# TWISS & MOORES, Chapter 12, Kinematic Models of Folding

Deformation may generally be divided into two categories. During homogeneous deformation, straight and parallel lines remain straight and parallel; during inhomogeneous deformation this is not the case. More specific cases include simple shear, which is a two-dimensional deformation in which volume is conserved; and flattening, in which (in profile) one side is shortened and the other lengthened (this latter type may be called pure shear when homogeneous and when in profile area is conserved). Competence describes the resistance of a ductile material to deformation.

Flexural, passive-shear and volume-loss folding of a layer; homogeneous flattening

Class 1B fold geometry is common and may be explained by two models, collectively known as flexural folding. (Two types of folding subsumed by the models are: bending, which results from the application of two equal and opposite torques, that create the fold; and buckling, which results from the application of compressive stresses parallel to the layer.)

1. orthogonal flexure occurs when all lines perpendicular to the layer prior to folding remain perpendicular after folding; this is common of open folds found in competent layers
2. flexural shear (flexural flow) occurs when folding is accomplished by simple shear parallel to the layer

Passive-shear folding (= passive-flow folding, flow folding) typically occurs in layers of low competence and takes place by inhomogeneous simple shear; the fold axis and hinge are not related to the direction of shear, and the model permits no shortening normal to the shear planes. This results in class 2 (similar) folds.

Volume-loss folding is a process by which folds are created or amplified by the dissolution of particular zones of the folded layer; this process may also be called solution folding. Because the final form of the fold depends on where material is removed, this kinematic model does not produce a single resultant fold geometry (class). It may also produce the illusion that shearing has occurred, though none necessarily has.

When homogeneous flattening may be combined with the processes above to create new fold geometries. For example, a class 1B fold, when subject to flattening perpendicular to the hinge, is transformed in to a class 1A fold. However, a class 2 fold remains such when subject to flattening.

The folding of multilayers by flexural shear and passive-shear

In the folding of multilayers, both the competence contrast and mean competence of the layers should be kept in mind; styles of folding have particular domains in the bivariate space defined by these two measures. Additionally, if the competence contrast is zero, then the stack of layers behaves as a single layer according the above kinematic models. Finally, the friction between layers is an important determinant of the folding process.

If the layers have the same high competence and friction between them is low, deformation occurs by flexural-slip folding, because effectively a high competence contrast is produced. Relative slip between layers is greatest at the inflection points and lowest at the hinge. This model differs from flexural shear folding in that slip is concentrated along layer surfaces. It commonly produces mineral slickenlines and slickenside lineations and a class 1B fold.

If a multilayer consists of intercalated beds of highly contrasting competence, then as a group they deform by flexural-slip folding, with interlayer slip taken up by deformation in the incompetent layers. The result if a class 1C fold. As the thickness ratio of incompetent to competent layers increases, the requirement that the adjacent surfaces of competent-layer folds be the same is relaxed, because flow in the incompetent layer occurs; this may result in the divergence of dip isogons and hence class 3 folds. When incompetent layers are much thicker than the competent ones, disharmonic ptygmatic folds result. If incompetent layers completely dominate a multilayer, then deformation occurs by passive-shear with flattening, and a class 2 fold results. Thus, it is clear that competence contrast (planar mechanical anisotropy) is important in the formation of class 1 and 3 folds.

Kink and chevron folds

Kink and chevron folds are most commonly developed in sequences of interbedded or laminated sequences with significant mechanical anisotropy. The former occur in pairs with a short segment connecting two longer, displaced segments.

Two models of kink formation involve the migration of the kink band boundary; two other models describes kink formation as the expansion of a shear zone, the boundaries of which are kink bands. The second type of model is experimentally well supported. There are two models to explain chevron folds. In the first, conjugate pairs of kink bands intersect and combine to form a chevron fold. The second model assumes infinitesimal laminations and describes a process essentially like flexural shear.

Whether kink or chevron folds form depends on whether the direction of compression is parallel or oblique to the laminations. Incompetent material may flow from limb to hinge to accommodate the lack of correspondence between the upper and lower surfaces of the folded competent layers.

Fault-bend, fault-propagation, and drag folds

In the following discussion several assumptions are made: no gaps are created during slip; fault bends have zero bluntness; layer thickness and length are conserved; and the layers are undeformed prior to faulting. A bending model of folding with layer-parallel (flexural) shear is frequently assumed, and this is the one geometry for which flexural folding can produce class 2 folds.

Initially, two kink bands form, and they grow as displacement continues. Two of the axial planes are fixed in the hanging-wall block, two in the footwall block. The fault-bend fold eventually reaches a maximum amplitude, with continued displacement causing migration of the hanging-wall layers through the fold. Analysis of surficial dip domains may be used to constrain fault structures at depth, and this is most useful when additional data form seismic studies, wells, etc. are incorporated. Also, for fault-bend folding, the maximum possible cutoff angle is 30° , given the assumptions previously stated. It must be emphasized that most interpretations here are not unique. Similar analysis can illumine the structure at depth of fault duplexes and imbricate thrusts as well as fault-propagation folds, which have slightly different geometries.

Drag folds are thought to form as a result of the velocity gradient in a shear zone; they are often non-cylindrical, asymmetric, disharmonic folds whose sense of asymmetry reflects the direction of shear. This latter fact can be used to determine the sense of slip along a fault (known as Hansen’s method).

The geometry of superposed folding

Superposed folds occur when one generation of folds is overprinted by a later generation. Generally the youngest generation of folding has planar axial surfaces, while the axial surfaces of earlier generations are folded by all episodes younger than themselves (this is basically just an application of the "law of cross-cutting relationships").

For competent layers, which typically deform by flexural folding, superposed folding tends to produce complex and less regular geometries. This is not true of incompetent layers that deform by passive-shear and flattening; in this case, outcrop patterns are display regular interference patterns. Several such interference patterns are discussed, but these are merely end-members in a continuum of possible patterns.

Folding from each generation may not be expressed at in a given area, and so correlations, when attempted, are more reliable when based on the style of folding rather than counting generations.

Diapiric flow

Diapirs, as we have seen earlier, are elliptical structures in cross-section and form when relatively low-density material flows upward through higher-density material; this is driven by buoyancy. Salt domes may occur when thick salt (evaporite) deposits are overlain by sequences of other sediments or volcanics. Salt flows laterally toward the zone of upwelling, producing tight, reclined to recumbent folds that are oriented radially. Shifts in the flow regime produce convolute folds. Similar structures may also be produced by shale diapirs, which may be formed when unconsolidated mud comes under high overburden and pore pressures rise dramatically. Mantled gneiss domes are often seen in the core zones of orogens and in some cases may be diapirs.