The development of asymmetrical folds in a cross-laminated siltstone

A group of folds in alternating pelites and cross-laminated siltstones is described. An interpretation of the finite strain state, in the competent silt layers, is proposed on the basis of an analysis of the angle between cross-lamination and the principal surface of accumulation. Strain magnitudes are greatest in the fold hinge where domains of layer parallel shortening and layer parallel extension are separated by a neutral surface. Strain magnitudes in the fold limbs are small and are largely related to the development of the asymmetry of the folds. In the incompetent pelitic layers, strain in the fold limbs has a large, layer parallel shear component. Deformation in the pelites is accompanied by, and presumably partially achieved by, migration of quartz from areas where there is a tendency for volume to decrease, to areas where it is tending to increase. This process involves local increases in volume of more than 50%.A kinematic model is proposed for development of the folds. It involves early development of small symmetrical folds followed by their modification to asymmetrical, parasitic structures on the limbs of later folds. In the late stages of folding, continued shortening perpendicular to the axial surface orientation is achieved by development of a conjugate crenulation cleavage.     

Analyses of fold profiles by changing weight parameters of NURB curves

Analyses of Non-Uniform Rational B-spline (NURB) curve by varying weights at its nodal points and projection ratio produce several kinetically plausible symmetric and asymmetric fold morphologies in 2D promptly and efficiently with varied overall geometries, curvature of limbs, sharpness/bluntness of hinges, extent of hinge zone, tightness/interlimb angles, etc. Some of these folds are new geometries what other approaches, such as those with Bézier curve, did not produce so far. Natural fold profiles can be matched with NURB curves from photographs.     

Hinge migration as a mechanism of superimposed folding

Paraffin wax analogue modelling of superimposed folding shows how early fold shape and orientation determine fold-axis orientation, type of interference pattern and mechanism of superposed folding. During two successive deformations, the behaviour depends on the angle between the first and second compression directions. (i) When they are perpendicular to each other, classic superposed folding with either domes and basins, or folds with vertical axes develop, depending on whether the earlier folds were open or closed. (ii) When the two compression directions are oblique, the earlier folds rotate. The degree of rotation depends on the angle between the first folds and the later compression direction and is proportional to the amount of strain. The orientations of the new folds are close to those of the earlier open folds. The final deformation pattern consists of domains where the orientations of the axes depend on whether the early folds were previously either open or closed. Many early folds are reused to become later folds by the mechanism of hinge migration.These results are consistent with the pattern of superimposed folding observed in the Devoluy structure of the French Alps. They show that simply by studying the directions of fold axes in areas of superposed folding, it is not possible to define compression directions. Moreover there is the possibility that superposed folding may go unnoticed if hinge migration has occurred.     

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.     

褶皱相关断裂构造形成条件与发育机制:燕山中部露头尺度变形研究为例

总结了褶皱相关断裂发育机制的3个构造几何学模型:同心圆褶皱模型、膝折带褶皱模型和弯流褶皱模型。基于燕山中部中、新元古界地层中发育的5个露头尺度褶皱及其中、小型断裂构造的实例剖析,探讨了收缩变形过程中褶皱与断裂构造发育时序与褶皱相关断裂构造的产生机制。研究指出,规模与所在褶皱构造相当或略小的断裂构造当中,既有形成时间早于褶皱变形的断层,也有在褶皱变形过程中调节褶皱不同部位应变差异的褶皱相关断裂构造,而且卷入后期变形的早期断裂可能成为制约褶皱成核位置的影响因素,以及成为枢纽叠覆楔构造的形成方式之一。断层位移-距离曲线特征和断层与褶皱变形几何学、运动学关系分析,可用来判断断层、褶皱变形发生相对时序。认为影响褶皱相关断裂构造发育的机制主要有3种:(1)纵弯滑褶皱作用中,翼部顺层滑动受到限制而无法持续时,将通过断层向上切层的方式予以调节,从而形成翼部或转折端揳入逆冲断裂以及背离向斜和指向背斜逆冲断层;(2)各种因素导致的褶皱曲率变化是褶皱相关断裂产生的重要机制之一,褶皱曲率变化可由褶皱轴面的合并和新生直观反映,轴面合并引起褶皱曲率变化的层位,可能是诱发褶皱相关断裂,如背离向斜和指向背斜逆冲构造开始产生的重要部位;(3)能干性差异和强硬层之间距离较大的岩层组合发生纵弯褶皱变形时,软弱岩系在褶皱核部的聚集和逃逸,是迫使递进收缩的强硬层产生褶皱相关断裂构造的重要机制。     

The geometrical classification of noncylindrical folds

The majority of naturally occurring folds are noncylindrical if definitions are strictly applied. A new classification of noncylindrical folds using a triangular plot and based on measurements of interlimb angle and hinge angle is proposed. The end-members of the triangular plot are planes, cylindrical isoclines, and isoclinal domes. An infinite range of cylindrical and noncylindrical plane fold shapes may be represented. Noncylindrical nonplane folds may be represented on the plot using proportional circles to signify the degree of non-planarity. The triangular diagram is used to classify large-scale folds from north Norway and their origin is discussed.     

Kinematic interpretation of folds in alpine-type peridotites

From a general understanding of the flow mechanisms in alpine-type peridotites, it is possible to describe without ambiguity the general flow regime and its directions in a massif. This result provides the means for an investigation of the origin of the folding in pyroxenitic layers independent of any preconceived theory on folding.The folds are usually isoclinal and of the flexural-flow type as demonstrated by petrofabric studies in hinges. Their axes are always parallel or subparallel to a mineral lineation which in turn is parallel or close to the orientation of the fabric elements defining the flow line. Their axial plane, which usually coincides with the foliation, is parallel to or close to the flow plane. This conclusion, also supported by paragenetic observations, shows that the folds were formed or transposed during the plastic flow responsible for the development of structures (foliation and lineation), textures and preferred mineral orientations. In the case of the Lanzo Massif and a few other Iherzolite massifs, the flow occurred during the intrusion from the mantle. The mapping in Lanzo yields evidence of a large-scale U-shaped fold with a remarkable pattern of mesoscopic folds attached to it: the tight isoclinal folds are restricted to the limbs of the largescale structure, and the open folds locally refolding former isoclinal ones to the hinge area where the angle between the folded pyroxenitic layering and the axial-plane foliation is large. Stereograms of the field structures in this hinge area clearly illustrate the geometric relations mentioned above.This folding, characterized by its axis and axial plane respectively close to the flow line and flow plane, can be explained either by rotation towards the flow line of non-cylindrical-fold axes or by direct formation in a non-plane flow when the flow line is initially contained in the layering or close to it. In this respect, the folding may bring information on the minor flow component, complementary to that given on the major flow component by considering the textures and fabrics. Finally this folding is shown to be ubiquitous in plastically deformed peridotites. It is proposed that these conclusions be extended to other domains submitted to intense non-plane flow.     

A new isogon-cleavage classification and its application to natural and model fold studies

Traditional methods of studying natural folds are reviewed. A new method of describing cleavage attitude in folds is presented; the β plot. The combined graph of dip isogon angle ϕ (Hudleston 1973) and cleavage angle β is proposed as a linked classification of fold and cleavage geometry. Plots of β and βϕ are given for three natural fold examples. The classification is extended to the geometry and strain attitude (βϕ₅) of two finite-element models and the classical folding models. Results are compared and some tentative conclusions drawn on the relationship of cleavage, the XY plane of strain and dip isogons.     

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.     

Cleavage-fold relationships and their implications for transected folds: an example from southwest Virginia,U.S.A.

A non-coaxial deformation involving pre-folding initiation of cleavage perpendicular to bedding is proposed to explain non-axial planar cleavage associated with mesoscopic folds in part of the Appalachian foreland thrust-belt of southwest Virginia. Folds are gently plunging, asymmetric, upright to slightly inclined, sinusoidal forms with non-axial fanning cleavage. They show extreme local variations in type and degree of transection and the consistency of transection direction. These relations are further complicated by hinge migration.Cleavage-fan angles, bedding-cleavage angles and δ transection values appear influenced by fold tightness, and in part by fold flattening strain. Fold flattening increments are considered simultaneous with folding. Axial surface traces, and not cleavage traces, coincide with the principal extension direction in fold profiles. Geometric modelling of cleavage fanning and bedding-cleavage angle variations for various theoretical folding modes suggest that folding in limestone and sandstone layers was by tangential longitudinal strain. Significant shape modification and change in bedding-cleavage relations occurred after limb dips of 40 and 50° were attained in limestone and sandstone respectively. Mud-rock class 1C folds with convergent cleavage fans show features transitional between buckling and flexural flow. Initiation of ‘cleavage’ fabrics during layer-parallel shortening prior to significant folding may be important for cleavage evolution in some deformed rocks.     

The glaciotectonic deformation of Quaternary sediments by fault-propagation folding

Fault-propagation folding is an important yet seldom recognised structural style within sediments affected by glacier-induced deformation. Fault-propagation folds develop in the hanging wall of low angle thrust faults and compensate part of the slip along the fault. Field examples are recognised across northern Europe, in glaciotectonic complexes of north Germany, Wales and the Isle of Man. The recognition of the fault-propagation fold mechanism in glaciotectonic deformation is important because resultant structures are related to exactly the same phase of deformation (i.e. the same phase of ice advance), and thus play a critical role in analyses of the temporal and spatial evolution of glacier-induced deformation. Some field examples show monoclinal geometries that are in good agreement with predictions of trishear kinematic theory. The trishear approach is appropriate to model these structures because the structures analysed in the field and simulated below show characteristics that are compatible with fault-propagation folds that were produced by trishear kinematics. The curved forelimb and the monocline geometry of the fault-propagation folds fit to the trishear model. The occurrence of footwall synclines is also in good agreement with trishear kinematics. These synclines show the typical thickening of the strata in the hinge. With respect to the modelling output, most important factors for the structural evolution of the fault-propagation folds is the ramp angle of the thrust, the position of the tip line and the propagation-to-slip ratio along the fault. This fits to observations made by previous studies at large scale fault-propagation folds in fold-and-thrust belts.     

On the production of two inclined cleavages during a single folding event; Stirling Range, S.W. Australia

In any one area of the Stirling Range Proterozoic low-grade fold-foreland, the first phase of folding to be associated with cleavage development has generated two inclined tectonic fabrics each of which is closely related in geometry to the folds. The most likely fold history has been determined by comparing predictions of theoretical fold mechanisms against the observed field relations and strain states seen in an arenite and minor mudrock multilayer. In an initial phase of folding dominated by layer-parallel shortening, a well-spaced mica-band cleavage was, initiated, intensified, and able to maintain a near axial plane relationship, until body rotation of limbs took over at a fold dihedral angle of about 140°. The resultant 70° angle between solution cleavage and bedding on the fold limbs was preserved by flexural slip until the fold had tightened to about 100° when, for mechanical reasons, flattening rapidly became important. During this phase, a mica-film cleavage, with grainscale spacing, developed approximately axial planar and the solution cleavage/bedding angle on the limbs was reduced to 55°.     

Deformation history of the Hampden Synform in the Eastern Fold Belt of the Mt Isa terrane

The moderately metamorphosed and deformed rocks exposed in the Hampden Synform, Eastern Fold Belt, in the Mt Isa terrane, underwent complex multiple deformations during the early Mesoproterozoic Isan Orogeny (ca 1590–1500 Ma). The earliest deformation elements preserved in the Hampden Synform are first‐generation tight to isoclinal folds and an associated axial‐planar slaty cleavage. Preservation of recumbent first‐generation folds in the hinge zones of second‐generation folds, and the approximately northeast‐southwest orientation of restored L¹ ₀ intersection lineation suggest recumbent folding occurred during east‐west to northwest‐southeast shortening. First‐generation folds are refolded by north‐south‐oriented upright non‐cylindrical tight to isoclinal second‐generation folds. A differentiated axial‐planar cleavage to the second‐generation fold is the dominant fabric in the study area. This fabric crenulates an earlier fabric in the hinge zones of second‐generation folds, but forms a composite cleavage on the fold limbs. Two weakly developed steeply dipping crenulation cleavages overprint the dominant composite cleavage at a relatively high angle (>45°). These deformations appear to have had little regional effect. The composite cleavage is also overprinted by a subhorizontal crenulation cleavage inferred to have developed during vertical shortening associated with late‐orogenic pluton emplacement. We interpret the sequence of deformation events in the Hampden Synform to reflect the progression from thin‐skinned crustal shortening during the development of first‐generation structures to thick‐skinned crustal shortening during subsequent events. The Hampden Synform is interpreted to occur within a progressively deformed thrust slice located in the hangingwall of the Overhang Shear.     

Geometric analysis of fold development in overthrust terranes

Fault-bend folding, fault-propagation folding, and detachment (or décollement) folding are three distinct scenarios for fold-thrust interaction in overthrust terranes. Simple kink-hinge models are used to determine the geometric associations implicit in each scenario. Bedding maintains constant thickness in the models except in the forelimb of the fold. The forelimb is allowed to thicken or thin without limit. The models address individual folds, and the calculated fold geometries are balanced structures.Each mode of fold-thrust interaction has a distinct set of geometric relationships. Final fold geometry is adequate in itself to discern many fault-bend folds. This is not the case for fault-propagation and detachment folds. These two fold forms have very similar geometric relationships. Some knowledge of the nature of the underlying thrust or décollement zone is usually needed to distinguish between them. The geometry of a fold is altered, in a predictable fashion, by transport through an upper ramp hinge and by fault-parallel shearing of the structure. The shearing results in a tighter fold, whereas transport through the ramp hinge produces a broader fold.The viability of the geometric analysis technique is demonstrated through its application to a pair of detachment folds from the Canadian Cordillera. The geometric analysis is also used to evaluate cross-sections through subsurface structures. In an example from the Turner Valley oil field, the analysis indicates how the interpretation should be altered so as to balance the cross-section. The analysis reveals hidden assumptions and specific inconsistencies in structural interpretations.     

Inversion of fold-hinge in superposed folding: An example from the Precambrian of central Rajasthan,India

Axial culminations and depressions of folds are common in regions of superposed deformations involving two sets of folds at high angles to each other. If the intensity of the later folding in these cases exceeds a particular limit, plunge reversal of the early folds gives way to “plunge inversion”. In such instances, segments of early folds rotate through end-on or reclined geometry while being refolded. And instead of plunge reversal at the hinge zones of later folds, the early folds plunge in the same direction in both limbs of the later folds. As a result, an antiform will pass along the axial trend to a synform. A particularly clear instance of plunge inversion has been noted from the “Sawar outlier” comprising a metasedimentary sequence within the older Banded Gneissic Complex in central Rajasthan. In Sawar, the southern segment of a south-southwest-trending synformal early fold has been inverted to attain an antiformal geometry because of superposition of a later fold at high angles to the early fold axes and axial planes. The deformation history of the large-scale folds has been traced and the stratigraphic implications of the plunge inversion discussed. From the movement pattern, it seems justifiable to correlate the metasedimentary sequence of the outlier with the Late Precambrian Delhi Group of parametamorphic rocks.     

Growth-strata geometry in fault-propagation folds: a case study from the Gafsa basin, southern Tunisian Atlas

The structural and sedimentological study of fault-propagation folds in Southern Tunisia highlights a special geometry of the growth strata (strata deposited simultaneously with the formation or growth of a fold). This distinct geometry is visible in the uppermost growth-strata beds and consists of one flank with unconformity as opposed to the other flank with perfect conformity. This geometry can be explained by the mechanism of fault-propagation folding, with asymmetrical flank dips and hinge migration kinematics. This kinematics was originally predicted by the fault-propagation fold model, which facilitates the study of this special geometry in a narrow domain of sedimentation-to-shortening ratios. A plot projection provides a generalisation of the results of all types of fault-propagation folds by revealing the expected geometry of the growth strata. This study constitutes one of the most complete examples of kinematic model validation on a field scale.     

Variation of interlayer slip in space and time during flexural folding

This paper describes the results of an experiment which was performed with a Plasticine model to investigate the progressive evolution of flexural-slip folds. The model analyses the relationship between bulk shortening and the amount of flexural slip on fold limbs and in hinge zones. In the light of the experimental results, the theoretical relationship between limb dip and angular shear strain proposed by Ramsay (1967, p. 393) needs modifying to take into account the effect of hinge dilation and limb thinning at large deformations.     

江西赣中铁矿“红绸带”式铁矿体形态成因及其找矿预测

江西赣中新余铁矿是我国重要的铁矿类型之一,产于震旦纪火山-沉积浅变质岩系硅铁建造中。铁矿体普遍呈现"红绸带"式形态,前人认为是多期次褶皱叠加的结果。本文通过野外调查,在整个铁矿区发现,区域透入性的拉伸线理、A型褶曲十分发育,局部地段甚至出现鞘褶皱;系统测量表明,区域拉伸线理、A型褶皱的脊线走向稳定在295°~320°之间,倾角一般小于25°。推测赣中铁矿经历了强烈的塑性流变,"红绸带"式铁矿体是塑性流变,而非多期褶皱叠加变形的结果;整个铁矿区的原始形态应是一个鼻端向南封闭的巨形鞘褶皱,但变形期后不均匀的构造抬升和剥蚀,导致了不同铁矿区现今地表出露了原始形态的不同部位。结合褶皱构造对铁成矿物质的控制作用和矿区的地层出露状态分析,认为大陂-陂头、寨口-太平山-良山一带皆处于鞘褶皱的前缘部位,具有寻找富大厚矿体的找矿前景,松山-杨家桥处于鞘褶皱的西翼,平剖面上都发育小型鞘褶皱和红绸带式重叠矿体,因而也具有良好的找矿前景。     

A unified kinematic model for the evolution of detachment folds

Detachment folds represent a major structural element in a number of fold belts. They are common in the Jura Mountains, the Zagros fold belt, the Central Appalachian fold belt, the Wyoming fold-belt, the Brooks Range, the Parry Islands fold belt, and parts of the SubAndean belt. These structures form in stratigraphic packages with high competency contrasts among units. The competent upper units exhibit parallel fold geometries, whereas the weak lower unit displays disharmonic folding and significant penetrative deformation. Two distinct geometric types, disharmonic detachment folds, and lift-off folds have been recognized. However, these structures commonly represent different stages in the progressive evolution of detachment folds. The structures first form by symmetric or asymmetric folding, with the fold wavelength controlled by the thickness of the dominant units. Volumetric constraints require sinking of units in the synclines, and movement of the ductile unit from the synclines to the anticlines. Continuing deformation results in increasing fold amplitudes and tighter geometries resulting from both limb segment rotation and hinge migration. Initially, limb rotation occurs primarily by flexural slip folding, but in the late stages of deformation, the rotation may involve significant internal deformation of units between locked hinges. The folds eventually assume tight isoclinal geometries resembling lift-off folds. Variations in the geometry of detachment fold geometry, such as fold asymmetry, significant faulting, and fold associated with multiple detachments, are related to variations in the mechanical stratigraphy and pre-existing structure.