The deformation of a clast in a folding rock can be described in general, in terms of four kinematic components: (1) A bulk pure shear orthogonal with the axial plane of the fold (Fig. 8d). (2) A simple shear component parallel to bedding due to a flexural slip component of the folding (Fig. 8c). (3) A rigid body rotation due to rotation of the fold limb (Fig. 8b). (4) A simple shear parallel to the clast long dimension engendered by traction on the clast boundary due to rotation relative to its matrix.

Fig. 8 Summary of the interpretation of the foliation development. (a) Initial fabric with shale clasts (red) slightly inclined to either side of bedding (horizontal). (b-d) Kinematic components causing rotation of the long dimension of the clasts. (b) Spin of fold limb; clasts do not rotate with respect to bedding, but rotate relative to the axial plane of the fold (vertical). (c) Bedding-parallel shear; both clasts rotate anticlockwise with respect to bedding, but clast 1, having already reached parallelism with the shear plane is in a meta-stable orientation. (d) Bulk pure shear component with horizontal shortening; both clasts rotate with respect to bedding and the axial plane and their direction of rotation is determined by their orientation relative to the shortening direction. (e-i) Diagrammatic representation of the interpreted sequence of events during folding, showing contrasting histories of clasts 1 and 2. (e) Initial bedding-parallel shortening and clockwise and anticlockwise rotation of clasts 1 & 2 respectively. (f-h) Rotation of clasts relative to bedding and the fold axial plane at dips of 20 , 45 & 60 . A combination of the limb-spin (b), simple shear (c) and pure shear (d) components has been assumed. (i) Additional pure shear component. (j & k) Diagrammatic representation of the deformation within crenulated clasts derived from clasts 2 & 1 respectively. The three stages in each represent initial shortening, rotation and subsequent shortening in a different direction. In reality, rotation and shortening are synchronous, but never-the-less non coaxial. See text for further discussion.

In the situation where S_se and S₂ are approximately perpendicular, in a symmetrical fold hinge, it is reasonable to assume that the bulk shortening was approximately parallel to bedding throughout the deformation. In such a situation a clast that was oriented with its long dimension and S_i foliation exactly parallel to the bulk shortening direction would shorten symmetrically by crenulation of the clast and its internal foliation (Fig. 4c & f). This would result in an irregular outline to the clast (Figs. 4f & 5c & d). There would be no rotation of the clast because of the symmetry with respect to the pure shear shortening component and because there is no bulk rotation of bedding or shear parallel to bedding as on a fold limb. There would therefore be no simple shear component within the clast. However, such clasts would be in a state of unstable equilibrium, with respect to the bulk shortening direction, in that the slightest clast-scale perturbations in flow, may jostle the clasts out of this special orientation. Such perturbations are inevitable in materials as mechanically heterogeneous as a sediment. When no longer parallel to the bulk shortening direction the clasts would begin to rotate, and the kinematics would become more complicated as discussed below.

In the same situation with respect to the fold, but with a clast initially slightly inclined to bedding or jostled into such an orientation, the clast is inclined to the pure shear shortening direction. Its history now becomes more complex and its long dimension will rotate (Fig. 4b & e). It may do so passively, i.e. the strain of clast and matrix may be homogeneous with no stain discontinuity along the clast boundary. Alternatively rotation may be active in that it has a rigid body rotation component relative to its matrix. Such an actively rotating clast may also be undergoing shortening parallel to the bulk shortening direction and there may also be an internal simple shear component parallel to its long dimension. The relative importance of the components at any given stage in the history will depend on the orientation of the clast relative to the bulk strain axes at that stage.

Starting with a clast that was close, but not exactly parallel to the bulk shortening direction, the pure shear component would tend to shorten the clast and to rotate (passive rotation) its long dimension (Fig. 4b & e). Shortening would produce symmetrical or near symmetrical crenulations and the nearer the initial orientation of the long dimension of the clast to the bulk shortening direction the better developed the crenulations would be. If the clast experienced a component of active rotation there would be shear parallel to its long dimension and the crenulations would become asymmetrical (e.g. Bayly, 1965). Passive rotation would also result in the crenulations becoming asymmetrical, but the two situations can be distinguished theoretically because active rotation results in overturning of the crenulations relative to the vertical S_2e (Fig. 8j & k). Unfortunately it has not been possible to make this distinction in an actual fold hinge. Most clasts in the hinge tend to be the symmetrical type (Fig. 4f), and the few asymmetrical clasts that do occur are not truly diagnostic because of irregularities and heterogeneity of strain. However, the crenulations look more like the passive type suggesting that there has been no active rotation. This is consistent with the fact that there is no reason to believe that the shale clasts are more competent than the matrix.

It is to be expected that the initial angle between some clasts and the bulk shortening direction would be sufficiently large that no crenulations would develop (Fig. 4a & d). Obviously this is true where the initial orientation of the long dimension is in the instantaneous stretching field of the bulk strain. However, even at lower angles, crenulations might not develop, simply because the magnitude of the shortening was insufficient; in experimental deformation there is generally a significant (15% plus) amount of shortening before crenulations become apparent. Further, if very open crenulations developed while the foliation was in the shortening field they could be unfolded, once the enveloping surface to the crenulations rotated (passively or actively) into the extensional field (cf. Williams and Schoneveld, 1981). Consequently it is to be expected that some clasts would rotate without evidence of crenulation. These clasts would rotate towards parallelism with S_2e and would increase in length as they rotated. The result would be a clast of increased length with its long dimension, S_si and S_i all parallel, and approximately parallel to S_2e (Fig. 4d). Such clasts would tend to have smooth outlines since their initial outline was probably smooth and there is no micro-scale folding to modify it (Fig. 3).

On the limb of a fold there are further complications. Clasts undergo a rigid body rotation (Fig. 8b), together with the rest of the fold limb, relative to the axial plane, and therefore relative to the bulk pure shear component. In addition there is potentially a component of simple shear parallel to bedding (Fig. 8c), which will tend to deform the clasts. If rotation of the limb is clockwise the simple shear component will result in anticlockwise rotation of a clast with respect to bedding (Fig. 8c). The pure shear component will rotate the clasts both ways relative to the axial plane depending on the orientation of the clast with respect to the shortening direction (Fig. 8d). The net rotation is the sum of the three components. There are too many unknowns to analyse the relative significance of these components in detail, however some general comments can be made.

Three of the kinematic components affecting clasts are shown diagrammatically in Figure 8. The fourth one, shear within the clasts in response to their active rotation relative to their matrix, is omitted because it is thought to be negligible in the Woody Island rocks. The points were already made that there is no obvious competence contrast and therefore no reason for active rotation, and that the geometry of crenulations in the hinge suggests that there is no active rotation. On the limbs the clast geometry (Fig. 4e) indicates that the clasts have undergone a non coaxial straining (see Fig. 9). However, in the limb environment the non coaxial deformation need not be a product of traction due to active rotation of the clasts, because the combined affect of the bedding parallel simple shear and the bulk pure shear can result in the overturned appearance (Fig. 8j & k). In view of this and the lack of evidence of competency contrast it is assumed that the rotation of the clasts is passive.

In Figure 8a two clasts dip gently in opposite directions symmetrical about the bedding plane. Only clast 2 is capable of developing an antithetic crenulation cleavage anticlockwise of the long dimension of the clast (see Fig. 8j). For clast 1 to develop such a geometry it would first have to rotate through the horizontal or through the axial plane and there is no mechanism for it to do so. Either clast has the potential to rotate without crenulating so that its long dimension is parallel to S_2e if initially inclined to bedding at a sufficiently large angle. Figure 8e-i shows a possible sequence of events that would lead to the observed characteristics of the foliation and clasts. Initial pure shear shortening rotates both clasts away from the bedding orientation towards the normal to bedding. Initially both clasts are shortened and there is the potential for crenulations to develop if the strain magnitude is sufficient. Folding, and therefore limb-rotation, starts (probably after a small amount of bedding-parallel shortening), so that clast 1 is rotated towards the pure shear extensional axis, and clast 2 is rotated towards the shortening axis. However, both rotations are reduced by the simple shear component, and the rotation of clast 2 is also reduced by the pure shear component. Given the right balance of the different components, orientations of clast 1 in the shortening field and clast 2 in the extensional field can be maintained without clast 2 rotating through the shortening axis (Fig. 8f-h). As the folds tighten and lock-up, the limb-rotation and limb-parallel shear decrease in importance and the pure shear component continues to rotate both clasts towards the extension direction (Fig. 8i). Since clast 2 spent much of its history in the shortening field it can be expected to be crenulated and by the end of deformation the crenulations will generally be asymmetrical and antithetic. In contrast clast 1 might have rotated into the extensional field early enough to remain uncrenulated. Similarly oriented clasts more nearly parallel to bedding might stay in the shortening field long enough to crenulate before rotating into the extensional field (Fig. 8k). In the Woody Island rocks these would be the rare clasts, which having rotated the opposite way to the limb, have a synthetic cleavage (Fig. 8k).

Fig. 9 Diagram showing that the observed morphology of the clasts cannot be achieved simply by a pure shear deformation. In (a) a clast has been shortened sufficiently to produce symmetrical crenulations. (b & c) Continued shortening perpendicular to the axial plane (parallel to S2e) of developing F2 folds, results in the crenulations becoming increasingly asymmetrical, as is observed in the Woody Island material. However, the resultant foliation S2i (see c) is essentially parallel to S2e and does not have the typical appearance of the asymmetrical crenulations. (Note that S2i is parallel to the axial plane of the crenulations). (d - f) represents a different approach; (d) is the typical observed morphology with S2i anticlockwise of S2e, and (e & f) represent stages in its unstraining, assuming pure shear. When almost parallel to bedding (horizontal) the crenulation is seen (f) to be very asymmetrical, which is considered unacceptable for the initial microstructure. See text for further discussion.

Finally, there is the possibility for some clasts, even on the fold limb, to deform symmetrically without any rotation. On the limb, this would be a fortuitous situation and therefore rare but given the right balance of rotations it is possible. This would explain the symmetrically crenulated clasts observed in the Woody Island fold limbs. If strain were large enough such clasts would be the ones that have a penetrative foliation (S_2i) perpendicular to S_si.

Several lines of evidence indicate that penetrative foliation on Woody Island has developed by this process of micro-transposition. First, the penetrative foliation is most common in high strain domains such as the concave side of competent layer folds or in clasts that have S_si approximately parallel to S_se, but are nevertheless elongate parallel to S_2e, suggesting high strain. Second, all gradations between crenulation, crenulation cleavage and the S_2e-parallel penetrative foliation are observed in different clasts. More significantly, the same gradation can be observed in a single tapered clast, the broad end of which, is protected from the strain experienced by the narrow end, by an adjacent strong clast. In the strain shadow area there is a crenulation cleavage which changes progressively into a penetrative foliation as traced into the high strain area (Fig. 6).

Thus the S₂ foliation in the Woody Island rocks is believed to have developed by a process of transposition at various scales. The transposed foliation is an early surface mimetic after a sedimentary foliation, defined by the preferred orientation of clasts and matrix micas and by S_i within the clasts. At clast-scale, transposition involves flattening and/or rotation of clasts as well as folding of bedding (S_se). Commonly, rotation of clasts involves no internal folding so that S₂ is defined by S_i which, if modified at all, is simply accentuated by flattening perpendicular to its original orientation (Fig. 4d). Elsewhere, deformation of clasts has produced symmetrical crenulations within the clasts which rotate S_i into the S_2i orientation (Fig. 4f). Mostly however, initial symmetrical crenulations have been converted by a complex interplay of the three kinematic components into asymmetrical crenulations (Fig. 4e). In domains where the strain magnitude is large enough the crenulations may become too tight to recognise as such and transposition may result in a penetrative S_2i. Mostly however, rare relic crenulations indicate the transposition origin.

The model outlined above was developed by conceptually forward modelling the deformation of an assumed initial fabric based on undeformed sediments. Where alternatives were possible a choice was made that was most consistent with the observations. The result is a model that is capable of explaining all features of the observed microstructures including the relative abundance of end-member types in the fold hinges and limbs. End-member 1 (Fig. 4f) is most common in the fold hinges because there is less tendency for clasts in that environment to rotate relative to the bulk pure shear component of deformation. It is the least common end-member on the fold limbs where end-member 3 (Fig. 4d) is the most common, because the tendency for rotation relative to the bulk pure shear component is large on the fold limbs.

This model is presented as the most reasonable interpretation of the microstructure of the Woody Island rocks.