Crenulation cleavage development by partitioning of deformation into zones of progressive shearing (combined shearing, shortening and volume loss) and progressive shortening (no volume loss): quantification of solution shortening and intermicrolithon-movement

TECTONOPHYSICS ELSEVIER

Tectonophysics 281 (1997) 125-140

Crenulation cleavage development by partitioning of deformation into zones of progressive shearing (combined shearing, shortening and volume loss) and progressive shortening (no volume loss): quantification of solution shortening and intermicrolithon-movement L.K. Stewart * Department of Earth Sciences, James Cook UniversiO' of North Queensland, Townsville, QLD. 4811, Australia Received 11 June 1996; accepted 20 February 1997

Abstract An analytical method for determining amounts of cleavage-normal dissolution and cleavage-parallel shear movement that occurred between adjacent microlithons during crenulation cleavage seam formation within a deformed slate is developed for the progressive bulk inhomogeneous shortening (PBIS) mechanism of crenulation cleavage formation. The method utilises structural information obtained from samples where a diverging bed and vein are offset by a crenulation cleavage seam. Several samples analysed using this method produced ratios of relative, cleavage-parallel movement of microlithons to the material thickness removed by dissolution typically in the range of 1.1-3.4: 1. The mean amount of solution shortening attributed to the formation of the cleavage seams examined is 24%. The results indicate that a relationship may exist between the width of microlithons and the amount of cleavage-parallel intermicrolithon-movement. The method presented here has the potential to help determine whether crenulation cleavage seams formed by the progressive bulk inhomogeneous shortening mechanism or by that involving cleavage-normal pressure solution alone.

Keywords: crenulation cleavage; mathematical method; solution; movement

1. Introduction Mechanisms that can explain cleavage-parallel offsets of bedding, veins and other structures associated with crenulation cleavages can be divided into two categories. (1) Those in which the intermicrolithon-strain is purely the result of a volume loss with the apparent cleavage-parallel offset of features across cleavage domains attributed to the removal of material * Fax: +61-77-251501 ; E-mail: x-gllks @jcu.edu.au

by pressure solution (e.g., Durney, 1972; Groshong, 1975, 1976; Cosgrove, 1976; Gray, 1979a; Gray and Durney, 1979; Price and Cosgrove, 1990; Wright and Henderson, 1992). For such mechanisms, the apparent offset of a straight feature across the cleavage domain would be a function of the amount and direction of dissolution and the orientation of the feature. Note, offsets may also arise through the preferential removal of one limb of a crenulation fold by pressure solution (e.g., Cosgrove, 1976; Gray, 1979b). (2) Those in which the intermicrolithon-strain is the result of a volume loss and a shear movement be-

0040-1951/97/517.00 © 1997 Elsevier Science B.V. All rights reserved. PII S 0 0 4 0 - 1 95 1 ( 9 7 ) 0 0 0 4 1-3

126

L.K. Stewart/Tectonophysics 281 (1997) 125-140

tween microlithons (e.g., Means and Williams, 1972; Williams, 1972, 1976, 1990; Hobbs et al., 1976; Bell, 1981, 1985; Dennis and Secor, 1987; Murphy, 1990; Rajlich, 1993; Hobbs et al., 1994). In this category, a component of the offset will be due to a cleavage-parallel shear movement between microlithons (intermicrolithon-movement) that is independent of the orientation of the feature. The deformation mechanisms in both of the above-mentioned categories can qualitatively produce the fabrics associated with crenulation cleavages and, consequently, a problem exists in determining which actually operates within rocks. It is for distinguishing between the various mechanisms that a quantification of volume loss and intermicrolithonmovement may be useful. Within this study a method is developed for quantifying the amounts of cleavage-normal dissolution and cleavage-parallel intermicrolithon-movement associated with crenulation cleavage seam formation within a specific rock system that is assumed to have deformed through the progressive bulk inhomogeneous shortening (PBIS) mechanism of crenulation cleavage formation, as defined by Bell (1981, 1985). This study represents the first part of an ongoing investigation into whether theoretical mechanisms of crenulation cleavage formation can be distinguished on the basis of their respective measures of dissolution in deformed rocks. It is planned to geometrically evaluate the amount of dissolution within the same set of rock specimens (Stewart, 1997) under the alternative hypothesis that the cleavages formed due to solution-deposition processes. If the average measures of dissolution relating to the two geometrical analyses are, statistically, significantly different then they can be compared to a third measure of solution shortening that is independent of the mechanism of deformation, being a geochemical analysis. Agreement between the geochemically derived level of dissolution within the specimens and one of the geometrical analyses could be viewed as support for that mechanism of deformation being responsible for the structures observed with the specimens studied. 1.1. The PBIS deformation mechanism

In the conceptual PBIS mechanism, rock deformation is partitioned, due to primary or secondary

heterogeneity of the rock, such that different zones of the rock take up (Fig. la); (1) no strain; (2) primarily progressive shortening strain; (3) progressive shortening plus shearing strain; (4) progressive shearing strain (Bell, 1981, 1985). The high-strain zones (3 and 4) anastomose and are represented by the cleavage seams and the low-strain zones (1 and 2) by the microlithons. During deformation, shear and shortening within the higher-strain zones results in strain-induced dissolution and volume loss (e.g., Bell, 1981; Bosworth, 1981; Engelder, 1982; Meike, 1990a,b,c). Intermicrolithon-movement resuits across the high-strain domains and is aided by the presence of micaceous minerals whose crystallographically dominant basal cleavage plane accommodates some of the simple shear component of the deformation (Bell, 1981). In other theoretical mechanisms of crenulation cleavage development intermicrolithon-movement (e.g., Murphy, 1990; Hobbs et al., 1994) occurs when, during deformation, the foliation lies at some angle to the X - Y plane of the finite strain ellipsoid (Ghosh, 1982). However, Bell (1981) suggested that in most instances foliations form parallel or sub-parallel to the X - Y plane of the finite strain ellipsoid (Cloos, 1947; Wood, 1974; Gray and Durney, 1979). The theoretical considerations of Williams (1976) indicated that this would be impossible in a bulk non-coaxial situation where there is a large shear component approximately parallel to the foliation. Bell (1981), by differentiating between the local and bulk strain ellipsoids, rationalised this apparent inconsistency. During progressive bulk inhomogeneous shortening, at the local scale (i.e., at the scale of a foliation) the anastomosing foliation can track or be close to parallel to the finite local X - Y plane (Bell, 1981). As the foliations represent zones of shear, adjacent microlithons will be displaced relative to one another resulting in the X - Y plane of the bulk strain ellipsoid lying at an angle to the local X-Yplane and therefore the foliation (Fig. la). Thus, conceptually, the local X - Y plane lies almost parallel to the foliation yet is able to act as a plane of shear (Bell, 1981). Fig. I shows the conceptual distribution of strain during non-coaxial deformation of rock by the PBIS mechanism. The PBIS mechanism leads to structural relationships such that, in adjacent microlithons, segments

L.K. Stewart/Tectonophysics 281 (1997) 125-140

(a)

127

(b)

Vein

Fig. 1. (a) Strain diagram (modified from Bell, 1985) showing the conceptual distribution of strain associated with non-coaxial progressive bulk inhomogeneous shortening. Zones described by dashed lines take up no strain (zone 1 in text). The zones between the dashed and dotted lines take up predominantly coaxial strain (zone 2 in text). The areas between dotted lines take up non-coaxial shearing and shortening (zones 3 and 4 in text). The anastomosing strain-field lines are analogous with foliations. The conceptual orientations of local strain-ellipses within these different zones are displayed as small black ellipses. The large ellipse represents the bulk strain-ellipse. (b) Sketch of a strain diagram (modified from Bell, 1985) showing how, during non-coaxial progressive bulk inhomogeneous shortening, deformation may partition around relatively competent heterogeneities within the rock, such as the areas where veins and beds intersect. The zones of deformation partitioning are delineated in the same manner as in (a).

o f v e i n and b e d d i n g display a cleavage-parallel offset across the c o m m o n c r e n u l a t i o n cleavage seam. In this study the analytical m e t h o d that is developed is applied to several e x a m p l e s that display such relationships. Data pertaining to the calculated a m o u n t s of dissolution and i n t e r m i c r o l i t h o n - m o v e m e n t associated with the cleavage seams e x a m i n e d are presented and discussed.

2. Description of specimens The s p e c i m e n s described herein were o b t a i n e d from a lower greenschist-facies p o l y d e f o r m e d slate w i t h i n the Silurian Chesleigh f o r m a t i o n n e a r Sofala, N.S.W., Australia. Gray (1979b) studied rocks from this location as part o f a wider investigation of crenulation cleavage and attributed the cleavage-parallel offsets of veins and b e d d i n g to the process of buck-

128

L.K. Stewart/Tectonophysics 281 (1997) 125-140

Fig. 2. An example of crenulation cleavage that cuts an intersecting thin psammitic bed and vein, thus allowing the calculation of the amount of dissolution and intermicrolithon-movement.The cleavage seams lie roughly parallel to the short sides of the image. Dip indicators show the orientation of the vein, bed and cleavagerelative to the thin-section. ling of the vein combined with subsequent cleavage-normal (Gray, 1979a) pressure solution. However, Bell and Johnson (1992, fig. 8) attributed the structural relationships in a sample from the same location to intermicrolithon-movement and dissolution associated with PBIS. The specimens consist of interbedded pelitic and psammitic layers cross-cut by crenulated quartz veins (Fig. 2). The differentiated crenulation cleavage seams primarily occur within the pelitic layers and are associated with the crenulated quartz veins (Gray, 1979b). The quartz veins appear to predate, or have formed early synchronous with, the deformation event that produced the crenulation cleavages because the veins control the distribution of the cleavage seams (i.e., the cleavage seams intensify and converge against the veins), In thin-section the crenulation cleavage appears to be the result of the most recent deformation as no subsequent events are evident. Also, there does not appear to have been any cleavage-parallel intermicrolithon-movement post-dating the cleavage seams (i.e., cleavage

seams anastomose and there is no evidence of brittle deformation following some and cutting through others). At the scale of interest the quartz veins and beds that are cut by the crenulation cleavage appear to have been relatively straight prior to the cleavage forming event. This is evidenced by most beds and veins only showing significant curvature near the higher-strain zones associated with the boundaries of the microlithons (e.g., Fig. 2). In general, the crenulation cleavage does not cut the thicker psammitic layers (>2 mm) and this may result from strain in these layers being accommodated by layer-parallel shear (Hobbs et al., 1976). In assuming deformation by PBIS this relationship is attributed to reactivation (Bell, 1986) of the bedding-parallel cleavage predominantly at the cleaved pelite/psammite interfaces (Fig. 3). Some thinner psammitic beds (< 2 mm thick in section) were crosscut by the crenulation cleavage. At the locations where a thin psammitic layer, a vein and a crenulation cleavage seam intersect (Fig. 2), it was possible to calculate the amount of cleavage-normal dissolution

L.K. Stewart/Tectonophysics 281 (1997) 125-140

129

Fig. 3. Photomicrograph showing the contact between a thick psammitic layer and pelite. Reactivation of the bedding-parallel cleavage is evident at the psammite/pelite interface. The white lines indicate the orientations of (a) the reactivated bedding-parallel cleavage and (b) the crenulation cleavage. Note also the curvature of the crenulation cleavage into the orientation of the psammite/pelite contact due to accommodation of shear along this interface during reactivation. and cleavage-parallel intermicrolithon-movement attributable to development of the cleavage seam (under the assumption of deformation by PBIS).

3. Structural relationships within specimens In the PBIS mechanism of deformation the mineral stretching lineation gives an indication of the relative displacement vector for adjacent microlithons (Belt, 1986; Bell et al., 1986). Therefore, the analysis of the structure is easiest in sections that contain both the intermicrolithon-displacement vector and the normal to the dissolution seam (Fig. 4). Consequently, the rocks used in this study were sec-

tioned such that the long axis of minerals on the cleavage plane and the cleavage-normal lay at low angle to the plane of the thin-section. Additionally, when sectioned in this manner, the planes of bedding and veining lay at high angle to the thin-section. Fig. 4 shows the approximate structural relationships present within the specimens with respect to the ideal thin-section plane. In thin-section, a sample of structures suitable for analysis consists of adjacent microlithons and the intervening cleavage domain such that: (a) both microlithons contain segments of a diverging vein and bed; (b) the vein and bed are both offset across the common cleavage seam; (c) the intersection of

130

L.K. Stewart/Tectonophysics 281 (1997) 125-140

Stretching

lineation

Normal to cleavage

cleavage plane

Fig. 4. Diagramshowingthe generalrelationshipsbetweenbedding, veining and cleavageplanes within the rocks studied and the ideal thin-section plane. Ideally the thin-section should be oriented such that it is normal to the cleavageand containsthe stretchinglineation. the vein and bed occurs, or appears to have occurred, within the bounds of the sample (e.g., Figs. 2 and 5). Fig. 6a shows the idealised structural relationships expected between bed, vein and cleavage in samples found within a thin-section containing the movement and dissolution direction vectors. A cartesian coordinate system superimposed over the section such that the Y-axis parallels the cleavage seam (Fig. 6a) allows the following structural information to be recorded: Tb = offset of bed across cleavage seam; Tv = offset of vein across cleavage seam; 0b = angle of bed to X-axis; 0v ---- angle of vein to X-axis. Measured from the X-axis angles are given a clockwise-positive sign convention.

4. Methodology 4.1. Assumptions

The method for calculating values of cleavagenormal dissolution and relative intermicrolithonmovement within the described samples is based on the following assumptions. (a) The direction of dissolution is perpendicular to the mean surface of dissolution (cleavage seam). Considering the study of Gray (1979a), outlined above, this assumption is reasonable for the samples obtained from the described location.

(b) The orientation of veins and psammitic beds preserved within the adjacent microlithons represent, at their respective mid-points, the approximate pre-cleavage-formation orientations of those features. This assumption is valid in the context of the PBIS deformation mechanism. The psammitic beds show signs of having been relatively competent with respect to the pelite because evidence of earlier cleavage reactivation can be found at the boundaries between the two (Fig. 3). Within the primarily pelitic matrix a relatively competent psammitic bed and vein in proximity to one another would form a relatively competent cell around which the deformation would partition extensively (e.g., Fig. lb), thus protecting the core of the microlithon from significant internal strain. Note that in order to be consistent with the assumption of a relatively undeformed microlithon-core the feature should be reasonably straight within those areas of the sample (e.g., Figs. 2 and 5). (c) The cleavage seam between the offset features is straight. Considering the small distances involved and examining some of the samples analysed (e.g., Figs. 2 and 5) this assumption is reasonable. (d) Along the cleavage seam each feature has undergone an equal amount of actual displacement by intermicrolithon-movement. No evidence to invalidate this assumption was observed within the samples. (e) The transport direction, as determined by the long axes of the minerals on the cleavage plane, is the same for each sample. Assuming deformation by PBIS, the mineral elongation direction within the plane of the most recently developed cleavage should indicate the transport direction unless there is evidence of reactivation of that cleavage. As there is no evidence for subsequent events or reactivation of the crenulation cleavage this assumption is conceptually valid. (f) The feature was reasonably straight over the extent of the sample prior to the crenulation cleavage forming event. 4.2. The method

Using the information obtained from the idealised case shown in Fig. 6a the thickness of material removed by dissolution, in the direction perpendicular

L.K. Stewart / Tectonophysics 281 (1997) 125-140

131

Fig. 5. Photomicrographs of typical structural relationships analysed within the study. In both cases the thin psammitic beds and veins are offset across a cleavage seam. Dip indicators show the orientation of the vein, bed and cleavage relative to the thin-section.

L.K. Stewart/Tectonophysics 281 (1997) 125-140

132

(a)

the above we can write the simultaneous equations: Tb = - h tan(0b) + M /Cleavage

(1)

and

seam

Tv = - h tan(0v) + M

(2)

where M is the actual displacement of the features by intermicrolithon-movement and h is the thickness of material removed by dissolution in the direction of the cleavage normal. Solving these equations gives:

Bed

h =

Tb- Tv tan(0v) - tan(0b)

and

X", Vein

*- X M = Tb --

(b) Y

Future dissolution zone

I,- h -d Apparent l" " [ /''- movement t

(3)

|

~

--'htan(Ob)

Vein

:

i [

;

i

I

J

~ movement =h tan(Or) I~ X

Fig. 6. (a) Idealised diagrammatic representation of the structural relationships that may be found within suitable samples and the measurements made. Tb = offset of bed across cleavage seam; Tv = offset of vein across cleavage seam; 0b = angle of bed to X-axis; 0v = angle of vein to X-axis. If there is actual relative displacement of adjacent microlithons (in the Y-direction) as well as a zone of material removed by dissolution then the evident displacement of each feature will comprise two components, one real and one apparent. (b) Diagram showing the apparent movement of features due to removal of a zone of thickness, h, by dissolution.

to the cleavage seam, and the amount of intermicrolithon-movement can be calculated. The offset of each feature across the cleavage seam comprises two components (Murphy, 1990). One component is apparent movement due to dissolution of the inclined feature (Fig. 6b) that involves no real physical displacement of this feature parallel to the cleavage. The other will be due to displacement of the features by intermicrolithon-movement (e.g., Fig. 6a). Given

Tb- Tv

tan(0b) (4) tan(0b) -- tan(0v) The above equations are based on the idealised case where the elements of bedding and vein preserved within the microlithons are straight. However, it is more common for these features to be sigmoidally shaped within the microlithon (i.e., they become curved near the boundaries of the microlithon; Fig. 7). Within the conceptual framework of the PBIS deformation mechanism this is due to a gradient in both shear strain and dissolution or 'strain spreading' from the high-strain zone (that will become the cleavage seam) into the lower-strain zone of the microlithon. The zone of strain spreading encompasses the zones of progressive shortening and shearing (zones 2, 3 and 4 in Fig. la). Ideally, the deflection of the tail-ends of the features, caused by strain spreading, will be limited to a zone near the microlithon-boundary (Fig. 7), leaving the core of the microlithon relatively undeformed, particularly in the presence of a competent heterogeneity (see assumption b and Fig. lb). The deflection of the tail-ends of the features due to strain spreading means that the offsets when measured along the cleavage-seam/Y-axis will not reflect the total amount of intermicrolithon-movement and dissolution that has occurred. Consequently, the offsets of each feature were not determined in this manner. They were instead calculated from the orientation of the feature within the core of the microlithon and the relative positions of the feature's mid-points within adjacent microlithons (Fig. 8). Calculating the offsets in this manner is meaningful. The effect of any intermicrolithon-movement and dissolution that occurs across the zone

LK. Stewart /Tectonophysics 281 (1997) 125-140

[

133

Y

Microfithon

X

,

(Xb2' Yb2)'~

7, Ybl)

/Cleavage I

i

i

......

'(x , y

[

~

Cleavage seam

. . . . . . . . Effective feature orientation ~1~

~

~-~

Limit of strain spreading Preserved microlithon core and features

b5

-------22

,x

) b5

T

( be, Y b6) m

X

Fig. 8. The deflection of a feature's ends means that not all strain due to intermicrolithon-movement and dissolution is accumulated in the cleavage seam. This problem can be remedied by calculating the distance along the cleavage seam between the intersection of straight lines (that within each microlithon, parallel and pass through the feature at its mid-point) with the common cleavage seam. These points of intersection are shown as hollow spots. The distance between the hollow spots defines an offset, Tb, of the feature that represents the strain due to dissolution and intermicrolithon-movement within both the cleavage domain and the adjoining zones of strain spreading. T~ is calculated by subtracting the lengths a and e from c. The solid spots define the end and mid-point coordinates of the structures, these coordinates are necessary for the calculation of the revised feature offset (T~).

Zone of strain spreading

Fig. 7. Diagram shows how the end portions of the preserved features of interest may have been deflected by strain spreading. The zones of strain spreading may extend only a short distance into the microlithon. Where features within the portion of microlithon unaffected by strain spreading were not straight they were assumed, Ior the purpose of analysis, to have an orientation defined by a straight line connecting the points of intersection between the feature and the boundary of the strain spreading zone (e.g., an orientation defined by the dashed line between the spots in the diagram).

of strain spreading will be represented as a deflection of the feature from the orientation represented within the core of the microlithon. When measured on the cleavage-seam/Y-axis the real and apparent components of the offset of a feature, due to intermicrolithon-movement and dissolution, respectively, are independent. Given the above, we can define straight lines that, in each microlithon-core, parallel the feature and pass through its mid-points. The distance between the two points defined by the intersection of these lines with the common cleavage

seam (e.g., Fig. 8) will then represent the observed offset plus an offset that represents any intermicrolithon-movement and dissolution represented as strain within the zones of strain spreading. Thus, the calculated offset will represent all intermicrolithonmovement and dissolution across the strained zone that lies between the microlithon-cores. The expressions for the revised bedding and vein offsets, T~ and Tv', respectively, across a cleavage seam are: T~ ---- Yb2

-- Yb5

t tan(0bj) +

tan(0b2)

(5) and Tv = Y v 2 - - Y v 5

+ (Xv3 -/vl2 ~/tan(0vl)

+(xv6-Xv4)tan(Ov2) (6)

L.K. Stewart/Tectonophysics 281 (1997) 125-140

134

where: xsi and ysi represent x, y coordinates of the feature-end and mid-points: i E (1 . . . . . 6), s (b, v); 0sl represents the angle of the feature at its mid-point to the X-axis (Fig. 8). The calculated offsets T~ and T" are used in place of Tb and Tv in Eqs. 1 and 2 thus allowing for the presence of sigmoidally shaped features (strain spreading). In some examples the mid-point orientation of a reasonably straight feature preserved within the microlithon-core did not reflect the general orientation of this feature (Fig. 7). In such cases these features were assumed to have the orientation as defined in Fig. 7. Also, it is evident from the equations of the revised feature offsets that the angle between a feature and the X-axis can vary slightly within adjacent microlithons (the average difference in orientation for the samples examined was 8.2°). However, solution of the simultaneous Eqs. 1 and 2, requires the angle of such a feature to the X-axis to be the same in adjacent microlithons. Therefore, the average orientation of a feature in adjacent microlithons is used to represent the angle to the X-axis in Eqs. 1 and 2 (differences in orientation of a particular feature between microlithons were fully considered in the calculation of the variation associated with the results). After these substitutions are made the simultaneous equations describing the system are:

T~=-h

t a n ( 80~ +8o2)2 + M

(7)

(0,1 + 0v2) + M 2

(8)

Solving these equations gives: h =

(9)

N

and ,

M=T(,-tan xtan(

r

-L'

(80' +( 802) 2 - tan

801

0vl +2 0v2 )

+0b2)2

(10)

Eqs. 9 and l0 allow a mathematically based estimate of the amounts of intermicrolithon-movement and dissolution that have occurred across a cleavage seam between adjacent microlithons.

5. Analysis of samples and results In total eleven samples were analysed. Many other samples were considered for analysis but were deemed unsuitable as it was considered that the errors involved in their analysis would be too large to provide useful data. Typical representations of the samples analysed are shown in Figs. 2 and 5. Sixteen measurements are required from each sample to provide the data necessary to calculate the amount of intermicrolithon-movement and dissolution that occurred. This data was entered into a software spreadsheet that was programmed to manipulate the information to provide intermicrolithon-movement and dissolution values. The results of the analyses for the eleven sampies examined are displayed in Table 1. The average

and Tv' = - h tan

T~ - Tv' tan (0vl +2 0v2 ) - t a n ( 801+ 802

Table 1 Calculated values of thickness of material removed by solution shortening, intermicrolithon-movement, relative solution shortening and associated variation (also shown is average microlithon-width)

h (mm) Variation in h ( ~ m m ) M (mm) Variation in M (-4-mm) W(mm) (i0.02) RSS (%) Variation in RSS (4-%)

1

2

3

4

5

0.81 0.37 0.97 0.51 1.28 39 18

0.70 0.39 1.78 0.57 2.35 23 13

0.83 0.64 1.91 0.81 2.42 26 20

0.76 0.30 1.63 0.33 2.13 26 lI

0.54 0.41 1.63 0.44 2.35 19 14

6

0.49 ' 0.30 1.66 0.44 2.48 16 10

7

8

9

10

11

0.13 0.20 1.58 0.71 2.31 5 8

0.48 0.41 1.40 0.38 1.55 24 20

1.20 0.65 2.38 0.48 3.08 28 15

0.53 0.29 0.60 0.34 2.79 16 9

1.66 0.53 1.95 0.42 2.08 44 14

Key: h = thickness of material removed by solution shortening; M = amount of intermicrolithon slip; W = microlithon width; RSS = amount of relative solution shortening.

L.K. Stewart/Tectonophysics 281 (1997) 125-140 Le, angle of mineral stretch

thickness of material removed by dissolution was 0.74 mm. The average amount of intermicrolithonmovement was 1.59 mm. In each of the samples examined the intermicrolithon-movement is greater than the thickness of material removed by solution shortening, with a ratio typically in the range 1.13.4: 1. 5.1. Variation associated with the results

Due to the uncertainties of orienting and cutting thin-sections they were, after preparation, evaluated to determine their orientation relative to the ideal thin-section plane. If the thin-section was cut accurately it will contain both the stretching lineation and cleavage normal (Fig. 9a). However, if this is not the case the structural information obtained from the thin-section will contain unwelcome variation. This variation can be minimised if the orientation of the stretching lineation within the cleavage plane and the angle of that plane to the cut thin-section plane are known. A stereo-net can be used to calculate the angular relationships between the cleavage seam and feature within the ideal thin-section plane. The offsets of features across the cleavage seam in the ideal plane can be found by using the following relationship: corr T~ =

T~' × sin(asc), sin(180 - Lc - Asc)

for ( L c - Asc) ¢

180

where: corrT~ = the offset of a feature across the cleavage seam in the ideal thin-section plane; T" = offset of a feature across the cleavage in the non-ideal thin-section plane, s 6 (b, v); Lc = angle of mineral stretch to the non-ideal thin-section plane measured in cleavage plane; Asc = angle of the plane of the feature to non-ideal thin-section plane measured in the cleavage plane (Fig. 9b). An indication of the relationship between the corrected (corr T') and original (T') offsets for various Lc and Asc is shown in Fig. 10. The corrected data can then be used in the quantitative analysis, thus minimising the variation associated with the determination of dissolution and intermicrolithon-movement values.

135 Ideal

thin-section plane

Ion-ideal n-section

plane

Angle of c to non-ideal

,lane

//I

Mineral stretch

Cleavage normal

(a)

t hjN°ns;dctia2n

Structure ~

(b)

- -

defines T" s

"Cleavageplane

- - - defines corrT' s

Fig. 9. (a) Diagram showing relationships between a non-ideal thin-section plane and the ideal thin-section plane. The ideal thin-section plane will contain the cleavage normal and stretching lineation. (b) Diagram showing the difference in feature offset when measured in the non-ideal (offset = 7~) and ideal (offset = corrT~!) thin-section planes. Asc, the angle between feature and non-ideal thin-section plane is given by ABC. Lc, the angle between the mineral stretching lineation and the non-ideal thin-section plane is defined by BAC. Arrows show relative movement of microlithons across the cleavage plane.

The quantifiable variation (including that associated with the process of data correction) relevant to the calculated values of dissolution and intermicrolithon-movement is shown in Table 1. In each case the variation can be separated into two primary components. There is a component associated with the physical measurement of lengths (e.g., microlithon-widths), angles (e.g., between feature and X-axis) and the orientation of structure (e.g., mineral stretch). There is also a component resulting from

L.K. Stewart/Tectonophysics 281 (1997) 125-140

136

Ratio of corrT' s to T' s against L c for various Asc 2°'T

"--'~-'-7-IA==

/

1.5.-[

150

.,,,,,~Asc = 135

A,,c= 120

k..

Asc: 105 1.0.

A=:= 90

O t~

A,,~= 75 A,== 60

A~¢= 45 0.5. A ~ = 30

0.0

(0

1'5

2'0

i 25

Lc Fig. 10. Plot showing the ratio of actual offset of a feature within the ideal thin-section plane to the measured offset against Lc for various Asc.

using the average angle of each feature across the microlithon-pair as the representative angle of the feature to the cleavage normal. The second component becomes larger as the difference in the orientation of a feature within adjacent microlithons becomes larger. Fig. 1 l provides a visual indication of the level of representation of each of the two components for all the samples examined. There may also be some unaccounted variation that is due to the fact that the features being analysed are not actually planes and the cleavage seams, in

thin-section, are assumed straight. Cleavage planes anastomose in three dimensions and local variation away from the average orientation of the cleavage surfaces could result in the cleavage surface not lying perpendicular to the ideal thin-section plane. Also, local perturbations in the dip of beds and veins relative to the ideal thin-section plane could exist. Either or both such occurrences would produce unaccounted variation in the data pertaining to the cleavage-parallel offsets of the beds and veins. In view of this, a crude 'sensitivity analysis' was

L.K. Stewart/Tectonophysics 281 (1997) 125-140

performed. The local dips of the 'planar' features were assumed to be different from the data values used by an amount of ten degrees and values for dissolution and intermicrolithon-movement were then calculated. These 'sensitivity analysis' values were compared to the original data. The introduction of the local variation in dip resulted in values of disso-

Variation a

in h

]

Variation due to measurement

]

Variationdue to intermicrolithon

error

E 0.75 E

<

0.5

L.,

0.25

2

3

4

5

6

8

7

9

10

11

Sample no.

Variation

E

in M

0.75

E

< +

5.2. Relative solution shortening

%shortening =

.9

>

lution and intermicrolithon-movement differing from the originals by an average of 17% (minimum 5, maximum 39), and 12% (minimum 5, maximum 30), respectively. It is difficult to estimate the amount of unaccounted variation that may be due to the assumption that the cleavage seams are straight over the area of interest. However, it is evident that the sum of unaccounted variation has the potential to be significant with respect to the accuracy of the analysis.

Values for percentage relative shortening through dissolution were obtained for each sample (Table 1) using the following relationship:

deviation of feature orientation

+ t.'-

137

0.5

.9

100h ½(BL A- BR) + h

(12)

where: h = thickness of material removed by dissolution; BL = thickness of left-hand nficrolithon; BR ~--- thickness of right-hand rnicrolithon. The data give a mean value of 24% relative solution shortening but individual values can be as high as 44%. The standard deviation of the percentage relative solution shortening data is 11%. Fig. 12 is a graph of intermicrolithon-movement against the mean width of the adjacent pair of microlithons for each example examined. The most common microlithon-width in the examples analysed was approximately 2.3 mm. The graph shows a consistent level of intermicrolithon-movement (approximately 1.7 mm) to be associated with that microlithon-width. Excluding the one outlying point the data suggest a relationship may exist between microlithon-width and interrnicrolithon-movement. Graphs of the amount of dissolution to microlithon-width and dissolution to interrnicrolithonmovement are shown in Figs. 13 and 14, respectively. In both cases, within the variation limits of the data,

c~

>¢~

0.25

2

3

4

5

6

7

Sample no.

8

9

10

11

Fig. 11. Bar graphs displaying the accountable variation associated with the measurement of (a) the thickness of material removed by dissolution, h, and (b) relative movement between adjacent microlithons, M, for all samples. For each sample the components of variation associated with measurement and the differences in orientation of a feature between adjacent microlithons are shown.

L.K. Stewart/Tectonophysics 281 (1997) 125-140

138

Movement

to

width

Dissolution

to

width

4-~ 4-

E E

E E e-

T

1

/l T

o

2

T T

1

±

I

I

I

I

!

2

3

4

i

1

5

0

0

Microlithon width

T

±

I

I

I

I

1

2

3

4

5

(mm)

Fig. 12. Scatter plot of intermicrolithon-movement, M, against microlithon-width. The 'error' bars represent the amount of quantifiable variation associated with the data.

Microlithon width

(ram)

Fig. 13. Scatter plot of thickness of material removed by dissolution, h, against rnicrolithon-width. The 'error' bars represent the amount of quantifiable variation associated with the data.

no evidence was found for a relationship between either of these parameter pairings.

Dissolution

to

movement

5

6. Discussion The conceptual PBIS mechanism is one of several used to explain the fabrics and microstructures associated with crenulation cleavages. To date, little work has been done to quantify the levels of intermicrolithon-movement and dissolution for this mechanism of rock deformation. The method described here provides a means of determining approximate amounts of dissolution and intermicrolithon-movement within rocks assumed to have deformed by the PBIS mechanism of crenulation cleavage formation. As in any model of a physical process, assumptions must be made so as to maintain simplicity of the model. The most important assumption that relates to applying the method to physical samples is that the orientations of beds and veins preserved in cores of microlithons are close to their approximate pre-cleavage-formation orientations. Within the scope of the PBIS mechanism of deformation it is possible for the cores of some microlithons to un-

E E t.-

0

0

1'

t

2

3'

M (mm) Fig. 14. Scatter plot of thickness of material removed by dissolution, h, against intermicrolithon-movement, M, for each sample. The 'error' bars represent the amount of quantifiable variation associated with the data.

L.K. Stewart/ Tectonophysics 281 (1997) 125-140

dergo progressive shortening (Bell, 1981; Bell and Johnson, 1992). If there is evidence to suggest that significant rotation of the features from their original orientations has occurred through progressive shortening then the significance of any results will be affected. Such rotation of the features analysed would (using the work of Ghosh and Ramberg, 1976, as a guide to the rotational behaviour of the features) be likely to result in an underestimation of the thickness of material removed by dissolution and an overestimation (by the same proportion) of the amount of intermicrolithon-movement. 6.1. Results and the PBIS mechanism

The data from the small number of samples analysed suggest that a relationship may exist between the amount of cleavage-parallel intermicrolithonmovement and microlithon-width. With the exception of one sample point in Fig. 12 the larger intermicrolithon-movements were associated with larger microlithon-widths. Such a relationship would be expected with deformation by the PBIS mechanism as, in general, the 'coarser' the partitioning of a given deformation the greater the simple-shear component that the zones of relatively higher strain would need to accommodate. However, such a relationship cannot be used as proof of intermicrolithon-movement. The removal, during crenulation-cleavage formation by the solution-deposition mechanism, of each steep limb of a sample of asymmetric folds with a reasonably consistent orientation and asymmetry index (Hudleston, 1973) would result in a similar relationship between microlithon-width and 'apparent' cleavage-parallel intermicrolithon-movement. As the calculated cleavage-parallel intermicrolithon-movements for the PBIS mechanism of crenulation cleavage formation are not independent of the original 'apparent' offsets they cannot be used as proof of intermicrolithon-movement. Only limited conclusions can be drawn from the data displayed in Figs. 13 and 14 because of the small number of data points and the respective measures of variation. The small number of samples analysed reflects the difficulty in finding suitable examples for analysis. This difficulty arose because the method requires that the sample of interest has two inclined features reasonably well preserved in

139

the cores of adjacent microlithons. As a result many examples need to be examined in order to find one suitable for analysis. When the method is applied to suitable samples it provides a measure of the amount of solution shortening that should have occurred if the formation of crenulation cleavage seams was by the PBIS mechanism. Potential exists for this measure to be compared to those relevant to the pressure-solution mechanism of crenulation cleavage formation (e.g., Gray, 1979a; Henderson et al., 1986; Wright and Henderson, 1992; Stewart, 1997). If, in a common set of rock samples, the respective measures of solution shortening for the PBIS and pressure-solution mechanisms are found to be significantly different then the mechanisms can be quantitatively separated. The samples could then be examined using nondestructive geochemical analysis (e.g., Gratier, 1979; Erslev and Ward, 1994) to provide a third independent measure of solution shortening. If the geochemically obtained values of solution shortening agreed with either the PBIS or the pressure-solution mechanism this could be viewed as support for that mechanism of crenulation cleavage formation.

Acknowledgements I gratefully acknowledge the assistance of Mike Hordern in directing me to the location at which the samples that were the focus of this study could be found. I thank Prof. Tim Bell, Dr. Brett Davis and Dr. Ken Hickey for their assistance in interpretation of the deformation history of the specimens and for pre-submission reviews of the manuscript. Prof. Terry Engelder, Dr. Rick Groshong, Dr. Jean-Pierre Gratier and an anonymous reviewer are thanked for their constructive and helpful reviews of the manuscript. I particularly thank Paul Williams for the assistance given with an earlier draft of the manuscript.

References Bell, T.H., 1981. Foliation development -- the contribution, geometry and significanceof progressivebulk inhomogeneous shortening. Tectonophysics,75: 273-296. Bell, T.H., 1985. Deformation partitioning and porphyroblast rotation in metamorphic rocks: a radical reinterpretation. J. Metamorph. Geol., 3:109-118.

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L.K. Stewart/Tectonophysics 281 (1997) 125-140

Bell, T.H., 1986. Foliation development and refraction in metamorphic rocks: reactivation of earlier foliations and decrenulation due to shifting patterns of deformation partitioning. J. Metamorph. Geol., 4: 421-444. Bell, T.H. and Johnson, S.E., 1992. Shear sense: a new approach that resolves conflicts between criteria in metamorphic rocks. J. Metamorph. Geol., 10: 99-124. Bell, T.H., Flemming, P.D. and Rubenach, M.J., 1986. Porphyroblast nucleation, growth and dissolution in regional metamorphic rocks as a function of deformation partitioning during foliation development. J. Metamorph. Geol., 4: 37-67. Bosworth, W., 1981. Strain induced preferential dissolution of halite. Tectonophysics, 78: 509-525. Cloos, E., 1947. Oolite deformation in the South Mountain Fold, Maryland. Bull. Geol. Soc. Am., 58: 843-918. Cosgrove, J.W., 1976. The formation of crenulation cleavage. J. Geol. Soc. London, 132: 155-178. Dennis, A.J. and Secor, D.T., 1987. A model for the development of crenulations in shear zones with applications from the Southern Appalachian Piedmont. J. Struct. Geol., 9:809-817. Durney, D.W., 1972. Solution transfer an important geological deformation process. Nature, 235: 315-317. Engelder, T., 1982. A natural example of the simultaneous operation of free-face dissolution and pressure solution. Geochim. Cosmochim. Acta, 46: 69-74. Erslev, E.A. and Ward, D.J., 1994. Non-volatile element and volume flux in coalesced slaty cleavage. J. Struct. Geol., 16: 531-553. Ghosh, S.K., 1982. The problem of shearing along axial plane foliations. J. Struct. Geol., 4: 63-67. Ghosh, S.K. and Ramberg, H., 1976. Reorientation of inclusions by combinations of pure and simple shear. Tectonophysics, 34: 1-70.

Gratier, J.P., 1979. Mise en 6vidence de relations entre changement de composition chimique des roches et intensit6 de leur drformation. Bull. Soc. Geol. Fr., XXI(1): 95-104. Gray, D.R., 1979a. Microstructure of crenulation cleavages: an indicator of cleavage origin. Am. J. Sci., 279: 97-128. Gray, D.R., 1979b. Geometry of crenulation-folds and their relationship to crenulation cleavage. J. Struct. Geol., 1: 187205. Gray, D.R. and Durney, D.W., 1979. Investigations on the mechanical significance of crenulation cleavage. Tectonophysics, 58: 35-80. Groshong, R.H., 1975. 'Slip" cleavage caused by pressure solution in a buckle fold. Geology, 3:411-413. Groshong, R.H., 1976. Strain and pressure solution in the Martinsburg Slate, Delaware Water Gap, New Jersey. Am. J. Sci., 276: 1131-1146. Henderson, J.R., Wright, T.O. and Henderson, M.N., 1986. A

history of cleavage and folding: An example from the Goldenville Formation, Nova Scotia. Bull. Geol. Soc. Am., 97: 1354-1366. Hobbs, B.E., Means, W.D. and Williams, P.E, 1976. An Outline of Structural Geology. Wiley, New York, NY, 571 pp. Hobbs, B.E., Zhang, Y., Miihlhaus, H.-B. and Ord, A., 1994. The evolution of folds and the development of crenulation cleavage. SGTSG Field Conference, Jindabyne, Deformation Processes in the Earth: from Microcracks to Mountain Belts, February 6-11. Geological Society of Australia, Conference Abstracts, 36. Hudleston, P.J., 1973. The analysis and interpretation of minor folds developed in the Moine rocks of Monar, Scotland. Tectonophysics, 17: 89-132. Means, W.D. and Williams, P.F., 1972. Crenulation cleavage and faulting in an artificial salt-mica schist. J. Geol., 80: 569-591. Meike, A., 1990a. Considerations for quantitative determination of the role of dislocations in selective dissolution. Earth-Sci. Rev., 29: 309-320. Meike, A., 1990b. A micromechanical perspective on the role of dislocations in selective dissolution. Geochim. Cosmochim. Acta, 54: 3347-3352. Meike, A., 1990c. Dislocation enhanced selective dissolution: an examination of mechanical aspects using deformation-mechanism maps. J. Struct. Geol., 12: 785-794. Murphy, EX., 1990. The role of pressure solution and intermicrolithon-movement in the development of disjunctive cleavage domains: a study from Helvick Head in the Irish Variscides. J. Struct. Geol., 12: 69-81. Price, N.J. and Cosgrove, J.W., 1990. Analysis of Geological Structures. Pergamon Press, Cambridge, 502 pp. Rajlich, P., 1993. Riedel shear: a mechanism for crenulation cleavage. Earth-Sci. Rev., 34:176-195. Stewart, L.K., 1997. Using crenulated quartz veins with axial plane crenulation cleavage to determine the average amount of relative solution shortening associated with cleavage seam development. Tectonophysics, under revision. Williams, P.E, 1972. Development of metamorphic layering and cleavage in low grade metamorphic rocks at Bermagui, Australia. Am. J. Sci., 272: 1-47. Williams, P.F., 1976. Relationships between axial-plane foliations and strain. Tectonophysics, 30: 181-196. Williams, P.E, 1990. Differentiated layering in metamorphic rocks. Earth-Sci. Rev., 29: 267-281. Wood, D.S., 1974. Current views of the origin of slaty cleavage. Annu. Rev. Earth Planet. Sci., 2: 369-401. Wright, T.O. and Henderson, J.R., 1992. Volume loss during cleavage formation in the Meguma Group, Nova Scotia, Canada. J. Struct. Geol., 14: 281-290.