Growth trishear model and its application to the Gilbertown graben system, southwest Alabama

Fault-propagation folding associated with an upward propagating fault in the Gilbertown graben system is revealed by well-based 3-D subsurface mapping and dipmeter analysis. The fold is developed in the Selma chalk, which is an oil reservoir along the southern margin of the graben. Area-depth-strain analysis suggests that the Cretaceous strata were growth units, the Jurassic strata were pregrowth units, and the graben system is detached in the Louann Salt.The growth trishear model has been applied in this paper to study the evolution and kinematics of extensional fault-propagation folding. Models indicate that the propagation to slip (p/s) ratio of the underlying fault plays an important role in governing the geometry of the resulting extensional fault-propagation fold. With a greater p/s ratio, the fold is more localized in the vicinity of the propagating fault. The extensional fault-propagation fold in the Gilbertown graben is modeled by both a compactional and a non-compactional growth trishear model. Both models predict a similar geometry of the extensional fault-propagation fold. The trishear model with compaction best predicts the fold geometry.     

The glaciotectonic deformation of Quaternary sediments by fault-propagation folding

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

断层相关褶皱的三维构造几何学分析:以川西三维地震工区为例

现有的断层相关褶皱理论均基于平衡剖面原理而建立的二维几何学模型。所谓的假三维模型则是通过一系列的二维剖面复合而成的,真正意义上的三维断层相关褶皱理论尚未确立,仍然处于探索阶段。本文采用Trishear 4.0和GoCad软件,分别构建一系列不同位移量的断层转折褶皱和三剪断层传播褶皱的二维正演剖面,将这些正演剖面按照一定的线性位移梯度平行排列,从而建立起断层转折褶皱和三剪断层传播褶皱的假三维理论模型并加以分析和讨论。进而选取川西南盆地中三维地震勘探所覆盖的邛西断层转折褶皱和盐井沟断层传播褶皱,作为真三维实际解释模型的两个实例。研究表明,邛西背斜是一个典型的剪切断层转折褶皱,盐井沟背斜是一个典型的三剪断层传播褶皱;断层相关褶皱的假三维理论模型与实际解释模型的对比分析,可以看出沿背斜走向的位移梯度是控制三维构造几何学特征的基本因素,然而自然界断层面几何学的复杂多变以及岩层力学性质的各向异性,是造成断层相关褶皱真三维理论模型难以建立的主要原因。     

Pseudo 3-D modeling of trishear fault-propagation folding

Basement structures, to which trishear fault-propagation models have most successfully been applied, are commonly three-dimensional folds formed at the tip-line of a fault. We present here a ‘pseudo-3D’ trishear model in which various parameters are permitted to vary along strike and oblique-slip can be modeled. These variations may be combined in an infinite number of ways, facilitating the simulation of many real structures. A thrust changing from blind to emergent can be produced by a change in the slip or propagation-to-slip (P/S) along strike. Folds with forelimbs changing from overturned to upright along strike can be modeled either by changing the slip, P/S or trishear angle. Also some minor folds perpendicular or oblique to the main structure can result from changes in the trishear angle or fault angle along the strike. Models including growth strata show that it is practically impossible to distinguish between growth and pre-growth strata using the map patterns. As a field test, we have modeled the oblique slip East Kaibab monocline, demonstrating a good fit between the field observations and model predictions.     

Experimental (clay) models of inversion structures

Experimental modeling is used to study the geometry and evolution of inversion structures. Two main types of inversion structures are analyzed:

1. (1) structures formed by fault-propagation folding; and

2. (2) structures formed by fault-bend folding on listric faults.

Fault-propagation inversion structures initially develop as broad drape folds with possible fault breakthrough during an early extensional phase. Syn-extensional strata deposited in the hanging wall typically thicken away from the fault. Compressional reactivation results in reversal of slip on the master and secondary faults, their rotation to shallower dips, and the development of a compressional fault-propagation fold. Key features of the fault-propagation fold are basinward thickening of syn-extensional units and resulting steep dips of the front limb of the structure. Fault-bend inversion structures initiate as rollover folds within extensional half-graben. Deformation is primarily localized along a system of antithetic faults. Syn-extensional strata typically thicken across the fault but also thin basinward away from the fault. During compression, the extensional rollover folds are folded into compressional fault-bend folds. Key features of this structure are thinning of syn-extensional units into the basin. Inversion of more symmetric graben results in a doubly-convex geometry of syn-extensional units. These observations of bed geometry and thickness provide predictive models for interpreting the geometries of inversion structures in areas of poor data quality.     

伸展断层相关褶皱的几何学分析及其在车镇凹陷中的应用

本文总结了伸展断层相关褶皱的发育类型,主要包括伸展断层传播褶皱与伸展断层转折褶皱(也叫断弯褶皱)等.伸展断层传播褶皱多形成在较陡的正断层之上,正断层向上传播使断层顶部地层弯曲,进而形成一个伸展的断层传播褶皱,其发育模式与三剪变形发育模式一致.车镇凹陷是渤海湾盆地南部一个典型的中新生代半地堑盆地.本文通过对横穿车镇凹陷的...     

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.     

Geometry and architecture of faults in a syn-rift normal fault array: The Nukhul half-graben, Suez rift, Egypt

The geometry and architecture of a well exposed syn-rift normal fault array in the Suez rift is examined. At pre-rift level, the Nukhul fault consists of a single zone of intense deformation up to 10 m wide, with a significant monocline in the hanging wall and much more limited folding in the footwall. At syn-rift level, the fault zone is characterised by a single discrete fault zone less than 2 m wide, with damage zone faults up to approximately 200 m into the hanging wall, and with no significant monocline developed. The evolution of the fault from a buried structure with associated fault-propagation folding, to a surface-breaking structure with associated surface faulting, has led to enhanced bedding-parallel slip at lower levels that is absent at higher levels. Strain is enhanced at breached relay ramps and bends inherited from pre-existing structures that were reactivated during rifting. Damage zone faults observed within the pre-rift show ramp-flat geometries associated with contrast in competency of the layers cut and commonly contain zones of scaly shale or clay smear. Damage zone faults within the syn-rift are commonly very straight, and may be discrete fault planes with no visible fault rock at the scale of observation, or contain relatively thin and simple zones of scaly shale or gouge. The geometric and architectural evolution of the fault array is interpreted to be the result of (i) the evolution from distributed trishear deformation during upward propagation of buried fault tips to surface faulting after faults breach the surface; (ii) differences in deformation response between lithified pre-rift units that display high competence contrasts during deformation, and unlithified syn-rift units that display low competence contrasts during deformation, and; (iii) the history of segmentation, growth and linkage of the faults that make up the fault array. This has important implications for fluid flow in fault zones.     

Propagation history of the Osaka-wan blind thrust,Japan, from trishear modeling

Mapping the nucleation and 3D fault tip growth of the active Osaka-wan blind thrust provides an opportunity to asses how reactivated thrusts build slip from preexisting faults and the threat they pose as sources of large earthquakes. Analysis of folded growth strata, based on 2D trishear inverse modeling allows a range of best-fit models of the evolution of slip and propagation of the fault to be defined. The depth of the fault tip at 1200 ka varies between ∼1.5–4.5 km, suggesting the fault grew upward from high in the crust, and that it is reactivated. From its onset at ∼1500 ka, the fault grew rapidly along strike in ∼300 ky, and upwards with a P/S ratio of 2.5–3.0, but variable fault slip in space and time. Shallower depths of the fault tip at initiation and thinner basin fill correlates with slower propagation with time, contradicting models that argue for sediments as inhibitors of fault growth. Results also suggest the displacement profile of the currently active thrust is offset from its predecessor, assuming shallower depths to the original fault correlate with greater displacement in its prior history. These results suggest reactivated faults may accrue slip differently than newly developed ones, based on the history of upward fault propagation.     

Effect of initial fault geometry on the development of fixed-hinge, fault-propagation folds

This paper describes how a model of fixed-hinge, basement-involved, fault-propagation folds may be adapted to apply to thin-skinned thrust faults to generate footwall synclines. Fixed-hinge, fault-propagation folding assumes that the fold-axial surfaces diverge upwards, fold hinges are fixed in the rock, the fault propagated through the forelimb, thickness changes occur in the forelimb and the forelimb progressively rotates with increasing displacement on the underlying fault. The original model for fixed-hinge, fault-propagation folds was developed for the case of a planar fault in basement with a tip line that was at the interface between basement and the overlying sedimentary cover rocks. The two geometries applicable to thin-skinned thrusts are for the cases where a fixed-hinge fault-propagation fold develops above an initial bedding-parallel detachment, and an initial fault ramp of constant dip which flattens down-dip into a bedding-parallel detachment.     

川西盐井沟断层传播褶皱的三维构造建模与磁组构分析

当前断层相关褶皱研究的发展方向是从二维向三维的转换。文中基于Arcgis、Discovery以及Gocad等三维软件平台,对川西盐井沟地区地震资料进行精细的解析,得出盐井沟背斜是一个典型的三剪断层传播褶皱,并建立了它的三维模型。同时考虑到单纯符合几何约束的构造解释普遍存在着多解性和不确定性,结合几何学的三维建模和动力学的有限应变分析研究断层相关褶皱。在川西盐井沟地区18个采样点钻取了184块定向岩心样品,通过磁组构的分析结果发现,盐井沟地区的磁组构基本上都是弱应变的初始变形组构,褶皱前翼应变强度比后翼略强。断层传播褶皱三剪带是有限应变最为集中的区域,在模型预测的三剪带内,磁组构反映的有限应变也较为强烈。磁组构所指示的构造应力场大致为NW-SE向挤压缩短,与断层相关褶皱的几何学与运动学模型的预测相一致。     

Three-dimensional Evolutionary Models of the Qiongxi Structures, Southwestern Sichuan Basin, China: Evidence from Seismic Interpretation and Geomorphology

Fold terminations are key features in the study of compressional fault-related folds. Such terminations could be due to loss of displacement on the thrust fault or/and forming a lateral or oblique ramp. Thus, high-quality seismic data would help unambiguously define which mechanism should be responsible for the termination of a given fault-related fold. The Qiongxi and Qiongxinan structures in the Sichuan Basin, China are examples of natural fault-propagation folds that possess a northern termination and a structural saddle between them. The folds/fault geometry and along-strike displacement variations are constrained by the industry 3-D seismic volume. We interpret that the plunge of the fold near the northern termination and the structural saddle are due to the loss of displacement along strike. The fault geometry associated with the northern termination changes from a flat-ramp at the crest of the Qiongxinan structure, where displacement is the greatest, to simply a ramp near the northern tip of the Qiongxi structure, without forming a lateral or oblique ramp. In this study, we also use the drainage pattern, embryonic structure preserved in the crest of the Qiongxinan structure and the assumption that displacement along a fault is proportional to the duration of thrusting to propose a model for the lateral propagation of the Qiongxinan and Qiongxi structures. Specifically, we suggest that the structure first initiated as an isolated fault ramp within brittle units. With increased shortening, the fault grows to link with lower detachments in weaker shale units to create a hybridized fault-propagation fold. Our model suggests a possible explanation for the lateral propagation history of the Qiongxinan and Qiongxi structures, and also provides an alternative approach to confirming the activity of the previous Pingluoba structure in the southwestern Sichuan Basin in the late Cenozoic.     

Constraining slip rates and spacings for active normal faults

Numerous observations of extensional provinces indicate that neighbouring faults commonly slip at different rates and, moreover, may be active over different time intervals. These published observations include variations in slip rate measured along-strike of a fault array or fault zone, as well as significant across-strike differences in the timing and rates of movement on faults that have a similar orientation with respect to the regional stress field. Here we review published examples from the western USA, the North Sea, and central Greece, and present new data from the Italian Apennines that support the idea that such variations are systematic and thus to some extent predictable. The basis for the prediction is that: (1) the way in which a fault grows is fundamentally controlled by the ratio of maximum displacement to length, and (2) the regional strain rate must remain approximately constant through time. We show how data on fault lengths and displacements can be used to model the observed patterns of long-term slip rate where measured values are sparse. Specifically, we estimate the magnitude of spatial variation in slip rate along-strike and relate it to the across-strike spacing between active faults.     

Segment,Linkage,and Extensional Fault-Related Fold in Western Liaodong Bay Subbasin,Northeastern Bohai Sea,China

The western Liaodong (辽东) Bay subbasin displays examples of segment,linkage of extensional fault,and fault-related folds.The Liaoxi (辽西) extensional fault system consists of a series of NNE- and NE-trending segments that were linked through relay ramps.The fault hanging walls are characterized by a series of en echelon synclines with axial traces sub-parallel to the faults.The synclines are doubly plunging located on the hanging wall of normal faults,with the strata dip sub-parallel to the fault.These folds result from along-strike displacement variations of the individual fault segments,as well as from extensional fault-related folding.In the study area,the synclines are separated by transverse intra-basin highs and relay ramps that formed where segment linkage occurred.These hanging wall synclines and their relation to fault displacement variations indicate that they are formed by extensional fault-related fold.     

Displacement transfer from fault-bend to fault-propagation fold geometry: An example from the Himalayan thrust front

The leading edge of the ENE-trending Himalayan thrust front in Pakistan exhibits along-strike changes in deformational style, ranging from fault-bend to fault-propagation folds. Although the structural geometry is very gently deformed throughout the Salt Range, it becomes progressively more complex to the east as the leading edge of the emergent Salt Range Thrust becomes blind. Surface geology, seismic reflection, petroleum well, and chronostratigraphic data are synthesized to produce a 3-D kinematic model that reconciles the contrasting structural geometries along this part of the Himalayan thrust front. We propose a model whereby displacement was transferred, across a newly-identified lateral ramp, from a fault-bend fold in the west to fault-propagation folds in the east and comparable shortening was synchronously accommodated by two fundamentally different mechanisms: translation vs. telescoping. However, substantially different shortening distribution patterns within these structurally contrasting segments require a tear fault, which later is reactivated as a thrust fault. The present geometry of this S-shaped displacement transfer zone is a combined result of the NW–SE compression of the lateral culmination wall and associated tear fault, and their subsequent modification due to mobilization of underlying ductile salt.     

Inverse trishear modeling of bedding dip data using Markov chain Monte Carlo methods

We present a method for fitting trishear models to surface profile data, by restoring bedding dip data and inverting for model parameters using a Markov chain Monte Carlo method. Trishear is a widely-used kinematic model for fault-propagation folds. It lacks an analytic solution, but a variety of data inversion techniques can be used to fit trishear models to data. Where the geometry of an entire folded bed is known, models can be tested by restoring the bed to its pre-folding orientation. When data include bedding attitudes, however, previous approaches have relied on computationally-intensive forward modeling. This paper presents an equation for the rate of change of dip in the trishear zone, which can be used to restore dips directly to their pre-folding values. The resulting error can be used to calculate a probability for each model, which allows solution by Markov chain Monte Carlo methods and inversion of datasets that combine dips and contact locations. These methods are tested using synthetic and real datasets. Results are used to approximate multimodal probability density functions and to estimate uncertainty in model parameters. The relative value of dips and contacts in constraining parameters and the effects of uncertainty in the data are investigated.     

伸展断层传播褶皱研究现状

伸展断层传播褶皱是伸展环境中重要的一种褶皱类型,是由于隐伏基底正断层活化向上传播而引起上覆地层发生的弯曲。多年的研究认为这是一种向上变宽的三角形分布式剪切调节过程,断层的上端点限定了三角剪切区的顶点。运用三角剪切的速度模型很好地拟合和描述变形区内物质的运动,三角剪切区的顶角和断层向上传播/断层向下滑移比值（p /s）是控制伸展断层传播褶皱变形过程和几何形态的重要的运动学参数。伸展断层传播褶皱的发育过程可以根据断层是否切穿上覆盖层而划分为两个阶段。在沉积过程中,伸展断层传播褶皱作用对生长地层的几何形态和叠置样式有较强的控制作用。通过对保留的生长地层几何形态的分析,可以确定隐伏基底断层的初始破裂点和断层传播量,并最终重建伸展断层传播褶皱的变形过程。     

Trishear for curved faults

Fault-propagation folds form an important trapping element in both onshore and offshore fold-thrust belts, and as such benefit from reliable interpretation. Building an accurate geologic interpretation of such structures requires palinspastic restorations, which are made more challenging by the interplay between folding and faulting. Trishear (Erslev, 1991; Allmendinger, 1998) is a useful tool to unravel this relationship kinematically, but is limited by a restriction to planar fault geometries, or at least planar fault segments. Here, new methods are presented for trishear along continuously curved reverse faults defining a flat–ramp transition. In these methods, rotation of the hanging wall above a curved fault is coupled to translation along a horizontal detachment. Including hanging wall rotation allows for investigation of structures with progressive backlimb rotation. Application of the new algorithms are shown for two fault-propagation fold structures: the Turner Valley Anticline in Southwestern Alberta, and the Alpha Structure in the Niger Delta.     

Main Frontal thrust deformation and topographic growth of the Mohand Range,northwest Himalaya

The Main Frontal thrust (MFT) uplifts the Himalayan topographic front. Deciphering MFT deformation kinematics is crucial for understanding how the orogen accommodates continuing continental collision and assessing associated hazards. Here, we (a) detail newly discovered fault-zone exposures along the MFT at the Mohand Range front in northwestern India and (b) apply contemporary fault zone theory to show that the MFT is an emergent fault with a well-developed fault zone overlain by uplifted Quaternary gravels over a horizontal length of ∼700 m. Northward from the front, the fault zone grades from a central, gouge-dominated core to a hanging-wall, rock-dominated damage zone. We observed incohesive, non-foliated breccia, fault gouge, and brittle deformation microstructures within the fractured country rocks (Middle Siwaliks) and outcrop scale, non-plunging folds in the proximal hanging wall. We interpret these observations to suggest that (1) elastico-frictional (brittle) deformation processes operated in the fault zone at near surface (∼1–5 km depth) conditions and (2) the folds formed first at the propagating MFT fault tip, then were subsequently dismembered by the fault itself. Thus, we interpret the Mohand Range as a fault-propagation fold driven by an emergent MFT in contrast to the consensus view that it is a fault-bend fold. A fault-propagation fold model is more consistent with these new observations, the modern range-scale topography, and existing erosion estimates. To further evaluate our proposed structural model, we used a Boundary Element Method-based dislocation model to simulate topographic growth from excess slip at a propagating fault tip. Results show that the frontal topography could have evolved by slip along a (a) near-surface fault plane consistent with the present-day MFT location, or (b) blind MFT at ∼3 km depth farther north near the drainage divide. Comparing modelled vs. measured high resolution (∼16 cm) topographic profiles for each case provides permissible end-member scenarios of an either dynamically-evolving, high erosion, northward-migrating frontal scarp or a static, low, and symmetric, MHT-related fold, respectively. Our integrated approach is expected to deliver an improved understanding of coupled fault-generated deformation and topographic growth that may be applied more broadly across the entire Himalayan front.     

High precision analysis of an embryonic extensional fault-related fold using 3D orthorectified virtual outcrops: The viewpoint importance in structural geology

Image-based 3D modeling has recently opened the way to the use of virtual outcrop models in geology. An intriguing application of this method involves the production of orthorectified images of outcrops using almost any user-defined point of view, so that photorealistic cross-sections suitable for numerous geological purposes and measurements can be easily generated. These purposes include the accurate quantitative analysis of fault-fold relationships starting from imperfectly oriented and partly inaccessible real outcrops. We applied the method of image-based 3D modeling and orthorectification to a case study from the northern Apennines, Italy, where an incipient extensional fault affecting well-layered limestones is exposed on a 10-m-high barely accessible cliff. Through a few simple steps, we constructed a high-quality image-based 3D model of the outcrop. In the model, we made a series of measurements including fault and bedding attitudes, which allowed us to derive the bedding-fault intersection direction. We then used this direction as viewpoint to obtain a distortion-free photorealistic cross-section, on which we measured bed dips and thicknesses as well as fault stratigraphic separations. These measurements allowed us to identify a slight difference (i.e. only 0.5°) between the hangingwall and footwall cutoff angles. We show that the hangingwall strain required to compensate the upward-decreasing displacement of the fault was accommodated by this 0.5° rotation (i.e. folding) and coeval 0.8% thickening of strata in the hangingwall relatively to footwall strata. This evidence is consistent with trishear fault-propagation folding. Our results emphasize the viewpoint importance in structural geology and therefore the potential of using orthorectified virtual outcrops.