Foliation development — The contribution, geometry and significance of progressive, bulk, inhomogeneous shortening

Tectonophysics, 75 (1981) 273-296 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

273

FOLIATION DEVELOPMENT - THE CONTRIBUTION, GEOMETRY AND SIGNIFICANCE OF PROGRESSIVE, BULK, INHOMOGENEOUS SHORTENING

T.H. BELL Department

of Geology, James Cook University P.O., Townsville, Qld. 4811 (Australia)

(Received June 3,198O;

revised version accepted January 29,1981)

ABSTRACT Bell, T.H., 1981. Foliation development - the contribution, geometry and significance of progressive, bulk, inhomogeneous shortening. Tectonophysics, 15: 273-296. The geometric consequences of modelling deformation histories involving pure shear, simple shear, inhomogeneous simple shear and bulk inhomogeneous shortening are reviewed. It is shown that zones of rock affected by these deformation histories have similar discontinuities on most of their boundaries with unaffected rock. The “space problem” of progressive pure shear and bulk inhomogeneous shortening can only be resolved if the maximum finite elongation plunges down the dip of any associated foliation plane. However, many fold belts and a number of mylonite zones possess this property and consequently bulk shortening deformation histories must be considered in such cases. The strain field in these models does not account for the inherently heterogeneous nature of deformation on all scales and they generally cannot accommodate the anastomosing character of foliations as it reflects variation in strain. Hence a model is required that provides a solution to the boundary discontinuities associated with bulk shortening and which can accomodate the heterogeneous and anastomosing nature of strain in rocks. An unusual geometry called a “millipede microstructure” preserved in crenulated and crenulation cleavages and also in inclusion trails in plagioclase porphyroblasts is described in Bell and Rubenach (1980). This structure represents a specific deformation history which involved bulk inhomogeneous shortening. A number of constant-area (volume) models of the possible strain in this structure were developed that accommodate the effects of change and/or redistribution of volume, variation in strain and a heterogeneous distribution of inhomogeneity. They also provide a solution to the boundary discontinuities of progressive bulk inhomogeneous shortening. Some of the implications of these models are as follows: (1) Mylonite zones can form by progressive, bulk, inhomogeneous shortening with or without a large noncoaxial component. (2) Foliations formed by progressive, bulk, inhomogeneous shortening must anastomose if the foliation is to remain planar on the average and that this reflects strain variation, both in degree and orientation. (3) Metamorphic differentiation associated with crenulation cleavage development may be controlled directly by strain, strain rate and local strain history variation and only indirectly by stress. (4) Foliations develop on the local scale parallel or nearly parallel to the XY plane of the strain ellipsoid whether they be slaty or crenulation cleavages, schistosity, gneissosity 0040.1951/81/0000-OOOO/$

02.50 0 1981 Elsevier Scientific Publishing Company

or mylonitic foliations. However on the bulk scale of a I’old limb the!- w11i commonly lie at a low angle to the XY plane of the strain ellipse. (5) The microstructure of individual mineral species nlay pruv~tit~ ~‘t‘~t~~r~at’or clistitl guishing strain history, and individual minerals in favouretl orientations for slip control subsequent development of heterogeneity. (6) Geometric criteria exist on various scales which allow tlifferc~ntintion between bulk shortening and shear strain histories. (7) Many arcuate fold belts can be readily explaned by non-plane strain ttur~nc thrir development.

INTRODUCTION

In recent years the significance of the deformation history associated with foliation development has been emphasized (e.g. Donath and Wood. 1976: Hobbs et al., 1976; Williams, 1976). Williams, from a theoretical point of view, also considered in some detail the relationship between axial plane foliations and strain. He concluded that foliations, including slaty cleavage and schistosity, are not precisely parallel to a principal plane of finite strain in the general case such as on fold limbs. He suggested that the apparent conflict arising from this with regard to strain measurements made in slate belts, which appear to show that the slaty cleavage is precisely parallel to the XY plane of the strain ellipse (e.g. D.S. Wood, 1974), could be resolved in a variety of ways (see Williams, 1976, p. 194). Williams (1976) and more recently Gray and Durney (1979) also considered the mechanical significance of crenulation cleavage, and hence ultimately its deformation history. Bulk strain history measurements made by Gray and Durney have shown that small scale crenulation cleavage can follow with no detectable discordance, the orientation of the bulk progressive strain ellipse in highly non-coaxial deformation. They recorded a maximum deviation of 4 degrees from it at more advanced strains due to a tendency for the cleavage to behave in a passive manner. Hence, they suggested that the concept of crenulation cleavage as a plane of shear needs to be re-examined as the cleavage cannot be normal to the direction of greatest total shortening if this is the case. A widely accepted view on mylonitic foliations is that whilst they conform with the XY plane of the bulk strain ellipsoid, they are products of a deformation history involving dominantly shear rather than shortening (e.g. Bak et al., 1975; Escher et al., 1975; Wilkinson et al., 1975). This is partly a function of their common association with major thrusts. However, it is also due to the boundary discontinuities and space problems associated with bulk shortening (e.g. Escher and Watterson, 1974). Such problems appear daunting if one considers a large component of bulk shortening in mylonite production, because of the huge strain involved. This paper is an attempt to rationalize and resolve the “boundary” and

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“space” problems associated with progressive, bulk, inhomogeneous shortening, and to encourage due consideration of this shortening during foliation development. It also appears to provide a possible solution to some of the problems associated with foliation development discussed by Williams, Gray and Durney. REVIEW

OF STRAIN

MODELS

The strain models which have been described in the literature (e.g. Ramsay, 1963, 1967; Escher and Watterson, 1974) are drawn so that their broad outlines mimic known or conceivable geometries. They are constructed to conserve area, and hence volume in three dimensions because if the model is possible at constant volume it can certainly be modified to accommodate diiation or reduction. The reverse procedure of course, is not necessarily the case. Construction of models at constant area/volume, however, places very tight constraints on the possible geometry of strain especially when the model is expanded to simulate a mass of fold belt dimensions. The geometric effects of a variety of the deformation histories, modified from Ramsay (1963), are shown in Fig. 1. This figure includes the strain

b

c

Fig, 1. Sketches, modified from Ramsay (1963), of strain fields generated in a block of originally undeformed rock (a), by deformation histories which involved; (b) progressive simple shear, (c) progressive, inhomogeneous, simple shear, (d) progressive pure shear, (e) coaxial progressive, bulk, inhomogeneous shortening (Ramsay’s 1963 inhomogeneo~ form of pure shear), and (f) non-coaxial progressive, bulk, inhomogeneous shortening.

276

Fig. 2. Sketch showing the boundary d&continuities associated wrth progressive purta shear. Note that faults or possibly shear zones would form on al1 boundaries of an isolated block of rock that underwent this type of deformation history. Two of these, at the base and top can be ‘accommodated if the zone of rock affected extends all the way through the lithosphere. There would be no space problem provided the deformation involved approximately plane strain and the maximum finite elongation plunged steeply as shown. The lithosphere would simply thicken up and down with erosion taking place at the surface.

fields resulting from: (1) Progressive simple shear - non-coaxial, plane strain (Fig. 1 b), (2) Progressive, inhomogeneous, simple shear - non-coaxial *, plane strain (Fig. 1~). (3) Approximately progressive, simple shear --- non-coaxial, non-plane strain (Fig. lb). (4) Approximately pro~essive, inhomogeneous, simple shear ----noncoaxial *, non-plane strain (Fig. lc). (5) Progressive pure-shear - coaxial, plane or non-plane strain {Fig. Id). (6) Progressive, bulk, inhomogeneous shortening (flattening). This divides into two main categories where: (a) the centres of bulk boundaries are displaced relative to the average direction of flattening as shortening occurs -. non-coaxial on the bulkscale - plane or non-plane strain (Fig. If); (b) the centres of bulk boundaries are not displaced relative to the average direction of flattening as shortening occurs - coaxial on the bulk scale - plane or nonplane strain (Fig. le). (N.B. Any of the above deformation histories can be combined with volume change.) The discontinuities that occur between zones of rock affected and unaffected by progressive pure and simple shear are shown respectively in Figures 2 and 3. It is immediately evident from these figures that progressive pure shear, as opposed to progressive simple shear, has an extra boundary discontinuity. For the former to occur, faults or shear zones must develop on all margins of the rocks affected by it. This mode of deformation also creates a space problem (Fig. 2). However, this can be accommodated by * These deformations can in special circumstances have coaxial strain paths on the bulk scale where the principal strain axes do not rotate during the deformation. Non-coaxial and coaxial refer to whether the principal axes, at the scale of consideration of the strain, do or do not rotate respectively during the deformation.

277

b

Fig. 3. Sketches showing the boundary discontinuities and their possible solution for progressive simple shear (these apply to progressive inhomogeneous simple shear also). This mode of deformation has all the boundary discontinuities of pure shear, except the two boundaries which in this model are parallel to the shear plane. Two of the other boundary discontinuities at the base and top in (a) and (b) can be accommodated if the zone of rock affected extends all the way through the lithosphere. There would be no space problem in (a) if the maximum finite elongation was steeply plunging. However, if it was horizontal, as in (b) the zone of deformation would have to end in fold and thrust belts (c), rift zones (d), mid-ocean ridges or arcs. Note that these zones can also end in a zone of deformation which involved a large component of progressive, bulk, inhomogeneous shortening. In these situations the problems arise of how to distinguish where along the zone progressive simple shear with no component of shortening has occurred or, if indeed, this happened at all.

thickening of the crust as long as the maximum finite elongation plunges steeply down the dip of the foliation produced. Such a deformation history is possibly quite rare in nature. Progressive simple shear and inhomogeneous simple shear produce simple displacements across zones of intense deforma-

278

tion with no boundary discontinuities parallel to the shear plane (Fig. 3). However, they have similar problems to progressive pure shear in the other directions and their XZ oriented boundaries along the Y direction must end in faults or shear zones {Fig. 3a). If X (the maximum finite elongation direction) approximately follows the strike (Fig. 3b), they must end in fold belts, rifts, subduction zones or mid-oceanic ridges (Fig. 3c and d). Ramsay (1963, Figs. 5/2, 5, 6, and 7) featured a number of models of strain in folded layers which could have resulted from progressive, bulk, inhomogeneous shortening. These models do not conserve volume at their concave cores and therefore could only apply to certain layers in a folded mass. If strain distribution patterns could be constructed for these core regions without decollements they would have unusual geometries. While such anomalous strain distributions may occur, as suggested for example, by unusual cleavage orientations in schists or slates in the concave hinges of folds in quartzites, they have not been recorded in a total rock mass of relatively uniform composition. Accordingly, it appears unlikely that such models can be applied on the scale of an entire fold belt unless decollements are present. Ramsay (1967, fig. 7.104) featured another interesting strain model. Its construction, however, entailed uniform flattening in the upper pat of the diagram which introduces most of the boundary discontinuities of pure shear for this segment. Ramsay’s (1963) model of inhomogeneous pure shear (Fig. 4a) solves two of the boundary problems of pure shear. This geometry would result from a special form of progressive, bulk, inhomogeneous shortening. The lateral boundaries in the third dimension, parallel to the X2 plane, have to be accommodated by faults or shear zones (Fig. 4b). Provided this mode of deformation extends down to the upper mantle, there is no difficulty in accommodating strain at the base of the zone affected. However, if it only affects an upper portion of the crust, a decollement zone or fault must occur at its base, The space problem can be resolved as long as the maximum finite elongation plunges approximately down the dip of the foliation produced by such a deformation history. Crustal thickening would be natural consequence of this (Fig. 4a and c), Since downward thickening is likely to require greater force than that necessary to overcome gravity, a larger upward component could occur resulting in uplift, isostatic readjustment and erosion. However, some problems are associated with this model. These are as follows: (1) Constant extension is required along any line parallel to the flow direction. If this had not occurred the vertical parallel lines in Figure 4 would have splayed out or converged on the axial plane of the fold as is illustrated by Fig. 5. Rocks are heterogeneous on all scales ranging from grain boundaries to rheological variation associated with change in temperature and pressure in a section through the earth’s crust. Hence the possibility of a constant extension along any line parallel to the flow direction (i.e. up the axial plane of a fold) from the base of the crust to the earth’s surface, or even over a distance

279

b

Fig. 4. Sketches showing Ramsay’s model of an inhomogeneous form of pure shear (a), and modifications to it. This is a special type of progressive, bulk, inhomogeneous shortening. (b) shows the boundary discontinuities of this model in three dimensions which are similar to those for progressive simple shear (c.f. Fig. 3). Two of them (at the base and top) can be accommodated provided the zone of rock affected extends all the way through the lithosphere. There would be no space problem provided the maximum finite elongation plunged down the dip of the axial plane and the deformation involved approximately plane strain. The crust would thicken but could only do so upwards. However, the model shown in (c) would allow thickening in both directions. (d) shows how strain variation can be accommodated in the Y direction by anastomosing the axial planes and how that the fold axes would change plunge as their axial planes curved if this could occur. (e) shows a solution to the remaining boundary discontinuities.

280

Fig. 5. Sketches taken from Tulhs tion of foliation which developed sections sketched were cut through axis of compression. (a) underwent shortening. Note how the foliation vertical

in both

et al.‘s (1973) fig. la and 1 d. They show the orientaduring experimental deformation of quartzite. The the centre of the deformed cylinders parallel to the 34% sample shortening; (b) underwent 53% sample whorls off towards the axis of compression which is

diagrams.

of one metre along a foliation plane, on the scale of grain boundaries, is unlikely. This is due to the interaction between grains in different orientations and of different composition in which the grain boundaries (and kink-band boundaries) are the most highly strained regions where recrystallization begins, whereas the grain centres are less strained (White, 1979). This phenomenon has been experimentally confirmed and evaluated by Ch. Spiers (personal communication, 1979). (2) Tectonic foliations almost always anastomose in three dimensions, usually on a range of scales. For example, slaty cleavages anastomose on the scale of phyllosilicate trails around quartz-feldspar or calcite rich ellipsoidal pods. Mylonitic foliations behave similarly on the scale of finely recrystallized new grains around megacryst remains of older grains. They also anastomose on the scale of kilometres as zones of intense mylonite enveloping less deformed ellipsoidal pods of country rock (Bell, 1978a). Gneissic foliations, schistosities and crenulation cleavages always anastomose to some degree. If the anastomosing foliations reflect approximately sinusoidal variation in the orientation of the XY plane of the strain ellipsoid then this model does not accommodate it. (3) Fold belts occur which do not end along strike in faults or shear zones. This model can possibly accommodate variation in strain in the Y direction from one X2 section to the next through the zone of deformation. Under restricted circumstances this could produce an anastomosing effect in the YZ plane (Fig. 4d) without generating the same in the X2 plane. It would cause the fold axes and their axial planes to vary significantly in orientation (Fig. 4d and e). If the strain decreased along the length of the fold belt to zero the axial planes would have to diverge considerably as the folds reduced in profile as shown in Figure 4e. It must be emphasized that generally when the fold axis changed its plunge the axial plane would change its orientation. It is this last characteristic which caused problems with this model as fold axes

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commonly bend in their own axial planes which remain planar (Sanderson, 1973; Bell, 1978a). (4) Continuous reduction is required in fold profile amplitude from the surface down (Fig. 4a). This phenomenon has not been investigated thoroughly but it does not occur in many fold structures in terrains where foliation has developed. In the circumstance shown in Figure 4c the amplitude would decrease to zero and then begin to increase again at one point down the axial plane. A more applicable model of progressive bulk inhomogeneous shortening must be able to accommodate heterogeneities in the development of strain on all scales from grain boundaries upward. It must also maintain, on average, a planar foliation yet provide for an anastomosing foliation. It should ideally be flexible enough to accommodate any fold profile. A NEW MODEL

Bell and Rubenach (1980) recorded an unusual geometry preserved in inclusion trails in “millipede porphyroblast microstructures”. A number of strain models of the geometry produced by progressive, bulk, inhomogeneous shortening have been developed by attempting to simulate this microstructure. These models were constructed for a bulk strain ratio of 21 : 1 using a digitizer to maintain constant area for each original square after the “millipede microstructure” had been reduced to the minimum pattern repeat required to develop it. Figures 6 and 7 show the geometric changes in a block of squares when affected by such a deformation history. These models maintain constant area (volume in 3-D). However, area (volume in 3-D) change and/or redistribution could readily occur and allow much greater flexibility in the geometry. It should be emphasized that once an inhomogeneity in strain is established a very specific strain field within the scale of that heterogeneity is developed. This geometry mimics that recorded in natural rocks and it may be quite common on a variety of scales. Of course a strain marker such as bedding or foliation can only reflect the strain field shown in Fig. 6 if it initially lay approximately at right angles to the foliation which developed during that particular deformation. The strain field shown in Fig. 6 on the bulk scale is coaxial whereas that in Fig. 7 is noncoaxial. Effects

of a change and/or redistribution

of volume

The strain fields possible with no change in area (volume) are quite restricted within an individual anastomosed unit (or cell). If volume can change and/or be redistributed then any geometry could be achieved. An interesting corollary to this is that a heterogeneous progressive, inhomogeneous, bulk shortening deformation history could possibly drive volume changes and/or redistribution (see later).

Fig. 6. Three constant area. (a) to (b) to the model and

Effects

microstructure geometry constructed at strain models of the “millipede” The bulk strain ratio in each case is 21 : 1 for the section shown. From (c) the anastomosing zone of higher strain has been spread over more 01’ hence the strain is less inhomogeneously distributed

of a change in strain

Changes in the amount of strain can readily be accommodated. These are in any case inherent even for a bulk uniform strain. A change from no strain to a bulk ratio of 2: : 1 in the X2 plane is shown in Fig. 8. Effects

of heterogeneous

distribution

in inhomogeneity

Any degree or scale of inhomogeneity can be accommodated by this model, especially if volume changes and/or redistribution occur (Fig. 9a). The space problem Provided the maximum finite elongation direction plunges down the dip of the foliation, this problem can be resolved by thickening of the crust. In fact, down dip mineral elongation lineations which reflect the maximum finite elongation are common in the youngest and hence unreoriented foliations in many fold belts (Cloos, 1947, 1971; Wood, 1974: Bell, 197813) and

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Fig. 7. A modification of Fig. 6A for a non-coaxial situation (constructed at constant area) is shown. Note that this geometry can occur on any scale in a rock from the grain scale upwards. Very similar geometries commonly occur in some crenulation cleaved rocks (e.g. Weber, 1976, plate 4, figs. 2,3,4 and 6). Fig. 8. Strain model constructed at constant area showing a transition from unstrained to strained with a bulk strain ratio of 2: : 1. This model is drawn to represent the X2 plane of strain. However, it could equally well represent the YZ plane if extension occurred in Y. Even if extension did not occur on the bulk scale in Y the strain pattern in this section could still be anastomosing. This model provides a possible solution for the two boundary discontinuities unique to progressive pure shear.

some mylonite zones (Johnson, 1960; Christie, 1963; Bryant and Reed, 1969; Bell, 1978a). If the progressive, bulk, inhomogeneous shortening involves non-plane strain on the scale of a fold belt and extension or contraction occurs in the Y direction, then the fold belt will bulge or neck, or curve in a sinusoidal fashion. This can occur without affecting the country rock away from the fold belt. The strain in YZ must anastomose in a similar fashion to X2 and can decay to zero as shown in Fig. 8. Locally the bulk strain in Y could range considerably either side of plane strain in association with its anastomosing character. This could readily average out on the bulk scale of the fold belt to plane strain in which case the belt would be linear in plan,

284 SIGNIFICANCE

This model of progressive, bulk, inhomogeneous shortening, and modifications of it due to change and/or redistribution of volume and heterogeneity, has some possibly quite significant implications for foliation development and geometry, and various processes such as metamorphic differentiation, which may have occurred in naturally deformed rocks. These are described and discussed below.

Mylonite or shear zones have been increasingly regarded in recent years as zones with a relatively straightforward strain history involving progressive simple shear or inhomogeneous simple shear (Ramsay and Graham, 1970; Escher and Watterson, 1974). This approach has difficulty explaining the gross deviation from plane strain that has been recorded in a number of mylonites (e.g. James, 1979). A possible solution to the boundary problems of bulk shortening for the high strains involved in mylonite zones is shown in Fig. 8. Consider this figure has a width scale of 100 km. The individual high strain zones within it could be mylonites with a large component of shear and shortening. However, the overall deformation of the 100 km wide block of rock could have proceeded by bulk, coaxial, inhomogeneous shortening (cf. Fig. 9a taken from Mitra, 1979). Another possibility is that Fig. 8 (with a width scale of 1 km) represents the edge of a mylonite zone which developed by coaxial, bulk, inhomogeneous shortening. Figure 7 shows the type of geometry that could be derived in a mylonite with a highly non-coaxial deformation history. These geometries are quite similar to those observed on a large variety of scales in many individual mylonite zones (e.g. Fig. 9b). Ramsay and Graham (1970) showed that if the walls of a shear zone are undeformed and volume change is unimportant, such zones can only be formed by the process of heterogeneous simple shear. However, it may be difficult to tell whether the walls are undeformed. The model presented in Fig. 6a shows that the strain on the margins of the less deformed ceil adjacent to the zones of high strain is very low and hence may not be distin~ishable in an outcrop. Yet the zone of intense deformation (shear zone) has quite a large component of bulk shortening combined with the shear. Not only that, on the bulk scale relative to this figure, the strain is coaxial. Hence one may not be able to readily apply Ramsay and Graham’s criteria in the field without detailed strain analyses. Mitra (1979) has described a deformed basement in the Appalachians which has shortened by the production of ductile deformation zones. These zones are geometrically, extremely heterogeneous examples of the type of strain pattern described here and could have been readily produced by progressive, inhomogeneous, bulk shortening (Fig. 9a).

a

“ductile deformation zones” or Fig. 9. a. Sketches of extreme examples of anastomosing mylonite zones after Mitra (1979) which are associated with a radically inhomogeneous distribution of strain. Note that both senses of shear are apparent in these sketches and hence the zones of intense deformation can readily accommodate bulk shortening as indeed was claimed by Mitra. b. Photograph of a more homogeneous example of an anastomosing mylonite (Bell, 1978a) where the strain variation is spread out over a greater distance and hence the foliation follows a smoother path (c.f. Figs. 6a and 7).

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An interesting development from this model is a possible explanation as to why foliations anastomose. In the special case considered by Ramsay (fig. le) the flow lines are parallel. That is, the component of shortening is constant along any line parallel to the axial plane, but varies along any other line. Consequently foliations defined by elongated and/or preferentially oriented platy grains which developed in association with such a geometry would be expected to be very planar. Any single variation in the component of shortening along any line parallel to the axial plane would cause a cumulative effect through ail parts of the structure beyond that point. The flow lines would curve away from one another producing a geometry like that shown in Fig. 5. If strain heterogeneities occurred during the deformation along the axial plane of a fold as well as across it, then any local increase in strain must be accommodated in an adjacent region by a local decrease. Since rock bodies are extremely inhomogeneous on all scales, an equally wide range of strain heterogeneities could be developed. The zones of higher strain must anastomose back and forth on a similar range of scales to remain planar on average. Consequently, the elongated and aligned grains which define t?hr folia.. tion in these zones must also anastomose (Figs. 6 and 7). Mylonitic rocks contain the most extreme examples of anastomosing foliation. They also contain the greatest local variations in strain intensity. Yet on average, mylonitic foliations have commonly quite a planar distribution. Consider that the deformation producing a mylonitic foliation requires that. the foliation on the average remains approximately planar over large distances, yet the strains involved are very great and very inhomogeneous in their distribution. Consider also that the deformation history was dominantly progressive, bulk, inhomogeneous shortening. Applying the geometric model developed here, and for a start maintaining constant volume, one finds that the zones of high strain must anastomose to an extreme degree (Fig. 9a). Consequently the foliation must anastomose to an extreme degree also (Fig. 9a and b). This can preserve large areas of relatively unstrained material in between the zones of intense deformation. The converse effect is seen in the development of a pervasive slaty cleavage. In rocks affected by such a deformation the foliation anastomoses on a very fine scale giving very planar mesoseopit cleavage planes on a hand specimen scale, viz., roofing slates. If the slaty cleavage developed via a progressive, bulk, shortening strain history, and if the foliation is to remain on average planar on the scale of roofing slates, then the model requires that the distribution of anastomosing zones of high strain be developed on a very fine scale. The same applies to pervasive crenulation cleavages, developed by such a strain history. Of course, the strain in mylonites is extremely heterogeneous even on the scale of grains and consequently they anastomose far more on a thin section scale than slates do.

287

Metamorphic differentiation Metamorphic differentiation associated with crenulation cleavage development is spatially related to the strain pattern produced in the crenulated cleavage. That is, even rocks containing crenulations but no crenulation cleavate are sometimes differentiated. This is directly associated with the microfold geometry with limbs being differentiated with respect to hinges (c.f. Hobbs et al., 1976; p. 251, Marlow and Etheridge, 1977). Dieterich (1969) has shown that the pattern of lines drawn perpendicular to the maximum principal component of stress (01) and shortening (Cl) respectively (in 2-D) are different in certain regions of a fold (compare figs. 2 and 3B in Dieterich, 1969). This is especially so in the limbs. Lines drawn perpendicular to Cl in these regions diverge in orientation away from the axial plane of a fold in a much more pronounced manner. That is, the anastomosing character is much more pronounced in the strain than the stress pattern. Hence, if stress and strain vary relative to one another around a macroscopic fold with an axial plane crenulation cleavage, then it is apparent that any differentiation relates directly to the strain and only indirectly to the stress pattern. This implies that although the stress provides the driving force that generates differentiated crenulation cleavage, variation in strain and/or strain rate and/or strain history controls its local development. Consider the model of progressive bulk inhomogeneous shortening presented here (e.g. Figs. 6 and 7). The anastomosing pattern and heterogeneity of strain shown were obtained from a specimen containing crenulation cleavage (fig. 2 in Bell and Rubach, 1980). The crenulation cleavage followed the zones of high strain to either side of the ellipsoidal pods of lower strain which contained the relic crenulated cleavage. Therefore, when this specimen was deformed large strain gradients were progressively developed between the microlithons of crenulation cleavage and the zones of crenulated cleavage. The variation in dislocation density generated by this would have produced chemical potential gradients. Large strain rate gradient may also have developed across these zones of strain heterogeneity. These would have enhanced the chemical potential gradients established by the strain variation. The noncoaxial component of the deformation would have increased with the strain. In fact it changed from virtually zero in the lower strained ellipsoidal pods to a similar order of magnitude to the shortening component in the anastomosing high strain zones. This may have induced different deformation mechanisms to operate in the high strain zones and thus have enhanced diffusion of ions away from them in response to the chemical potential gradients established by the progressive development of strain, and probably strain rate, variation. Metamorphic differentiation could then have occurred and this would explain its intimate spatial relationship to the observed strain. Another possible control on differentiation is simply the geometrical constraints imposed on the rocks undergoing metamorphic differentiation by the more competent rocks surrounding them. For example, consider an

288

interbedded quartzite-pelite sequence undergoing a crenulation cleavage producing deformation. The pelite is constrained to conform to the geometry of the more competent quartzite. This may induce volume redistribution and/or change in the pelite because the heterogeneities of strain set up during the deformation are not sufficient alone to accommodate the geometry imposed on it. Hence, in conforming to the geometry of the competent quartzite members, volume redistribution and/or change is produced by the resultant strain rate differentials. This mechanism is possible but seems less likely than that already postulated because: (a) differentiation is intimately spatially associated with small scale crenulation cleavage; (b) differentiated crenulation cleavage occurs in rocks containing no quartzite or more competent units; (c) variation in the scale of heterogeneities within a body would predictably accommodate any fold geometry by setting up in effect in 3-D minor volume redistribution due to strain variation, without volume change being required.

Significance

of this model as to foliation

Coaxial versus non-coaxial

development

in general

strain paths

The concepts of coaxial and non-coaxial strain paths during deformation are scale dependent and could be important on one scale but not on another. For example, consider a macroscopic fold. The bulk strain history in the hinge region may have been approximately coaxial whereas that in the limb was non-coaxial. However, the axial plane foliation forming processes in both regions may have been similar and independent of whether the strain was coaxial or non-coaxial on the bulk scale. What may have been more important was the degree of coaxiality or non-coaxiality on the much smaller scale of individual or small groups of foliation planes and the heterogeneity of the strain development within the hinge and limb regions. For example, compare Figs, 6 and 7. The bulk strain in the former is coaxial whereas that in the latter is highly non-coaxial. The long axes of the ellipsoidal pods are parallel to the bulk XY plane of the strain ellipse within the pod. These pods in both figures have undergone similar coaxial deformation histories. The zones with a high component of shear strain which lie in between these ellipsoidal pods have undergone non-coaxial but somewhat similar deformation histories. However, in Fig. 6 the sense of shear changes along a zone whereas in Fig. 7 it stays the same. The difference between these two zones with respect to foliation development appears to be far less important than that between them and their neighbouring coaxially deformed ellipsoidal pods.

The relationship

of foliation

to the XY plane of the strain ellipse

Let us consider the problem of whether the foliation planes are parallel to the XY plane of the strain ellipse or parallel to planes of shear (recently reviewed by Williams, 1976, and Gray and Durney, 1979). If the foliation forms by progressive, bulk, inhomogeneous shortening then both arguments

289

appear to be correct depending on the scale of consideration of the strain (see below). The quantitative data on strain in deformed rocks would suggest that foliations form in most instances parallel or close to parallel to the XY plane of the strain ellipse (e.g. Cloos, 1947, 1971; Wood, 1974; Gray and Durney, 1979) whether they be slaty or crenulation cleavages, schistosity, gneissosity or mylonitic schistosity. However, theoretical considerations with respect to foliation development would indicate that this is impossible in a bulk non-coaxial situation (Williams, 1976) where there is a large shear component roughly parallel to the foliation, such as in crenulation cleavage. Let us consider a crenulation cleavage in the context of Figs. 6 and 7. Crenulation cleavage can form at close to constant volume with no solution transfer taking place in both bulk coaxial and non-coaxial situations - e.g. the slaty (crenulation) cleavage with no associated recrystallization in the phyllosihcate rich rocks of the northern Rheinisches Scheifergebirge (Weber, 1976, plate 1, figs. 1 and 2 -possibly coaxial - and plate 4, figs. 2, 3, 4 and 6 - noncoaxial). Hence, if the deformation involved progressive, bulk, inhomogeneous shortening, Figs. 6 and 7 could reflect the strain field in such crenulated rocks. Careful examination of these figures reveals that the ellipsoidal pods, which equate with microlithons of crenulated cleavage, are parallel and can track the XY plane of the local strain ellipsoid on the scale of the pod. Consequently the anastomosing zones with a large component of shear strain, which equate with the crenulation cleavage, can on average also track this plane on the scale of a pod. It is emphasized, however, that the strain models as drawn are for constant area (hence volume) and therefore no solution transfer. If volume changes and/or solution transfer do occur this can be readily accommodated in the strain model and the same geometric relationships would apply. In the coaxial situation (Fig. 6) the crenulation cleavage would on the bulk scale track the XY plane of the strain ellipse. However, in the noncoaxial situation (Fig. 7) this is impossible and the XY plane of the bulk strain ellipse will lie at some angle to the foliation depending on the component of shear relative to shortening in the anastomosing zones. If solution transfer and/or volume change can occur then this angle could be further reduced. This divergence of the bulk strain ellipse from the finite local XY plane and hence the foliation, is due to the heterogeneity of the strain distribution. Since the component of shear is confined to narrow zones which also have a large component of shortening, the XY plane of the strain ellipse within them is on average skewed at a very low angle relative to the foliation towards the fold hinges. However these zones displace the ellipsoidal pods in Fig. 7 relative to one another thus inducing on a larger scale than the pods, a rotation of the XY plane of the strain ellipse from the average foliation direction greater than that within the anastomosing zones themselves. Thus depending on the scale of consideration and the local degree of noncoaxiality across more than one crenulation cleavage plane, the foliation can track or be very close to parallel to the local XY plane of the strain ellipsoid

290

on average, yet be a plane of shear. Because these zones of high strain are anastomosing there is no problem of developing components of shear strain along them especially if Dieterichs’ (1969) theoretical results on divergence of the ~7~5~ and XY planes of stress and strain do occur in fold limbs during deformation.

Significance of this model during deformation

with regard to the role played by mineral species

The role of individual mineral species during deformation of pelitic rocks, for example, is often, quite varied. Consider the different roles of quartz and mica during the production of a slaty cleavage. The behaviour varies slightly from slate-belt to slate-belt, but these two mineral species commonly show a relationship whereby a quartz grain or aggregate of grains forms an ellipsoidal pod with (001) of mica wrapping around it. The strain on that scale of the quartz is analogous to that in the core of the millipede microstructure described here (e.g. figs. 1 and 2 in Bell and Rubenach, 1980). The strain in the mica is possibly analogous to that in the high strain zones where there is a large shear component combined with the shortening. In other words, when these two minerals are growing and/or deforming together in a slate the crystallographic characteristics of one appears to have caused it to accommodate the shear dominated portion of the strain history whereas the other deforms relatively slightly and accommodates a shortening dominated portion. Of course, the crystallographically dominant (001) plane in mica means that this mineral is an ideal recipient for any shear component to a deformation. It is a poor recipient for shortening especially when this occurs perpendicular to (001). Quartz, however, can play the role of mica in a slate when a iess micaceous rock such as a granite is deformed. Often in this situation the quartz will have provided the anastomosing framework around the less ductile feldspar grams. It commonly does this by deforming to long thin grain shapes or recrystallizing to a finer aggregate of grains that can accommodate the heterogeneities of strain around the feldspar margins with greater ease than a single elongate crystal. Perhaps the behaviour of individual species of minerals around others could be used to achieve a comprehension of the relative component of shortening in the strain history. For example, if a mica was compressed against a quartz or garnet grain as shown in Fig. ZOa, it could be forced to shear towards the extensional margin of this grain, causing a kink-band pattern to develop in mica as depicted in Fig. 10b and thus conserve volume across the zone. The pattern of asymmetry of the kinks with respect to (001) could be expected to be quite specific as shown in Fig. 10b if the thin section was cut parallel to the mineral elongation lineation but perpendicular to the schistosity. The asymmetry on the other side of the quartz or garnet grain should be opposite to that in Fig. lob, provided the deformation was coaxial with respect to the foliation on the bulk scale and involved progres-

291

a

b

Fig. 10. Sketches of the predicted behaviour of mica (001) deformed against ellipsoidal quartz, garnet or feldspar during approximately coaxial progressive bulk inhomogeneous shortening. Note the opposite asymmetry of kink axial planes to (001) on either side and along either edge of the ellipsoidal grain. This geometry would be expected in any section perpendicular to the foliation.

sive, bulk, inhomogeneous shortening (Fig. 10~). This would even be the case for some grains if the deformation was similar but non-coaxial. However, the strain history involved in progressive ~homogeneous simple shear could not produce this geometry if the quartz or feldspar (whatever) grain was changed to a simple ellipsoidal shape during the deformation (Fig. lla). The asymmetry of kinks of (001) of mica would be the same on either side of the elliptical end of the quartz or feldspar grain (Fig. lib and c) because of the geometry of shear during this mode of deformation. Hence, one may be able to use such microstructures to discern the deformation history. Progressive, bulk, inhomogeneous shortening could have generated either structure depending on the degree and/or dist~bution of the non-coaxial component of the strain. However, progressive shear can only produce the

cl

b

Fig. 11. Sketches of the possible (a and b) and predicted (c) behaviour of mica (001) deformed against ellipsoidal quartz, garnet, or feldspar during progressive, inhomogeneous, simple shear. Note the identical asymmetry of the kink axial planes to (001) on either side and along either edge of the ellipsoidal grain which reflects the shear couple. This geometry could be expected in a section cut parallel to mineral elongation and perpendicular to foliation.

292

one. The geometry shown in Fig. 10b and c, could theoretically form during progressive simple shear if the foliation was a product of antithetic rotation within the shear zone (c.f. figs. 31a and 32 in Weber, 1976). However, such a deformation history can be precluded if the scale of the microstructure is greater than the average width between foliation planes. Consider the asymmetry of highly elongate and folded quartz grains such as those which occur in some mylonites, around an ellipsoidal but more competent grain such as a feldspar. Since the quartz does not have a strong anisotrophy equivalent to (001) in mica, it would be expected to behave differently. Its deformation geometry could in fact be expected to appear as shown in Fig. 12a, asa result of progressive, bulk, inhomogeneous shortening. If the deformation involved progressive inhomogeneous simple shear the geometry could be expected to appear as shown in Fig. 12b. It would be necessary to check that this was a fold geometry by rotating the stage under cross polarizers and observing how the extinction moved across the quartz grain. It is emphasized that progressive, bulk, inhomogeneous shortening could give either geometry depending on the degree and/or distribution of the non-coaxial component of the strain. A.V.A. diagrams have been used by structural geologists since the 1920’s to map the distribution of variously oriented individual mineral species. They characteristically show diamond (in 2dimension) patterns, the origin of which has remained enigmatic since their discovery. However, their presence in all deformed rocks for which A.V.A. studies have been made indicates that they are a fundamental result of deformation. The model developed here suggests that these diamond shaped arrays simply reflect anastomosing variation in strain intensity on a scale larger than that of a single grain or aggregate of grains or individual foliation laminae. The orientation of individual grains in a deformed rock partially reflects the local strain

cl

b

Fig. 12. Sketches of the predicted possible geometries of highly elongate and folded quartz grains around ellipsoidal feldspar in mylonitic rocks deformed by (a) approximately coaxial, progressive, bulk, inhomogeneous shortening; (b) progressive, inhomogeneous, simple shear. These geometries could occur for both deformation histories in a section cut parallel to mineral elongation and perpendicular to foliation. However, the geometry shown in (a) could possibly occur for this deformation history in any section cut perpendicular to foliation. Note the opposite asymmetry to either side and along either edge of the feldspar in (a) and the identical asymmetry in these locations in (h).

293

environment. Certain grains may be oriented such that they control the local distribution of strain. For example, certain grains in a rock will have orientations that enable them to strain more readily should deformation initiate. Such grains will partly control the distribution of strain around them and in fact, may localize strain to their immediate vicinity. This could set up the anastomosing patterns of strain described and modelled here. Such a control has been espoused and confirmed experimentally by Ch. Spears (personal communication, 1979). Arcuate

fold belts

Arcuate fold belts (Ries and Shackleton, 1976) are not uncommon in continental areas around the world. The major bend in the Appalachian fold belt northwest of Baltimore is a good example (Cloos, 1947, 1971). Such macroscopic structures can be readily explained by progressive, bulk, inhomogeneous shortening. Consider the deformation which produced the fold belt is non-plane strain at a bulk scale equal approximately to the width of the belt. The elongation in the horizontal direction (for a deformation involving a steeply plunging direction of maximum finite elongation such as that which occurs in the Appalachians) parallel to the trend of the fold belt will generate a strain field in the YZ plane similar to that shown in Fig. 6, Such a pattern accommodates the non-plane strain by generating a bend in the fold belt, yet need not fold the continen~l interior further away. In fact, such a d~t~bution of regional strain may apply about the arc in the Appalachian fold belt (Geiser, 1979). Criteria which indicate that a bulk inhomogeneous occurred during a deformation

shortening strain history

This paper has shown and predicted a few geometric criteria which could be used to indicate the presence of a progressive, bulk, inhomogeneous shortening strain history. If such geometries cannot be found, this strain history is not precluded, since they may not be present when the progressive strain has a large non-coaxial component in which case the geometries developed would be similar to those of progressive, i~omogeneous, simple shear. A summary of these geometries and other that give similar information is given below. (1) Millipede microstructure (Fig. 6). (2) Folds on any scale that change from a synform to an antiform through an unfolded layer along their axial plane. (3) Fold axes that bend in a closed circle in their own axial plane (Bell, 1978a). (4) Folds that refold a strongly anastomosing foliation produced by the same deformation where the asymmetry changes along the axial plane parallel to the mineral elongation (depicted in Bell, 1978a, fig. 13~).

294

(5) Mica kink band asymmetry against quartz, garnet, feldspar and so on as shown here in Fig. 10~. (6) Asymmetric fold shapes in highly elongate quartz against more competent grains such as feldspar as occur in some mylonites (Fig. 12a). SUMMARY

Various models associated with a range of deformation histories are reviewed and their boundary and space problems described. In particular, those models which treat bulk, inhomogeneous, shortening are considered in detail. A strain model is presented which mimics a particular geometry called a “millipede microstructure”. This geometry provides a solution to boundary discontinuities unique to progressive, bulk, inhomogeneous shortening. The significance and implications of this model with respect to a wide range of structural phenomena are described and discussed in detail. Some of the main conclusions derived from this are as follows: (1) Mylonite zones can form by progressive, bulk, inhomogeneous shortening if the maximum finite elongation plunges approximately down the dip of the foliation. However, vertical mylonites zones with horizontal maximum finite elongation must be products of progressive simple or heterogeneous simple shear. (2) Foliations formed by bulk, inhomogeneous shortening strain histories must anastomose if the foliation is to remain on the average, planar in orientation. This anastomosing character corresponds to local variation in strain intensity. (3) Metamorphic differentiation associated with crenulation cleavage development may be controlled directly by strain, strain rate and local strain history variation and only indirectly by stress. (4) Most foliations develop on the local scale parallel or nearly parallel to the XY plane of the strain ellipsoid. However, on the bulk scale of a fold limb they will commonly lie at a low angle to the XY plane of the strain ellipsoid. (5) The geometry of individual mineral species with respect to others is extremely important information on a par with field orientation data. It can give us criteria for distinguishing a progressive, bulk, inhomogeneous shortening strain history from a progressive shear history and some of these are delineated in the text. Individual minerals in favoured orientations for deformation preferentially slip and control and localize subsequent deformation generating local strain inhomogeneity. A.V.A. diagram diamond shaped patterns appear to reflect this strain inhomogeneity on a scale greater than that of grains or foliation planes. (6) A number of distinctive geometric criteria exist which allow differentiation between progressive, bulk, inhomogeneous shortening and a strain history involving simple or inhomogeneous simple shear.

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(7) Arcuate fold belts could be readily explained by non-plane strain during progressive, bulk, inhomogeneous shortening. The strain ellipsoid pattern for such a geometry can be predicted and work currently under way on strain measurement around the arc in the Appalachians N.W. of Baltimore tends to confirm this. ACKNOWLEDGEMENTS

I would like to thank the many people with whom I have had stimulating arguments and discussions on this subject, in particular Mike Coward and others on the Barcelona Shear Zone Conference Excursion, David Elliott, Paul Karabinos, Richard Lisle, Gordon Lister, Chris Spiers, Harry Stehl, Klaus Weber and Paul Williams. I would also like to acknowledge the A.R.G.C. for grant number E7715647 which funded the project from which this paper is a partial result. Andrew Duncan, John Fawckner, Peter Jones, Mike Rubenach and Nelleke Swager of James Cook University read and criticized the paper for a structural discussion session and I thank them for their comments and suggestions for improvement of the manuscript. I also greatly appreciated critical reviews by Professors J.G. Ramsay and M. Friedman and the manuscript was improved considerably as a result of their comments. REFERENCES Bak, J., Korstgard, J. and Sorenson, K., 1975. A major shear zone within the Nagssugto gidian of West Greenland. Tectonophysics, 27: 191-209. Bell, T.H., 1978a. Progressive deformation and reorientation of fold axes in a ductile mylonite zone: the Woodroofe Thrust. Tectonophysics, 44: 285-320. Bell, T.H., 1978b. The development of slaty cleavage across the Nackara Arc of the Adelaide Geosyncline. Tectonophysics, 51: 171-201. Bell, T.H. and Rubenach, M.J., 1980. Crenulation cleavage development - evidence for microstructures in the progressive bulk inhomogeneous shortening from “millipede” Robertson River Metamorphics. Tectonophysics, 68: T9-T15. Bryant, B. and Reed, J.C. Jr., 1969. Significance of lineation and minor folds near major thrust faults in the southern Appalachians and the British and Norwegian Caledonides. Geol. Mag., 106: 412-429. Christie, J.M., 1963. The Moine thrust zone in the Assynt region, northwest Scotland. Calif. Univ. Publ. Geol. Sci., 40: 345-419. Cloos, E., 1947. Oolite deformation in the South Mountain Fold, Maryland. Bull. Geol. Sot. Am., 58: 843-918. Cloos, E., 1971. Microtectonics along the Western Edge of the Blue Ridge, Maryland and Virginia. Johns Hopkins Press, Baltimore, Md., 234 pp. Dieterich, J.H., 1969. Origin of cleavage in folded rocks. Am. J. Sci., 267: 155-165. Donath, F.A. and Wood, D.S., 1976. Experimental evaluation of the deformation path concept. Philos. Trans. R. Sot. London, Ser. A., 283: 187-201. Escher, A. and Watterson, J., 1974. Stretching fabrics, folds and crustal shortening. Tectonophysics, 22: 223-231. Escher, A., Escher, J. and Watterson, J., 1975. The reorientation of the Kangamiut Dike Swarm, West Greenland. Can. J. Earth Sci., 12: 158-173.

296 Geiser, P.S., 1979. Present knowledge of strain distribution in the Appalachian orogen. In: The Caledonides in the U.S.A., Conf., Blacksburg, Va., 6-9 September, Abstr. Gray, D.R. and Durney, D.W., 1979. Investigations on the mechanical significance of crenulation cleavage. Tectonophysics, 58: 35-80. Hobbs, B.E., Means, W.D. and Williams, P.F., 1976. An Outline of Structural Geology. Wiley, New York, 571 pp. James, P.R., 1979. Strain and microfabric development m a sheared mcgacrystic granite gneiss from the Eyre Peninsula, South Australia. In: International Conference on Shear Zones in Rocks, Barcelona, 15-17th May, Abstr. Johnson, M.R.W., 1960. The structural history of the Moinr Thrust Zone at Loch Carron. Western Ross. Trans. R. Sot. Edinburgh 64: 139-168. Marlow, P.C. and Etheridge, M.A., 1977. Development of a layered crenulation cleavage in mica schists of the Kanmantoo Group near Macclesfield, South Australia. Geol. Sot. Am. Bull., 88: 873-882. Mitra, G., 1979. Ductile deformation zones in Blue Ridge Basement rocks and estimation of finite strains. Geol. Sot. Am. Bull., 90: 935-951. Mitra, S., 1976. A quantitative study of deformation mechanisms and finite strain in quartzites. Contrib. Mineral. Petrol., 59: 203-226. Ramsay, J.G., 1963. Structure and metamorphism of the Moine and Lewisian rocks of the north-west Caledonides. In: M.R.W. Johnson and F.H. Stewart (Editors). The British Caledonides. Oliver and Boyd, London, pp. 143-175. Ramsay, J.G., 1967. Folding and Fracturing of Rocks. McGraw-Hill, New York, 660 pp. Ramsay, J.G. and Graham, R.H., 1970. Strain variation in shear belts. Can. J. Earth Sci., 7: 786-813. Ries, A.C. and Sackleton, R.M., 1976. Patterns of strain variation 111 ai-cuatr fold belts. Philos. Trans. R. Sot. London, Ser. A, 283: 281-288. Tullis, J., Christie, J.M. and Griggs, D.T., 1973. Microstructures and preferred orientations of experimentally deformed quartzites. Geol. SOC. Am. Bull.. 84: 297--314. Weber, K., 1976. Gefiigeuntersuchungen an transversal geschieferten Gesteinen aus dem ijstlichen Rheinischen Schiefergebirge. Geol. Jahrb., 15: 3-98. White, S., 1979. Grain and subgrain size variations across a mylonitr zone. (Iontrib. Mineral. Wilkinson,

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A.M.,

1975.

143-158. between

axial

views of the origin

Skolithos plane

of slaty

pipes

foliations

cleavage.

as strain and strain.

Annu.

markers

in

Trctono-

Rev. Earth

Planet.