Trishear Zone Research Articles

Geomechanical modeling of fault-propagation folds: A comparative analysis of finite-element and the trishear kinematic model

Fault-propagation folds are common structures within fold and thrust belts. The trishear kinematic model has been widely used to understand the kinematics and geometry of these folds, effectively reproducing various characteristics. However, the resulting geometry of natural prototypes may diverge from the predictions of the trishear model depending on the rheological properties involved in the deformation. In order to address this limitation, finite element viscoplastic numerical models were implemented. The analysis revealed that in models with a 15° fault angle, these simulations develop a mechanically weaker discontinuity, which is defined as the low viscosity zone (LVZ). The LVZ induces faulting and absorbs slip, causing deviations of velocity vectors from parallel alignment with the main reverse ramp. In models with fault angles set at 25° or 35°, the kinematic vectors of the hanging wall aligned parallel to the ramp, and a zone of progressive rotation of the velocity vectors was observed in the forelimb, resembling the theoretical trishear zone. In these scenarios, the resulting folds exhibited greater symmetry. However, in cover layers with a viscosity equal to 1020 Pa s, the forelimb exhibits the highest velocities, which is attributed to material flow toward the footwall.

Numerical investigation of the roles of gravel fabric on composite strata deformation induced by thrust faulting

In historical earthquakes, fault ruptures have caused significant ground deformation and infrastructure damage. Because the occurrences of earthquakes are hard to predict, it is critical to assess the area influenced by fault propagation for disaster resistance. Based on trench excavations in active fault zones, earthquake faults propagated through the composite strata with gravel deposits are common. However, the stratigraphy change of the overburden strata and the non-spherical granular particles of the gravel deposit are rarely considered in most case studies. This study proposes a procedure that utilizes digital image analysis and discrete element modeling to estimate the composite strata deformation induced by thrust faulting. The procedure is demonstrated through a series of small-scale sandbox modeling and a case study of the Chushan excavation site in Taiwan. The gravel fabric, including gravel volumetric content, aspect ratio and initial long-axis orientation, are considered in the parametric study as well as the configuration of the strata composition. Simulations show that fault propagation restricts in the overburden because the faulting-induced kinematic energy is mostly dissipated by clast rotation, resulting in a lower fault extended distance and a wider tri-shear zone. The rotation of the gravels shows good agreement with the range of the tri-shear zone, indicating that the long-axis orientations of gravels can be an indicator to interpret the faulting history. Overall, it is feasible to construct a reasonable numerical model for assessing fault rupture-composite strata interaction (FR-CSI) once the outcrop photo data are available. The proposed procedure is useful for efficient and reliable scenario modeling regarding earthquake hazard mitigation.

Strain modelling of extensional fault-propagation folds based on an improved non-linear trishear model: A numerical simulation analysis

This paper focuses on the strain modelling of extensional fault-propagation folds to reveal the effects of key factors on the strain accumulation and the relationship between the geometry and strain distribution of fault-related folds. A velocity-geometry-strain method is proposed for the analysis of the total strain and its accumulation process within the trishear zone of an extensional fault-propagation fold. This paper improves the non-linear trishear model proposed by Jin and Groshong (2006). Based on the improved model, the distribution of the strain rate within the trishear zone and the total strain are obtained. The numerical simulations of different parameters performed in this study indicate that the shape factor R, the total apical angle, and the P/S ratio control the final geometry and strain distribution of extensional fault-propagation folds. A small P/S ratio, a small apical angle, and an R value far greater or far smaller than 1 produce an asymmetric, narrow, and strongly deformed trishear zone. The velocity-geometry-strain analysis method is applied to two natural examples from Big Brushy Canyon in Texas and the northwestern Red Sea in Egypt. The strain distribution within the trishear zone is closely related to the geometry of the folds.

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.

Strain variation with progressive deformation in basement-involved trishear structures

Basement-involved structures associated with reverse, vertical and normal faults commonly involve non-parallel shear within a triangular deformation (trishear) zone located on the front limbs of the structures. Deformation within the trishear zone is characterized by shear gradients and an associated decrease in the dips of the beds in stratigraphically higher units. Geometric models suggest that the layer-parallel strain within the trishear zone depends on the type of fault (normal, reverse, or vertical), the dip and throw of the fault, the dip of the anticlinal or synclinal axial surfaces, and the distance of any unit above the initial tip of the trishear zone, located at the basement-sediment contact. At any given location, reverse faults typically show increasing layer parallel shortening, followed by decreasing layer parallel shortening and a transition to extension, with increasing throw. The transition from contraction to extension occurs at lower values of throw for stratigraphically lower units and also for faults with smaller dips. Vertical and normal faults exhibit increasing layer-parallel extension of all units with increasing throw, with larger extension for stratigraphically lower units. Experimental models suggest that the trishear zone can expand with increasing fault throw. The strain within the trishear zones is accommodated largely by secondary faults, which are rotated with progressive deformation. The strain variations in the experiments closely mimic those predicted by the geometric models for reverse, vertical, and normal faults.

Løvehovden fault and Billefjorden rift basin segmentation and development, Spitsbergen, Norway

AbstractThe Carboniferous Billefjorden rift basin is a well-known example of a suite of Carboniferous basins on the Barents Shelf and NE Greenland. The basin has a clastic, carbonate and evaporite fill with complex and disputed stratigraphic relationships, especially regarding the Ebbadalen and Minkinfjellet formations. Geometrically, the basin is considered a simple half-graben. A N–S-trending fault and monocline structure within the northern portion of the basin, the Løvehovden fault, has lithological and thickness differences across it within the Minkinfjellet and possibly Ebbadalen formations. The fault shows W-side-down movement, defining a sub-basin within the larger half-graben. Significant along-strike changes occur. Down-throw to the west is at least 150 metres and possibly 400 metres, as shown by across-fault thickness differences of Ebbadalen and/or Minkinfjellet formations. To the east of the fault, the contact between the Ebbadalen and Minkinfjellet formations is a disconformity with significant local relief, and is interpreted to represent exposure from footwall uplift, and associated near- or at-surface solution, producing basal stratiform breccias. A similar contact is not exposed west of the fault. Monoclinal deformation and thickening of the younger Wordiekammen Formation above and across the monocline constrain a later movement component. Kinematic data and the structural style clearly indicate the Løvehovden fault is a normal fault with associated tri-shear zone development, consistent with the regional Carboniferous rift setting. Earlier interpretations describe the Løvehovden fault and monocline as Tertiary contractional features. In contrast, our work advocates that they are an important architectural basin element, defining a sub-basin within the Billeforden Trough during Minkinfjellet Formation deposition, with insignificant, if any, Tertiary reactivation. The Løvehovden fault is aligned with and represents the southern termination of the Lemströmfjellet fault to the north. Thus, the Billefjorden basin changes from a narrow graben to a broader half-graben to the south. These along-strike changes have important implications for the stratigraphic architecture of the basin, and for palaeogeographic reconstructions. These results and application of 3-D models for extension related tri-shear zones may help inform interpretation of other Carboniferous basins on the Barents Shelf.

Three Dimension Construction and Magnetic Fabric Analysis of the Yanjinggou Fault-propagation Fold in Western Sichuan, China

Recently, there is a transition trend of the research on the fault-related fold from 2D to 3D. Based on ARCGIS, DISCOVERY and GOCAD software platform, we built a 3D geological model of the Yanjinggou anticline using 3D seismic data in the area. It was found that Yanjinggou anticline was a typical trishear fault-propagation fold. Because the structural interpretation of the 3D model only is of non-uniqueness and uncertainty due to geometric constraint, the finite strain analysis was also applied in the structural interpretation. 184 oriented samples have been drilled at 18 sampling sites in Yanjinggou, western Sichuan. AMS of these samples disclosed: (1) that most of the magnetic fabrics were the initial deformation fabric; (2) that deformation in the forelimb was relatively stronger than that in the rearlimb; and (3) that the finite strain was strong within the trishear zone of the fault-propagation fold, in accordance with demonstration in the 3D geometric model. The tectonic stress field indicated by the magnetic fabrics suggested a NW-SE compression and shortening, which was consistent with the prediction of the 3D geometric model.

An improvement of the too cold tongue in the tropical Pacific with the development of an ocean-wave-atmosphere coupled numerical model

The anisotropy of magnetic susceptibility (AMS) is a quick, effective and sensitive technique used to measure the weakly deformed sedimentary rocks, and also a reliable method to reveal the deforming mechanisms of fault-related folds. In Longmenshan front belt, a typical cross-section of fault-related folds is chosen to study the AMS. A total of 224 oriented specimens have been drilled at 23 different sampling sites which were distributed at the key structural positions of this structural section developed in the Xujiahe formation of the upper Triassic. Six elementary types of magnetic fabrics are recognized and established through this AMS study: 1) a sedimentary fabric; 2) an initial deformation fabric; 3) a pencil structure fabric; 4) a weak cleavage fabric; 5) a strong cleavage fabric; 6) a stretching lineation fabric. It has been found that most of magnetic fabrics are characterized by fabrics of weak deformation which belong to the pure-shear results of a pre-folding layer parallel shortening (LPS). In the fault-bend fold, almost all magnetic fabrics are the initial deformation fabrics of weak deformation, and denote that the deformation in the forelimb is stronger than that in the backlimb and no finite strain is shown in the footwall. While in the fault-propagation fold, finite strains are concentrated in the trishear zone where magnetic fabric results are approximately consistent with the estimated consequences of the kinematic model. The tectonic stress field indicated by the magnetic fabrics is basically the same along the whole structural section and shows a NW to SE compression and shortening which is accordant with the regional compressive stress field of the Longmenshan fold-thrust belt.

Trishear kinematic modeling of extensional fault-propagation folding

We present a new non-linear 2-D numerical trishear model that is capable of modeling both symmetrical and asymmetrical trishear zones and a strain prediction approach based on the velocity field within the trishear zone. A simple relationship exists between the shape factor ( r) of the velocity field, the hanging wall apical angle, and footwall apical angle. The implication of this relationship is that when dealing with a real deformed state cross-section, one can measure the hanging wall and footwall apical angles to determine the r value to specify the velocity field within the trishear zone for either the forward modeling or restoration. The new trishear model can accurately reproduce the geometry of two experimental clay models and an extensional fault-propagation fold from the Gulf of Suez. Predicted strain is greatest directly above the fault tip and decreases with distance from the fault tip, as in the experimental models. Greater strain occurs in the hanging wall because of the greater velocity gradient there, whereas the footwall is much less intensely deformed. Consequently, secondary faulting and fracturing, if present, should be better developed along the fault tip line or in the hanging wall. The orientation of fractures or minor faults can be predicted from the strain ellipses calculated from the trishear velocity field.

Paleoseismology of the Chelungpu Fault during the past 1900 years

The 1999 earthquake brought about 80-km-long surface ruptures along the Shihkang, Chelungpu, and Tajienshan Faults, central Taiwan. Several trenches have been excavated across the Chelungpu Fault of the middle segment. The surface ruptures display clear scarps ranging from 0.2 to 4 m high, showing a complex geomorphic pattern due to coseismic faulting and folding. In the study, measurement of the vertical offset or structural relief was taken with reference to the hanging wall beyond the trishear deformation zone. Therefore we suggest that, for the measurement of offset, we should disregard the trishear zone, and that structural relief on the hanging wall should be represented as a real vertical offset. The net slip is then calculated from the structural relief and dip angle of the thrust on a vertical plane along the slip direction. Through the excavation of a pineapple field across the Chelungpu Fault, we are able to provide evidence of at least four earthquake events for the past about 1900 years, including the 1999 earthquake. Furthermore, based on the radiocarbon dates and historical record, the timing of the penultimate event is bracketed to be between 430 and 150 years ago, and the average recurrence interval is less than 700 years. These data indicate that the average slip rate is about 8.7 mm/yr for the past 1900 years.

Velocity field for the trishear model

A general method for the derivation of velocity fields consistent with the basic kinematics of the trishear model of fault-propagation folding is given. We show that the fields can be written as explicit functions of position within the deformation zone. To demonstrate the approach, several different linear and non-linear velocity fields are derived and plotted. We show that the trishear zone need not be symmetric and that the trishear model produces 1/ r singular strain rates, consistent with results for cracks in elastic–plastic materials. A continuous formulation of heterogeneous trishear is also presented.

Inverse and forward numerical modeling of trishear fault‐propagation folds

Fault‐propagation folds commonly display footwall synclines as well as changes in stratigraphic thickness and dip on their forelimbs, features that cannot easily be explained by simple parallel kink fold kinematics. An alternative kinematic model, trishear, can explain these observations, as well as a variety of other features which have long intrigued structural geologists. Trishear has received little attention until recently, in part because it must be applied numerically rather than graphically. A new computer program has been developed to analyze trishear and hybrid trishear‐fault‐bend fold deformation. Trishear fold shape can vary considerably by changing the apical angle of the trishear zone and/or the propagation to slip ratio (P/S) during the evolution of the structure. Breakouts, anticlinal and synclinal ramps, and inversion structures can also be modeled, tracking the kinematics with growth strata. Strain within trishear zones can be used to predict fracture orientations throughout the structures as demonstrated by comparison with analog clay models. Also presented is a method for inverting data on real structures for a best fit trishear model by performing a grid search over a six‐parameter space (ramp angle, trishear apical angle, displacement, P/S, and X and Y positions of the fault tip line). The inversion is performed by restoring a key bed to a planar orientation by least squares regression. Because trishear provides a bulk kinematic description of a deforming zone, it is complementary to, rather than competing with, other kinematic models.