Pitfalls among the promises of mechanics-based restoration: Addressing implications of unphysical boundary conditions

Mechanics-based restoration has been seen by some in the structural geology community as a panacea – a new technology that melds the retrodeformational merits of kinematic balancing with principles of continuum mechanics. The method has been touted for its ability to simulate complex 3D systems without assumptions of plane strain, allowing for heterogeneous fault slip distributions and mechanical interaction of fault segments. It has been suggested as a means to predict distributions of geologic strain and associated small-scale structures; however, we demonstrate that the kinematics of restoration models may differ significantly from forward deformation. Restoration models are governed by boundary conditions that are different from the forces driving forward geologic deformation. Models may be improved by supplementing restoration boundary conditions with loads that attempt to reverse tectonic strain, but unphysical artifacts persist. Mechanics-based restoration may be an appropriate tool for traditional applications of kinematic models including validation of structural interpretation and modeling geometric evolution; however, more subtle features, particularly strain distribution, should be treated with skepticism. Restoration models may provide insights to the initial configuration of forward mechanical models with physically appropriate boundary conditions and non-linear material behavior. Forward models provide the best means for simulating deformation and predicting subsidiary structures.     

Deformation Localization-A Review on the Maximum- Effective-Moment (MEM) Criterion

The essential difference in the formation of conjugate shear zones in brittle and ductile deformation is that the intersection angle between brittle conjugate faults in the contractional quadrants is acute(usually ~60°) whereas the angle between conjugate ductile shear zones is obtuse(usually 110°). The Mohr-Coulomb failure criterion, an experimentally validated empirical relationship, is commonly applied for interpreting the stress directions based on the orientation of the brittle shear fractures. However, the Mohr-Coulomb failure criterion fails to explain the formation of the low-angle normal fault, high-angle reverse fault, and the conjugate strike-slip fault with an obtuse angle in the σ1 direction. Although it is ten years since the Maximum-Effective-Moment(MEM) criterion was first proposed, and increasingly solid evidence in support of it has been obtained from both observed examples in nature and laboratory experiments, it is not yet a commonly accepted model to use to interpret these antiMohr-Coulomb features that are widely observed in the natural world. The deformational behavior of rock depends on its intrinsic mechanical properties and external factors such as applied stresses, strain rates, and temperature conditions related to crustal depths. The occurrence of conjugate shear features with obtuse angles of ~110° in the contractional direction on different scales and at different crustal levels are consistent with the prediction of the MEM criterion, therefore ~110° is a reliable indicator for deformation localization that occurred at medium-low strain rates at any crustal levels. Since the strain–rate is variable through time in nature, brittle, ductile, and plastic features may appear within the same rock.     

CHEMICAL DISTINCTIONS BETWEEN THE THREE PRINCIPAL SERIES OF BASALTIC ROCKS

We present an outcrop-scale example of a localized contractional fault geometry that developed as part of an imbricate normal fault system in response to regional extension. Although extensional regions are dominated by abundant normal faulting, local thrust duplication may occur during the same phase of deformation, and on a regional scale may concentrate important quantities of hydrocarbons. Characteristics of extension-related fold belts have mostly been derived from seismic sections; thus fault geometries, mechanisms of formation, and kinematics of these structures are not precisely understood. Abundant kinematic indicators and complete exposure of an extended sedimentary sequence within the Dead Sea Transform, however, provide the opportunity to examine these fault geometries and mechanisms in detail. The local contractional geometry developed within an imbricate normal fault system, as a result of an out-of-sequence normal fault that detached at a higher structural level. The out-of-sequence normal fault offset pre-existing faults, but was deflected into a contractional geometry upon encountering an earlier-formed rollover anticline, whose curved bedding surface served as a convenient ramp. Consequently, displacement across the out-of-sequence fault generated coeval extensional and contractional geometries along the same detachment surface. Geometries and kinematics derived from the outcrop structural analysis may serve as important analogs for larger structures identified as potential targets for hydrocarbon exploration.     

Kinematics-Based Mathematical Model for Deforming Thrust Wedges

Given the wealth of data concerning the kinematics of deforming fold-thrust belts (FTBs), first-order generalizations about how the major strain components vary within a deforming thrust wedges are considered. These generally observed strain patterns are used to constrain a general, kinematics-based, FTB-wedge model. We considered five strain components within a deforming thrust sheet: (1) thrust-parallel simple shear, (2) horizontal contractional strain, (3) thrust-normal reaction strain, (4) gravitational strain, and (5) a lateral confining boundary condition. After making assumptions about how these strain components vary within a model FTB-wedge, the incremental deformation matrix can be calculated for any given point within the deforming wedge. Thus, the material path of a given marker can be determined and an initially spherical marker’s strain path can be calculated as it moves through the deforming wedge. Furthermore, by illustrating various kinematic parameters of many initially spherical markers (for example, Flinn’s k-value, incremental octahedral shear strain, transport-perpendicular stretch), we have assembled representations of the kinematic properties of the entire model wedge. By including a flat-ramp-flat fault surface geometry for the model wedge, we are able to examine the kinematic effects of this relatively common structural geometry. Within the fault ramp segment there are greater incremental strain magnitudes, out-of-the-plane motion, and flattening strains. Additionally, data from this model suggests that gravitational strains potentially have a significant effect on the strain distribution within a deforming thrust wedge. M. Mookerjee is formerly Matthew Strine.     

三角剪切断层传播褶皱作用理论与应用

基底断层在沉积盖层中传播所形成的褶皱形态难以用平行膝折褶皱理论进行解释,这在于两者的流变学性质有很大差异。Erslev提出了三角剪切断层传播褶皱理论,认为下伏断层的脆性强破裂变形为向上变宽的三角形分布式剪切所调节,三角形顶点固定于断层端点。Hardy和Ford拓展了这一理论并成功地建立数字模拟模型,Allmendinger进一步建立与完善了三角剪切的正演模型与反演方法。通过运动学模型预测结果与天然构造观察和相似模拟实验结果的对比分析,以及通过一系列力学模型对运动学模型的检验,三角剪切断层传播褶皱理论被证实并获得了广泛应用。对前陆盆地、克拉通盆地和走滑盆地的基底卷入型构造与走滑或斜向滑动构造,都可以应用三角剪切断层传播褶皱理论来分析变形样式及其分布特征。该理论可以有效地预测隐伏断层的初始破裂点、断层传播量与发育部位,已成功地应用于工程地质与地震灾害预报等方面。     

Strain refraction in layered systems

Strain refraction across competence contrasts is presented as a simple model consisting of two components, a homogeneous strain and a heterogeneous simple shear. For Newtonian materials, the ratio of the layer-parallel simple shear component in adjacent layers is the inverse of their viscosity ratio. Strong changes in ellipsoid size, shape and orientation are predicted across viscosity contrasts.The geological implications of strain refraction theory are considered within the context of the ‘cleavage/strain debate’. The particular relationships of relative competence and strain revealed by the refraction model may contribute to the problem of why cleavages of different morphologies in rocks of different lithologies (and kinematic histories) should appear to be subparallel to the XY planes of measured strain ellipsoids. Competent rocks should develop dominantly layer-orthogonal strain, and incompetent layers shear-dominated deformation. A variety of structural features ranging from cleavage refraction, changing lineation orientations, folds transected by cleavage, changes from coaxial to non-coaxial deformation, and ramp-flat fault geometry may be the result of stress and strain refraction in rocks.     

Structural pattern and kinematic framework of deformation in the southern Nallamalai fold–fault belt,Cuddapah district,Andhra Pradesh,Southern India

An association of westerly verging asymmetric folds, easterly dipping cleavages and contractional faults control the pattern and intensity of structures at different scales in the southern Nallamalai fold–fault belt, Cuddapah district of Andhra Pradesh, Southern India. Variation in structural geometry is manifested across the section by the occurrence of relatively low amplitude folds, sometimes only a monocline and by the near absence of contractional faults in the WSW, but tight to isoclinal folds with frequent fold–fault interactions through the central areas towards ENE.The relationships of structural elements in terms of orientation, style, sense of movement and general vergence indicate their development under a progressive contractional deformation. The structures are interpreted to result from a combination of bulk inhomogeneous shortening across the belt and a top-to-west, variable simple shear. Localized developments of crenulation cleavage, rotation of cleavage in the shorter limbs of some mesoscale asymmetric folds and general variation of structural elements in morphology and associations across the belt, indicate partitioning of deformation and a varying degree of non-coaxiality in discrete domains of the bulk deformation.     

Comments on the interpretation of deformation textures in rocks

In rocks that undergo ductile deformation, preferred orientation develops as a result of intracrystalline slip and mechanical twinning. The orientation distribution is a consequence of the microscopic mechanisms and of the strain path. It can be used to get some insight into the deformation history; however it is never unique. The interpretation relies largely on polycrystal plasticity theory. The concepts of stress equilibrium and strain compatibility, which are two extreme assumptions made to model deformation, are discussed. New approaches such as the viscoplastic self-consistent theory are a compromise and may be applicable to mineral systems which display a high degree of plastic anisotropy. Important extensions allow for heterogeneous deformation in the polycrystal from grain to grain and even within grains in correspondence with microstructural observations. All these theories defy the popular notion which is becoming entrenched in the geological literature, that the microscopic slip plane normal aligns with the axis of maximum principal compressive stress, and that in simple shear the crystallographic slip plane rotates into the macroscopic shear plane and the slip direction into the macroscopic shear direction, an orientation referred to by geologists as ‘easy glide’. It is emphasized that future work on texture development of rocks should be based on rigorous physics rather than ingenious intuition, in accordance with an old recommendation of Walter Schmidt.     

The unusual 3D interplay of basement fault reactivation and fault-propagation-fold development: A case study of the Laramide-age Stillwell anticline,west Texas (USA)

Subsurface fault geometries have a systematic influence on folds formed above those faults. We use the extraordinarily well-exposed fold geometries of the Laramide-age Stillwell anticline in west Texas (USA) to develop a strain-predictive model of fault-propagation fold formation. The anticline is a 10-km long, NW-trending, NE-vergent, asymmetric fold system with an axis that displays a map-view left-stepping, en echelon pattern. We integrated field observations, geologic and structural data, cross-sections, and 2D kinematic modeling to establish an unusual 3D two-stage model of contractional fold formation, including: 1) reverse reactivation of a pre-existing, NW-striking, SW-dipping, left-stepping, en echelon normal fault system in Paleozoic basement rocks to generate monoclinal flexures in overlying layered Cretaceous carbonate rocks; and 2) the formation of a subsequent flat-ramp fault system that propagated horizontally along a mechanically-weak, clay-rich Cretaceous unit before ramping up at the hinge of the pre-existing monocline system. Strain is focused within the forelimb of the system, in front of the propagating fault tip, and is accommodated by a combination of interlayer slip, flat-ramp faulting, and fracturing proximal to planes of slip. This strain predictive model can be applied to similar, less-well-exposed contractional systems worldwide and provides a new, unusual example of Laramide-age contractional deformation.     

谈调整构造

调整构造是伸展型沉积盆地和造山带中普遍存在的构造，它与走向构造一起，控制了沉积盆地或造山带的基本轮廓与内部结构。调整构造横切走向构造，并与之共同控盆、控岩、控矿，并间隔开两侧不同的构造样式。它以长时期、多阶段活动，具有高渗透性为主要特征，是控制矿带展布与矿床就位的重要构造，也是固定成矿预测区与找矿靶区的重要依据之一，本文以鲁西、中亚及乌拉山—大青山地区、兰坪─思茅盆地区及右江盆地区为例，论述了调整构造的基本特征及控矿作用。     

Development of quartz c-axis crossed/single girdles under simple-pure shear deformation: Results of visco-plastic self-consistent modeling

Quartz c-axis fabrics are widely used to determine the shear plane in ductile shear zones, based upon an assumption that the shear plane is perpendicular to both the central segment of quartz c-axis crossed girdle and single girdle. In this paper the development of quartz c-axis fabric under simple-pure shear deformation is simulated using the visco-plastic self-consistent (VPSC) model so as to re-examine this assumption. In the case of no or weak dynamic recrystallization, the simulated crossed girdles have a central segment perpendicular or nearly perpendicular to the maximum principal finite strain direction (X) and the XY finite strain plane, and at a variable angle relative to the imposed kinematic framework that is dependent on the modeled flow vorticity and finite strain. These crossed girdles have a symmetrical skeleton with respect to the finite strain axes, regardless of the bulk strain and the kinematic vorticity, and rotate in a way similar to the shear sense with increasing bulk strain ratio. The larger the vorticity number the more asymmetrical their legs tend to be. In the case of strong dynamic recrystallization and large bulk strain, under simple shear the crossed girdle switches into single girdles, sub-perpendicular to the shear plane, by losing the weak legs. The numerical results in our models do not confirm the above-mentioned assumption.     

结构面力学性质的定量鉴定

变形带力学性质的鉴定是地质力学研究中的先行基础步骤.近来出现一些新的概念和方法,可用以定量表征变形带的力学性质.天然变形带通常是一般剪切作用的产物,是纯剪切(共轴缩短或伸展)和简单剪切的组合.为了定量说明两者间的相对贡献,提出了运动学涡度(W_k)这一物理量,并简单地定义为cos υ.υ是主变形面内两特征方向间的夹角.纯剪切的υ=90°,W_k=0;简单剪切的υ=0°,W_k=1.一般剪切的υ介于0°和90°之间,W_k为0到1.运动学涡度符号的正负分别代表变形带的减薄和增厚.υ可通过极摩尔圆法求出.主压应力(σ₁)方向与W_k的关系为W_k=sin2ξ.ξ是σ₁与变形带法线间的夹角.因此,可用以确定变形带的W_k和力学性质.根据最大有效力矩准则,韧性变形带与主压应力(σ₁)方向间的夹角为55°,可用以确定古应力轴的方向,并可能确定变形时差应力的大小.      

Ouachita, Appalachian, and Ancestral Rockies deformations recorded in mesoscale structures on the foreland Ozark plateaus

Mesoscale structures in Paleozoic rocks of the Ozark plateaus reveal four Pennsylvanian deformation episodes in midcontinent North America. The two earliest episodes can be assigned to progressive northwestward docking of the Ouachita terrane with North America. Early extensional structures (Event 1) indicate a northwest/southeast maximum horizontal stress (Hmax) during Early Pennsylvanian Ouachita terrane advance. Event 2 extensional and strike-slip structures indicate Hmax across the Ozark plateaus that varies systematically from north-northwest/south-southeast in the south to northeast/southwest in the north. This suggests development of a slip-line deformation field in response to minor northeastward lateral escape of lithospheric blocks away from the northwestward-moving Ouachita terrane's leading edge, which acted as an indenter in western Arkansas, southeastern Oklahoma, and Texas. Younger contractional and strike-slip structures of Event 3 indicate northeast/southwest Hmax across the entire Ozark plateaus, and deformation orientation and intensity are not readily assigned to Ouachita foreland deformation and may be related to Middle Pennsylvanian Ancestral Rockies contractional deformation. Finally, Event 4 contractional structures indicate northwest/southeast Hmax consistent with southern Appalachian late stage convergence.Deformation episodes are localized along basement fault zones, particularly at major bends, suggesting minor restraining-bend uplifts along strike-slip faults. Geometries of conjugate normal fault and hybrid shear joint arrays indicate localized areas of high differential stress consistent with basement block uplift at these bends. High-angle faults reactivated in a reverse sense and bedding-parallel veins suggest tensile minimum stresses and pore fluid pressures exceeding lithostatic stress, consistent with brine pulses driven into the midcontinent during Late Paleozoic orogeny (as proposed by other authors).     

库车坳陷-南天山盆山过渡带的收缩构造变形模式

用地面露头、地震和CEMP(连续电磁剖面法)勘探资料揭示的库车坳陷-南天山盆山过渡带构造变形特征难以用经典的“A型俯冲”冲断褶皱楔变形模型来解释,因而文中提出一种“分层变形、垂向叠置”的“非俯冲”收缩构造解释模型。所谓分层变形是指受古近系膏盐岩层和侏罗系含煤地层等软弱岩层分隔,不同深度的岩层发育不同的收缩变形样式;所谓垂向叠置是指不同层次的强变形带在垂向上叠置,不存在区域性大位移的拆离断层。位于盐岩层之上的新生界以滑脱褶皱变形为主,而盐下层的中生界沉积层及盆地基底则以收缩断裂变形为主。浅部的滑脱褶皱表现出紧闭背斜和宽缓向斜组合,背斜具有不对称形态,其核部在古近系盐岩层或侏罗系含煤地层中滑脱,可在陡翼发育破冲断层或缓翼发育顺层滑脱逆冲断层。深层断裂变形以向山脉倾斜的高角度基底卷入逆冲断层为主干断层,断层上盘形成冲断隆起,次级断层相对较少,下盘则发育一系列同向倾斜的次级逆冲断层构成楔状叠瓦冲断构造。深层断层向上延伸在古近系盐岩层中尖灭,部分次级断层向下延伸并在侏罗系含煤地层中或盆地基底面滑脱,但是主干逆冲断层高角度切入基底,向上则对应于浅层背斜的核部。基底卷入的高角度主干逆冲断层可能利用了先存正断层发生反转位移,并成为控制局部构造变形的主要构造要素。天山上升引起的垂直剪切作用是导致库车坳陷-南天山盆山过渡带发育高角度逆冲断层或促成先存正断层的反转的可能原因。     

Vector analysis of fault bends and intersecting faults

An analogy is drawn between intersecting faults or shear zones and triple junctions of lithospheric plates. Vector analysis shows that fault intersections are always unstable for rigid fault blocks but can be stabilized by the presence of zones of kinking or volume change within the fault blocks.The method allows rapid assessment of the likely location and orientation of wall-rock strains for any fault geometry and should be used to test kinematic models erected to account for field data.     

High temperature fracturing and ductile deformation during cooling of a pluton: The Lake Edison granodiorite (Sierra Nevada batholith,California)

In the Bear Creek area of the Sierra Nevada batholith, California, the high temperature postmagmatic deformation structures of the Lake Edison granodiorite include steeply-dipping orthogneiss foliations, joints, and ductile shear zones that nucleated on joints and leucocratic dykes. Exploitation of segmented joints resulted in sharply bounded, thin shear zones and in large slip gradients near the shear zone tips causing the deformation of the host rock at contractional domains. The orthogneiss foliation intensifies towards the contact with the younger Mono Creek granite and locally defines the dextral Rosy Finch Shear Zone (RFSZ), a major kilometre-wide zone crosscutting the pluton contacts. Joints predominantly strike at N70–90°E over most of the Lake Edison pluton and are exploited as sinistral shear zones, both within and outside the RFSZ. In a narrow (∼250 m thick) zone at the contact with the younger Mono Creek granite, within the RFSZ, the Lake Edison granodiorite includes different sets of dextral and sinistral shear zones/joints (the latter corresponding to the set that dominates over the rest of the Lake Edison pluton). These shear zones/joints potentially fit with a composite Y–R–R′ shear fracture pattern associated with the RFSZ, or with a pattern consisting of Y–R-shear fractures and rotated T′ mode I extensional fractures. The mineral assemblage of shear zones, and the microstructure and texture of quartz mylonites indicate that ductile deformation occurred above 500 °C. Joints and ductile shearing alternated and developed coevally. The existing kinematic models do not fully capture the structural complexity of the area or the spatial distribution of the deformation and magmatic structures. Future models should account more completely for the character of ductile and brittle deformation as these plutons were emplaced and cooled.     

Origin and tectonic interpretation of multiple fault patterns

It is shown that in two-dimensional and three-dimensional deformation accommodated by fracture, the symmetry of the fault patterns is an intrinsic attribute because it reflects the symmetry of either stress or strain tensors. The deformation accommodated by sliding along pre-existing planes, when there is kinematic interaction between that planes, forms multiple fault pattern and multiple slickenline sets during a single deformation event. These fault patterns have no restrictions with respect to symmetry, number of fault sets or fault orientation.

The kinematic analysis developed here shows that an interacting system is formed by two cross cutting faults and three slickenlines. One slickenline must be parallel to the intersection line between the planes. Also, it is demonstrated that the slickenlines generally do not correspond to the shear stress solution on the planes. Thus, the interaction between planes does not satisfy the assumption of parallelism between shear stress and slip vector. We conclude that the inversion methods to calculate paleostress tensors can lead to erroneous interpretations in structurally complex zones with many pre-existing planes of weakness.

We propose four possibilities to form multiple fault patterns: (1) two or more events of faulting obeying Coulomb's law with a change of orientation of the principal stresses in each event; (2) reactivation of non-interacting planes according to the Bott (1959) model; (3) one three-dimensional strain event that obeys the “Slip Model”; this mechanism will form an orthorhombic four-fault pattern and two slickenline sets in a single strain event; and (4) one or more events obeying the interacting block model proposed here, with or without rotation of the principal stresses. We propose the last origin as the most common in continental regions.     

谈调整构造

调整构造是伸展型沉积盆地和造山带中普遍存在的构造,它与走向构造一起,控制了沉积盆地或造山带的基本轮廓与内部结构。调整构造横切走向构造,并与之共同控盆、控岩、控矿,并间隔开两侧不同的构造样式。它以长时期、多阶段活动,具有高渗透性为主要特征,是控制矿带展布与矿床就位的重要构造,也是固定成矿预测区与找矿靶区的重要依据之一,本文以鲁西、中亚及乌拉山-大青山地区、兰坪─思茅盆地区及右江盆地区为例,论述了调整构造的基本特征及控矿作用。     

Stochastic Structural Modeling

A consistent stochastic model for faults and horizons is described. The faults are represented as a parametric invertible deformation operator. The faults may truncate each other. The horizons are modeled as correlated Gaussian fields and are represented in a grid. Petrophysical variables may be modeled in a reservoir before faulting in order to describe the juxtaposition effect of the faulting. It is possible to condition the realization on petrophysics, horizons, and fault plane observations in wells in addition to seismic data. The transmissibility in the fault plane may also be included in the model. Four different methods to integrate the fault and horizon models in a common model is described. The method is illustrated on an example from a real petroleum field with 18 interpreted faults that are handled stochastically.     

Sequential growth of deformation bands in carbonate grainstones in the hangingwall of an active growth fault: Implications for deformation mechanisms in different tectonic regimes

Deformation bands in porous sandstones have been extensively studied for four decades, whereas comparatively less is known about deformation bands in porous carbonate rocks, particularly in extensional settings. Here, we investigate porous grainstones of the Globigerina Limestone Formation in Malta, which contain several types of deformation bands in the hangingwall of the Maghlaq Fault: (i) bed-parallel pure compaction bands (PCB); (ii) pressure solution-dominated compactive shear bands (SCSB) and iii) cataclasis-dominated compactive shear bands (CCSB). Geometric and kinematic analyses show that the bands formed sequentially in the hangingwall of the evolving Maghlaq growth fault. PCBs formed first due to fault-controlled subsidence and vertical loading; a (semi-)tectonic control on PCB formation is thus documented for the first time in an extensional setting. Pressure solution (dominating SCSBs) and cataclasis (dominating CCSBs) appear to have operated separately, and not in concert. Our findings therefore suggest that, in some carbonate rocks, cataclasis within deformation bands may develop irrespective of whether pressure solution processes are involved. We suggest this may be related to stress state, and that whereas pressure solution is a significant facilitator of grain size reduction in contractional settings, grain size reduction within deformation bands in extensional settings is less dependent on pressure solution processes.