Patterns of fold interference: influence of early fold shapes

Model experiments were specifically designed to test the effect of different profile shapes of early folds on refolding patterns. Comparison of natural examples with experimental results and analogy with engineering information on buckling of fold shapes suggest that, when layers are mechanically active during refolding, the profile shape of the early folds markedly affects the patterns of fold interference. Open rounded folds tend to refold to form dome and basin patterns of interference whereas isoclinal folds tend to refold by folding their axial plane, forming type 2 patterns of interference. Hence, the dimensions and shape of the profile of the early folds control the preferred buckling mode during refolding.     

Fold propagation in single embedded layers

This paper investigates the folding of single competent layers embedded in a less competent matrix, where the competence contrast is about 10: 1. Folds result from buckling during layer-parallel compression. A geometrical study of natural examples shows that individual folds tend to be grouped into fold complexes.The amplitude varies from a maximum at the centre of a complex to a minimum at each end. Each complex is often centred about a sedimentary lens or nodule which may have triggered the folding and localized the complex. The formation of folds of this kind has been simulated experimentally by deformation of models made from paraffin waxes of known rheological properties. Early in the deformation of a model, buckling starts at a localized site of disturbance, producing only one fold. With further deformation, new folds appear at either side of the initial one. The buckling then propagates along the layering, further folds appearing serially in time and distance. The end result is a complex with many individual folds and a regularly periodic shape.With a competence contrast of 10: 1, the rate of fold propagation is slow, and formation of a periodic complex requires an overall shortening of at least 15%. The shapes of folds formed experimentally are similar to those formed naturally.     

An energy calculation concerning the roundness of folds

The calculation estimates the energy consumed in a representative fold in an extended layered sequence of two alternating lithologies, during buckling through finite amplitudes (limb inclinations up to 70°). By estimating separately the energy quantities comsumed in different parts of a fold, it is concluded:

1. (1) that angular folds (chevrons, kinks etc.) do not require brittleness or any localized material abnormality for their development; they have the most economic profile as regards energy-consumption even in strictly Newtonian materials, particularly at high limb inclinations;

2. (2) where a fold profile approximates a circular-arc hinge section and a straight limb, the ratio (length of curved part/total length of profile) is a useful parameter, that can be linked in a systematic way to the mechanical properties of the assemblage at time of folding;

3. (3) measurements so far made in outcrop are compatible with the calculations and with published opinions about possible mechanical properties of rocks.

The discussion presented is merely exploratory; further study of the ratio mentioned is likely to throw light on the folding process.     

Successive development of plane noncylindrical folds in progressive deformation

In the history of superposed deformations of the iron formations at the western border of the Kolar Gold Field in S India, an important event was the successive growth of broadly coaxial plane noncylindrical folds in course of a progressive deformation concomitant with development of ductile mesoscopic shear zones. The noncylindrical folds were initiated as active folds by the creation of a buckling instability at successive stages on newly developed foliation surfaces. The nucleation of noncylindrical folds and the subsequent axial-plane folding of the tightened mature folds are explained by the mechanical inhomogeneity of the rocks and the heterogeneous character of strain. The correlation between increasing tightness and increasing noncylindricity of the folds indicates that the initial curvatures of hinge lines were accentuated by an extension parallel to the subhorizontal stretching lineation. From the patterns of deformed lineations over folds of varying tightnesses, it is concluded that the passive accentuation of hinge-line curvatures was mostly achieved when the folds had already become isoclinal or very tight.     

Mega arrowhead interference patterns in the central part of the Yanshan Orogenic Belt,North China

The Chengde-Pingquan region is located in the central part of the Yanshan Orogenic Belt (YOB). At Daheishan and Pingquan in the central YOB, thrusts and folds of variable trends are displayed in 2 km-scale fold interference patterns. Detailed field mapping was conducted to decipher the geometry of these two superimposed structures. Map-view geometry and stereonet plots for outcrop-scale folds indicate that the superimposed structures form arrowhead interference pattern where NW-SE-trending F₁ folds are refolded by later ENE-WSW F₂ folding. After remove the effects of later faulting, restored map-views of the superimposed structures show that when the F₁ folds have inclined axial surfaces but with no an overturned limb, an arrowhead interference pattern (here called modified type-2 pattern) can form. Our field data and reinterpretation of the findings of previous studies suggest that five major shortening phases have occurred in the Chengde-Pingquan region. The first two phases, which formed the superimposed folds, occurred earlier than the Late Triassic (D1) and during the Late Triassic to Early Jurassic (D2). These two phases were followed by three deformation phases that are mainly characterized by thrusting and strike-slip faulting, which strongly modified the large-scale fold interference patterns.     

An approach to folding kinematics from the analysis of folded oblique surfaces

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.     

Folding of passive layers and forms of minor structures near terminations of blind thrust faults—application to the central Appalachian blind thrust

The existence of detachment surfaces or décollement zones beneath folded rocks of the Valley and Ridge and Plateau provinces of the Appalachians has been recognized as an important condition of folding. Large folds at the border between the two provinces resulted primarily from repetition of strata by thrusting of blocks over ramp faults that connect detachement surfaces at different horizons. Some investigators have suggested that folds in the Plateau province of Pennsylvania were produced by splay faults arising from detachment surfaces, but field observations and theoretical analyses by Sherwin and by Wiltschko & Chapple suggest that the folds are a result of buckling of multilayered rocks above a décollement. An exception may be the Burning Springs anticline in West Virginia, which appears to have formed at the termination of a detachment surface.Investigation of the translation of an homogenous, viscous material above a flat detachment surface that terminates laterally indicates that the termination produces a broad, low-amplitude anticline in passive layering as a result of thickening induced by a gradient of shear stresses in the vertical direction. This thickening above the termination of a detachment is a mechanism of folding. If the viscous fluid contained mechanical layering, the fold would become amplified by buckling. Computations of stresses in the material indicate that minor faults should be generated first near the termination of the flat detachment surface. The Burning Springs anticline probably was initiated by termination of a detachment surface and subsequently amplified by buckling.     

Foliations developed during slump deformation of Miocene marine sediments,Cyprus

Foliations within a Miocene slumped bioclastic sandstone unit of the Pakhna Formation, southern Cyprus, were investigated in order to assess the importance of slump strain, liquifaction and compaction in their generation. There are two approximately orthogonal sets of folds, F₁ and F₂. F₁ folds are upright to inclined slump folds formed during slope-failure translation of the sediment. The cores of upright F₁ folds have a steeply dipping macroscopic fabric defined by the axial surfaces of small tight folds in compositional layering. F₂ folds occur on steeply-dipping limbs of F₁ folds. F₂ folds are small and asymmetric with flat-lying axial surfaces, and are interpreted as compaction generated. A pervasive flat-lying microscopic fabric defined by grain and pore long axis orientation is found in both fold sets, and is probably a liquifaction fabric enhanced by compaction. A pervasive steeply-dipping microfabric parallel to the axial planes of slump folds is not present in any of the slumps investigated.     

Relationships between garnet shape, rotational inclusion fabrics and strain in some Moine metamorphic rocks of Skye, Scotland

Study of rotational inclusion fabrics in garnet porphyroblasts demonstrates that angles of rotation are dependent not only on the amounts of strain suffered by the host rocks but also on porphyroblast shape: near-spherical crystals suffer considerably more rotation than discoidal for a given amount of strain. Angles ranging from 160° to 0° have been measured but rotation took place during two distinct phases of deformation each associated with the formation of folds and attendant axial planar fabrics.The rotational inclusion fabrics permit a study to be made of the geometry and state of strain around two minor folds and thus suggest that the main mechanism of fold development was flexural flow. The differences in the amounts of strain, as recorded by rotational inclusion fabrics, around the two folds further suggest that there was unequal limb rotation during fold development and that the maximum compressive stress lay obliquely to the layering at the onset of folding.     

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.     

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.     

Pressure-solution deformation of the purgatory conglomerate,rhode island (u.s.a.): quantification of volume change,real strains and sedimentary shape factor

Pressure solution has caused substantial volume redistribution within the Purgatory Conglomerate from Rhode Island. Material has been removed from quartzite cobble surfaces parallel to the fold axes and mostly redeposited as fibrous pressure shadows at the long axis terminations of the cobbles. In the hinges of folds, 23% of the mean cobble volume has been removed, and in highly deformed and overturned fold limbs up to 55% volume reduction has occurred. The initial cobble shape and orientation can be measured at an undeformed locality and the deformation path can be easily deduced; thus these are real cobble volume reductions. Apparent volume losses (initial shapes not removed) range from 70% to 89%. Real strains for cobbles (axial ratios ranging from 1:0.65:0.38 to 1:0.47:0.15) have values of e_x, e_y, e_z which range from 0%, −20%, −11% to 0%, −37%, −42%, respectively, depending on structural position. The conglomerate itself has been extended parallel to the fold axes (e_r), but the extension is not recorded by the cobble shapes.     

塔里木盆地西南缘构造样式及其主导因素

塔里木盆地西南缘是西昆仑山前北北西—近东西向的构造变形带.具有南北3带、东西3段、上下3层的展布特点.各带、段和层以基底卷入的冲断构造和盖层滑脱的断层相关褶皱为主,包括:破冲褶皱、断层扩展褶皱、断层滑脱褶皱和断层弯曲褶皱等.通过识别地震剖面上不整合面和同构造沉积现象,认为构造变形时间在上新世—第四纪;第一排背斜带形成于...     

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.     

Archaean greenstone belts: A structaral test of tectonic hypothesis

Tectonic hypotheses for Archaean greenstone belts are tested against structural data from the Agnew belt, Western Australia. This belt shows the following critical features:

1. (1) A sialic infrastructure, formed by semi-concordant tonalitic intrusions, was present before tectonism began.

2. (2) An early deformation formed recumbent folds and a flat-lying schistosity; a second deformation formed major upright folds and steep ductile shear zones that outline the present tectonic belt. Neither deformation caused major disruptions in the stratigraphy. Both were accompanied by metamorph ism under upper greenschist to amphibolite facies conditions and low pressure.

3. (3) The belt is bounded on either side by tonalitic gneiss of unknown age, emplaced along steep shear zones.

Comparison with Phanerozoic orogenic belts representing a subduction complex, a collisional suture zone, and a collapsed marginal basin, indicates that the belt was not formed in any of these plate-tectonic environments.The second deformation in the belt resulted from regional crustal distortion, accomplished by right-lateral ductile wrenching along major N- to NNW-trending shear zones. Associated en-echelon buckle folding formed large granite-cored anticlines and tight synclines. The detailed structural pattern is not consistent with a diapiric origin for these folds. The ductile wrench faults may have been related to mantle flow patterns in a manner analogous to modern transform faults.     

The structural evolution of sheath folds: A case study from Cap de Creus

It has long been recognised that within zones of intense non-coaxial deformation, fold hinges may rotate progressively towards the transport direction ultimately resulting in highly curvilinear sheath folds. However, there is a surprising lack of detailed and systematic field analysis of such “evolving” sheath folds. This case study therefore focuses on the sequential development of cm-scale curvilinear folds in the greenschist-facies El Llimac shear zone, Cap de Creus, Spain. This simple shear-dominated dextral shear zone displays superb three dimensional exposures of sheath folds defined by mylonitic quartz bands within phyllonite. Increasing amounts of fold hinge curvature (δ) are marked by hinge segments rotating into sub-parallelism with the mineral lineation (Lm), whilst the acute angle between the axial-planar hinge girdle and foliation (ω) also displays a sequential reduction. Although Lm bisects the noses of sheath folds, it is also clearly folded and wrapped-around the sheath hinges. Lm typically preserves a larger angle (θ) with the fold hinge on the lower limb (L) compared to the upper (U) limb (θL > θU), suggesting that Lm failed to achieve a steady orientation on the lower limb. Adjacent sheath fold hinges forming fold pairs may display the same sense of hinge arcing to define synthetic curvature, or alternatively opposing directions of antithetic curvature. Such patterns reflect original buckle fold geometries coupled with the direction of shearing. The ratio of long/short fold limbs decreases with increasing hinge curvilinearity, indicating sheath folds developed via stretching of the short limb, rather than migrating or rolling hinge models. This study unequivocally demonstrates that both hinges of fold pairs become curvilinear with sheaths closing in the transport direction recording greater hinge-line curvilinearity compared to adjacent return hinges. This may provide a useful guide to bulk shear sense.     

The development of folds in bedded chert and related rocks in the Malaguide Complex, southern Spain

Folds and folding mechanism in a chert sequence and related rocks of the Maláguide Complex (the uppermost tectonic unit of the Betic Zone) have been investigated. The geometric study shows that folds that developed in the chert sequence are usually angular in shape and asymmetric. Chevron and conjugate folds are common.Folding in bedded chert is explained in terms of a suggested model:

1. (1) Development of folds by kink and conjugate kinking.

2. (2) As the shortening increases, the interlimb angles decrease; in the kink folds this is caused by a reduction of the angle between the layers within the kink and the kink boundaries. There seems to be a relationship between this angle and the asymmetrical thinning-out in the limbs of many folds: the smaller is the angle between the kink boundary and the layers within the kink band, the larger is the reduction of the thickness in these layers.

Single limestone layers embedded in slate deform very probably by a buckling mechanism, implying tangential longitudinal strain and an additional flattening.     

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.