape

A new method to estimate strain and competence contrast from natural fold shapes is developed and verified by analogue and numerical experiments. Strain is estimated relative to the nucleation amplitude, A_N, which is the fold amplitude when the amplification velocities caused by kinematic layer thickening and dynamic folding are identical. A_N is defined as the initial amplitude corresponding to zero strain because folding at amplitudes smaller than A_N is dominantly by kinematic layer thickening. For amplitudes larger than A_N, estimates of strain and competence contrast are contoured in thickness-to-wavelength (H/λ) and amplitude-to-wavelength (A/λ) space. These quantities can be measured for any observed fold shape. Contour maps are constructed using existing linear theories of folding, a new nonlinear theory of folding and numerical simulations, all for single-layer folding. The method represents a significant improvement to the arc length method. The strain estimation method is applied to folds in viscous (Newtonian), power-law (non-Newtonian) and viscoelastic layers. Also, strain partitioning in fold trains is investigated. Strain partitioning refers to the difference in strain accommodated by individual folds in the fold train and by the whole fold train. Fold trains within layers exhibiting viscous and viscoelastic rheology show different characteristic strain partitioning patterns. Strain partitioning patterns of natural fold trains can be used to assess the rheological behaviour during fold initiation.     

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.     

Strain distribution in superposed buckling folds and the problem of reorientation of early lineations

Two series of experiments were carried out with soft model-materials in order to assess the relative importance of initial homogeneous strain, external rotation and late-stage strain in reorienting early lineations during superposed buckle-folding. In the first series cylindrical buckling folds were produced in embedded planar sheets containing a “lineation”. In the second series noncylindrical folds were produced by compression of a set of cylindrical folds. The experiments indicate that the ratio of buckle shortening to layer-parallel strain is much smaller when the principal extension is parallel to the fold-axis than in the case when the principal extension is perpendicular to the fold-axis. In very competent rocks, the reorientation of old lineations is mainly by external rotation and by the associated concentric longitudinal strain. In moderately competent rocks, the orientation of early lineations always changes by initial homogeneous strain before buckling becomes significant. Because of the unlike amounts of initial strain in layers of different competences, orientations of unrolled lineations may not be parallel in disharmonically folded layers of unlike competences. Under certain conditions the early lineation may become virtually parallel to the later fold-axis. The experiments indicate that the effects of late-stage strain in buckle-folding are largely restricted to the incompetent layers of a multilayer. Hence, if orientation data of early lineations in both competent and incompetent rocks are lumped together, the pattern of orientation may become quite complex. Even for a single competent layer, the pattern of early lineations can locally become complex because of the complex nature of concentric longitudinal strain (and strain resulting from stretching of middle surface of the layer), development of conical folds, development of shear strain along hinge zones of deformed early folds and also because of the development of different orders of folds in both the first and the second deformations.     

Experimental analysis of folding in simple shear

Six experiments of single-layer folding with simple-shear boundary conditions were completed. Using materials of ethyl cellulose, the viscosity ratio of the stiff layer to matrix ranged from 20 to 100. The experiments were monitored by 10–14 photographs taken at equally spaced time intervals. Strain distributions in both the stiff layer and matrix were calculated from the displacements of over 300 ink dots distributed over the surface of each experiment. Both incremental strain (calculated from the relative displacements of the dots between successive photographs) and accumulating strain were determined on the two-dimensional profile of the materials as they folded.Symmetrical fold wavelengths occur and seem to be controlled by the wavelengths of initial perturbations in the stiff layer. If the Biot wavelength was not present initially, it will not occur in the final waveform. Consequently, in a group of natural folds, the mean value of wavelength/thickness ratios apparently reflects the initial perturbations. The mean value should not be confused with the Biot wavelength and should not be used to calculate viscosity ratios in naturally deformed rocks.Substantial layer thickening occurred only with viscosity ratios of 20. The amount of layer thickening also depends on initial perturbations of the stiff layer. If these perturbations are near the Biot wavelength, they are greatly amplified, the folds grow rapidly and layer thickening is small. If the perturbations are not near the Biot wavelength, amplification is small, the folds grow slowly and layer thickening is much greater.Principal elongations of the accumulated strain in the cores of some of the folds are not symmetrically distributed about axial planes and may cut across the axial plane at angles up to 20°. Strain shadows in the matrix, near the convex side of fold hinges, are also prominent. These triangular-shaped regions of low strain are not symmetrically disposed about fold axial planes, in contrast to strain shadows occurring in folds produced under pure-shear boundary conditions.The rotation of accumulating principal elongations in the stiff layer was calculated at fold inflections. Even though the folds themselves are generally symmetrical, these rotations at opposite fold inflections are not. One fold limb exhibits little rotation of principal elongations during folding while the other has rotations up to 70°. In contrast, folds formed in pure-shear boundary conditions have rotations of principal directions on opposite fold limbs equal in magnitude.     

低级变质沉积岩区压溶作用在褶皱变形中的意义

拉卡兰褶皱带中,发育于Ballarat-Bandigo冲断带中的低级变质砂、泥岩的宏观构造以间离劈理和人字形褶皱为特征,而且劈理在褶皱中呈扇形发育。劈理和褶皱的几何关系分析显示:劈理和褶皱的形成为压溶作用、压扁作用、弯曲作用和被动旋转共同作用的结果,而褶皱砂、泥岩中变形构造则以与压溶作用和再沉淀过程有关的显微构造为其典型特征。Fry法进行的全岩应变测量显示,褶皱砂岩的内部应变相当低(X/Z=1.40—1.83),褶皱应变格局给出变形机制的信息包括:缩短过程中的压扁作用和压溶作用、褶皱过程中由弯滑导致的层平行剪应变、以及褶皱后期发育阶段内弧区强烈的压溶作用。宏观构造、显散构造以及应变特征多方面信息证明:低级变质的沉积岩在褶皱变形过程中,压溶作用为一重要的变形机制。应变分解显示在30％—50％的总地壳水平缩短量下,弯曲导致的缩短最为14％—36％,压扁导致的缩短量为3％—14％,压溶导致的缩短量为8％—26％,而且压溶作用主要发生在褶皱内弧区。     

Strain distribution across an experimental single-layer fold

Experiments have been carried out to study the effects of progressive deformation on the shape of folds and the variation in two-dimensional strains on cross-sections of singlelayer folds in a less competent matrix, in a pure-shear plane-strain deformation box with no volume change. The layer shortening continues after buckling has set in, leading to thickening of the fold hinge and with progressive buckling the layer elongates. During the layer elongation stage of folding the hinges continue to thicken, whereas the limbs thin out. Concentric folds are a combination of Class 1a type in the outer arc which gradually change to Class Ib type and then to Class 3 folds of Ramsay (1967) in the inner arc. Tangential longitudinal strains and shearing strains predominate in the fold-hinge zone and in the fold limbs of the buckling layer, respectively. Initially, uniform layer-flattening strains perpendicular to the layering develop which become extensive strains in the outer fold arc and compressive strains in the inner fold arc with progressive buckling. In the outer fold arc the extensive strains are distributed laterally over a wider zone and are of a lower magnitude than the compressive strains which are restricted to a narrow zone in the inner fold arc. The neutral surface first appears when the initial layer-flattening strains are removed due to extensive strains on the outer arc and with progressive buckling migrates towards the inner fold arc and extends laterally on the outer fold arc.     

Strain analysis in folds (Infrahelvetic complex,Central Alps)

Strain analysis based on initially uniformly oriented elliptical particles in an oolitic limestone (Blegi oolite) was used to study the homogeneity of the state of strain on various scales, kinematics of folding and deformation mechanisms. A computer (reduced means) method for strain analysis is presented which is based on deforming a population of ellipses with shape and orientation properties of measured undeformed ooids. The strain values obtained with this method are within an accuracy of about 10% (in terms of axial ratios) and are in good agreement with the ones obtained with existing graphical methods. The state of strain is homogeneous on the scale of a thin section, handspecimen and outcrop, provided that regions around relatively strong fossils and regions of marked variations in lithology are avoided. Whole rock strains and strains as indicated by ooids alone are similar. Strain patterns in folds in limestones embedded in sandstones, shales and marl are compatible with bending accompanied simultaneously with a shortening perpendicular to the axial surface. The shortening may be attributed to the shear strains related to fold asymmetry and overthrusting. Strains on the outer arcs of a competent dolomite layer compare well with theoretical and experimental fold models; strain patterns include complex contact strains and change along the fold hinge line across a transverse fault which was active during the folding process. Strains parallel to the hinge line are more or less uniform but do not necessarily represent a plane strain state. Volume change took place during deformation. It was accomplished by pressure solution processes, the pressure solved material being partly redeposited. Pressure solution accounts for only a relatively small fraction of the bulk finite strain and was accompanied by plastic flow. Intracrystalline deformation together with grain boundary sliding and/or grain boundary migration went hand in hand with recrystallization (noteably grain growth).     

Strain analysis and fold shape in a limestone layer and implications for layer rheology

Folds are developed in thin limestone layers within slates of the McKay Formation exposed to the east of the Rocky Mountain Trench, British Columbia, Canada. They possess geometrical characteristics expected of development by buckling. Strain in the profile plane of a selected fold is similar to that predicted by tangential longitudinal strain, except that magnitudes are too low for the observed curvature. This is attributed to inhomogeneity of strain on the scale of measurement, largely because of pressure solution. Material removed by pressure solution from the inner arc of the fold appears to form veins perpendicular to the hinge, a direction of tectonic stretching. Bedding-parallel stylolites developed diagenetically prior to tectonism.Layer-parallel shortening during the initiation of buckling was less than 20%, and probably less than 10%. The mean arclength/thickness ratio is 6.5 and 7.1, with a dispersion of 0.48 and 0.37 for local and regional populations of 29 and 212 folds, respectively. Application of buckling theory to this data suggests that folding followed a non-linear flow law. The viscosity contrast between limestone and slate would be higher and the power law exponent lower, if initial irregularities in the layers were in the form of a constant amplitude spectrum rather than one of white roughness. The data do not allow a choice of initial amplitude spectrum to be made, nor do they closely constrain estimates of n the power law exponent and viscosity contrast.Deformation in the limestone layers was accommodated by intracrystalline flow (twin gliding), pressure solution, and extensional veining (the last two linked by diffusive mass transfer). The first two dominated deformation in the profile plane of the fold and the last, in association with fracturing, allowed for extension parallel to the hinge. Experimental and theoretical considerations suggest that deformation by a combination of these processes should be non-linear. The non-linear flow law deduced from buckling analysis is consistent with expectations based on observations of active deformation mechanisms.     

Centrifuge modelling of deformation of a multi-layered sequence over a ductile substrate: 1. Style and 4D geometry of active cover folds during layer-parallel shortening

Centrifuge analogue modelling illustrates the progressive development of active folds in multilayers upon a ductile substrate during layer-parallel shortening. Models simulate folding of a mechanically stratified sedimentary sequence upon migmatitic gneisses in a large hot orogen, or upon a thick basal evaporite ± shale sequence in deeper levels of fold belts. The absence of a weak low-viscosity and low-density layer at the interface promotes infolding of the cover sequence and ductile substrate, whereas a planar upper surface to the basal ductile substrate is preserved when it is present. Whilst fold style, wavelength, and deformation of the interface with the ductile substrate differ depending on whether a low-viscosity and low-density layer is present at the base of the cover sequence, there is no marked systematic curvature of fold axes as seen in previous sandbox models for fault-bend or fault propagation folding during bulk shortening. Bulk shortening of a layered sequence with relatively thick individual layers above a ductile substrate promotes a regular and upright train of buckle folds, whereas thinner layers promote a more irregular distribution of buckle folds with variable vergence, style, and amplitude. Buckle folds above a ductile substrate progressively develop during bulk shortening from open and upright, to angular and tight, and may further develop into cuspate structures above relatively weak horizons. Relatively thick weak horizons within the layered sequence during bulk shortening interrupt regular fold patterns up structural section and allow out-of-phase folds to develop above and below the weak horizon.     

Strain distribution in a fold in the West Norwegian Caledonides

Strain has been measured from clasts within a deformed conglomerate layer at 17 localities around an asymmetric fold in the Rundemanen Formation in the Bergen Arc System, West Norwegian Caledonides. Strain is very high and a marked gradient in strain ellipsoid shape exists. To either side of the fold, strain within the conglomerate bed is of the extreme flattening type. In the fold, especially on the lower fold closure, the strain is constrictional. Mathematical models of perturbations of flow in glacial ice have produced folds of the same geometry as this fold, with a strikingly similar pattern of finite strain. The fold geometry and strain pattern, as well as other field observations, suggest that the fold developed passively, as the result of a perturbation of flow in a shear zone, where the strain was accommodated by simple shear accompanied by extension along Y.     

Microstructures and evolution of folds in SC-mylonites from Dudatoli-Almora crystallines of Garhwal Himalaya

In the Lesser Garhwal Himalaya, the North Almora Thrust separates the overlying medium-grade Dudatoli-Almora crystallines of Precambrian age from the unmetamorphosed to partly metamorphosed rocks of the Garhwal Group of Late Precambrian age. The crystalline nappe sheet consists of flaggy to schistose quartzites, granite gneisses and garnetiferous mica schist members in an ascending order. In different localities. different members of the Dudatoli-Almora crystallines are exposed along the thrust plane. Southwest of Adbadri fine-grained mylonitized schistose quartzites of Dudatoli-AImora crystallines are in contact with the underlying metabasites of the Garhwal Group. The mylonitized schistose quartzites consist of alternating thick (1 to 2m) quartzite and thin (10 to 20cm) micaceous quartzite bands. The micaceous quartzites can be further differentiated into alternating quartz-rich (0-5 to 2.0 cm thick) and mica-rich (0.2 to 1.0 cm thick) layers. In the quartzites the C-surfaces are parallel to the S-surfaces defined by the alternating quartz-rich and mica-rich layers. Further, the S-surfaces exhibit almost similar folds with multiple wavelengths where the axial planes are nearly parallel and enveloping surfaces are oblique to the lithological layering. The evolution of these folds has been envisaged in three phases of deformation on the basis of field evidence, fold geometry and microstructures. During the first phase buckle folds (F ₁) developed in thin micaceous quartzite layers. whereas thick quartzite bands underwent only layer parallel shortening. During the second phase the stress orientation changed and the limbs ofF ₁ folds were folded (F ₂). During the third phase of deformation which coincided with thrusting, the rocks were sheared, mylonitized and developed microstructures exhibiting dynamic recrystallization by the processes of subgrain rotation, and continual and discontinuai grain boundary migration. This phase was also responsible for the development of C-surfaces parallel to the lithological layering. Further, in the folded micaceous quartzite layers shearing resulted in the development of C-surfaces parallel to the axial planes ofF ₂ folds.     

3D fold growth rates

Geological folds are inherently 3D structures; therefore, they also grow in three dimensions. Here, fold growth in all three dimensions is quantified by numerically simulating upright single‐layer folds in 3D Newtonian media. Horizontal uniaxial shortening leads to a buckling instability, which grows from a point‐like initial perturbation in all three dimensions by fold amplification (vertical), fold elongation (parallel to fold axis) and sequential fold growth (parallel to shortening direction) of secondary (and further) folds adjacent to the initial isolated fold. The two lateral directions exhibit similar averaged growth rates, leading to bulk fold structures with aspect ratios in map view close to 1. However, fold elongation is continuous with increasing bulk shortening, while sequential fold growth exhibits jumps whenever a new sequential fold appears and the bulk fold structure therefore suddenly occupies more space. Compared with the two lateral growth directions, fold amplification exhibits a slightly higher growth rate.     

Aspects of strain history in folded sediments from the Schefferville Mining District, Labrador Trough, Canada

Preferred orientations of phyllosilicate grains in the shaley rocks of the Labrador Trough were studied using a pole-figure goniometer. Transmitted X-rays permit determination of the basal planes of chlorite and muscovite. From their preferred orientation, strain is calculated according to March's theory. By choosing samples in successively more strongly deformed domains, a strain history can be recognized which started with compaction by loss of pore volume under an overburden and was later followed by an early homogeneous tectonic shortening parallel to bedding and at a right angle to the fold axis. Buckling occurred next, with strain in the limbs becoming different from that in the hinges; the limbs were lengthened parallel to bedding and nearly normal to the fold axis. Continuing appression, finally, led to pervasive shortening normal to the axial plane with concurrent stretching both updip along the axial plane and along the fold axis. This latter stretching may have occurred when variable-plunge basin and dome structures of the Labrador Trough were formed.     

Structures in the banded iron-formation of the southeastern Bababudan Hills, Karnataka, India

The banded iron-formation in the southeastern Bababudan Hills display a macroscopic synformal bend gently plunging towards WNW. The bedding planes in smaller individual sectors show a cylindrical or conical pattern of folding. The dominant set of minor folds has WNW-ESE trending axial planes and the axes plunge towards WNW at gentle to moderate angles, though there is considerable variation in orientation of both axes and axial planes. A later set of sporadically observed folds has N-S trending axial planes. The macroscopic synformal bend within the study area forms the southeastern corner of a horseshoe shaped regional synformal fold closure which encompasses the entire Bababudan range. The minor folds are buckle folds modified to a varying extent by flattening. In some examples the quartzose layers appear to be more competent than the ferruginous layers; in others the reverse is true. The folds are frequently noncylindrical and the axes show curvature with branching and en echelon patterns. Such patterns are interpreted to be the result of complex linking of progressively growing folds whose initiation is controlled by the presence of original perturbations in the layers. Domes and basins have at places developed as a result of shortening along two perpendicular directions in a constrictional type of strain. Development of folds at different stages of progressive deformation has given rise to nonparallelism of fold axes and axial planes. The axes and axial planes of smaller folds developed on the limbs of a larger fold are often oriented oblique to those of the latter. Progressive deformation has caused rotation and bending of axial planes of earlier formed folds by those developed at later stages of the same deformational episode. Coaxial recumbent to nearly reclined fold locally encountered on the N-S limb of the macroscopic fold may belong to an earlier episode of deformation or to the early stage of the main deformation episode. The E-W to ESE-WNW strike of axial plane of the regional fold system in the Bababudan belt contrasts with the N-S to NNW-SSE strike of axial planes of the main fold system in the Chitradurga and other schist belts of Karnataka.     

A theory of concentric,kink, and sinusoidal folding and of monoclinal flexuring of compressible,elastic multilayers: III. Transition from sinusoidal to concentric-like to chevron folds

A basic, sinusoidal solution to the linearized equations of equilibrium for compressible, elastic materials provides solutions to several problems of folding of multilayers. Theoretical wavelengths are comparable to those predicted by Ramberg, using viscosity theory, and to those predicted by elementary folding theory. The linearized analysis of buckling of a single, stiff, elastic layer, either isolated or within a soft medium, suggests that wavelengths computed with elementary beam theory are remarkably similar to those computed with the linearized theory for wavelength-to-thickness ratios greater than about five. This is half the limit of ten normally assumed for use of the elementary theory.The theory and experiments with deep beams of rubber or gelatin indicate that thick, homogeneous layers folded with short wavelengths assume internal forms strikingly similar to those of the ideal concentric fold. Thus, mechanical layering clearly is not required to produce concentric-like forms.Further, the theory suggests that “arc and cusp” structure, or “pinches”, at edges of deep beams as well as chevron-like forms in single or multiple stiff layers are a result of a peculiar, plastic-like behavior of elastic materials subjected to high normal stresses parallel to layering. In a sense, the elastic material “yields” to form the hinge of the chevron fold, although the strain vanishes if the stresses are released. Accordingly, it may be impossible to distinguish chevron forms produced in elastic-plastic materials, such as cardboard or aluminum and perhaps some rock, from chevron forms produced in purely elastic materials, such as rubber.Analysis of the theory shows that, just as high axial stresses make straight, shortened multilayers the unstable form and sinusoidal waves the stable form, stresses induced by sinusoidal displacements of the multilayer make the sinusoidal waveform unstable and concentric-like waves the stable form. Thus, concentric-like folds appear to be typical of folded multilayers according to our analysis. Further, where the layers have short wavelengths in the cores of the concentric-like folds, the stiff layers “yield” elastically at hinges and straighten in limbs. Thus the concentric-like pattern is replaced by chevron folds as the multilayer is shortened. In this way we can understand the sequence of events from uniform shortening, to sinusoidal folding, to concentric-like folding, to chevron folding in multilayers composed of elastic materials.     

Folding of a detachment and fault – Modified detachment folding along a lateral ramp,southwestern Montana,USA

The inversion of the Middle Proterozoic Belt sedimentary basin during Late Cretaceous thrusting in Montana produced a large eastwardly-convex salient, the southern boundary of which is a 200 km-long oblique to lateral ramp subtended by a detachment between the Belt rocks and Archean basement. A 10 km-long lateral ramp segment exposes the upper levels of the detachment where hanging wall Belt rocks have moved out over the Paleozoic and Mesozoic section. The hanging wall structure consists of a train of high amplitude, faulted, asymmetrical detachment folds. Initial west-east shortening produced layer parallel shortening fabrics and dominantly strike slip faulting followed by symmetrical detachment folding. “Lock-up” of movement on the detachment surface produced regional simple shear and caused the detachment folds to become asymmetrical and faulted. Folding of the detachment surface after lock-up modified the easternmost detachment folds further into a southeast-verging, overturned fold pair with a ramp-related fault along the base of the stretched mutual limb.     

Early formed regional antiforms and synforms that fold younger matrix schistosities: their effect on sites of mineral growth

In the metamorphic cores of many orogenic belts, large macroscopic folds in compositional layering also appear to fold one or more pervasive matrix foliations. The latter geometry suggests the folds formed relatively late in the tectonic history, after foliation development. However, microstructural analysis of four examples of such folds suggests this is not the case. The folds formed relatively early in the orogenic history and are the end product of multiple, near orthogonal, overprinting bulk shortening events. Once large macroscopic folds initiate, they may tighten further during successive periods of sub-parallel shortening, folding or reactivation of foliations that develop during intervening periods of near orthogonal shortening. Reactivation of the compositional layering defining the fold limbs causes foliation to be rotated into parallelism with the limbs.Multiple periods of porphyroblast growth accompanied the multiple phases of deformation that postdated the initial development of these folds. Some of these phases of deformation were attended by the development of large numbers of same asymmetry spiral-shaped inclusion trails in porphyroblasts on one limb of the fold and not the other, or larger numbers of opposite asymmetry spirals on the other limb, or similar numbers of the same asymmetry spirals on both limbs. Significantly, the largest disparity in numbers from limb to limb occurred for the first of these cases. For all four regional folds examined, the structural relationships that accompanied these large disparities were identical. In each case the shear sense operating on steeply dipping foliations was opposite to that required to originally develop the fold. Reactivation of the folded compositional layering was not possible for this shear sense. This favoured the development of sites of approximately coaxial shortening early during the deformation history, enhancing microfracture and promoting the growth of porphyroblasts on this limb in comparision to the other. These distributions of inclusion trail geometries from limb to limb cannot be explained by porphyroblast rotation, or folding of pre-existing rotated porphyroblasts within a shear zone, but can be explained by development of the inclusion trails synchronous with successive sub-vertical and sub-horizontal foliations.     

Buckling stability of a viscous single-layer system,oblique to the principal compression

A new theory is developed for single-layer buckling, where the layer is not parallel to the principal stresses. The model chosen consists of a single layer with Newtonian viscosity η embedded in an infinite matrix of viscosity η₁. The layer lies at an angle θ to the bulk principal compressive stress in the embedding medium. It is deformed in equal-area plane strain, with the direction of no strain and the third principal bulk stress, parallel to the layer; hence the obliqueness to the principal stresses is only in two dimensions. It is shown that stress refraction is a necessary condition for this system, and an expression is derived for its value in terms of η, η₁ and θ. Buckling stability equations are completely developed which satisfy the Navier-Stokes equilibrium equations for the buckling layer, and the condition of stress continuity at the layer-embedding medium interface. The dominant wavelength of the buckles is shown to be independent of θ, but the stress required increases with θ.The results of this work have an important bearing on natural folds, since there is no evidence that rock layers are initially parallel to the stresses which fold them, an assumption made in former buckling theories. It is suggested that refraction of stresses and the resulting incremental strains gives rise to the finite structure of cleavage refraction so common in deformed rocks, and that the progressive development of folds in layers oblique to the principal bulk stresses gives rise to asymmetry.