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.     

Model experiments showing simultaneous development of folds and transcurrent faults

Simultaneous development of noncylindrical folds and transcurrent fractures has been studied using model techniques. A plasticine model was compressed in one direction and an initial formation of folds was followed by the initiation of conjugate sets of transcurrent fractures. It was recorded that with progressive deformation the length of each fracture and the displacement along it increase steadily and the rate of displacement varies at different stages of deformation. Individual fold geometries vary along their hinge lines and these geometrical variations appear to be due to interference of folds with the transcurrent fractures. These interference effects also change the amount of rotation of fractures. Fold structures are different on either side of the fault plane. A natural example from the Bude area, England, shows similar geometrical features.The method of determining fault displacement by comparing the positions of fold hinge lines on either side of a fault is discussed in the light of the above results.     

An additional criterion in the aberrant fold relationship

From a re-analysis of aberrant folds in southwest Scotland the divergence of host fold axes from the regional b-axis, i.e. regional deviation, emerges as an additional factor determining the magnitude of the incongruous relationship in an assemblage of noncylindrical megascopic folding.     

Noncylindrical flexural slip folds in nature and experiment

Some naturally formed folds in North Cornwall, England, show the following geometrical features:

1. (a) each fold is noncylindrical;

2. (b) the profile shape varies along the hinge-line (chevron-shaped at culmination, rounded at terminations);

3. (c) hinge-lines and axial surfaces of some folds curve strongly in certain restricted areas. Micro-structures indicate that the folds formed by geometric bending and flexural slip.

The progressive development of folds like these has been simulated by subjecting multilayered plasticine models to layer-parallel compression in coaxial stages. This technique allows folds to be observed and measured after each deformation stage. The folds initiate at irregularities in the layering or stress-field. As each fold amplifies, it acquires a characteristic three-dimensional shape: generally the profile is chevron-shaped at the point of maximum amplitude and is rounded at the terminations. Growth of a fold also involves a lengthening of the hinge-line by propagation of the terminations (e.g. into areas of previously unfolded layering). Individual folds also tend to trigger the development of new folds at either side, eventually forming a fold complex with regular wavelength. Propagating fold complexes may interfere by processes of linking and blocking that are not strictly the same as interference effects in other wavelike processes. The interference of fold complexes is described with reference to layer surfaces and crosssections. Causes of noncylindricity are examined. Geometrical aspects of naturally formed folds are analyzed in the light of the experimental findings.     

Eocene simple shear and plio-quaternary pure-shear folding in the Central-Eastern Algerian Atlas

Tertiary folds of the central and eastern part of the Algerian Atlas were studied in order to assess their kinematics and regimes of deformation. Folds developed following two main phases of deformation during the Eocene and the Pliocene. The NE-SW trending Eocene folds show a clockwise rotation of fold axis with depth, noncylindrical geometry and a right-stepping en echelon configuration. Early secondary structures inside each fold are also rotated clockwise with respect to the younger folds. These data are in agreement with progressive ‘simple shear’ deformation. Pliocene folds strike E-W and display a cylindrical geometry. Associated Plio-Quaternary brittle structures show no rotational path. These observations are compatible with ‘pure shear’ style of deformation. These results, in combination with focal mechanism solutions, have important implications for the understanding of the kinematic evolution of the western segment of the African-European plate boundary. For Algeria they imply that transcurrent motion during the Paleogene was followed by coaxial shortening with a NNW direction during Neogene-Quaternary times. Comparison with published data for Morocco and Tunisia suggests that this transcurrent regime developed from west to east continuing from the Middle Jurassic through to the Miocene.     

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.     

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.     

Progressive development of structures in a ductile shear zone

In the Singhbhum Shear Zone of eastern India successive generations of folds grew in response to a progressive ductile shearing. During this deformation a mylonitic foliation was initiated and was repeatedly transposed. The majority of fold hinges were formed in an arcuate manner at low angles to the Y-axis in an E-W trending subhorizontal position and major segments of the fold hinges were then rotated towards the down-dip northerly plunging X-axis. The striping and intersection lineations were rotated in the same manner. The down-dip mylonitic lineation is a composite structure represented by rotated early lineations and newly superimposed stretching lineations. The consistent asymmetry of the folds, the angular relations between C and S surfaces and the evidence of two-dimensional boudinage indicate that the deformation was non-coaxial, but with a flattening type of strain with λ₁ ⪢ λ₂. The degree of non-coaxiality varied both in space and time. From the progressive development of mesoscopic structures it is concluded that the 2–3 km wide belt of ductile shear gave rise to successive anastomosing shear zones of mesoscopic scale. When a new set of shear lenses was superimposed on already sheared rocks, the preexisting foliation generally lay at a low angle to the lenses. No new folds developed where the acute angle was sympathetic to the sense of shear displacements. Where the acute angle was counter to the sense of shear, the pre-existing foliation, lying in the instantaneous shortening field, was deformed into a set of asymmetric folds.     

褶皱构造的曲率分析及其裂缝估算--以江汉盆地王场褶皱为例

曲面曲率的几何意义可以反映曲面一点邻近区域的具体形态和变形特征,因而可以用来研究褶皱层面的变形特征、构造样式及其可展性.褶皱面裂缝发育主要为一组张裂系,张裂隙走向与最大主曲率的方向垂直.褶皱构造的主曲率在一定程度上可以反映与褶皱有关的张裂隙的发育情况.对于圆柱状褶皱可以估算与褶皱有关的裂缝孔隙度和渗透率.以王场褶皱构造面为例,通过计算二次趋势面的特征值和特征向量得到褶皱构造面主曲率的大小和方向,确定该褶皱为圆柱状褶皱,并对与之相关的裂缝孔隙度和渗透率进行了估算.     

Internal geometry of a thrust sheet,eastern Proterozoic belt,Godavari Valley,South India

A small thrust sheet, named Pedda Gutta thrust sheet, consisting of calcareous to cherty argillites and cherts, and juxtaposed against tidal-intertidal cross-bedded quartzites and stromatolitic and sileceous limestone in the eastern Proterozoic belt, Godavari Valley, exhibits structures comparable in style to those of the external zone of a fold-thrust mountain belt. A wide spectrum of periodic and aperiodic mesoscopic folds varying from upright ones with rounded hinges and attenuated limbs, through noncylindrical kinks to whalebacks and sheath-like forms have developed within the small volume of the thrust sheet, the preserved thickness of which is of the order of 50 metres (comparable in scale to cleavage duplexes). Cleavage development is also heterogeneous across the width of the sheet. Displacement transfer from faults to folds and vice-versa is a common feature. On the basis of the distribution of the mesoscopic structures of varying style within the sheet and localization of fault rocks, three slices (wedges) have been recognized, each bounded on the east by a thrust which is steep at the current erosion level but interpreted to be of listric form making the thrust network comparable in architecture, though not in scale, to a hinterland (west) dipping imbricate fan.     

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.     

Sequence and style of major post-nappe structures, Simplon—Pennine Alps

In the Upper Pennine nappe complex of the Simplon—Pennine Alps (Switzerland and Italy), at least three phases of major post-nappe folding (in places associated with thrusting) can be distinguished. These are superimposed on an earlier-formed, partly chaotic, complex of tectonic units, including the Bernhard and Monte Rosa continental flakes and the Zermatt—Saas and Antrona ophiolite complexes. The earliest post-nappe folds were essentially isoclinal throughout the whole region and were accompanied by a strong schistosity which is the main foliation in most areas. Later, two successive phases of back-folding led to the present overall structure. Both phases typically show rapid variations in style from open folds lacking axial planar schistosity to very tight structures with complete foliation transposition. This has been demonstrated by systematically mapping the major axial traces over the whole region. Successively removing the major structures in reverse order shows that the ophiolite complexes were originally part of a continuous unit marking an important suture between the Bernhard and Monte Rosa nappes.     

Structure of the Abercrombie beds south of Reids flat,new South Wales

The Late Ordovician Abercrombie Beds, south of Reids Flat, New South Wales, and adjacent to the Wyangala Batholith, show evidence of three successive fold episodes. First generation folds are tight to isoclinal, with fold axes ranging from vertical to horizontal and north‐trending, and steep axial‐plane slaty cleavage. Second generation folds are steeply plunging, tight to open with north‐striking axial planes. In pelitic rocks the axial plane structure is a crenulation cleavage which overprints the slaty cleavage. The first two fold episodes were accompanied by greenschist‐facies metamorphism. Granite emplacement occurred prior to the second fold episode. A third deformation was of relatively mild intensity and produced open, north‐trending folds with axial planes dipping moderately to the east, and crenulation cleavage as the axial plane structure in pelitic rocks. These latest folds are correlated with the latest folds in the Abercrombie Beds north of the Abercrombie River. The mapped area has no apparent macroscopic structure and may be considered as a single domain.     

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.     

西准噶尔野鸭沟地区褶皱冲断构造的特征及意义

西准噶尔地区的褶皱冲断带多被认为是向东南逆冲的。在东部野鸭沟发育的褶皱冲断构造中识别出顶端指向北西的褶皱组合。褶皱自北西向南东逐渐由直立褶皱转变为斜歪褶皱,最后褶皱北西翼发生倒转而倾向南东,表明它们的极性指向北西;褶皱翼间角也由110°转变为60°左右,显示野鸭沟褶皱自北西向南东变形程度逐渐增强。根据卷入褶皱冲断带最年轻的地层为石炭系,又被307Ma的闪长岩穿切的事实,认为该褶皱冲断带形成于晚石炭世的顶端指向北西的剪切环境。     

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.     

An alternative interpretation for the formation of doubly plunging folds in sandstone terrains

Folds are marvellous features of mountain terrains, but despite extensive research, many fundamental problems have still not been solved. In terrains of sandstone, fold hinges are rarely straight lines but curved, forming a pattern characterized by doubly plunging, elliptical dome‐and‐basin structures. Such structures are an obvious manifestation of coeval or successive shortening deformation in two orthogonal principal directions in the horizontal plane. Based on an anatomic investigation of the fold pattern of sandstone beds at the rocky beaches of Saint‐Jean‐Port‐Joli (Quebec, Canada), we propose that the doubly plunging folds may result from a transition from a plane deformation to a constrictional deformation due to auxetic effects of quartz‐rich rocks. The sandstone beds possessed potentially such negative values of Poisson's ratio that, when placed under compression in one direction, they become contracted in the transverse direction, producing a series of doubly plunging folds. Further work is needed to approve or disapprove the interpretation.     

Tectonic structures — a classification

By considering the ways (symmetric, asymmetric and antisymmetric) in which layer interfaces can mutually deflect (see Fig.2.), and the relative curvatures which occur in waves of each of the interfaces (Fig.1), it is possible to generate a classification of structures which covers a wide range of buckle fold shapes, load casts and interface buckles, some types of boudins and asymmetric folds, in one three-dimensional plot.     

Parallel, similar and constrained folds

Theoretical analysis of folding of viscous multilayers with free slip or bonding at layer contacts indicates that folds in such multilayers can be described in terms of three end-members:parallel, in which orthogonal thicknesses of layers are largely constant;similar, in which vertical thicknesses of layers and shapes of successive interfaces are essentially constant; andconstrained, in which amplitudes of anticlines and synclines decrease to zero at upper and lower boundaries. Constrained,internal folds form if the multilayer is confined by rigid media; parallel,concentric-like folds form if the multilayer is confined by soft media, provided soft interbeds are sufficiently thin for the stiff layers to fold as an ensemble. Similar,sinusoidal orchevron folds form throughout much of the thickness of a multilayer, for any stiffness of confining media, provided wavelengths of folds are short relative to the thickness of the multilayer or soft interbeds are sufficiently soft and thick for the stiff layers to act independently. The analysis shows that multilayer folds may have the same form regardless of whether the layer contacts are freely slipping or bonded.

The forms of folds in multilayers confined by media with different viscosities above and below depend on the viscosity contrast of the media. For no medium above and a rigid medium below, the forms are concentric-like in the upper part and internal in the lower part of the multilayer. For no medium above and a soft medium below, the folds are concentric-like throughout the multilayer.

The theory indicates that a useful way to analyze forms of folds in rocks or in experiments is in terms of component waveforms, as defined, for example, by Fourier series. The distributions of amplitudes of component waveforms throughout the multilayer appears to be diagnostic, reflecting contrasts in properties of the multilayer and its confining media. Analysis of a large fold in the central Appalachians, Pennsylvania, and of a smaller fold in the Huasna syncline, California, indicates that at least three component waveforms are required to produce the gross forms of those folds.

The theory closely predicts wavelengths and shapes of folds produced in analogous elastic multilayers, indicating that nonlinearities in material behavior, which are inherent in the elastic material but are absent in the viscous material, are less significant than nonlinearities in the boundary conditions, which are the same in elastic and viscous materials.     

渤海湾地区的中生代盆地构造概论

根据 1∶5 0万渤海湾新生代盆地区基岩地质图揭示的残留中生代地层的分布及构造变形特征 ,渤海湾地区的中生代盆地可以分为 5期。早—中三叠世、晚三叠世盆地为克拉通内部大型坳陷盆地 ,其中晚三叠世盆地仅分布在渤海湾西南部地区。早—中侏罗世盆地分布于印支运动形成的向斜坳陷核部 ,属于压陷挠曲型盆地。晚侏罗世—早白垩世盆地分布广泛 ,属于裂陷盆地 ;晚白垩世盆地属于后裂陷阶段的坳陷盆地。这些盆地受印支运动、燕山运动影响而发生反转。印支运动在渤海湾地区的东、西部的表现有明显差异。西部变形弱、以近EW向宽缓褶皱变形为主 ,东部变形强、并叠加了NE向褶皱和逆冲断层变形。早燕山运动使渤海湾地区形成宽缓的大型NE向褶皱变形 ,并使早—中侏罗世盆地发生反转和逆冲断层变形 ;中、晚燕山运动基本没有在渤海湾地区形成褶皱构造变形 ,而是表现为晚侏罗—早白垩世盆地和晚白垩世盆地的区域性反转隆升。下—中侏罗统沉积之后 ,渤海湾地区的构造格局发生基本变革 ,进入以裂陷盆地为主的构造演化时期。