SUPPORTING MATERIAL

Terminology of Folds

Amplitude Half the height of the structure measured from crest to trough.

Arc length The distance between two hinges of the same orientation measured over the folded surface.

Axial surface The surface containing the hinge lines from consecutive folded surfaces.

Crest The topographically highest point of a fold, which need not coincide with the fold hinge.

Cross section A vertical plane through a fold.

Culmination High point of the hinge line in a non-cylindrical fold.

Cylindrical fold Fold in which a straight hinge line parallels the fold axis; in other words, the folded surface wraps partway around a cylinder.

Depression Low point of the hinge line in a non-cylindrical fold.

Fold axis Fold generator in cylindrical folds.

Hinge The region of greatest curvature in a fold.

Hinge line The line of greatest curvature.

Inflection point The position in a limb where the sense of curvature changes.

Limb Less curved portion of a fold.

Non-cylindrical fold Fold with a curved hinge line.

Profile plane The surface perpendicular to the hinge line.

Trough The topographically lowest point of a fold, which need not coincide with the fold hinge.

Wavelength The distance between two hinges of the same orientation.

MORE EXPLORATION

We can quantify fold shape by using a method called dip-isogon analysis. Dip isogons connect points on the upper and lower boundary of a folded layer where the layers have the same dip relative to a reference frame (Figure S8.1).

FIGURE S8.1. Fold classification based on dip isogon analysis. In Class 1A (a) the construction of a single dip isogon is shown, which connects the tangents to the upper and lower boundary of the folded layer with equal angle (α) relative to a reference frame; dip isogons at 10° intervals are shown for each class. Class 1 folds (a–c) have convergent dip isogon patterns; dip isogons in Class 2 folds (d) are parallel; Class 3 folds (e) have divergent dip isogon patterns. In this classification, parallel (b) and similar (d) folds are labeled as Class 1B and Class 2, respectively. [10.12]

The construction method is explained step by step in all structural geology laboratory manuals, to which you are referred. Graphically, the dip isogon classification plots angle α versus normalized distance between the two tangents defining a dip isogon. Three classes are recognized: convergent dip isogons (Class 1), parallel dip isogons (Class 2), and divergent dip isogons (Class 3). The terms “convergence” and “divergence” are used with respect to the core of the fold when the dip isogons intersect in a point in the core of the fold, the fold is called convergent, and vice versa. Dip isogons that are perpendicular to bedding throughout the fold define a parallel fold, whereas dip isogons that are parallel to each other characterize a similar fold.

Strain-modified Biot-Ramberg Equation

We simplify this effect in our analysis by inferring that a component of layer thickening occurs before folding instabilities arise. Recalling the effect of layer thickness on LW (Equation 8.1), we therefore must include a strain component in Equation 8.1:

Eq. S8.1

where RS is the strain ratio X/Z. This modified Biot-Ramberg equation, also known as the Sherwin-Chapple equation, gives a good prediction for the shape of natural folds in rocks with low viscosity contrast, such as one finds in metamorphic regions.

The respective roles of viscosity contrast and layer thickening during shortening are also well illustrated in numerical models of folding. The advantage of mathematical models is their ability to vary parameters with relative ease. These calculations also show that wavelength becomes less and the folding layer increasingly thickens, with the added advantage of computer modeling that we can track the strain field as well. The strain pattern becomes increasingly homogeneous with decreasing viscosity contrast. Indeed, no viscosity contrast (ηL/ηM = 1) reflects the situation in which there is no more mechanical significance to the layer (see the foam-only box experiment in Chapter 8).

READING

Biot, M. A., 1961. Theory of folding of stratified viscoelastic media and its implication in tectonics and orogenesis. Geological Society of America Bulletin, 72, 1595–1620.

Dietrich, J. H., 1970. Computer experiments on mechanics of finite amplitude folds. Canadian Journal of Earth Sciences, 7, 467–476.

Hudleston, P. J., and Lan, L., 1993. Information from fold shapes. Journal of Structural Geology, 15, 253–264.

Latham, J., 1985. A numerical investigation and geological discussion of the relationship between folding, kinking and faulting. Journal of Structural Geology, 7, 237–249.

Price, N. J., and Cosgrove, J. W., 1990. Analysis of geological structures. Cambridge University Press: Cambridge.

Ramberg, H., 1963. Strain distribution and geometry of folds. Bulletin of the Geological Institute, University of Uppsala, 42, 1–20.

Ramsay, J. G., and Huber, M. I., 1987. The techniques of modern structural geology, volume 2: folds and fractures. Academic Press.

Sherwin, J., and Chapple, W. M., 1968. Wavelengths of single layer folds: a comparison between theory and observation. American Journal of Science, 266, 167–179.

Thiessen, R. L., and Means, W. D., 1980. Classification of fold interference patterns: a reexamination. Journal of Structural Geology, 2, 311–316.

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