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_Journal of Structural Geology 32 (2010) 2042e2071_ _Contents lists available at ScienceDirect_ _Journal of Structural Geology_ _journal homepage: www.elsevier.com locate jsg_ _Review Article_ _Information from folds: A review_ _Peter J. Hudleston a,*, Susan H. Treagusb a Department of Geology and Geophysics, University of Minnesota, Minneapolis, MN 55455, USA b School of Earth, Atmospheric and Environmental Sciences, University of Manchester, Manchester M13 9PL, UK_ _article info_ _Article history: Received 13 January 2010 Received in revised form 24 July 2010 Accepted 22 August 2010 Available online 8 September 2010_ _Keywords: Folds Folding Deformation history_ _abstract_ _Folds are spectacular geological structures seen on many different scales. To mark 30 years of the Journal of Structural Geology, we review information gained from studies of folds in theory, experiment and nature. We first review theoretical considerations and modeling, from classical approaches to current developments. The subject is dominated by single-layer fold theory with the assumption of perfect layer-parallel shortening, but we also review multilayer fold theory and modeling, and folding of layers oblique to principal stresses and strains. This work demonstrates that viscosity ratio, degree of non-linearity of the flow law, anisotropy, and thickness and spacing distribution of layers of different competence are all important in determining the nature and strength of the folding instability. Theory and modeling provide the basis for obtaining rheological information from natural folds through analysis of wavelength thickness ratios of single layer folds and fold shapes. They also provide a basis for estimating bulk strain from folded layers. Information about folding mechanisms can be obtained by analyzing cleavage and fabric patterns in folded rocks, and the history of deformation can be revealed by understanding how asymmetry develops in folds, by how folds develop in shear zones, and how they develop in more complex three-dimensional deformations._ _? 2010 Elsevier Ltd. All rights reserved._ _1. Introduction_ _Folds are spectacular structures in deformed rocks affecting single or multiple layers on all scales, and on a small scale commonly seen affecting veins, schistosities and foliations (Figs. 1 and 2). They have played an important part historically in understanding episodes of deformation in orogenic belts. To mark 30 years of the Journal of Structural Geology, we combine forces and indulge our separate love of folds to review information gained from studies of folds in theory, experiment and nature._ _It was probably Hall (1815) who first used the word "folds" in connection with rock structures. He described models he had made from layered cloths confined between boards and laterally compressed, simulating folded rocks observed on the Berwickshire coast of Britain. He wrote: “The consequence was that the strata were constrained to assume folds, bent up and down, which very much resemble the convoluted beds exhibited in the crags of Fast Castle.” Among early studies of folds are outstanding contributions by Willis (1891) on mechanics and Van Hise (1894) on geometry. Much of the work on folds in the first half of the 20th century was concerned with developing geometrical methods for representing folds. Details can be found in textbooks by Leith (1923), Nevin (1931), Hills (1963) and de Sitter (1964). A review of work on the mechanics of folding through the mid 1970s can be found in Johnson (1977: Chapter 1)._ _In this review, we concentrate on information provided by folded rocks and their analysis: information on rheology, strain and deformation history, locally or regionally. Much of this information stems from developments in fold theory and modeling over the course of the last 50 years, beginning with work of Biot (1961, 1965a, 1965b), who developed theories for single and multilayer folding in viscoelastic and viscous media, with applications to rocks. Currie et al. (1962) developed models of elastic folding and structural lithic units related to folds in the Appalachians, and Ramberg (1959, 1963, 1964, 1970), who made significant contributions to modern understanding of folding mechanisms based on theory and model experiments. These studies together form the foundations of modern fold theory and modeling, expanded below._ _In their papers on buckling, Biot (1961, 1965a) and Ramberg (1964, 1970, 1981) extended their analysis to include the influence of gravity. In this paper we do not consider gravitational forces, which may become important for large folds and certainly so for folds affecting the Earth’s surface. In the last_ _P.J. Hudleston, S.H. Treagus Journal of Structural Geology 32 (2010) 2042e2071_ _2043_ _Fig. 1. Examples of small-scale buckle folds: (a) Quartz veins in slate, Trondheim, Norway; scale bar 20 cm. (b) Quartz veins in schist, Cap de Creus, Spain; coin 2 cm. (c) Mylonitized pegmatite vein in mylonites, Cap de Creus, Spain, showing wavelength decreasing with thickness; scale bar 10 cm. (d) Single-layer buckling in thin white pegmatitic veins modified by multilayer effects of banding in gneisses of the Maggia nappe, Ticino, Switzerland; coin 2.3 cm._ _Fig. 2. (a) Multilayer folds in Moine schists with wavelengths determined by competent white quartzo-feldspathic veins of different thickness (v) that have buckled largely independently; Loch Monar, Scotland; scale bar 20 cm. (b) Multilayer folds in anisotropic gneiss, Maggia nappe, Ticino, Switzerland; hand lens 5 cm. (c) Multilayer folding in the New Harbour Formation psammitic schists, Silver Bay, Anglesey, UK; lens cap 5 cm. (d) Multilayer buckle folds of chevron style and variable asymmetry in siltstone and slates, Boscastle, Cornwall, England; scale bar 20 cm. The overall fold style is similar (Class 1C, Ramsay, 1967, p. 367), but the stiff siltstone layers have parallel shapes (Class 1B)._ _2044_ _P.J. Hudleston, S.H. Treagus Journal of Structural Geology 32 (2010) 2042e2071_ _decade or so, work on large-scale buckle folding has focused on the whole lithosphere (e.g., Burg and Podladchikov, 1999; Cloetingh et al., 2002), at which scale gravitational forces are of great importance._ _2. Theoretical considerations and modeling_ _2.1. Single-layer fold theory_ _Single layer fold theory concerns the buckling of isolated layers subjected to layer-parallel compression, developed for the case of a stiff or competent viscous layer in a less stiff or less competent matrix (Biot, 1961; Biot et al., 1961; Ramberg, 1961, 1963; Chapple, 1968; Fletcher, 1974, 1977; Smith, 1975, 1977, 1979; Johnson and Fletcher, 1994) and for the corresponding cases of elastic and viscoelastic layers and matrix (Biot, 1961, 1965a; Currie et al., 1962; Johnson, 1977; M?hlhaus et al., 1994, 1998; Hunt et al., 1996, 1997; Schmalholz and Podladchikov, 1999, 2000; Jeng and Huang, 2008). Classical theory predicts that if the layer is given small sinusoidal perturbations of different wavelengths, one such perturbation will amplify at a greater rate than all others. The wavelength of this perturbation is termed the dominant wavelength, ld. For Newtonian viscous layer and matrix in plane strain, with maximum shortening parallel to the layer and ignoring gravity and inertial effects, ld depends only on the ratio of viscosities of layer to matrix. The thin-plate approximation for ld is:_ _ld = 2p x186mmLM x191_3;_ _(1)_ _where h is layer thickness and mL and mM are the viscosities of layer and matrix (Biot, 1961; Ramberg, 1961). This approximation holds for both welded and free-slip contacts between layer and matrix. It is good for mL mM ! 100, but becomes increasingly inaccurate as mL mM is decreased and the assumptions of the thin plate formulation become untenable. (Note in this regard that Eq. (1) gives a dominant wavelength for the case when mL mM ? 1, which is not physically meaningful). Under suitable conditions, including sufficiently large strain rates, the elastic properties of rocks may influence the folding instability. The thin-plate expression for the dominant wavelength of an elastic layer in an elastic matrix is identical in form to Eq. (1) (e.g., Currie et al., 1962; Jeng and Huang, 2008)._ _ld = 2p EL x18_6EM x191_3_;_ _(2)_ _where EL and EM are the elastic moduli of layer and matrix. Elastic behavior by itself is obviously inappropriate for rocks, in which folds represent permanent inelastic deformation. If an elastic layer is embedded in a viscous matrix, the dominant wavelength is dependent on applied load (or alternatively rate of deformation). It is given by:_ _ld ? p x18_6h !1_2_ _x191_3_;_ _(3)_ _where nL is Poisson’s ratio and P is the layer-parallel stress in the stiff layer (Biot, 1961; Turcotte and Schubert, 1982). Note that the dominant wavelength in this case is independent of the viscosity of the matrix. If the layer is viscoelastic (Maxwell rheology, equivalent to a spring and a dashpot in series) and the matrix viscous, Schmalholz and Podladchikov (1999) showed that whether the folding is controlled largely by its viscous properties (with ld given by Eq. (1)) or largely by its elastic properties (with ld given by Eq. (3)) depends on the ratio of the viscous to elastic dominant wavelengths. If the ratio, R ? ldv lde < 1, ld is given approximately by Eq. (1) and if R ? ldv lde > 1, ld is given approximately by Eq. (3)._ _A buckling instability is in fact one of a family of dynamic instabilities that result from either compression or extension of an isolated layer that is either more or less viscous than its matrix, as shown by Smit_ Ключевые слова: buckle, dominant wavelength, ramberg, stress exponent, nite amplitude, stress history, stiff, schmid, zone, power-law rheology, parasitic fold, weiss, multiple layer, treagus, black dot, exural, america memoir, mancktelow, perry, mm, stify conned, small, layer matrix, transected fold, rock property, geometry, quartz vein, membrane stress, tectonophysics, shear-sense indicator, earth, elastic property, treagus journal, limb dip, shear, vein, folding, society, m?hlhaus, bedding-plane slip, american association, case, small-scale fold, ampli?cation, data, lan hudleston, single-layer, cleavage, viscosity contrast, strain, law, shortening, individual fold, sharp-hinged fold, viscous property, chevron, fold shape, viscoelastic medium, geological structure, wavelength, viscoelastic rheology, package behaves, reply journal, buckling, viscosity, rheological contrast, geology, fletcher, smith, wavelength selection, american, model, parallel, initial irregularity, crossover strain, elastic control, principal stress, structural geology, geological society, shear zone, ha, axial plane, preferred wavelength, secondary, lisle, flinn, contact strain, power-law layer, single layer, poissons ratio, geophysical, multilayers, deformation, rheological property, journal structural, cylindrical waveform, layer, competent, result, fault-related fold, minor fold, structure, relative bandwidth, simple shear, effective viscosity, change, hobbs, ramsay, exural slip, cobbold, anisotropy, bulletin, cleavage trace, perturbation, initial perturbation, ratio, soper, power-law behavior, srivastava, instability, competent bed, power-law exponent, limb, viscosity ratio, ?ow, pattern, latham, contrast, larger fold, watkinson, analysis, crossover amplitude, journal structural geology, property, london, johnson, analytical solution, single-layer fold, sheath fold, numerical modelling, biot, shear band, buckle fold, elastic, refolded fold, rock, amplitude, chevron style, tectonics, theory, science, numerical model, schmalholz podladchikov, modeling, larger-scale fold, growth, fold grows, dominant, single, direction, stretch, york, shape, plane, natural, geological, material, multilayer, anisotropic, structural, hudleston treagus, growth rate, fold developing, hinge, thermal-mechanical feedback, eds interactions, alternating stiff, free-slip contact, ?nite, development, anisotropic rock, hinge region, dip, journal, power-law, ghosh, numerical, mechanism, orogenic belt, folded, initial amplitude, stiff layer, hinge migration, initial, shear viscosity, hall, fold, podladchikov, geological structures, rheology, hudleston, ductile rock, calcite vein, matrix, stress level, thickness, kink band, numerical simulation, earths crust, viscous, study, stress, strain rate, multilayered rock, lan, softer layer, interfering fold, growth factor, rate, schmalholz