A theory of concentric, kink and sinusoidal folding and of monoclinal flexuring of compressible, elastic multilayers: VI. Asymmetric folding and monoclinal kinking

One of the rules of thumb of structural geology is that drag folds, or minor asymmetric folds, reflect the sense of layer-parallel shear during folding of an area. According to this rule, right-lateral, layer-parallel shear is accompanied by clockwise rotation of marker surfaces and left-lateral by counterclockwise rotation. By using this rule of thumb, one is supposed to be able to examine small asymmetric folds in an outcrop and to infer the direction of axes of major folds relative to the position of the outcrop. Such inferences, however, can be misleading. Theoretical and experimental analyses of elastic multilayers show that symmetric sinusoidal folds first develop in the multilayers, if the rheological and dimensional properties favor the development of sinusoidal folds rather than kink folds, and that the folded layers will then behave much as passive markers during layerparallel shear and thus will follow the rule of thumb of drag folding. The analyses indicate, however, that multilayers whose properties favor the development of kink folds can produce monoclinal kink folds with a sense of asymmetry opposite to that predicted by the rule of thumb. Therefore, the asymmetry of folds can be an ambiguous indicator of the sense of shear.The reason for the ambiguity is that asymmetry is a result of two processes that can produce diametrically opposed results. The deformation of foliation surfaces and axial planes in a passive manner is the pure or end-member form of one process. The result of the passive deformation of fold forms is the drag fold in which the steepness of limbs and the tilt of axial planes relative to nonfolded layering are in accord with the rule of thumb.The end-member form of a second process, however, produces the opposite geometric relationships. This process involves yielding and buckling instabilities of layers with contact strength and can result in monoclinal kink bands. Right-lateral, layer-parallel shear stress produces left-lateral monoclinal kink bands and left-lateral shear stress produces right-lateral monoclinal kink bands. Actual folds do not behave as either of these ideal end members, and it is for this reason that the interpretation of the sense of layer-parallel shear stress relative to the asymmetry of folds can be ambiguous.Kink folding of a multilayer with contact strength theoretically is a result of both buckling and yielding instabilities. The theory indicates that inclination of the direction of maximum compression to layering favors either left-lateral or right-lateral kinking, and that one can predict conditions under which monoclinal kink bands will develop in elastic or elastic—plastic layers. Further, the first criterion of kink and sinusoidal folding developed in Part IV remains valid if we replace the contact shear strength with the difference between the shear strength and the initial layer-parallel shear stress.Kink folds theoretically can initiate only in layers inclined at angles less than to the direction of maximum compression. Here φ is the angle of internal friction of contacts. For higher angles of layering, slippage is stable so that the result is layer-parallel slippage rather than kink folding.The theory also provides estimates of locking angles of kink bands relative to the direction of maximum compression. The maximum locking angle between layering in a nondilating kink band and the direction of maximum compression is . The theory indicates that the inclination of the boundaries of kink bands is determined by many factors, including the contact strength between layers, the ratio of principal stresses, the thickening or thinning of layers, that is, the dilitation, within the kink band, and the orientation of the principal stresses relative to layering. If there is no dilitation within the kink band, the minimum inclination of the boundaries of the band is to the direction of maximum compression, or to the direction of nonfolded layers. Here α is the angle between the direction of maximum compression and the nonfolded layers. It is positive if clockwise.Analysis of processes in terminal regions of propagating kink bands in multilayers with frictional contact strength indicates that an essential process is dilitation, which decreases the normal stress, thereby allowing slippage and buckling even though slopes of layers are low there.     

A theory of concentric, kink and sinusoidal folding and of monoclinal flexuring of compressible, elastic multilayers: IV. Development of sinusoidal and kink folds in multilayers confined by rigid boundaries

This part concerns folding of elastic multilayers subjected to principal initial stresses parallel or normal to layering and to confinement by stiff or rigid boundaries. Both sinusoidal and reverse-kink folds can be produced in multilayers subjected to these conditions, depending primarily upon the conditions of contacts between layers. The initial fold pattern is always sinusoidal under these ideal conditions, but subsequent growth of the initial folds can change the pattern. For example, if contacts between layers cannot resist shear stress or if soft elastic interbeds provide uniform resistance to shear between stiff layers, sinusoidal folds of the Biot wavelength grow most rapidly with increased shortening. Further, the Biot waves become unstable as the folds grow and are transformed into concentric-like folds and finally into chevron folds. Comparison of results of the elementary and the linearized theories of elastic folding indicates that the elementary theory can accurately predict the Biot wavelength if the multilayers contain at least ten layers and if either the soft interbeds are at most about one-fifth as stiff as the stiff layers, or there is zero contact shear strength between layers.Multilayers subjected to the same conditions of loading and confinement as discussed above, can develop kink folds also. The kink fold can be explained in terms of a theory based on three assumptions: each stiff layer folds into the same form; kinking is a buckling phenomenon, and shear stress is required to overcome contact shear strength between layers and to produce slippage locally. The theory indicates that kink forms will tend to develop in multilayers with low but finite contact shear strength relative to the average shear modulus of the multilayer. Also, the larger the initial slopes and number of layers with contact shear strength, the more is the tendency for kink folds rather than sinusoidal folds to develop. The theoretical displacement form of a layer in a kink band is the superposition of a full sine wave, with a wavelength equal to the width of the kink band, and of a linear displacement profile. The resultant form resembles a one-half sine curve but it is significantly different from this curve. The width of the kink band may be greater or less than the Biot wavelength of sinusoidal folding in the multilayer, depending upon the magnitude of the contact shear strength relative to the average shear modulus. For example, in multilayers of homogeneous layers with contact strength, the Biot wavelength is zero so that the width of the kink band in such materials is always greater than the Biot wavelength. In general, the higher the contact strength, the narrower the kink band; for simple frictional contacts, the widths of kink bands decrease with increasing confinement normal to layers. Widths of kink bands theoretically depend upon a host of parameters — initial amplitude of Biot waves, number of layers, shear strength of contacts between layers, and thickness and modulus ratios of stiff-to-soft layers — therefore, widths of kink bands probably cannot be used readily to estimate properties of rocks containing kink bands. All these theoretical predictions are consistent with observations of natural and experimental kink folds of the reverse variety.Chevron folding and kink folding can be distinctly different phenomena according to the theory. Chevron folds typically form at cores of concentric-like folds; they rarely form at intersections of kink bands. In either case, they are similar folds that develop at a late stage in the folding process. Kink folds are more nearly akin to concentric-like folds than to chevron folds because kink folds form early, commonly before the sinusoidal folds are visible. Whereas concentric-like folds develop in response to higher-order effects near boundaries of a multilayer, kink folds typically initiate in response to higher-order shear, as at inflection points near mid-depth in low-amplitude, sinusoidal fold patterns. Chevron folding and kink folding are similar in elastic multilayers in that elastic “yielding” at hinges can produce rather sharp, angular forms.     

Opposite senses of fold asymmetry

If the orientation of the principal compressive stress is oblique to layering, viscous multilayers fold in response to the layer-parallel shortening and develop asymmetric interfaces in response to the layer-parallel shear. A theoretical analysis of folding of viscous multilayers with different slip laws at layer contacts shows that the sense of asymmetry of folds is determined largely by the behavior of the layer contacts and the sense of layer-parallel shear during folding.

For a given sense of layer-parallel shear, the sense of asymmetry of folds can be reversed by changing only the behavior of the layer contacts. If the slip rate is linearly proportional to the shear stress at layer contacts, the resistance to slip is the same everywhere along interfaces, and the folds develop the sense of asymmetry of drag folds. If the slip rate is a nonlinear function of the shear stress at layer contacts, however, the resistance to slip varies with position along interfaces, and folds develop the sense of asymmetry of monoclinal kink folds.

For a given variable resistance to slip at layer contacts, the sense of asymmetry depends on the sense and magnitude of the layer-parallel shear and on the thickness-to-wavelength ratio of the multilayer.

For finite multilayers with variable resistance to slip at contacts, an increase in the layer-parallel shear stress decreases the dominant wavelength and increases the amplification factor for the initial perturbation of the interface.

The multilayer consists of linear viscous layers and is confined by thick, viscous media. Resistance to slip at layer contacts is modeled theoretically by a powerlaw relationship between rate of slip and contact shear stress. The equations, derived to 2nd order in the slopes of the interfaces, describe the growth of asymmetric folds from initial, symmetric perturbations.     

A theory of concentric, kink, and sinusoidal folding and of monoclinal flexuring of compressible, elastic multilayers: I. Introduction

Most folds in stratified rock are similar in form to ideal kink, concentric or chevron folds, in which there are discontinuities in slope or curvature of bedding planes. In this respect most folds appear to be closely related to faults, traces of which can be considered to be lines across which there are discontinuities of displacement of layers. Further, the close association of reverse faults and folds or monoclinal flexures seems to indicate that theories of faulting and folding should be closely related.The theory of characteristics is a mathematical tool with which we can obtain insights into processes involving discontinuities. Theoretical characteristic lines are directions across which certain variables might be discontinuous and they are directions along which discontinuities propagate. The theory has been widely applied in plasticity theory and in fluid mechanics and theoretical studies of faulting have suggested that faults are analogous to the lines of discontinuity predicted by plasticity theory. Elasticity and viscosity theories, on which theories of folding have been founded, exclude the existence of characteristic lines in the materials unless the equilibrium equations, rheological properties or strains are nonlinear. However, all folding theories are nonlinear to some extent and the theories can be modified so that they predict lines of discontinuity for some conditions of loading and deformation.Theories of folding will be developed in subsequent papers of this series in order to predict conditions under which characteristic lines can exist in multilayered materials and in order to determine the conditions that must be satisfied across and along the characteristic lines. The theory should help us to recognize lines of apparent discontinuity in natural and experimental folds and study of these lines should provide further understanding of mechanisms of folding.Experimental studies of folding of a wide variety of materials, including alternating layers of rubber and gelatin, modeling clay and grease or graphite, and potter's clay and rubber or cardboard, suggest that the patterns of folding in these materials begin with sinusoidal forms, transform into concentric or kink forms and then into chevron forms as the multilayers are shortened axially. A suitable theory of folding of multilayers should account for these observations.     

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.     

Impact of mechanical anisotropy and power-law rheology on single layer folding

The infinitesimal and finite stages of folding in nonlinear viscous material with a layer-parallel anisotropy were investigated using numerical and analytical methods. Anisotropy was found to have a first-order effect on growth rate and wavelength selection, and these effects are already important for anisotropy values (normal viscosity/shear viscosity) < 10. The effect of anisotropy must therefore be considered when deducing viscosity contrasts from wavelength to thickness ratios of natural folds. Growth rates of single layer folds were found to increase and subsequently decrease during progressive deformation. This is due to interference between the single layer folds and chevron folds that form in the matrix as a result of instability caused by the anisotropic material behaviour. The wavelength of the chevron folds in the matrix is determined by the wavelength of the folded single layer, which can explain the high wavelength to thickness ratios that are sometimes found in multilayer sequences. Numerical models including anisotropic material properties allow the behaviour of multilayer sequences to be investigated without the need for resolution on the scale of individual layers. This is particularly important for large-scale models of layered lithosphere.     

A theory of concentric, kink and sinusoidal folding and of monoclinal flexuring of compressible, elastic multilayers: VII. development of folds within Huasna Syncline, San Luis Obispo County, California

Folds in the Huasna area of the southern Coast Ranges of California provide an opportunity to study different fold forms and to estimate dimensional and relative rheological properties of rocks at the time of folding. Plunging, concentric-like and chevron-like folds with wavelengths ranging from about 0.1 to 1 km are clearly visible in natural exposures at the south end of the Huasna syncline, which has a wavelength of 12–16 km. Examination of two fresh roadcut exposures in the Miocene Monterey Formation suggests that folding within part of the Monterey was accommodated primarily by layer-parallel slip between structural layers with thicknesses ranging from 30 to 43 m, even though lithologic layers range from a few mm to a few dm in thickness. This part of the Monterey is folded into a series of concentric-like folds, with chevron-like folds at their cores and with a ratio of wavelength to total thickness of layers of about . Theoretical analysis of multilayers, comprised of identical, elastic or elastic—plastic layers with frictionless contacts, indicates that the effective, or weighted-average thickness of structural layers corresponding with an ratio of 0.42 is about 41 m. Thus, the theoretical predictions are roughly in agreement with available data concerning these folds.Thicknesses of structural units in other folds of this area are inadequately known to closely check theoretical predictions, but most of the data are consistent with predictions. An exception is the Huasna syncline which has a larger wavelength than we would predict. There are several likely explanations for this discrepancy. Layers in the underlying Franciscan complex may have taken part in the folding, making our estimates of total thickness too small. The basement rocks may have been much softer, relative to the overlying sedimentary rocks, than we assumed. The Huasna syncline could be partly a result of gravitational instability of relatively low density, Miocene siliceous and porcelaneous shales, overlain by relatively high density, Pliocene sandstones.The Huasna syncline and some of the smaller folds in the Miocene rocks are doubly in the northwest—southeast direction. Further, the maximum compression was approximately normal to the traces of the large faults in this part of California.     

Parasitic folds with wrong vergence: How pre-existing geometrical asymmetries can be inherited during multilayer buckle folding

Parasitic folds are typical structures in geological multilayer folds; they are characterized by a small wavelength and are situated within folds with larger wavelength. Parasitic folds exhibit a characteristic asymmetry (or vergence) reflecting their structural relationship to the larger-scale fold. Here we investigate if a pre-existing geometrical asymmetry (e.g., from sedimentary structures or folds from a previous tectonic event) can be inherited during buckle folding to form parasitic folds with wrong vergence. We conduct 2D finite-element simulations of multilayer folding using Newtonian materials. The applied model setup comprises a thin layer exhibiting the pre-existing geometrical asymmetry sandwiched between two thicker layers, all intercalated with a lower-viscosity matrix and subjected to layer-parallel shortening. When the two outer thick layers buckle and amplify, two processes work against the asymmetry: layer-perpendicular flattening between the two thick layers and the rotational component of flexural flow folding. Both processes promote de-amplification and unfolding of the pre-existing asymmetry. We discuss how the efficiency of de-amplification is controlled by the larger-scale fold amplification and conclude that pre-existing asymmetries that are open and/or exhibit low amplitude are prone to de-amplification and may disappear during buckling of the multilayer system. Large-amplitude and/or tight to isoclinal folds may be inherited and develop type 3 fold interference patterns.     

Single layer folding in simple shear

Despite the common occurrence of simple shear deformation, laboratory and numerical simulations of folding have so far been almost exclusively in pure shear. Here we present a series of finite-element simulations of single layer folding in simple shear up to high shear strains (γ ≤ 4, and up to 75% shortening of the folding layer). In the simulations we vary the viscosity contrast between layer and its surroundings (25–100), the stress exponent (1 or 3) and the kinematics of deformation (pure- versus simple shear). In simple shear fold trains do not show a clear asymmetry, axial planes form perpendicular to the developing fold train and rotate along with the fold train. Differences in geometries between folds formed in simple and pure shear folds are thus difficult to distinguish visually, with simple shear folds slightly more irregular and with more variable axial plane orientation than in pure shear. Asymmetric refraction of an axial planar cleavage is a clearer indication of folding in simple shear. The main effect of an increase in stress exponent is an increase in effective viscosity contrast, with only a secondary effect on fold geometry. Naturally folded aplite dykes in a granodiorite are found in a shear zone in Roses, NE Spain. Comparison of the folded dykes with our numerical simulations indicates a viscosity contrast of around 25 and a stress exponent of 3. The natural folds confirm that at this moderate viscosity contrast, a significant amount of shortening (20–30%) is achieved by layer thickening instead of folding.     

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。     

A numerical investigation and geological discussion of the relationship between folding,kinking and faulting

The layer-parallel compression of a regular bilaminate consisting of layers with materials described by an incompressible power-law elastic model is considered. The average mechanical properties of this idealised multilayer are then represented by those of an equivalent anisotropic continuum with internal resistance to bending. Changes in material properties that accompany uniform finite shortening are accounted for. Interpretation of the internal instability analysis for such a continuum, introduced in the companion paper involves the use of a spectrum which at a given level of strain, scans all directions within the continuum for relative susceptibility to a heterogeneous simple shearing instability.Estimates of nonlinear material properties from reported experiments on the behaviour of various rocks in the time-independent deformation regime, and geometric parameters such as the volume fraction of each material and the number of confined layers are considered. The shapes of the resulting spectra may be used to predict natural conditions that will favour the initiation of repetitive buckle folds or more localized disturbances such as kink-bands and faults. Results suggest that for typical properties of sedimentary multilayers, kinking is strongly favoured over repetitive buckling where the weaker material occupies only a very small volume fraction of the multilayer. The effect of significant imperfections leading to slippage between layers is discussed.Finally, a simple classification of structure genesis is proposed in which the mechanical relationships between apparently diverse structures is illustrated.     

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.     

Kinematics of fault-related folding in a duplex,lost river range,Idaho, U.S.A.

The Doublespring duplex, located in the Lost River Range of Idaho, is a Sevier age fault-related fold complex in massive limestones of the Upper Mississippian Scott Peak Formation. Folds within the duplex closely resemble fault-bend fold geometrics, with open interlimb angles and low-angle bed cut-offs. Narrow, widely spaced, bedding-parallel shear zones with well-developed pressure solution cleavage alternate with massive, relatively undeformed layers on fold limbs. Shear zones are developed only on the limbs of anticlines, and have similar but unique morphologies in each of three different folds. Incremental strain histories reconstructed from antitaxial fibrous overgrowths and veins within the shear zones constrain the kinematics of folding. Shear zones experienced distributed bedding-parallel simple shear (flexural flow) towards pins near axial surfaces, while adjacent massive layers experienced rotation through an externally fixed extension direction. The absence of footwall synclines and morphological differences in shear zones from adjacent folds suggest that faulting preceded folding. Kinematic histories of folds that have experienced different translational histories are identical, and are not compatible with strain histories predicted from previous kinematic models of fault-bend folding. Shear zone development and fiber growth is instead interpreted to have occurred during low amplitude fixed-hinge buckling in response to initial resistance to translation of the thrust sheet. Fault-bend folding with mobile axial surfaces occurred with translation of the thrust sheets once the initial resistance to translation was overcome and resulted in no penetrative strain.     

Fault reactivation and superimposed folding in a proterozoic sandstone-volcanic sequence,davenport province,central Australia

The Davenport Province is a fluvial to shallow-marine sequence of weakly metamorphosed sandstone, rhyolite and basalt deposited in an ensialic basin that was probably initiated by continental extension. Isopach ridges and cut-offs suggest that synsedimentary normal and transfer faults controlled deposition. These faults were reactivated as reverse faults and strike-slip faults during deformation. Upright concentric folding took place in two episodes, initially about NW-trending axes and subsequently about generally NE-trending axes. Balanced cross-sections suggest that the folds die out downwards above the base of the sequence. However, units from well below the concentrically folded part of the sequence crop out in anticlinal cores, indicating that there is no through-going detachment horizon in the sequence. This is consistent with the rarity of clayey, silty and evaporitic sediments suitable for detachment. Hence, the faults probably cut the entire sequence and enter the basement. Interference of the folds formed dome-and-saddle and crescentic patterns. Thrust sheets, imbricate stacks and duplexes are not recognized in the province, and layer-parallel shortening is moderate (about 28%). These suggest a correspondingly low degree of earlier regional extension (about 40%). The folding may have been due to a sudden change in lithospheric plate velocity.     

Quaternary reactivation of flexural-slip folds by diapiric activity: example from the western Ebro Basin (Spain)

In the western sector of the Ebro Basin two types of structures deform the Quaternary terraces and pediments developed by the Ebro River and its tributaries: (1) folds up to 10 km long in the lower levels of fluvial terraces and (2) normal listric faults that produce tilting and rollover anticlines of the Quaternary deposits. Both types of structures are linked to the geometrical and lithological features of the Tertiary beds that underlie the Quaternary deposits. Quaternary folds, whose axes are parallel to the strike of the Tertiary beds, are the result of reactivation of Tertiary large-scale (60 km long) folds due to diapirism of their gypsum cores, where the gypsum units reach a maximum thickness of 3 000 m. This reactivation produced flexural-slip in some beds on the limbs of the folds, bringing about the folding of the overlying Quaternary terraces. The mechanism of Quaternary folding involves layer-parallel shear in alternating Tertiary units and folding linked to detachments and reverse layer-parallel faults. Normal listric faults are widespread throughout the studied area. They are partly parallel to low dipping Tertiary beds and are the result of a NNE-SSW tectonic extension, compatible with minor structures and focal mechanisms of recent earthquakes. The relationship between the two kinds of Quaternary structures indicates that diapirism of the gypsum cores of the anticlines was activated by extensional tectonics.     

白云鄂博叠加褶皱及其变形机制

华北地块北缘中上元古界的白云鄂博群尖山组，在白云鄂博群东南花果山一带褶皱变形十分复杂，为了研究其褶皱形态、变形机制，在原1：5万填图的基础上选近1km^2的范围进行1：2000大比例尺地质填图，以变质长石石英砂岩为标志层，确定了两期褶皱构造。综合区域资料表明：早期EW向褶皱以纯剪切、纯剪切＋简单剪切为主，是加里东运动的结果；晚期褶皱表现为EW向压扁，为印支运动所形成。     

华北克拉通东部地块和大别—苏鲁造山带印支期褶皱-逆冲构造与动力学背景

大别-苏鲁造山带不同岩片(块)经历了不同的褶皱变形.榴辉岩块(或透镜体)和硬玉石英岩片经历了高压-超高压背景下的两幕褶皱变形之后,在区域性第一幕变形期间主要发生透镜化为主,后期与围岩共同经历紧闭同斜第二幕褶皱.而其它岩片主要经历了现今野外可见的区域性三幕褶皱,其中区域性第一幕褶皱为片内残留褶皱,在斜长角闪岩透镜体中多见,宏观规律不明.区域性第二幕褶皱在露头尺度多见,轴面为折劈理,局部强烈置换成片理化带(复合片理或第二期片理),恢复第三幕褶皱改造作用后,揭示出各种岩片中的各级尺度的第二幕褶皱都为轴面北西倾南东倒、轴迹走向为NNE向的紧闭不对称褶皱,不对称性一致反映其指向与各种岩片向南东的逆冲运动有关.第三幕褶皱为以片理或折劈理为变形面的宽缓褶皱,轴迹走向NWW,枢纽向西倾伏.韧性剪切带为非透入性构造,分早晚两期,早期为韧性逆冲,新县穹隆以南,运动学标志指示向北逆冲,错切第二幕褶皱,结合新县穹隆北部向南的逆冲特征,反映这些韧性逆冲断层多数为第二幕大型褶皱翼部的次级逆冲断层;晚期为韧性滑脱带,其发育局限于几个岩性差异较大的接触带,带内伸展型折劈理发育,并对挤压构造样式有重要的改造作用.华北克拉通东部地块是华北克拉通的重要组成,其盖层古生界和三叠系在印支运动期间经历了一幕宽缓褶皱作用,其轴迹方向主体也为NWW向.这一褶皱构造明显在变形时间、变形样式和展布方向上都和大别-苏鲁造山带中的第三幕褶皱非常一致,说明它们具有动力学上的必然联系.同时,研究表明在华北克拉通东部地块中没有经历大别-苏鲁造山带中区域性第一、第二幕褶皱变形的记录,故本文认为印支期这两幕变形主要发生在华北板块东南缘的边界上,并没有波及到板内,而且从东向西高压-超高压岩石剥露具有穿时性.只有当华北板块和华南板块在第二幕变形之后构成了统一块体后,第三幕变形才波及华北板内.     

The geometry and kinematics of a suite of conjugate kink bands, southeastern Australia

A conjugate set of subvertical kink bands is exposed in coastal outcrops of well-foliated Ordovician turbidites near Mystery Bay, Australia. All kink bands with widths exceeding 3 cm have complex internal structures including compound and parasitic kinks, stepped kink boundaries, internal crenulations, variable kink angles and prismatic voids. The kink bands are interpreted to result from rotation of short foliation segments between fixed kink planes with subsequent widening and modification by layer-parallel shear external to the kink band. Layer-parallel shear of both sinistral and dextral sense accompanied kinking and indicates a variable stress system during kink band development.Conjugate kink bands are abundant and are used to estimate bulk strain orientations. In general, the dominant kink set of a conjugate pair is inclined at a lower angle to the external foliation than the weaker set and this angular disparity increases with increasing dominance of one set. These observations are at variance with relationships described from experimental bulk pure shear deformation of anisotropic materials. It is suggested that orthogonal constraints in these experiments restrict layer-parallel shear to within a developing kink band and are, therefore, unlike many natural kink systems. Simple shear experiments can produce structures geometrically similar to natural kink bands.     

Model studies of gravitational gliding tectonics

The paper presents the results of modelling deformations in stratified formations involved in gliding down a tilted base. The modelling is performed to simulate an “orogenic wave”. Gravity folding is compared to folding caused by horizontal compression from a rigid block. Various morphologic types of structure arise with gravitational gliding depending on the thickness and physical properties of the layers involved. These are kink, sine, chevron and fan-like folds, uplift-thrusted structures and selective folding. In similar strata similar deformations originate both in gravity gliding and by compression from a rigid block. The results of the experiments suggest that gravity gliding tectonics may be responsible fo a much wider variety of structure than has been previously envisaged.     

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.