Strain and competence contrast estimation from fold shape

A new method to estimate strain and competence contrast from natural fold shapes is developed and verified by analogue and numerical experiments. Strain is estimated relative to the nucleation amplitude, A_N, which is the fold amplitude when the amplification velocities caused by kinematic layer thickening and dynamic folding are identical. A_N is defined as the initial amplitude corresponding to zero strain because folding at amplitudes smaller than A_N is dominantly by kinematic layer thickening. For amplitudes larger than A_N, estimates of strain and competence contrast are contoured in thickness-to-wavelength (H/λ) and amplitude-to-wavelength (A/λ) space. These quantities can be measured for any observed fold shape. Contour maps are constructed using existing linear theories of folding, a new nonlinear theory of folding and numerical simulations, all for single-layer folding. The method represents a significant improvement to the arc length method. The strain estimation method is applied to folds in viscous (Newtonian), power-law (non-Newtonian) and viscoelastic layers. Also, strain partitioning in fold trains is investigated. Strain partitioning refers to the difference in strain accommodated by individual folds in the fold train and by the whole fold train. Fold trains within layers exhibiting viscous and viscoelastic rheology show different characteristic strain partitioning patterns. Strain partitioning patterns of natural fold trains can be used to assess the rheological behaviour during fold initiation.     

Experimental analysis of folding in simple shear

Six experiments of single-layer folding with simple-shear boundary conditions were completed. Using materials of ethyl cellulose, the viscosity ratio of the stiff layer to matrix ranged from 20 to 100. The experiments were monitored by 10–14 photographs taken at equally spaced time intervals. Strain distributions in both the stiff layer and matrix were calculated from the displacements of over 300 ink dots distributed over the surface of each experiment. Both incremental strain (calculated from the relative displacements of the dots between successive photographs) and accumulating strain were determined on the two-dimensional profile of the materials as they folded.Symmetrical fold wavelengths occur and seem to be controlled by the wavelengths of initial perturbations in the stiff layer. If the Biot wavelength was not present initially, it will not occur in the final waveform. Consequently, in a group of natural folds, the mean value of wavelength/thickness ratios apparently reflects the initial perturbations. The mean value should not be confused with the Biot wavelength and should not be used to calculate viscosity ratios in naturally deformed rocks.Substantial layer thickening occurred only with viscosity ratios of 20. The amount of layer thickening also depends on initial perturbations of the stiff layer. If these perturbations are near the Biot wavelength, they are greatly amplified, the folds grow rapidly and layer thickening is small. If the perturbations are not near the Biot wavelength, amplification is small, the folds grow slowly and layer thickening is much greater.Principal elongations of the accumulated strain in the cores of some of the folds are not symmetrically distributed about axial planes and may cut across the axial plane at angles up to 20°. Strain shadows in the matrix, near the convex side of fold hinges, are also prominent. These triangular-shaped regions of low strain are not symmetrically disposed about fold axial planes, in contrast to strain shadows occurring in folds produced under pure-shear boundary conditions.The rotation of accumulating principal elongations in the stiff layer was calculated at fold inflections. Even though the folds themselves are generally symmetrical, these rotations at opposite fold inflections are not. One fold limb exhibits little rotation of principal elongations during folding while the other has rotations up to 70°. In contrast, folds formed in pure-shear boundary conditions have rotations of principal directions on opposite fold limbs equal in magnitude.     

A finite-element study of fold propagation in a viscous layer

A finite-element model of a viscous layer contained in a viscous matrix and undergoing layer-parallel compression is used to examine the hypothesis that a long chain of folds, as found in real rocks, can originate from one initial perturbation to the layer geometry. This hypothesis is tested by determining the velocity with which a perturbation spreads along layers of various viscosities.An insight is gained into the roles played by local strain and local layer strength in the folding mechanism. The results show that for layers with viscosity ratios comparable with those of real rocks it is impossible for long chains of folds to originate from one perturbation. The authors conclude that rock layers contain many initial perturbations and folding originates at all perturbation sites simultaneously. The growth of such folds depends on the amplitude and shape of the initial perturbation and on subsequent interference between folds.     

3D numerical modeling of forward folding and reverse unfolding of a viscous single-layer: Implications for the formation of folds and fold patterns

The main aims of this study are to show (i) that non-cylindrical three-dimensional (3D) fold shapes and patterns can form during a single, unidirectional shortening event and (ii) that numerical reverse modeling of 3D folding is a feasible method to reconstruct the formation of 3D buckle-folds. 3D viscous (Newtonian) single-layer folding is numerically simulated with the finite element method to investigate the formation of fold shapes during one shortening event. An initially flat layer rests on a matrix with smaller viscosity and is shortened in one direction parallel to the layering. Forward modeling with different initial geometrical perturbations on the flat layer and different lateral boundary conditions generates non-cylindrical 3D fold shapes and patterns. The simulations show that, in reality, the initial layer geometry and the boundary conditions strongly control the final fold geometry. Fold geometries produced from the forward folding models are used as initial setting in numerical reverse folding models with parameters identical to those of forward models. These reverse models accurately reconstruct the initial geometry of forward models with also only one extension event parallel to the previous shortening direction. The starting geometry of the forward models is inaccurately reconstructed by the reverse models if a significantly different viscosity ratio than in the forward models is used. This work demonstrates that reverse modeling has a high potential for reconstructing the deformation history of folded regions and rheological constraints such as viscosity ratio. Reverse models may be applied to natural 3D fold shapes and patterns in order to determine if they formed (i) during a single or multiple deformation events and (ii) as active buckle-folds with a viscosity ratio 1 or as passive, kinematic folds without buckling. This approach may find much application to fold interference patterns, in particular.     

Layer shortening and fold-shape development in the buckling of single layers

The progressive development of folds by buckling in single isolated viscous layers compressed parallel to the layering and embedded in a less viscous host is examined in several ways; by use of experiments, an analogue model to simulate simultaneous buckling and flattening and by an application of finite-element analysis.The appearance of folds with a characteristic wavelength in an initially flat layer occurs in the experiments for viscosity ratios (μ_layer/μ_host = μ₁/μ₂) of between 11 and 100; progressive fold development after the initial folds have appeared is similar in the experiments and in the finite-element models. Except for the finite-element model for μ₁/μ₂ = 1,000 layer-parallel shortening occurs in the early stages of folding and a stage is reached where little further changes in arc length occur. The amount of layer-parallel shortening increases with decreasing viscosity contrast, and becomes relatively unimportant after the folds have attained limb dips of about 15°–25°.Thickness variations with dip are only significant here for the finite-element model with μ₁/μ₂ = 10, and in experiments for μ₁/μ₂ = 5 where the layer is initially in the form of a moderate-amplitude sine wave. The variations range from a parallel to a near-similar fold geometry, and in general depend on the viscosity contrast, the degree of shortening and the initial wavelength/thickness ratio. They are very similar to the variations predicted by the analogue model of combined buckling and flattening. The difference between the thickness/dip variations in a fold produced by buckling at low viscosity contrast and one produced by flattening a parallel fold is marked at high limb dips and very slight at low limb dips.Many natural folds in isolated rock layers or veins show thickness/dip relationships expected for a flattened parallel fold, and some show relationships expected for buckling at low viscosity contrasts. Studies of the wavelength/thickness ratios in natural folds have suggested that competence contrast is often low. Many folds in isolated rock layers or veins whose geometry may vary between parallel and almost similar, and may be indistinguishable from those of flattened parallel folds, have probably developed by a process of buckling at low viscosity contrasts.     

Opposite senses of fold asymmetry

If the orientation of the principal compressive stress is oblique to layering, viscous multilayers fold in response to the layer-parallel shortening and develop asymmetric interfaces in response to the layer-parallel shear. A theoretical analysis of folding of viscous multilayers with different slip laws at layer contacts shows that the sense of asymmetry of folds is determined largely by the behavior of the layer contacts and the sense of layer-parallel shear during folding.

For a given sense of layer-parallel shear, the sense of asymmetry of folds can be reversed by changing only the behavior of the layer contacts. If the slip rate is linearly proportional to the shear stress at layer contacts, the resistance to slip is the same everywhere along interfaces, and the folds develop the sense of asymmetry of drag folds. If the slip rate is a nonlinear function of the shear stress at layer contacts, however, the resistance to slip varies with position along interfaces, and folds develop the sense of asymmetry of monoclinal kink folds.

For a given variable resistance to slip at layer contacts, the sense of asymmetry depends on the sense and magnitude of the layer-parallel shear and on the thickness-to-wavelength ratio of the multilayer.

For finite multilayers with variable resistance to slip at contacts, an increase in the layer-parallel shear stress decreases the dominant wavelength and increases the amplification factor for the initial perturbation of the interface.

The multilayer consists of linear viscous layers and is confined by thick, viscous media. Resistance to slip at layer contacts is modeled theoretically by a powerlaw relationship between rate of slip and contact shear stress. The equations, derived to 2nd order in the slopes of the interfaces, describe the growth of asymmetric folds from initial, symmetric perturbations.     

Parasitic folds with wrong vergence: How pre-existing geometrical asymmetries can be inherited during multilayer buckle folding

Parasitic folds are typical structures in geological multilayer folds; they are characterized by a small wavelength and are situated within folds with larger wavelength. Parasitic folds exhibit a characteristic asymmetry (or vergence) reflecting their structural relationship to the larger-scale fold. Here we investigate if a pre-existing geometrical asymmetry (e.g., from sedimentary structures or folds from a previous tectonic event) can be inherited during buckle folding to form parasitic folds with wrong vergence. We conduct 2D finite-element simulations of multilayer folding using Newtonian materials. The applied model setup comprises a thin layer exhibiting the pre-existing geometrical asymmetry sandwiched between two thicker layers, all intercalated with a lower-viscosity matrix and subjected to layer-parallel shortening. When the two outer thick layers buckle and amplify, two processes work against the asymmetry: layer-perpendicular flattening between the two thick layers and the rotational component of flexural flow folding. Both processes promote de-amplification and unfolding of the pre-existing asymmetry. We discuss how the efficiency of de-amplification is controlled by the larger-scale fold amplification and conclude that pre-existing asymmetries that are open and/or exhibit low amplitude are prone to de-amplification and may disappear during buckling of the multilayer system. Large-amplitude and/or tight to isoclinal folds may be inherited and develop type 3 fold interference patterns.     

Impact of mechanical anisotropy and power-law rheology on single layer folding

The infinitesimal and finite stages of folding in nonlinear viscous material with a layer-parallel anisotropy were investigated using numerical and analytical methods. Anisotropy was found to have a first-order effect on growth rate and wavelength selection, and these effects are already important for anisotropy values (normal viscosity/shear viscosity) < 10. The effect of anisotropy must therefore be considered when deducing viscosity contrasts from wavelength to thickness ratios of natural folds. Growth rates of single layer folds were found to increase and subsequently decrease during progressive deformation. This is due to interference between the single layer folds and chevron folds that form in the matrix as a result of instability caused by the anisotropic material behaviour. The wavelength of the chevron folds in the matrix is determined by the wavelength of the folded single layer, which can explain the high wavelength to thickness ratios that are sometimes found in multilayer sequences. Numerical models including anisotropic material properties allow the behaviour of multilayer sequences to be investigated without the need for resolution on the scale of individual layers. This is particularly important for large-scale models of layered lithosphere.     

Theoretical analysis of large amplitude folding of a single viscous layer

We present a theoretical model for Large Amplitude Folding (LAF) of a single, viscous layer embedded in a viscous matrix. LAF analysis is rooted in the first order thick-plate analysis but extends it by incorporating two growth rate corrections. 1) Following Fletcher (1974), the growth rate is modified according to the evolution of the wavelength to thickness ratio. 2) A growth rate reduction is introduced based on the rate of arclength shortening, as originally developed by Schmalholz and Podladchikov (2000). Through comparison with numerical models, we show that the simultaneous application of the two corrections in LAF provides a good prediction of the evolution of fold geometry parameters up to large amplitudes irrespective of the particular initial perturbation geometry and viscosity ratio. In the case of the multiple waveforms perturbation, we predict a coupling of the evolution of waveforms. We show that the irregular (non-sinusoidal) or localized final fold shape, commonly observed in nature, can be predicted using LAF.     

Stress-induced viscosity changes and the existence of dominant wavelengths in folds

The theory of folding in stratified media presented by Biot and Ramberg has been extended by considering a more general type of material response. The model consists of a viscous layer embedded in a less viscous medium, compressed parallel to the layering. A transition from Newtonian to non-Newtonian behavior is considered and an approximate solution to the governing equation is discussed. The results give the effect of local, stress-induced changes in the viscosity on the profile of the fold. The results indicate that as the transition to non-Newtonian behavior proceeds, the wavelength selection process described by Biot and Ramberg breaks down; the wavelength of the fold which develops probably will not be the “dominant” wavelength defined by Biot.     

A theory of concentric, kink and sinusoidal folding and of monoclinal flexuring of compressible, elastic multilayers: IV. Development of sinusoidal and kink folds in multilayers confined by rigid boundaries

This part concerns folding of elastic multilayers subjected to principal initial stresses parallel or normal to layering and to confinement by stiff or rigid boundaries. Both sinusoidal and reverse-kink folds can be produced in multilayers subjected to these conditions, depending primarily upon the conditions of contacts between layers. The initial fold pattern is always sinusoidal under these ideal conditions, but subsequent growth of the initial folds can change the pattern. For example, if contacts between layers cannot resist shear stress or if soft elastic interbeds provide uniform resistance to shear between stiff layers, sinusoidal folds of the Biot wavelength grow most rapidly with increased shortening. Further, the Biot waves become unstable as the folds grow and are transformed into concentric-like folds and finally into chevron folds. Comparison of results of the elementary and the linearized theories of elastic folding indicates that the elementary theory can accurately predict the Biot wavelength if the multilayers contain at least ten layers and if either the soft interbeds are at most about one-fifth as stiff as the stiff layers, or there is zero contact shear strength between layers.Multilayers subjected to the same conditions of loading and confinement as discussed above, can develop kink folds also. The kink fold can be explained in terms of a theory based on three assumptions: each stiff layer folds into the same form; kinking is a buckling phenomenon, and shear stress is required to overcome contact shear strength between layers and to produce slippage locally. The theory indicates that kink forms will tend to develop in multilayers with low but finite contact shear strength relative to the average shear modulus of the multilayer. Also, the larger the initial slopes and number of layers with contact shear strength, the more is the tendency for kink folds rather than sinusoidal folds to develop. The theoretical displacement form of a layer in a kink band is the superposition of a full sine wave, with a wavelength equal to the width of the kink band, and of a linear displacement profile. The resultant form resembles a one-half sine curve but it is significantly different from this curve. The width of the kink band may be greater or less than the Biot wavelength of sinusoidal folding in the multilayer, depending upon the magnitude of the contact shear strength relative to the average shear modulus. For example, in multilayers of homogeneous layers with contact strength, the Biot wavelength is zero so that the width of the kink band in such materials is always greater than the Biot wavelength. In general, the higher the contact strength, the narrower the kink band; for simple frictional contacts, the widths of kink bands decrease with increasing confinement normal to layers. Widths of kink bands theoretically depend upon a host of parameters — initial amplitude of Biot waves, number of layers, shear strength of contacts between layers, and thickness and modulus ratios of stiff-to-soft layers — therefore, widths of kink bands probably cannot be used readily to estimate properties of rocks containing kink bands. All these theoretical predictions are consistent with observations of natural and experimental kink folds of the reverse variety.Chevron folding and kink folding can be distinctly different phenomena according to the theory. Chevron folds typically form at cores of concentric-like folds; they rarely form at intersections of kink bands. In either case, they are similar folds that develop at a late stage in the folding process. Kink folds are more nearly akin to concentric-like folds than to chevron folds because kink folds form early, commonly before the sinusoidal folds are visible. Whereas concentric-like folds develop in response to higher-order effects near boundaries of a multilayer, kink folds typically initiate in response to higher-order shear, as at inflection points near mid-depth in low-amplitude, sinusoidal fold patterns. Chevron folding and kink folding are similar in elastic multilayers in that elastic “yielding” at hinges can produce rather sharp, angular forms.     

Kinematics of fault-related folding in a duplex,lost river range,Idaho, U.S.A.

The Doublespring duplex, located in the Lost River Range of Idaho, is a Sevier age fault-related fold complex in massive limestones of the Upper Mississippian Scott Peak Formation. Folds within the duplex closely resemble fault-bend fold geometrics, with open interlimb angles and low-angle bed cut-offs. Narrow, widely spaced, bedding-parallel shear zones with well-developed pressure solution cleavage alternate with massive, relatively undeformed layers on fold limbs. Shear zones are developed only on the limbs of anticlines, and have similar but unique morphologies in each of three different folds. Incremental strain histories reconstructed from antitaxial fibrous overgrowths and veins within the shear zones constrain the kinematics of folding. Shear zones experienced distributed bedding-parallel simple shear (flexural flow) towards pins near axial surfaces, while adjacent massive layers experienced rotation through an externally fixed extension direction. The absence of footwall synclines and morphological differences in shear zones from adjacent folds suggest that faulting preceded folding. Kinematic histories of folds that have experienced different translational histories are identical, and are not compatible with strain histories predicted from previous kinematic models of fault-bend folding. Shear zone development and fiber growth is instead interpreted to have occurred during low amplitude fixed-hinge buckling in response to initial resistance to translation of the thrust sheet. Fault-bend folding with mobile axial surfaces occurred with translation of the thrust sheets once the initial resistance to translation was overcome and resulted in no penetrative strain.     

A unified kinematic model for the evolution of detachment folds

Detachment folds represent a major structural element in a number of fold belts. They are common in the Jura Mountains, the Zagros fold belt, the Central Appalachian fold belt, the Wyoming fold-belt, the Brooks Range, the Parry Islands fold belt, and parts of the SubAndean belt. These structures form in stratigraphic packages with high competency contrasts among units. The competent upper units exhibit parallel fold geometries, whereas the weak lower unit displays disharmonic folding and significant penetrative deformation. Two distinct geometric types, disharmonic detachment folds, and lift-off folds have been recognized. However, these structures commonly represent different stages in the progressive evolution of detachment folds. The structures first form by symmetric or asymmetric folding, with the fold wavelength controlled by the thickness of the dominant units. Volumetric constraints require sinking of units in the synclines, and movement of the ductile unit from the synclines to the anticlines. Continuing deformation results in increasing fold amplitudes and tighter geometries resulting from both limb segment rotation and hinge migration. Initially, limb rotation occurs primarily by flexural slip folding, but in the late stages of deformation, the rotation may involve significant internal deformation of units between locked hinges. The folds eventually assume tight isoclinal geometries resembling lift-off folds. Variations in the geometry of detachment fold geometry, such as fold asymmetry, significant faulting, and fold associated with multiple detachments, are related to variations in the mechanical stratigraphy and pre-existing structure.     

Single layer folding in simple shear

Despite the common occurrence of simple shear deformation, laboratory and numerical simulations of folding have so far been almost exclusively in pure shear. Here we present a series of finite-element simulations of single layer folding in simple shear up to high shear strains (γ ≤ 4, and up to 75% shortening of the folding layer). In the simulations we vary the viscosity contrast between layer and its surroundings (25–100), the stress exponent (1 or 3) and the kinematics of deformation (pure- versus simple shear). In simple shear fold trains do not show a clear asymmetry, axial planes form perpendicular to the developing fold train and rotate along with the fold train. Differences in geometries between folds formed in simple and pure shear folds are thus difficult to distinguish visually, with simple shear folds slightly more irregular and with more variable axial plane orientation than in pure shear. Asymmetric refraction of an axial planar cleavage is a clearer indication of folding in simple shear. The main effect of an increase in stress exponent is an increase in effective viscosity contrast, with only a secondary effect on fold geometry. Naturally folded aplite dykes in a granodiorite are found in a shear zone in Roses, NE Spain. Comparison of the folded dykes with our numerical simulations indicates a viscosity contrast of around 25 and a stress exponent of 3. The natural folds confirm that at this moderate viscosity contrast, a significant amount of shortening (20–30%) is achieved by layer thickening instead of folding.     

Parallel, similar and constrained folds

Theoretical analysis of folding of viscous multilayers with free slip or bonding at layer contacts indicates that folds in such multilayers can be described in terms of three end-members:parallel, in which orthogonal thicknesses of layers are largely constant;similar, in which vertical thicknesses of layers and shapes of successive interfaces are essentially constant; andconstrained, in which amplitudes of anticlines and synclines decrease to zero at upper and lower boundaries. Constrained,internal folds form if the multilayer is confined by rigid media; parallel,concentric-like folds form if the multilayer is confined by soft media, provided soft interbeds are sufficiently thin for the stiff layers to fold as an ensemble. Similar,sinusoidal orchevron folds form throughout much of the thickness of a multilayer, for any stiffness of confining media, provided wavelengths of folds are short relative to the thickness of the multilayer or soft interbeds are sufficiently soft and thick for the stiff layers to act independently. The analysis shows that multilayer folds may have the same form regardless of whether the layer contacts are freely slipping or bonded.

The forms of folds in multilayers confined by media with different viscosities above and below depend on the viscosity contrast of the media. For no medium above and a rigid medium below, the forms are concentric-like in the upper part and internal in the lower part of the multilayer. For no medium above and a soft medium below, the folds are concentric-like throughout the multilayer.

The theory indicates that a useful way to analyze forms of folds in rocks or in experiments is in terms of component waveforms, as defined, for example, by Fourier series. The distributions of amplitudes of component waveforms throughout the multilayer appears to be diagnostic, reflecting contrasts in properties of the multilayer and its confining media. Analysis of a large fold in the central Appalachians, Pennsylvania, and of a smaller fold in the Huasna syncline, California, indicates that at least three component waveforms are required to produce the gross forms of those folds.

The theory closely predicts wavelengths and shapes of folds produced in analogous elastic multilayers, indicating that nonlinearities in material behavior, which are inherent in the elastic material but are absent in the viscous material, are less significant than nonlinearities in the boundary conditions, which are the same in elastic and viscous materials.     

Strain analysis and fold shape in a limestone layer and implications for layer rheology

Folds are developed in thin limestone layers within slates of the McKay Formation exposed to the east of the Rocky Mountain Trench, British Columbia, Canada. They possess geometrical characteristics expected of development by buckling. Strain in the profile plane of a selected fold is similar to that predicted by tangential longitudinal strain, except that magnitudes are too low for the observed curvature. This is attributed to inhomogeneity of strain on the scale of measurement, largely because of pressure solution. Material removed by pressure solution from the inner arc of the fold appears to form veins perpendicular to the hinge, a direction of tectonic stretching. Bedding-parallel stylolites developed diagenetically prior to tectonism.Layer-parallel shortening during the initiation of buckling was less than 20%, and probably less than 10%. The mean arclength/thickness ratio is 6.5 and 7.1, with a dispersion of 0.48 and 0.37 for local and regional populations of 29 and 212 folds, respectively. Application of buckling theory to this data suggests that folding followed a non-linear flow law. The viscosity contrast between limestone and slate would be higher and the power law exponent lower, if initial irregularities in the layers were in the form of a constant amplitude spectrum rather than one of white roughness. The data do not allow a choice of initial amplitude spectrum to be made, nor do they closely constrain estimates of n the power law exponent and viscosity contrast.Deformation in the limestone layers was accommodated by intracrystalline flow (twin gliding), pressure solution, and extensional veining (the last two linked by diffusive mass transfer). The first two dominated deformation in the profile plane of the fold and the last, in association with fracturing, allowed for extension parallel to the hinge. Experimental and theoretical considerations suggest that deformation by a combination of these processes should be non-linear. The non-linear flow law deduced from buckling analysis is consistent with expectations based on observations of active deformation mechanisms.     

Fold propagation in single embedded layers

This paper investigates the folding of single competent layers embedded in a less competent matrix, where the competence contrast is about 10: 1. Folds result from buckling during layer-parallel compression. A geometrical study of natural examples shows that individual folds tend to be grouped into fold complexes.The amplitude varies from a maximum at the centre of a complex to a minimum at each end. Each complex is often centred about a sedimentary lens or nodule which may have triggered the folding and localized the complex. The formation of folds of this kind has been simulated experimentally by deformation of models made from paraffin waxes of known rheological properties. Early in the deformation of a model, buckling starts at a localized site of disturbance, producing only one fold. With further deformation, new folds appear at either side of the initial one. The buckling then propagates along the layering, further folds appearing serially in time and distance. The end result is a complex with many individual folds and a regularly periodic shape.With a competence contrast of 10: 1, the rate of fold propagation is slow, and formation of a periodic complex requires an overall shortening of at least 15%. The shapes of folds formed experimentally are similar to those formed naturally.     

Formation of dome and basin structures: Results from scaled experiments using non-linear rock analogues

Dome and basin folds are structures with circular or slightly elongate outcrop patterns, which can form during single- and polyphase deformation in various tectonic settings. We used power-law viscous rock analogues to simulate single-phase dome-and-basin folding of rocks undergoing dislocation creep. The viscosity ratio between a single competent layer and incompetent matrix was 5, and the stress exponent of both materials was 7. The samples underwent layer-parallel shortening under bulk pure constriction.Increasing initial layer thickness resulted in a decrease in the number of domes and basins and an increase in amplitude, A, arc-length, L, wavelength, λ, and layer thickness, H_f. Samples deformed incrementally show progressive development of domes and basins until a strain of e_Y=Z = −30% is attained. During the dome-and-basin formation the layer thickened permanently, while A, L, and λ increased. A dominant wavelength was not attained. The normalized amplitude (A/λ) increased almost linearly reaching a maximum of 0.12 at e_Y=Z = −30%. During the last increment of shortening (e_Y=Z = −30 to −40%) the domes and basins did not further grow, but were overprinted by a second generation of non-cylindrical folds. Most of the geometrical parameters of the previously formed domes and basins behaved stable or decreased during this phase. The normalized arc-length (L/H_f) of domes and basins is significantly higher than that of 2D cylindrical folds. For this reason, the normalized arc length can probably be used to identify domes and basins in the field, even if these structures are not fully exposed in 3D.