Strain and competence contrast estimation from fold shape

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

Flow pattern within a Permian submarine slump recorded by oblique folds and deformed fossils, Ulladulla, south-eastern Australia

The flow pattern within a slump in Permian marine rocks of the southern Sydney Basin, Australia, is recorded by folds and deformed fossils. Abundant brachiopod and bryzoan fossils in the slumped rocks are relatively undeformed, but fossil crinoid stems have been deformed by relative rotation of individual ossicles. Measurement of the strain indicates that the deformation of the crinoids is consistent with flexural flow folding within the slump. Previous models assume that curved slump fold axes remain parallel to the enveloping bedding surface of a slump sheet. Detailed measurements of the orientation of slump folds in this study found fold axes to be oblique to bedding, which is interpreted as a result of folds plunging downward towards the flanks of the slump or slump lobes. In the present model, fold axes are not generally parallel to the strike of the fold axial surface, and this can explain differences between the orientations of slump fold axes and axial surfaces when these are used as directional indicators of slump movement.     

单层褶皱变形过程中最大主应力与水平应变的变化及其影响因素

对地质构造进行定量半定量研究是地质工作者近几十年来一直努力的方向,构造数值模拟是有效的定量研究方法之一。褶皱是一种典型的构造类型,对褶皱构造进行定量半定量研究也一直是构造地质学家们所致力解决的研究课题。本文结合近年来单层褶皱构造数值模拟研究进展,以及笔者近几年来对单层褶皱所进行的数值模拟实验研究,主要论述了单层褶皱变形的影响因素,单层褶皱变形过程中的最大主应力与水平应变的变化及其影响因素等。数值模拟技术为褶皱变形提供了一种新的研究方法,该方法在构造地质领域将有很好的发展前景。     

Strain distribution in a fold in the West Norwegian Caledonides

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

The structure of the Sierras Australes (Buenos Aires Province, Argentina): An example of folding in a transpressive environment

The Sierras Australes of eastern Argentina record the progressive suturing of the Patagonian terrane with the South American craton during Permo-Triassic time. On the South American side of the suture, fold axes and axial plane cleavage show a systematic variation in orientation across the region, rotating counterclockwise from the southern and central segments to the northwestern segments. These data, in combination with finite strain measurements indicative of extension parallel to fold axes, suggest progressive, horizontal, simple shear with a left-lateral sense. Thus, the suturing probably had a strong, transpressive component. This conclusion explains the characteristic sigmoidal shape of the sierras and is supported by comparison with scale-model experiments conducted by other investigators. Furthermore, this interpretation is in agreement with paleomagnetic data.     

龙门山南段邛西断层转折褶皱磁组构及其有限应变

龙门山南段位于四川盆地以西,其新生代构造变形特征对于认识青藏高原东缘的变形机制具有一定的指示意义。磁组构是一种灵敏的应变指示计,在变形微弱的沉积岩地区尤为适用。在龙门山南段邛西断层转折褶皱不同构造部位选取48个采样点开展磁组构研究,分析断层转折褶皱的有限应变特征及区域构造变形机制。实验结果表明,邛西地区上白垩统中主要载磁矿物为高矫顽力的赤铁矿,背斜整体应变较弱,且存在3种类型的磁组构,以沉积磁组构和初始变形磁组构为主,铅笔状磁组构少见,主要存在于靠近褶皱中段的前翼部位,说明断层转折褶皱前翼较后翼和核部应变强,且中段地层应变较其他部位更为强烈。此外,各采样点磁线理的优势方位为近南北向（N10°E）,表明邛西断层转折褶皱的形成与龙门山南段晚新生代近东西向的地壳水平缩短有关,暗示龙门山南段的最大主压应力方向在晚新生代存在转变的可能。     

3-D geomechanical restoration and paleomagnetic analysis of fault-related folds: An example from the Yanjinggou anticline,southern Sichuan Basin

We examine the development of the Yanjinggou anticline, a fault-propagation-fold in the southern Longmen Shan, through an integrated study of structural geometry, strain, and paleomagnetism. The 3-D structural and strain restoration models generated in our analysis reveal that the NE-trending Yanjinggou fold has a curved map trace that is convex to the southeast. The fold has three distinct regions characterized by different strain patterns: contraction in the core of the fold, extension in the outer arc, and a forelimb with distributed shear. To further understand the kinematics of the Yanjinggou anticline, we performed paleomagnetic analysis on 184 oriented samples collected across the structure. Anisotropy of magnetic susceptibility (AMS) measurements and stepwise thermal demagnetization were conducted. A strike test was applied to the high temperature component (HTC) in order to identify rotation around the arc. The result indicates that the Yanjinggou anticline is a progressive arc, with a minor initial curvature and a dominant secondary curvature related to vertical-axis rotation synchronous with thrusting. The primary curvature and initial development of the structure correlates with the growth of the southern Longmen Shan in Late Miocene. The secondary curvature correlates with displacement extending since Late Pleistocene toward the southeast into the central basin along the detachments that underlie the structure. Lateral gradients in displacement along this underlying detachment provide a mechanism for producing the vertical rotation of the anticline. AMS results and historical earthquake analysis imply that the fault-propagation fold, along with other NE trending structures in the southern Sichuan basin, are tectonically active and accommodate east-west crustal shortening in the basin. By integrating 3-D structural and strain restoration modeling with systematic AMS and paleomagnetic methods using statistical analysis, we closely constrain how the Yanjinggou anticline developed, and provide insights into the formation of fault-related folds with curved shapes in map view, which are common in other fold-and-thrust belts around the world.     

龙门山南段邛西断层转折褶皱磁组构及其有限应变

龙门山南段位于四川盆地以西,其新生代构造变形特征对于认识青藏高原东缘的变形机制具有一定的指示意义。磁组构是一种灵敏的应变指示计,在变形微弱的沉积岩地区尤为适用。在龙门山南段邛西断层转折褶皱不同构造部位选取48个采样点开展磁组构研究,分析断层转折褶皱的有限应变特征及区域构造变形机制。实验结果表明,邛西地区上白垩统中主要载磁矿物为高矫顽力的赤铁矿,背斜整体应变较弱,且存在3种类型的磁组构,以沉积磁组构和初始变形磁组构为主,铅笔状磁组构少见,主要存在于靠近褶皱中段的前翼部位,说明断层转折褶皱前翼较后翼和核部应变强,且中段地层应变较其他部位更为强烈。此外,各采样点磁线理的优势方位为近南北向(N10°E),表明邛西断层转折褶皱的形成与龙门山南段晚新生代近东西向的地壳水平缩短有关,暗示龙门山南段的最大主压应力方向在晚新生代存在转变的可能。     

纵弯叠加褶皱地区岩石有限应变特征：以川东北地区典型叠加褶皱为例

纵弯叠加褶皱地区岩石有限应变特征是所受历次变形的综合结果.远离叠加区应变型式的伸长方向与褶皱轴向一致而缩短方向与褶皱轴垂直,叠加区应变型式不规则,且应变椭球伸长量和缩短量之差值较小.     

Strain analysis in folds (Infrahelvetic complex,Central Alps)

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

构造物理模拟和PIV有限应变分析对构造裂缝预测的启示

油气储层中构造裂缝发育与有限应变状态关系密切,为了探索有限应变分析与构造裂缝预测的新技术方法,此次研究设计完成了一组单侧挤压收敛模型的物理模拟实验,并引入粒子图像测速(PIV,Particle Image Velocimetry)技术对实验过程进行了定量化分析。实验模型在垂向上为含粘性层的多层结构,实验结果形成了一个肉眼可见的箱状褶皱。通过PIV技术可以获取实验模型变形演化过程中各阶段的位移场数据,计算出各阶段的增量应变,实现从初始状态到褶皱形成之后整个变形过程的有限应变分析,探讨构造裂缝成因机制和分布规律,进行定量化裂缝预测。挤压变形过程初期,应变分布范围很广,有限应变较弱(约4%~8%),在挤压方向上的线应变表现为弱压应变,在垂向上的线应变表现为弱张应变,这种现象是褶皱和断层产生前平行层缩短和层增厚的纯剪变形结果,也是区域型张裂缝和剪裂缝形成的主要机制。褶皱和断层即将发育之时至发育之后,应变局限在断层发育的剪切带及附近区域,有限应变表现为较强(达20%)的剪切应变和剪切张应变,是断层面附近简单剪切变形作用的结果,也是局部型剪裂缝和张剪裂缝形成的主要机制。     

Strain and rotation in a multilayered fold

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

构造流变计

根据构造形迹和应变式反演岩石流变性质的方法称为构造流变计,或简称流变计。目前提出的流变计主要有应变折射、能干层褶皱香肠构造、残斑翼尾样式。应变折射、能干层褶皱和香肠构造流变计已进入量化阶段。构造流变计 可用于研究不同尺度地质体的流变结构,也可用来研究地质体的流变学演化,具有很好的发展前景。     

Usage of strain and vorticity analyses to interpret large‐scale fold mechanisms along the Sanandaj–Sirjan HP‐LT metamorphic belt,SW Iran

3D finite strain analyses and kinematic vorticity measurements were carried out on the Loghon Anticline within the HP‐LT Sanandaj–Sirjan metamorphic belt (Neyriz area, SW Iran). Rƒ/φ and Fry methods were used on the strain markers (e.g. deformed fossils) to interpret geometric relationships between the fold axis, strain ellipsoid axes and shear zone boundaries. The results indicate the predominance of prolate strain in the anticline. Quantitative kinematic analyses show that the W_k parameter is 0. 67 ± 0. 06 (i.e. pure‐shear dominated non‐coaxial flow). This study quantitatively supports the establishment of a dextral transpressive system, which is responsible for the development of the large‐scale right‐lateral shear zones that strike sub‐parallel to the major folds. Flexural shear combined with regional dextral‐shear is suggested to be the most common mechanism of folding in this area. Copyright © 2011 John Wiley & Sons, Ltd.     

Heterogeneous constrictional deformation in a ductile shear zone resulting from the transposition of a lineation-parallel fold

We use new (micro-)structural, petrofabric, strain and vorticity data to analyze the deformation path in a mesoscopic quartz mylonite zone. The mylonite zone resulted from the complete transposition of a stretching lineation-parallel isoclinal fold. Symmetric cleft-girdle quartz c-axis fabrics were recorded in the middle domain, which occupies the inner limbs of the precursor isoclinal fold, while asymmetric cleft- and crossed-girdle fabrics were observed in the upper and lower domains that represent the outer limbs. Constrictional strain, with increasing k values towards the middle domain, is inferred from petrofabric and 3D strain data. Oblique grain shape fabrics yield vorticity estimates of 0.72–0.90 in the zone. However, in the middle domain, pure shear dominated deformation is suggested by orthorhombic crystallographic fabrics. Strain rate is constant throughout the zone; a strain decrease towards the zone center implies that deformation ceased earlier in the middle domain. The data indicates that fold transposition and subsequent mylonitization started as pure-shear-dominated constrictional deformation and progressively changed to simple-shear-dominated, plane strain. During this flow path the asymmetric quartz c-axis fabrics likely developed by depopulation of cleft-girdle maxima rather than from the synthetic rotation of fabric maxima itself.     

A cleavage triple point and its meso-scopic structures: the Mustio Sink (Svecofennides of SW Finland)

A cleavage-triple-point (CTP) structure is analyzed, located at the west side of the Mustio gneiss dome in the Svecofennides of southwest Finland. The presence of the CTP and the pattern of mesoscopic fold structures exclude the origin of the Mustio dome by successive interference of fold phases. The highly variable deformation structures are explained in a single-phase deformation model by using the theoretical specific strain environments of a CTP. These environments are (1) horizontal oblation on top of a dome, (2) transition from horizontal to vertical oblation on the flanks of a dome, and (3) vertical constriction in the center of the CTP. It is shown that each strain environment is associated with specific development of foliation, folds, mesoscopic fold interference and strain intensity. The theoretical strain environments are confirmed by strain analysis.     

Influence of structural position on fracture networks in the Torridon Group,Achnashellach fold and thrust belt,NW Scotland

In fold-and-thrust belts rocks undergo deformation as fold geometries evolve. Deformation may be accommodated by brittle fracturing, which can vary depending on structural position. We use 2D forward modelling and 3D restorations to determine strain distributions throughout folds of the Achnashellach Culmination, Moine Thrust Belt, NW Scotland. Fracture data is taken from the Torridon Group; a thick, coarse grained fluviatile sandstone deposited during the Proterozoic. Modelling infers a correlation between strain and simple curvature; we use simple curvature to infer how structural position and strain control fracture attribute variations in a fold and thrust belt.In high curvature regions, such as forelimbs, fracture intensities are high and fractures are short and oriented parallel to fold hinges. In low curvature regions fractures have variable intensities and are longer. Fracture orientations in these regions are scattered and vary over short distances. These variations do not relate to strain; data suggests lithology may influence fracturing. The strain history of fold structures also influences fracturing; structures with longer deformation histories exhibit consistent fracture attributes due to moderate-high strain during folding, despite present day low curvature. This is in contrast to younger folds with similar curvatures but shorter deformation histories. We suggest in high strain regions fracturing is influenced by structural controls, whereas in low strain regions lithology becomes more important in influencing fracturing.     

显微构造中应变标志物及应变测量

显微构造的运动学差别原理及方法目标已得到广泛应用，但其定量计算的标志还局限于石英颗粒、鲕粒、化石等球形物体及少数别的标志物。本文介绍的是书斜构造了、布丁构造、显微褶皱构造、揉皱构造和滑脱构造等5种显微构造的应变特征及测量方法，这些标志的识别和测量有助于提高平衡剖面和缩短量的计算精度。在这五种情况下，测量应变量首先要找到视域内代表最大应变方向的变形前和变形后的长度，然后计算不同视域下的变形量并找出最大应变量，利用应变公式计算变形率。例如：大别山构造带龟山组是一套单斜地层，它的显微变形很发育，显微褶皱显示其缩短变形量达57％，由于龟山组是单斜地层，其样品所代表的地层厚度内其缩短量为57％。     

Strain analysis in Jurassic argillites of the Monte Sirino area (Lagonegro Zone,southern Apennines,Italy) and implications for deformation paths in pelitic rocks

Analysis of strain in Jurassic argillites forming part of the folded and thrusted sedimentary succession of the Lagonegro basin (southern Italian Apennines) has been carried out using ellipsoid-shaped reduction spots as strain markers. Most of the determined finite strain ellipsoids are of oblate type and show a peculiar distribution of the maximum extension direction (X), with maxima either subparallel or subperpendicular to the local fold axes. Using the strain matrix method, two different deformation histories have been considered to assist the interpretation of the observed finite strain pattern. A first deformation history involved vertical compaction followed by horizontal shortening (occurring by a combination of true tectonic strain and volume loss), whereby all strain is coaxial and there is no change in the intermediate axis of the strain ellipsoid. By this type of deformation sequence, which produces a deformation path where total strain moves from the oblate to the prolate strain field and back to the oblate field, prolate strain ellipsoids can be generated and may be recorded where tectonic deformation has not been large enough to reverse pretectonic compaction. This type of deformation history may be of local importance within the study area (i.e. it may characterize some fold hinge regions) and, more generally, is probably of limited occurrence in deformed pelitic rocks. A second deformation sequence considered the superposition of pre-tectonic compaction and tectonic strain consisting of initial layer-parallel shortening followed by layer-parallel shear (related to flexural folding). Also in this instance, volume change during tectonic deformation and tectonic plane strain have been assumed. For geologically reasonable amounts of volume loss due to compaction and of initial layer-parallel shortening, this type of deformation history is capable of producing a deformation path entirely lying within the oblate strain field, but still characterized by a changeover, during deformation, of the maximum extension axis (X) from a position parallel to the fold axis to one perpendicular to it. This type of deformation sequence may explain the main strain features observed in the study area, where most of the measured finite strain ellipsoids, determined from the limb regions of flexural folds, display an oblate shape, irrespective of the orientation of their maximum extension direction (X) with respect to the local structural trends. More generally, this type of deformation history provides a mechanism to account for the predominance of oblate strains in deformed pelitic rocks.