Trishear Model Research Articles

Mechanical analysis of the geometry of forced-folds

A mechanical model of forced-folding, comprised of an anisotropic cover overlying displaced, rigid basement blocks, is used to investigate the influence of various parameters on theoretical fold form: shape and dip of basement fault, strength of basement-cover contact, and degree of anisotropy of the cover. We show that the degree of anisotropy in the cover largely influences the geometry of the forelimb of the forced-fold. Folds produced in isotropic cover display forelimbs that taper from large dip angles near the basement-cover contact to low dip angles at the ground surface. In contrast, dips in the forelimbs of folds in anisotropic cover are nearly uniform with depth. We show that the basement-cover contact and the shape of the basement fault largely influence the geometry of the backlimb. Backlimb rotation occurs in cover welded to the basement and in cover underlying curved basement faults. In addition, the kinematic features of the theoretical folds are compared with the fold geometry generated by parallel kink and trishear models. Folds in isotropic cover overlying straight basement faults closely resemble the fold forms produced by the trishear kinematic model while fold forms in anisotropic cover more closely resemble folds produced by parallel kink geometric constructions.

Mechanical models of trishear-like folds

Previous workers have formulated velocity descriptions of the trishear kinematic model of fault propagation-folds, which are inherently non-unique. We present two complete mechanical models of fault-related folding and assess the validity of the assumptions used in the assignment of velocities in the trishear description and to eliminate the untenable situation of an infinite number of possible solutions for velocity fields. The mechanical model of forced-folding, Forced Fold, based on viscous folding theory, is used to derive the velocity fields in an anisotropic sedimentary cover overlying faulted and displaced rigid basement blocks. The solution of displacements around a stress-free fault in an elastic body is used to model fault-arrest folds that form around a fault imbedded in a deformed medium. The results indicate that the velocity fields assumed in the trishear model more closely resemble the velocities derived in the mechanical Forced Fold model than the mechanical model of fault-arrest folding. The Forced Fold model produces a triangular region of concentrated deformation similar to the trishear region assumed in the kinematic models, while the deformation produced by the fault-arrest model is not concentrated within a triangular zone.

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.

Trishear kinematic model of fault-propagation folding and sequential development of minor structures; the Oupia Anticline (NE Pyrenees, France) case study

Abstract The Oupia anticline is a fault-propagation fold located at the northeastern tip of the Pyrenees. We show that this structure is suitably modelled using the trishear kinematic model rather than the self-similar kink-band model. In particular, the trishear model accounts well for the change in forelimb dip along strike as well as for sequential overall thickening and then thinning of the forelimb deduced from microtectonic analysis.

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.

Predicting the orientation of joints from fold shape: Results of pseudo–three-dimensional modeling and curvature analysis

We treat layers of sedimentary rock as elastic plates and predict the orientations of joints by assuming that they open parallel to the maximum instantaneous stretch of a layer. Because the direction of maximum instantaneous stretch is parallel to the maximum curvature of a surface, we hypothesize that joints will trend parallel to the minimum curvature of an elastically deformed layer. After constructing pseudo–three-dimensional trishear models of Laramide-style uplifts that grow self-similarly, we calculated the direction of minimum-curvature axes during the evolution of the fold. Our analysis of minimum-curvature axes in evolving folds suggests several important characteristics for fold-related joint sets: (1) joints that are neither parallel nor perpendicular to the fold axis may be induced by local fold-related strains; (2) at any time during folding, joint orientations may vary according to the structural position on a fold; (3) at any location on a fold, joint orientation may depend on when a joint forms during the evolution of the fold; and (4) joint patterns in trishear folds may vary with stratigraphic position. Natural folds that evolve along simple geometric pathways may develop fold-related joint sets, the orientation, dominance, abutting relationships, spacing, and continuity of which will vary systematically throughout the structure. This variation in joint-system architecture may reflect the history of fold growth.

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.

Numerical modeling of trishear fault propagation folding

In contrast to kink band migration modeling methods, trishear numerical models produce fault propagation folds with smooth profiles and rounded hinges. Modeled fold hinges tighten and converge downward, within a triangular zone of distributed deformation which is focused on the fault tip. Such features have been reported from field studies and are also seen in analogue models of compressional deformation. However, apart from its initial application to Laramide folds, little quantitative work has been undertaken on trishear fault propagation folding in other settings. In addition, no study has been undertaken into the growth strata which might be associated with such structures. This paper uses an equivalent velocity description of the geometric model of trishear, together with models of erosion and sedimentation, to investigate trishear fault propagation folding of both pregrowth and growth strata. The trishear model is generalized to include a variety of fault propagation to slip ratios and fault propagation from a flat decollement. The models show continuous rotation of the forelimb with the characteristic development of cumulative wedges within growth strata. When total slip on a structure is high, the model predicts overturned pregrowth and growth strata. During the initial stages of deformation, beds in the forelimb thicken but later thin when they become steep or overturned. The effect of variations in fault propagation to slip ratios on two‐dimensional finite strain in the models is assessed by the use of initially circular strain markers. High fault propagation to slip (p/s) ratios lead to narrow zones of high finite strain, while lower p/s ratios lead to more ductile deformation and broader zones of high strain. In all cases, hanging wall anticlines and footwall synclines originate as early ductile folds which are later cut by the propagating fault. Modeled structures are compared with natural examples.

Progressive evolution of a fault-related fold pair from growth strata geometries, Sant Llorenç de Morunys, SE Pyrenees

New structural-stratigraphical mapping constrains the three-dimensional kinematics and mechanisms of Eocene-Oligocene growth folding at Sant Llorenç de Morunys (NE Ebro basin, Spain). A 1 km wide sub-vertical panel of syntectonic alluvial gravels passes southwards via a highly asymmetrical growth fold-pair to shallowlydipping strata. The axial surface of the anticline comprises either continuous or en échelon segments while that of the syncline is concave and usually continuous. While converging upwards, the axial surfaces do not define growth triangles. Principal and subsidiary growth unconformities and thickness changes occur across both axial surfaces and the common limb. Dips within the common limb decrease up-stratigraphy and up-dip. Mesostructures indicate that internal deformation was ongoing during folding at all stratigraphical levels, and concentration of cleavage in the syncline indicates that this hinge was essentially fixed. Sequential restoration of three profiles shows that folds amplified principally by limb rotation but incorporated minor passive hinge migration. Particle movement vectors, generated by section restoration, are arcuate about a hinterland pinpoint. A new trishear model of fault propagation folding involving non-rigid limb rotation reproduces the rounded hinge forms, thickening geometries and limb dip variations observed. Simple kink band migration models (fixed axis and constant thickness theories) do not replicate these features.