Cleavage Refraction Research Articles

Rheological information determined from cleavage refraction in naturally deformed interlayered quartzites and phyllites

Abstract Cleavage refraction angles are used to estimate effective viscosity contrasts between interlayered quartzites and phyllites within the Baraboo Syncline, Wisconsin, USA. Both types of layers contain two major phases, quartz and pyrophyllite, with minor amounts of hematite. Quartz (with minor hematite) behaves as the strong phase and pyrophyllite acts as the weak phase. Cleavage refraction directly relates to mineralogy with a linear relationship between bedding/cleavage angle and strong-phase concentration. Mineralogy exerts first-order control over effective viscosity contrasts, which are generally small, in most cases <10. Effective viscosity contrasts are consistent across the fold, so are likely not to be highly strain dependent and indicate approximate linear viscous rheology. Microstructures suggest deformation was dominated by dislocation creep in layers with high quartz concentrations and diffusive mass transfer in layers with lower quartz concentrations, and that the transition of the deformation mechanism is gradual. Thus, the rheological flow laws at the small scale may not reflect the bulk flow law at the large scale over the span of the deformation. Effective viscosity contrasts allow an evaluation of samples compared to theoretical two-phase mixtures. The analysed samples most closely resemble the Reuss bound of two-phase mixtures, regardless of the mineralogy.

Sedimentological thickness variations within Silurian mudstone-dominated turbidite deposits and the effects on cleavage fanning (Anglo-Brabant Deformation Belt, Belgium)

The effect of vertical changes in lithology on cleavage refraction and cleavage fanning is relatively well understood. In contrast, the control that lateral changes in bed thickness and related multilayer characteristics have on cleavage fanning has not been widely documented. Mudstone-dominated Wenlock-age turbidites of the Anglo-Brabant Deformation Belt, Belgium, exhibit pronounced lateral thickness changes, which we attribute to intraslope flow ponding during foreland basin development. The mudstone-dominated nature of the turbidites is considered to reflect a particularly fine-grained source area, rather than a distal origin. Formation boundaries and lateral changes in lithofacies unit thickness are reflected in the amount of cleavage fanning. The degree of convergent cleavage fanning increases with an increase in thickness of the less competent units and with a decrease in thickness and number of the more competent units. As such, a detailed analysis of changes in cleavage–bedding angle aids in the distinction of different lithostratigraphic units of similar appearance, the location of their boundaries and identification of subtle lateral sedimentological changes. The utilization of cleavage and bedding data to recognize and describe vertical and lateral changes in a semi-quantitative way allows the linkage of subtle changes in multilayer rheology to finite strain trajectories. Supplementary materials: Details of position of lithological profiles are available at www.geolsoc.org.uk/SUP18708 .

Rheological implications of heterogeneous deformation at multiple scales in the Late Cretaceous Sierra Nevada, California

Late Cretaceous deformation in the east-central Sierra Nevada arc of California was heterogeneous at multiple scales. We quantify this heterogeneous deformation at centimeter, meter, and kilometer scales in the vicinity of the Gem Lake shear zone and infer variations in effective viscosity from our data. At the centimeter scale, variations in strain of different clast types in conglomerate suggest that effective viscosities varied by less than an order of magnitude. Lithology controlled the magnitude and nature of deformation recorded by clasts. At the meter scale, cleavage refraction between stratigraphic layers records variations in finite strain. Comparison of our observations with cleavage refraction models suggests a maximum effective viscosity contrast of ∼10 between layers. Bulk composition controls variations in deformation of the different layers. At the kilometer scale, variation in finite-strain magnitude and orientation in similar rock types both within and outside the shear zone demonstrates that deformation inside the zone was relatively intense. Comparing these results to numerical models of heterogeneous regional deformation, we estimate that the angle of oblique convergence inside the zone was ∼15 ± 10°, while outside it was greater than 60°. These kilometer-scale results imply regional deformation was moderately strike-slip partitioned during the Late Cretaceous and suggest regional effective viscosity varied by a factor between 6 and 17. At each scale of observation, the apparent range of effective viscosity varies by an order of magnitude or less. Consequently, we infer that relatively modest strength variations produced the structures observed at hand sample to tectonic scales.

Kinematic consequences of an angular unconformity in simple shear: an example from the southern border of the Lower Palaeozoic Rocroi inlier (Naux, France)

AbstractThe presence of an angular unconformity in combination with complex structures in the basement, lacking in the cover, is commonly seen as an indication for an orogenic event pre-dating the unconformity. The recognition of such an older orogenic event becomes, however, less evident in areas where both cover and basement were deformed together during an orogen post-dating the angular unconformity.The validity of this common interpretation has been evaluated at the southern border of the Lower Palaeozoic Rocroi basement inlier (Naux, northern France), where the basement-cover interface is very well exposed. This basement-cover interface, showing an angular unconformity, has classically been interpreted as evidence for an early Palaeozoic tectonometamorphic event, called the Ardennian orogeny, though only one penetrative cleavage, co-genetic with the structures present in both cover and basement, can be observed.A detailed geometrical study shows, however, that the presence of a tilted basement, involving the angular unconformity, provokes a rheological heterogeneity that causes a contrasting response of basement and cover with respect to the Variscan shortening. While Variscan progressive deformation gave rise to a rather regular cleavage refraction pattern in the subhorizontal multilayer cover sequence, a complex deformation, expressed by non-cylindrical folds, boudinage and shearing developed in the basement. The basement-cover interface itself played no rheological role, but has been passively sheared and folded as a consequence of the deformation of the basement. This study proves that the deformed basement-cover interface, allowing to link deformation in basement and cover, is a necessary tool to properly interpret complex deformation in the basement. With respect to the regional geodynamic evolution of the northern parts of the Central European Variscides, our kinematic model indeed demonstrates that this classical outcrop area bears no evidence for an early Palaeozoic orogenic event, and that the angular unconformity reflects the late Silurian – early Devonian onset of the Ardenne-Eifel basin development, rather than a middle Ordovician Ardennian orogeny.

Strain refraction, viscosity ratio and multi-layer deformation: A mechanical approach

A solution for the deformation of viscous layers during a two-dimensional general deformation is derived. Layer deformation is found to consist of components of pure shear, simple shear and pure rotation when considered with respect to the layer orientation. It is shown that for external bulk pure shear the layer deformation is typically vastly different to that outside the layer, ranging from pure to simple to super shear depending on layer orientation and viscosity contrast. Treagus' method for determining viscosity ratio from cleavage refraction is re-evaluated and is found to applicable under bulk pure shear. However, the presence of earlier LPS (layer-parallel shortening) can lead to erroneous viscosity ratio estimates. A new approach is developed, relying on the variation of cleavage orientation with layer orientation that is found to be robust with respect to LPS. The method is applied to examples from the Irish Variscides and the new approach has implications for determining whether or not LPS occurred in this foreland setting.

Distinguishing syn-cleavage folds from pre-cleavage folds to which cleavage is virtually axial planar: examples from the Cambrian core of the Lower Palaeozoic Anglo-Brabant Deformation Belt (Belgium)

Within the Cambrian Jodoigne Formation in the easternmost part of the Anglo-Brabant Deformation Belt, sub-horizontal to gently plunging folds occur within the limbs of steeply plunging folds. The latter folds are cogenetic with cleavage and are attributed to the Brabantian deformation event. In contrast, although cleavage is also (1) virtually axial planar to the sub-horizontal to gently plunging higher-order folds, shows (2) a well-developed divergent fanning across these folds, (3) an opposing sense of cleavage refraction on opposite fold limbs, and (4) only very small cleavage transection angles, an analysis of the cleavage/bedding intersection lineation suggests that these higher-order folds have a pre-cleavage origin. On the basis of a comparison of structural and sedimentological features these higher-order folds are interpreted as slump folds. The seemingly ‘normal’ cleavage/fold relationship across the slump folds within the limbs of the large steeply plunging folds is due to the very small angle between cleavage and bedding. As such, a ‘normal’ cleavage/fold relationship is no guarantee for a syn-cleavage fold origin. It is not unlikely that also within undeformed, recumbent slump folds, a well-developed compaction fabric, formed parallel to the axial surface of the slump folds, may show fanning and contrasting senses of cleavage refraction on opposite fold limbs.

From XY tracking to buckling: axial plane cleavage fanning and folding during progressive deformation

Folding of axial plane cleavage can occur during progressive deformation without a change in the overall background flow. Two field examples of upright (Lachlan Fold Belt, SE Australia) and recumbent (Naukluft Nappe Complex, central Namibia) folds are presented, in which strongly refracted pressure solution cleavage in competent layers on the fold limbs is buckled as a result of ongoing fold amplification. Finite element modelling confirms that cleavage refraction on limbs can be sufficient for cleavage planes to be subsequently shortened and therefore folded. Cleavage refraction is unequally developed on opposite limbs of asymmetric folds formed by oblique shortening of a layer in coaxial flow or by folding in a more general shear environment. The differences in finite strain on opposite limbs can be quite marked even when the fold shapes themselves are not obviously asymmetric. For folding in simple shear flow, as specifically modelled here, refraction is only strong on the fold limb that rotates against the imposed sense of shear. In known shear environments, this provides a potential kinematic indicator in folded units at relatively low strain (e.g. in simple shear, γ of around one), where other higher-strain indicators, typical of mylonites, are not yet sufficiently developed or are equivocal.

Influence of lithological heterogeneity, mechanical anisotropy, and magmatism on the rheology of an arc, North Cascades, Washington

Many aspects of crustal dynamics are dependent on changes in rheology and strength with depth in the lithosphere. Several of the controlling factors for rheology are difficult to study experimentally, particularly lithological heterogeneity, mechanical anisotropy, and magmatism, and we focus on these in a study of the deformation patterns in a thick crustal section (∼5- to 40-km paleodepth) through the Cretaceous Cascades core of the NW Cordillera. This magmatic arc consists of metamorphosed oceanic and arc terranes intruded by magmatic bodies ranging from <10-cm-thick sheets to large plutons. Heterogeneous brittle deformation marked by serpentinite melange characterizes the shallowest part of the crustal section, and the remainder of the section is characterized by heterogeneous, fold-dominated ductile deformation. Early tight to isoclinal recumbent folds and associated axial-planar fabrics are refolded by one or more cycles of nearly coaxial, open to isoclinal, upright to overturned folds. Layering played a mechanically active role during folding at all levels, as indicated by cleavage refraction, boudinaged layers, and kinematic indicators that record fold-related shear. Ductile deformation intensifies in the narrow structural aureoles of plutons, and SW-directed, reverse shear was partitioned into some of the aureoles. The poor strain memory of these magmatic bodies makes it difficult to determine if deformation was focused in the pluton magma chambers before they reached the solidus, as commonly predicted. All of the plutons have magmatic foliations that at least in part reflect regional strains, and these foliations are strong in the deeper plutons. The thinner sheets acted as competent bodies during folding and boudinage, after they reached the solidus, but generally did not cause marked strain gradients in their hosts. A relative strength profile constructed for the Cascades crustal section shows an overall decrease in strength with depth for the ductile part of the arc that fits idealized strength profiles. However, in more detail relative strengths are markedly variable. Units were able to accumulate large ductile strains, but even small variations in the physical properties of interlayered rock types exerted a strong influence on deformation patterns throughout the mid- to deep-crustal part of the profile. This profile thus emphasizes the complex vertical rheological stratification of arcs at the crustal to thin section scale, and should be applicable to many other magmatic arcs.

A new spin on ‘non-rotating’ porphyroblasts: implications of cleavage refraction and reference frames

It has been claimed that rigid porphyroblasts which grow before or during folding and concurrent cleavage development do not rotate with respect to the geographical reference frame (GRF), even if the straining is non-coaxial ( Bell 1985; Bell and Johnson 1990). The explanation offered is based on strain partitioning. It is argued that the initial orientations of early fabrics included as internal foliations (S i) in the porphyroblasts have been preserved after polyphase deformation, and even after successive orogenies. According to the strain partitioning model, the porphyroblasts are fixed in domains of coaxial straining (microlithons) and are isolated from the non-coaxial straining associated with the enveloping septa (S e). This hypothesis, and also its discussions both pro and contra, suffer from insufficient attention to reference frames. We therefore attempt to demonstrate: (a) the need for rigorous treatment of reference frames in geological interpretations; (b) that, in a folding situation, grains that do not rotate with respect to their immediate matrix generally rotate with respect to the GRF; (c) that lack of porphyroblast rotation with respect to the GRF demands a rare folding mechanism (slip fold model); and (d) that the non-rotation hypothesis is in conflict with heterogeneous deformation (cleavage refraction). Finally, we question the validity of the evidence in a study by Fyson (1980), cited in support of non-rotation with respect to the GRF during folding. Fyson reported orientations of S i that are constant, after folding, over a large area; this scenario is a product of selective data acquisition. In summary, our investigation shows that the lack of porphyroblast rotation with respect to a GRF during folding, while possible, is not universal. The development of microstructures (e.g. curved S i) is only related to the local deformation path, the characterisation of which does not rely on the GRF.

Are viscosity ratios of rocks measurable from cleavage refraction?

In this Questions contribution, I consider some of the accepted methods of measuring viscosity ratios in rocks, and pose a new one. For a wide range of strain and orientations, it can be shown that the bedding normal is immeasurably close to the XY plane, and this has applications to the relationship between cleavage and strain. I therefore propose that with some limitations, cleavage refraction can provide a measure of effective viscosity ratios in layered rocks. Examples show that cleavage refraction across competence contrasts yields surprisingly small viscosity ratios. This method might also provide a way of distinguishing Newtonian from non-Newtonian behaviour of rocks over time and space.

Competence contrasts in ductile deformation as illustrated from naturally deformed chert-mudstone layers

A sample of chert-mudstone layers provides a rare opportunity for quantitative analyses of competence contrasts in naturally deformed rocks. This sample contains deformed quartz veins, possibly formed subperpendicular to bedding during initial bedding-normal compaction, and abundant radiolarians as strain markers whose viscosity during deformation is approximated by that of chert. Under several assumptions these allow quantitative analyses of two types of competence contrast in ductile deformation, layer competence contrast and inclusion/matrix competence contrast. Layer competence contrast results in strain and cleavage refraction through the layers, while inclusion/matrix competence contrast is illustrated by the difference in strain state between radiolarians and their matrix. A quartz vein presumed to be initially perpendicular to bedding provides estimates of layer-parallel shear strains and chert/mudstone layer viscosity ratios which were also used as radiolaria/matrix viscosity ratios in different layers. Radiolarian shapes are factorized into cleavage strains and pre-cleavage shapes. Cleavage strains in matrix are then determined from radiolarian strains applying Eshelby's equations, and their variations as well as the refraction of cleavage through the layers are compared with Treagus's theoretical modeling of strain refraction. With decreasing layer competence, cleavage refracts toward bedding and increases in intensity so that cleavage-bedding intersections vary slightly but systematically through the layers, suggesting a threedimensional strain refraction. All three principal axes of radiolarian and matrix cleavage strain ellipsoids estimated indeed refract from layer to layer. Strain magnitude systematically increases with decreasing layer competence. These results are consistent with the strain refraction theory. However, no systematic change in strain ellipsoid shape associated with strain refraction is recognized.

Strain refraction in layered systems

Strain refraction across competence contrasts is presented as a simple model consisting of two components, a homogeneous strain and a heterogeneous simple shear. For Newtonian materials, the ratio of the layer-parallel simple shear component in adjacent layers is the inverse of their viscosity ratio. Strong changes in ellipsoid size, shape and orientation are predicted across viscosity contrasts. The geological implications of strain refraction theory are considered within the context of the ‘cleavage/strain debate’. The particular relationships of relative competence and strain revealed by the refraction model may contribute to the problem of why cleavages of different morphologies in rocks of different lithologies (and kinematic histories) should appear to be subparallel to the XY planes of measured strain ellipsoids. Competent rocks should develop dominantly layer-orthogonal strain, and incompetent layers shear-dominated deformation. A variety of structural features ranging from cleavage refraction, changing lineation orientations, folds transected by cleavage, changes from coaxial to non-coaxial deformation, and ramp-flat fault geometry may be the result of stress and strain refraction in rocks.

A history of cleavage and folding: An example from the Goldenville Formation, Nova Scotia

Temporal relationships between cleavage formation and folding in sedimentary rock sequences can vary from either phenomena preceding the other to both occurring simultaneously. Knowledge of this relationship, however, is required to understand fully the relationship of cleavage orientation to finite strain and the origin of cleavage refraction across competent-incompetent layers. Evidence from the Goldenville Formation provides an example of cleavage formed before folding by ∼50% pressure-solution removal of material, resulting in cleavage planes normal to bedding during active folding. This layer-parallel shortening was accompanied by excess pore pressure that in some cases, exceeded lithostatic pressure, causing formation of bedding-parallel quartz veins with crack-seal textures. Folds developed by a mechanism of differential flexural flow with no loss of coherence across bedding surfaces. En echelon veins formed sequentially across some beds during active folding and subsequently were deformed by various increments of bedding-parallel shear. After folds reached ∼80° limb dips, continued horizontal shortening was accommodated by additional pressure solution, but no recognizable new cleavage was formed. Because cleavage in the Goldenville Formation formed perpendicular to bedding before folding and was passively rotated and extended by bedding-parallel simple shear during fold amplification, the resulting cleavage planes cannot lie in the XY plane of the finite-strain ellipsoid. Differential shear between metagray-wacke and slate beds accounts for the observed cleavage refraction, and the bedding-cleavage angle provides a good estimate of the shearing across these beds during active folding. If cleavage can be shown to postdate folding in other examples, it is possible that cleavage planes will lie in the XY plane of the finite-strain ellipsoid.

“Fracture cleavage” in the Duluth Complex, northeastern Minnesota

An unusual cleavage is developed in troctolitic rocks of the late Precambrian Duluth Complex in northeastern Minnesota. It is localized in a zone −250 m wide, and it is parallel to the axes of gentle folds in rhythmic banding. The rocks show no textural signs of ductile deformation, and the cleavage is defined by fractures that are fairly straight and evenly spaced, but on a fine scale, somewhat irregular, multiple, anastomosing, and locally crosscutting. Textures indicate a purely extensional mode of development. Cleavage refraction across interfaces of bands of different composition is common. Serpentine coats the fracture surfaces and suggests that fluids were present to produce this alteration during formation of cleavage. The geological relationships and serpentinization suggest conditions of cleavage formation of 1.5–1.8 kb and 350 to 500 °C. The presence of extensional fractures indicates that cleavage formation involved crack propagation at high fluid pressures. The absence of shear fractures or ductile deformation features, and the nature of the cleavage refraction indicate that differential stresses were low. Localization of the cleavage seems to be due to the presence of a structure, probably a dike, below the layered intrusive rocks. This could have served to localize stresses and reactive fluids at high pressure during a late stage of continental rifting.

A theory of finite strain variation through contrasting layers, and its bearing on cleavage refraction

A theory of finite strain variation in contrasting viscous layers is presented. The theory is applicable to layers which are oblique to two principal strains, but parallel to the third, and is not restricted to plane strain. Results may be obtained algebraically or by use of the Mohr diagram for strain. Solutions are given for various examples of layering attitude and viscosity ratio, measured with respect to a reference layer. It is shown that the finite strain ellipsoid changes in shape and orientation across contrasting layers, and in some cases the principal axes may be exchanged. Low strain is indicated in relatively more viscous layers, and high strain with extension at a smaller angle to the layering, in less viscous layers; the latter may approximate simple shear parallel to layering if the strain is sufficiently high. The geological implications of the theory are strong strain variations in layered rock sequences. It is suggested that, in general, strain will be inhomogeneous from layer to layer both in orientation and amount. The relationship of strain and cleavage are reviewed in the Introduction to establish the validity of predicting cleavage patterns from strain data. Qualitative comparisons between the theoretical results of strain variation and natural cleavage refraction in layered rocks would appear to justify the assumption that cleavages of varied morphologies are sub parallel to the XY planes of strain. With this assumption, some three-dimensional features of planar and linear fabric refraction in contrasting rocks are predicted.

Une interprétation mécanique de la réfraction de la schistosité

Cleavage refraction is the difference in orientation of slaty cleavage of alternating layers of different lithology, such as shale and limestone. Observations in Oisans (French Alps) have shown that the cleavage-bedding intersection may have different orientations for different layers (Fig. 1). From observation of these orientations, it should be possible to derive information about the stress shape (i.e., ratio of the differences between the three principal components) and its orientation. For this, we assume that slaty cleavage in an isotropic layer: appears at right angles to the larger principal component of stress, and that this happened simultaneously in alternating layers, with different yield stresses (larger for limestone than for shale). With these assumptions, and for assumed values for the orientation and the shape of the stress in the first layer, a straight-forward calculation gives the principal orientations of the stress for the second layer. By derivation, the relation between the angular change of the cleavage-bedding intersection, and the change of cleavage-bedding angle is computed. The result is expressed by the value of angle A (see Fig. 2) of the direction in which the cleavage is shifted from one layer to the next. A set of graphs (Fig. 3), obtained by these calculations, gives the relations between the angles which can be measured (θ, angle between bedding and cleavage. A), and the unknowns: shape of the stress, as measured by ω; and orientation of the least principal component (which may be shown by the lineation). An actual example is given, in which several nearby observations are combined to obtain these two unknowns. Moreover, another set of graphs (Fig. 4), allows the computation of the ratio of the yield stress for the two alternating rock layers. Whenever cleavage refraction can be observed for incipient cleavage, these two sets of graphs may be used to obtain information about the stress. However, a large strain involves such changes in cleavage orientation that the basic assumption may no longer be valid, and our graphs should be used with caution.

Constraints on geological strain rates: Arguments from finite strain states of naturally deformed rocks

A summary of known finite strain states is presented; longitudinal strains (1 + e) as measured in many rocks often range from 1 to 40 and 1 to 0.025. The time span available to produce such measurable strains in young orogenic zones seems to be less than 10 m.y., possibly less than 1 m.y., which constrains conventional strain rates into the range of 10−13 s−1 to 10−15 s−1. For both pure and simple shear (the most efficient way and a much less efficient way to accumulate incremental strains, respectively) the ellipticity of the finite strain ellipse increases in a nonlinear manner. Finite strain variations in adjacent layers, which give rise to features such as cleavage refraction, arise with only slight differences in the strain rates within these layers.

Stylolitic cleavage and cleavage refraction in Lower Paleozoic carbonate rocks of the Great Valley, Maryland

Closely spaced stylolitic cleavage is developed in closures of folds in Lower Paleozoic carbonate rocks of the Great Valley, west of Hagerstown, Maryland. Stylolites which are perpendicular to bedding in beds of relatively competent microspar are refracted into a more penetrative cleavage in thin layers of less competent, dolomitic micrite. Cleavage refraction is a result of shear in the micrite layers which accommodated bedding slip between the more competent microspar beds by acting as Ramsay and Graham-type shear zones. The refracted cleavage is not normally parallel to the shear plane (bedding) but may approach parallelism in extremely thin shear zones. Refraction of cleavage between greywackes and slates of the overlying Martinsburg Formation, if due to the mechanism proposed for the carbonate rocks, is incompatible with a pre-lithification origin of the slaty cleavage.

Buckling stability of a viscous single-layer system, oblique to the principal compression

A new theory is developed for single-layer buckling, where the layer is not parallel to the principal stresses. The model chosen consists of a single layer with Newtonian viscosity η embedded in an infinite matrix of viscosity η 1. The layer lies at an angle θ to the bulk principal compressive stress in the embedding medium. It is deformed in equal-area plane strain, with the direction of no strain and the third principal bulk stress, parallel to the layer; hence the obliqueness to the principal stresses is only in two dimensions. It is shown that stress refraction is a necessary condition for this system, and an expression is derived for its value in terms of η, η 1 and θ. Buckling stability equations are completely developed which satisfy the Navier-Stokes equilibrium equations for the buckling layer, and the condition of stress continuity at the layer-embedding medium interface. The dominant wavelength of the buckles is shown to be independent of θ, but the stress required increases with θ. The results of this work have an important bearing on natural folds, since there is no evidence that rock layers are initially parallel to the stresses which fold them, an assumption made in former buckling theories. It is suggested that refraction of stresses and the resulting incremental strains gives rise to the finite structure of cleavage refraction so common in deformed rocks, and that the progressive development of folds in layers oblique to the principal bulk stresses gives rise to asymmetry.

Deformation structures in the Hovin Group schists in the Hommelvik-Hell region (Norway)

Measurement of wavelength/thickness ratios of buckle-folded veins in metasediments of the Upper Hovin Group showed that the ratios are rather constant within individual exposures although there are considerable variations from exposure to exposure. Straight and pinching and swelling veins usually make low angles with the cleavage, while veins showing the maximum degree of folding usually make high angles with the cleavage. Veins of an intermediate orientation show a moderate degree of folding. Such a relationship suggests that the cleavage is parallel to the plane of maximum extension in these rocks. The phenomenon of cleavage refraction is explained by variation in the nature of strain in beds of unlike competency. The attitude of cleavage depends chiefly upon three factors, viz.: 1. (1) layer-parallel compressive strain; 2. (2) shear strain generated during buckling; and 3. (3) rigid rotation of the competent layers. The diverging and converging attitudes of cleavages can be explained by the relative importance of these factors. From occurrence of stretched pebbles at an angle to cleavage, from presence of boudinage at hinges of folds, and from recognition of rotated tension gashes, it is suggested that the beds have undergone a period of stretching before the present system of folds had developed.