Descriptions of fold geometries are important because they allow comparisons within and between folds and allow us to recognize patterns in the occurrence and distribution of fold systems. For example, orogenic belts contain characteristic fold systems: along their flanks are large fold and thrust belts, with little metamorphism, but underlain by décollements; and in core zones where intense folding has been accomplished, accompanied by high-grade metamorphism under high temperature and pressure.
Geometry of folded surfaces and layers
Before proceeding we should define a number of terms used to describe the geometry of folded surfaces:
inflection line = the line along a surface across which the sense of curvature changes from concave to convex, or vice versa
antiforms and synforms in a series comprise a fold system
curvature is a measure of change in slope with distance (¶ 2z/¶ x2)
the hinge (line) connects points of maximum curvature along a fold
in a fold with a single hinge line, closure occurs at the hinge; a hinge zone is defined as the most highly curved portion near the hinge, while limbs are portions with the lowest curvature
crest and trough lines connect points of highest and lowest elevation on a fold and may not correspond with hinges; culminations and depressions connect points where crests and troughs go to maximum and minimum elevation
profile is the trace of a fold on a plane orthogonal to the hinge
in a cylindrical fold a line may be pulled parallel to the axial line along the fold surface without losing contact with it; in a conical fold is one in which the fold surface maintains a constant non-zero angle with a fixed linethe fold axis; non-cylindrical, non-conical folds dont possess such an axis
For multiple stacked folded surfaces, the above vocabulary must be modified. We speak, for example, of inflection surfaces, hinge and axial surfaces, and anticlines and synclines. Complexities are introduced for overturned beds.
Scale and attitude of folds
Key concepts regarding the scale and attitude of a fold include amplitude and wavelength, which may be defined for folds much like for waves. As for characterizing the attitude of folds:
upright, inclined and recumbent describe dipping of the axial surface normal to the hinge
horizontal, plunging and vertical refer to the angle the hinge makes with a horizontal surface
reclined fold = a fold with both plunging hinge and inclined axial surface
homoclines are essentially tilted (non-horizontal) planar surfaces; monoclines and structural terraces introduce increasing degrees of kinking and complixity
The elements of fold style
The geometric features of a given fold, in sum, constitute its style, and these features are the elements of fold style. A common angular measurement of folds is the interlimb angle i , which is related to the folding angle f :
i= 180 - f .
The cylindricity of a fold is a qualitative expression of the degree to which the fold approximates a purely cylindrical one; many are described as cylindroidal. A symmetric fold is one in which the fold limbs (in profile) are mirror images of one another across the axial surface. For asymmetric folds, the sense of asymmetry is by convention described looking in the down plunge direction; Z-folds have their axial surfaces rotated clockwise, while in S-folds the axial surface has been rotated counterclockwise. The sense of asymmetry may also be specified by vergence, which is the geographical direction of leaning of the axial surface.
There are three chief descriptors of a folded surface:
Ramsays classification is widely used to describe folded multilayers; in characterizing layers, one often compares the folding style between two surfaces of a layer (e.g., top and bottom). Three geometrical parameters are defined and used in classification:
These parameters are related by:
ta = Ta cos a
Ramsay divided folds into three classes, which are characterized as follows. Class 1 folds: evenly spaced dip isogons which converge toward the concave surface, and orthogonal and axial trace thickness increase away from the hinge. Class 2 folds: dip isogons are parallel to the axial trace throughout fold, and axial trace thickness remains constant. Class 3 folds: dip isogons diverge toward the concave surface, and axial trace thickness decreases away from the hinge.
Additional features may be defined for multiple, stacked, folded layers. Harmony, H, is the rate at which the fold dies out along the axial surface relative to the fold wavelength:
H = 2D/l .
Also, axial surfaces themselves may be curved or folded (i.e., they may not be planar), producing convolute folds, which usually reflect multiple episodes of deformation.
The order of folds
Folding usually develops simultaneously at different scales. The largest, usually regional folds are first order. Higher-order or parasitic folds are nested within these. The style and attitude of these smaller-scale folds typically approximate that of the lower-order folds, a relationship dubbed Pumpellys rule.
Common styles and associations
In the thrust-fold regions located parallel to orogenic belts, certain characteristic types of folds tend to develop; the folds themselves are usually cylindrical with horizontal hinges and are composed of largely unmetamorphosed rock. In the foreland, folds tend to be upright and open, while in the hinterland they tend to be isoclinal and inclined/recumbent, with vergence toward the hinterland. At depth these folds tend to die out at décollements and may be associated with fault-ramp folds, especially toward the foreland. Note: in regard to regions associated with plate convergence, foreland » backarc, and hinterland » forearc.
The strongly metamorphosed cores of orogens commonly contain cylindrical, asymmetric, convolute folds with angular hinges, that tend toward recumbent. Large-scale, isoclinal, recumbent folds are known as fold nappes, or, where continued compression has been accomodated by thrust faulting, thrust nappes. Folds with similar geometries may be associated with fault-ramp folds, especially toward the foreland.
Chevron and kink folds are (oddly enough) cylindrical and harmonic, with angular hinges. The former are symmetric, and both tend to be developed in rocks with strongly planar anisotropy. Ptygmatic folds affect individual layers, dikes, or veins in metamorphic rocks; they are disharmonic with rounded hinges.