Lecture index: Description of single folded surfaces. / Description of mutliple folded surfaces and fold style. / Kinematic analysis of folds in cross section. / Fold formation mechanisms. /

• Chapt. 10 in Van Der Pluijm and Marshak.
• Features of folded rocks p. 77-101 in Maley, T. S., 1994, Field Geology Illustrated, Mineral Land Publications, Boise, Idaho. This is beautifully illustrated book. which educates the eye.

List of key terms:

• fold types: cylindrical, concentric, conical, irregular, composite
• fold crest, fold hinge, fold axis, fold limbs
• axial plane, axial surface, axial trace
• vergence
• fold scale
• interlimb angle
• fold curvature - rounded to chevron, cuspate
• enveloping surfaces and wave characteristics
• antiform, anticline, synform, and syncline
• monoclines and structural terraces
• parallel vs. similar folds
• parasitic or secondary folds
• fold interference patterns
• fold transposition
• flexural slip
• buckle folds
• flow or viscous folds
• layer parallel compression

The adjacent photo is of folds evident in ice and debris material in Malaspina glacier, St Elias Mountains of Alaska. The folds reflect deformation, flowage in the ice, although another fator in the appearance here is that this is not a orthogonal cross section view, but a very oblique slice provided by a melting surface, and thus layer thicknesses are not true layer thicknesses. Indeed, given that moraine material is often of a stripe, character, the geometry is not simply that of folded layers. Photo source: http://libraryphoto.cr.usgs.gov/cgi-bin/show_picture.cgi?ID=ID.%20U.S.%20Geological%20Survey%20425 .

A common assumption is that layers start out as planar and horizontal strata. This is a good working assumption for many strata. When might it not be a good assumption? We will start out exploring how to describe the character of just a single folded surface. Such a surface might be represented by a surface contour map.

cylindrical geometry:

• idealized fold surface that can be reconstructed by rigid translation of a line through space. That line is the fold axis, an important symmetry element.
• serial orthogonal cross sections are identical.
• concentric is a special case, where fold axis follows part of circular arc.
• many folds approximately cylindrical.
• stereonet signature - great circle girdle of poles to the folded layer on stereonet.
• planar strain a possible approximation.
• can model surface in Excel.

conical geometry:

• fold surface reconstructed by rotating one line about another.
• cone axis and apical angle are important descriptors.
• change in serial cross sections (smaller amplitude).
• these folds die out along their length. - nonplanar strain.
• often a good approximation of the end of doubly plunging fold.
• stereonet signature - small circle girdle of poles on a stereonet.

irregular geometry:

• what it sounds like (a wrinkled blanket is a good example).
• occur in migmatitic rocks, a chaotic system?

composite geometry: e.g. a cylindrical middle portion and conical ends.

More complex patterns occur due to refolding and the variety of interference patterns that can develop.

Descriptors for concentric folds:

• fold crest, fold hinge, and fold axis. The first two are material lines with a specific position in the folded surface.
• enveloping surfaces. Can describe their orientation.
• fold limbs versus fold hinge.
• vergence = fold asymmetry, related to vorticity, and in some situations to simple shear sense. Inclination of axial trace to enveloping surfaces short vs. long limb asymmetry.

Description according to size (works with other structures).

• microscopic.
• mesoscopic-megascopic.
• macroscopic " covering bodies to large or too poorly exposed to be examined directly in their entirety" p. 16 Turner and Weiss.
• dependent on perspective, and on type of outcrops.
• alternative: thin section scale, hand specimen scale, outcrop scale, and map scale.

Description according to tightness or interlimb angle:

• Ramsey classification, used in literature:
  • 180-120 = gentle.
  • 120-70 = open.
  • 70-30 = closed.
  • 30-0 = tight.
  • 0 or parallel limbs - isoclinal.
• why not just give interlimb angle?
• significance? - gives some type of information about degree of strain and layer parallel shortening.

Description according to profile curvature:

• rounded.
• angular.
• chevron.
• cuspate.
• conjugate fold = box fold, multiple hinges and axial planes.
• mathematical - sine functions, harmonics and successive approximations. Provides complete description, but not easily accessible, and quite time consuming.
• wavelength, amplitude, geometry of enveloping surfaces.
• mechanical significance of above?

Description according to orientation and age relationships:

• antiform vs. synform.
• anticline vs. syncline.
• antiformal synclines and synformal syncline and viva la confusion.
• degree of plunge, and degree of axial plane inclination - Fleuty diagram.
• overturned folds = those with an overturned limb.
• monoclines and structural terrace.

axial plane: the limb bisector plane for simple geometries.

axial surface: the plane formed by the sum of all the fold hinge lines. Better descriptor to use, has distinct strain signficance.

axial trace on surface: the line formed by the intersection of the axial surface and the earth's surface; i.e. the map trace of the axial surface.

parallel folds :

• also known as concentric folds.
• thickness perpendicular to layer boundaries is maintained.
• Busk reconstruction method - one way of reconstructing fold profile geometries.
• disharmonic character - profile geometry changes along axial plane.

similar folds:

• t is constant for a given layer as measured parallel to the axial plane. Fold hinges appear thickened relative to thinned limbs.
• harmonic, ideally, different layers show the same profile geometry.
  

Composite fold forms are the most common, with some layers retaining layer thickness, and others not. This is due to differences in rock competency.

fold transposition:

• a compositional layering that was originally bedding, but where intense deformation has obliterated stratigraphic relationships and continuity.
• common in marbles, quartzites, and mica- rich metasediments.
• recognition criteria:
  • floating, isoclinal fold hinges - intrafolial folds.
  • cleavage and/or foliation parallel to bedding.
  • extreme flattening, or elongation of strain markers.
  • isolated boudins or pods of more competent material.
  • drag folds of opposite vergence in close proximity.
  • reversals of younging criteria in a short distance.
  • layers discontinuous as you trace them.
    

polyphase deformation and fold interference patterns.

• e.g. cross folding and domes and basins and saddles: exact geometry a function of wavelength and amplitudes of two fold phases.
• coaxial folding - potentially part of one phase, as a continuum. Rotation suggests a significant simple shear component to the deformation history.
• noncoaxial folding - infinite possibilities.
• sheath folds:
  • how to detect?
  • girdle pattern of fold axes on stereonet (folding of an earlier line). Great circle is shear plane. Associated with significant non-planar strain.
• example in Dalradian rocks of NW Ireland.
  

Basic assumptions for simple analysis:

• orthogonal cross-section.
• no out of the plane (cross section plane) movements (plane strain).
• parallel fold geometry helps.
• original geometry must be fairly well constrained

Shallow crustal level fold and thrust belts often meet these requirements.

Sinuous bed method:

• amount of shortening = original length - present map width.
• percentage of shortening = 1 - present length/original length.
• good idea to do several horizons at different stratigraphic levels in cross section.

Equal area method:

• can take into account unit internal deformation.
• need original stratigraphic thickness.
• present area / original strat. thickness = original length; then stick into above.
• calculation to depth of basal decollement (see overhead) t = A / (la - lc).

Typical amounts of shortening in fold-and-thrust belts = 10s to 100s of km.

Flexural slip folds:

• telephone book model.
• associated with layer parallel compression.
• produces parallel fold geometries.
• layers have strength and resist internal strain, whereas shear between layers is easier
• small inhomogeneties can cause parasitic folds to develop.
• bedding parallel striae or slickensides can develop.
• very common in fold-thrust belts.

Fault propagation folds:

• also called trishear folds.
• cored by a fault, whose tip propagates into the overlying fold with time.
• quantitative models by Allmendinger showing trishear fold evolution.
• slip on discrete fault becomes distributed to slip on bedding and smaller scale faults.

Fault bend folds:

• underlain by non-planar fault.
• points migrate into and out of 'deformation bands'.

Buckle folds:

• single layer situation where a more competent layer is surrounded by an incompetent material. The former is free to form buckle folds that have a parallel character, while the former will show another shape.
• Biot (1957) -- correspondence principle between elastic and viscoelastic materials (Newtonian viscosity), looks at stress-strain relationships in buckled layer.
• Ramberg (1959) -- approaches problem as one of fluid dynamics - particular function which satisfies both the biharmonic equation of a stream function and boundary conditions around a buckled layer.
• Both develop idea of dominant wavelength. Only valid for small % of strain, but then have inheritance principle;
• wd = 2 t ^3 ( µ1 / 6µ2 ) where wd is dominant wavelength, t is layer thickness, and µ1 and µ2 are the viscosities of the dominant layer and surrounding medium respectively.
• note that deviatoric stress plays no direct role.
• viscosity contrast, if < 5 get pure shortening.
• too high deviatoric stress get brittle failure, too low pure shortening.
• see this with ptygmatic folds in some outcrops; average wad/t ratio of 27.
• are folds with ratio around 5-7; possibly due to non-Newtonian viscosity.
• extrados and intrados of a beam - features that would indicate buckling.

Differential simple shear folds:

• card deck model.
• layer being folded is passive marker, and not a strong unit.
• similar fold forms, problems with vergence, and sense of shear.
• common in mid-crustal depths where good metamorphic anisotropies have developed, where deformation is often concurrent with metamorphism.
• expected in mylonite zones.

Flow or viscous folds:

• differ from simple shear folds in the number of possible shear planes that can operate. Van Mises criteria - 4 independent slip surfaces allow deformation to any shape.
• common in soft-sediment deformation and migmatitic terranes.

Accentuation of fold form by pure shear - e.g. by pressure solution, or as we will see by cleavage formation.

Copyright Harmon D. Maher Jr., This may be used for non-profit educational purposes as long as proper attribution is given. Otherwise, please contact me. Thank you.