Rigid-body translation of faulted blocks along non-planar fault surfaces leads to creation of voids (Figs. 13.1a, b). As noted earlier, large voids cannot be sustained in the crust. In order for the two faulted blocks across a non-planar fault surface to remain in tight contact with each other, there must be distortions within at least one of the fault blocks. Layered rocks may develop folds when they slip past a bend on a faulted surface (Figs. 13.1c, d). The fold geometry is controlled by the shape of the fault. These folds are called fault-related folds because folding is a consequence of faulting. Such folds are common in deformed sedimentary basins in both compressional and extensional tectonic settings. The emphasis here is on thrust-related folds because they have been described more frequently from fold-thrust belts.
Fracture
gap
(a) (b) gap
(c) (d)
Figure 13.1. Compatibility problem arising out of a rigid-body translation of hangingwall block along a fault with a sharp bend. (a) Incipient fracture with a sharp bend. (b) Gaps open up due to rigid-body translation of hangingwall block. (c, d) A kink band develops and fills up the gaps. The geometry of the kink band is controlled by the shape of the fault. Note that the gap above the footwall on the left side of (d) is yet to be filled up.
Since we do not understand mechanics in sufficient detail as yet, fault-related folds are usually modelled kinematically and the geometric consequences are evaluated
against naturally occurring folds and related structures. "Kinematics" is a branch of mechanics that treats motion in an abstract framework, without reference to force and mass. Since the publication of a classic paper by Suppe (1983), a number of kinematically valid related folding models have become available. However, fault-bend folding, fault-propagation folding and detachment folding may be considered as end-member models and they will be described in detail in this section.
13.1. Assumptions
For the purpose of kinematic modelling of fault-related folds several reasonable assumptions (or boundary conditions) must be made. This is a legitimate exercise for any kind of modelling.
• Fault shape: Faults are taken to have sharp bends leading to “ideal” stair-case trajectory although fault bends may not be as sharp as bends in ideal stair-case trajectories. Flat-ramp trajectories of thrust faults have approximately stair-case geometry. The fault bend controls the location and initiation of axial surfaces of fault-related folds.
• Fold shape: Folds are assumed to have kink fold geometry. Straight limbs and sharp hinges with infinite curvature of kink folds make the model calculations easier and simple. This is not a bad assumption because the folds in deformed sedimentary terrains usually have straighter limbs and hinges of small areal extent that approximate kink-fold geometry. The assumption of kink fold geometry does not introduce large error so long as axial surfaces and dip panels can be unambiguously determined.
• Layer thickness: Layer thickness, bed length and cross sectional area are assumed to remain constant during folding. In some models thickness of limbs are allowed to change during folding.
• Deformation: Plane strain is assumed, i.e., the material points are not allowed to move in and out of section plane. Deformation is essentially accomplished by slip parallel to bedding with or without simple shear perpendicular to bedding.
Rocks do not undergo any internal deformation, i.e., deformation is constant volume.
13.2 Kinematics of kink folds
Kink folding with constant layer thickness is commonly accomplished by flexural-slip mechanism wherein layers flexural-slip past each other (Figs. 13.2, 13.3). The type of layer-parallel slip in kink folds developed through layer-layer-parallel compression (i.e., buckling;
Fig. 13.2) is different from those developed due to faulting (Fig. 13.3). In buckling, the sense of slip on two limbs are opposite in the two limbs and amount of slip decreases from a high value near inflexion surface to zero at the axial surface Fig. (13.2). Material points cannot move past the axial surface.
Axial surface
(a) (b)
dextrally
sheared vein sinistrally sheared vein
Figure 13.2. Flexural-slip due to layer-parallel compression. Sense of shear on the two limbs is opposite to each other. The amount of slip (i.e. shear strain) decreases to zero at the hinge. Consequently, the material points cannot pass through the axial surfaces.
Any pre-existing vein will be displaced on the limbs and shear strain will be positive and negative in adjacent limbs (Fig. 13.2b). Further, sense of shear can be used to locate the hinge of the fold. The location and orientation of axial surfaces in fault-related folds are controlled by bends on the fault surface (Fig. 13.3). Sense of shear displacement will be same on both the limbs and material points can move past axial surfaces. Any pre-existing vein will show same sense shear displacement everywhere (Fig. 13.3c). Ramp portions will always have shear but the flat portions may or may not
have shear strain. In either case, if the layers across the axial surface maintain constant layer thickness, the axial plane must bisect the interlimb angle.
ψ ψ ψ' ψ
pre-deformation position post-deformation
position
material point
(a) (b)
(c)
sinistrally sheared vein
Figure 13.3. Flexural-slip during fault-related folding. The material points can roll through axial surfaces (a, b). (a) Shear strain is set up on the ramp part although there is shear on the flat part. (b) Shear strain in the ramp part is different from shear strain on the flat part. (c) Sense of shear displacements on the two limbs of the kink fold is same, as given by sheared veins.
13.3 Fault-bend folding
In the model of fault-bend folding (Suppe 1983), a fracture with a staircase or flat-ramp-flat trajectory forms rapidly followed by movement of one or both the fault blocks. If the rocks are layered they may fold in response to riding over a bend in the fault; the folds thus formed are called fault-bend folds. If we move the hangingwall keeping the footwall fixed, a flat-crested anticline forms over the ramp and the fold is called a ramp anticline (Figure 13.4). Names of different parts of ramp anticline and the angular parameters used for kinematic modelling of fault-bend folding are shown in Fig. 13.4.
Progressive development of a fault-bend fold (FBF) caused by a simple step in décollement with folding confined to the hangingwall block is shown in Fig. 13.5 (Suppe 1983). At the time of initiation of folding two axial planes B and B’ form at the
lower bend Y and two axial planes A and A’ form at the upper bend X. With continued slip, the axial plane B’ climbs up the ramp and axial plane A’ moves along the upper flat. The material points roll through axial planes A and B. The axial planes A and B do not move. Since the footwall is fixed and only hangingwall moves, we can say that axial planes A and B are attached to the footwall and axial planes A’ and B’ are attached to the hangingwall. As the axial planes B’ climbs up the ramp, the fold amplitude increases but the width of the flat crest is reduced. The width of the two kink bands AA’ and BB’ also increases with increasing slip. When Y’ reaches X (upper bend), the axial plane B’ gets attached to the footwall and stops moving. At the same instant, the axial plane A is transferred to the hangingwall and starts moving along the upper flat. The ramp anticline stops growing in amplitude but width of the flat crest keeps increasing with continued slip.
trailing
Figure 13.4. Different parts of and angular parameters in a ramp anticline. θ - initial cut-off angle, β - final cut-off angle, φ - change in the dip of fault (fault shape), γ - half of interlimb angle (Fold shape), δ - change in dip across axial surface.
Suppe (1983) recognized several angular parameters, which can be used to describe the fault and fold geometry (Fig. 13.4): change in dip of fault (φ), axial angle (i.e. half-interlimb angle) of fold (γ), initial cut-off angle (θ), final cut-off angle (β), and change in dip across axial surface (δ = 180° - 2γ). If the lower flat is parallel to bedding then θ is also the step-up angle. The angular parameters φ and γ represent fault and fold shapes respectively. For a simple step from one décollement to another (i.e., θ = φ), γ is related to θ by the following equation:
⎥ ⎦
Figure 13.5. Progressive development of fault-bend fold (after Suppe 1983)
Suppe (1983) provides a graph (Fig. 13.6), which is a pictorial representation of eqs.
13.1–13.3. The graph allows a quick analysis of possible range of solutions to a given