- Email: [email protected]
Skolithos pipes as strain markers in mylonites
Tectorzophysics, 28 (1975) 143-157 (9 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
SKOLITHOS
PIPES AS STRAIN
MARKERS
IN MYLONITES
P. WILKINSON, N.J. SOPER and A.M. BELL ~e~~rtrnen~ osteology,
Un~uers~tyof Sheffield, Sheffield (Great ~ritai~~
(Submitted February 6, 1975; revised version accepted ApriI 28, 1975)
ABSTRACT Wilkinson, P., Soper, N.J. and Bell, A.M., 1975. S~o~~~~ospipes as strain markers in mylonites. Tectonophysics, 28: 143-157. It is argued that mylonite zones result from translatory movements between rock masses and that the deformation mechanism is one of simple shear. Evidence is adduced to show that the mylonite zones in the Moine Thrust Belt of northwestern Scotland were developed in association with the inverted limbs of early Caledonian folds which trend parallel to the thrust front. On this basis a method is developed for the determination of shear strain from parameters which can be measured in mylonites which contain deformed Skolithos worm burrows. Very large strains are indicated (y 2 10). Some general implications are discussed.
INTRODUCTION
Many erogenic belts are hounded by thrust dislocations, which may be accompanied by mylonite zones. It is usually inferred that major displacements have occurred in these zones and their interpretation requires an estimate of the states of strain within them. Strain measurements in mylonites present considerable problems. Cataclastic flow tends to destroy such strain markers as may have been originally present in the rock. Very large strains lead to small angular discordances which are difficult both to interpret and measure. Reformation episodes earlier and later than the mylonitisation are a complicating factor. This paper presents an approach to the problem utilising S~~~~~~os worm burrows (‘pipes’) as strain markers in mylonitised Cambrian quartzite from the Moine Thrust Belt on the western margin of the British Caledonides in the Northwest Highlands of Scotland. It represents a development of the valuable pioneer work of McLeish (1971) on the same rocks. Mytonites
in the northern
part
of the Moine Thrust Belt
The Moine Thrust Belt comprises a number of nappe units which bave been displaced northwestwards relative to the Caledonian foreland on thrust planes
144
inclined gently to the southeast. The structurally highest (and most easterly) of these, the Moine Thrust, underlies the major Moine Nappe, which forms part of the interior of the orogen. On the northern coast of Scotland, at Loch Eriboll (Fig. l), the western part of this nappe, immediately overlying the Moine Thrust, is composed of 600-800 m of mylonite of greenschist facies, derived from both the Lewisian basement and Cambrian cover rocks as developed on the foreland to the west. The mylonites are overlain by Moine metasediments (Soper and Wilkinson, 1975). Four major Caledonian deformation episodes are recognized, of which the development of the mylonitic foliation is the earliest (D1) and displacement on the Moine Thrust the latest (D4). The deformation sequence is comparable with that recognised in more southerly parts of the thrust belt by Johnson (1957, 1960) and Barber (1965), although there the major development of mylonite is in the sub-Moine nappes.
THE
NORTHERN PART OF THE MOINE THRUST BELT
Forelond
SubMaine
Maine
thrust
Lew~uon. Torridoniar 8 Combro -0rdowic
napper
I
nappe
planer
0
5
Moinion mylonite
&
Lewirian
belt
-
Mo,ne
---------
Assynt -Amaboll Sole
IO
1.5 I
20
Kmr
Fig. 1. Sketch map of the Moine Thrust mentioned in the text.
Belt in northern
Scotland,
showing
localities
i45
The mylonite belt at the base of the Moine Nappe diminishes in thickness southwards from Loch Eriboll. At the Stat of Glencoul (Fig. 1) it is less than 100 m thick, rests on the Moine Thrust plane and is overlain by Moine psammites (see Christie, 1963, fig. 4). The lowest few metres of mylonite exposed on the northwest side of the Stat are very platy quartz-blastomylonites banded in grey and green. These were derived from the Pipe Rock Member of the Cambrian Eriboll Quartzite: highly deformed but still recognisable white Skolithos burrows are present (as originally noted by Clough in Peach et al., 1907, p. 504). The preservation of these trace fossils indicates that the colour banding represents bedding (Johnson, 1967). A strain study utilising the pipes has been made by McLeish (1971) on both mylonitised and non-mylonitised quartzites in the thrust belt. His evaluations of the states of strain in the Stat mylonites are based on the view (following Christie, 1963) that the deformed pipes lie parallel to the mylonitic foliation. The foliation comprises a penetrative planar microfabric plus an effectively coplanar colour banding (Johnson, 1967; Soper and Wilkinson, 1975). Since the colour banding represents bedding, to which the pipes were originally at right angles, this would imply infinite strain. The pipes in fact lie at a very small angle to the colour banding, and this is one of the key observations which rendered the present study possible. A complete strain solution is independent of assumptions regarding such factors as deformation mechanism, volume change or special types of strain. Unfortunately so few independent parameters can be measured in the mylonitised Pipe Rock that a complete finite-strain solution cannot even be approached. The problem can only be overcome by using geological evidence to select the most probable deformation mechanism and then making further simplifying assumptions. Deformation.
mechanism
of the mylonites
The origin of mylonite zones in the Moine Thrust Belt is controversal. The early view was that the mylonitic foliation represented closely spaced slip surfaces which developed in association with major thrust dislocations. This interpretation was modified by Barber (1965) who regarded the mylonite zones as shear belts located on the common limbs of northwesterly overturned primary (D1) folds, along which basement blocks or slices had been displaced upwards to the northwest relative to the foreland. Johnson (1967) adduced evidence to show that the mylonitic foliation had developed parallel to the XY-plane of the finite-strain ellipsoid, analogously to slaty cleavage, and proposed an irrotational ‘flattening’ rather than a rotational ‘movement zone’ mechanism for its generation. While accepting Johnson’s interpretation of the mylonite fabric in terms of strain, we favour a rotational mechanism for its development. Firstly, the mylonites of the thrust belt were produced in an environment in which large translatory movements demonstrably took place. Certain of the thrust planes
146
which predate the Moine Thrust (e.g. Glencoul, Arnaboll) are spatially associated with narrow mylonite zones, a metre or so in thickness. The morphology of these thin mylonite zones indicates that the strain in them was rotational and increased in intensity towards the failure plane. Although the main mylonite belt in the Moine Nappe was probably not developed synchronously with these lower thrusts and mylonite zones, it is reasonable to make a similar interpretation in terms of rotational strain. The principal difference is that in the main mylonite belt shear strain was distributed through a considerable thickness of rock (see Knopf and Ingerson, 1938) rather than confined to the vicinity of a discrete plane of failure. Secondly, the main mylonite belt is bounded above and below (where original relationships are not obscured by subsequent thrust faulting) by much less deformed rocks. It is difficult to envisage how irrotational strain could produce this degree of inhomogeneity. Thirdly, the mylonite belt is gently inclined and there is no evidence to indicate that it was not developed in approximately this attitude. Irrotational shortening would have been a response to subvertical compressive stress, presumably gravitational loading, which is unlikely to produce high strain zones of this type. We therefore consider that the mylonite belt results from large, northwesterly directed translatory movements. It is a shear belt in the sense of Ramsay and Graham (1970) the mechanism being essentially that of simple shear. The finite-strain state can be expressed as shear strain (y), together with the orientation of the shear plane and shear direction on that plane. The latter can be deduced from the geometry of the deformed rock; the sense of rotation is clockwise as viewed from the northeast. Orientation
of bedding and shear plane
The orientation of the shear plane cannot be deduced directly from the rock fabric. Geological considerations again allow certain simplifying assumptions to be made. The overall geometry of the Moine Thrust Belt and mylonite zones within it indicates that regionally the plane of simple shear was inclined gently to the ESE. Barber’s interpretation (1965, fig. 8) envisaged the mylonite belts to be associated with the common limbs of early folds and oriented so as to lie within the interlimb angle (Fig. 2a). Early fold pairs in the lower nappes trend NNE, face upwards to the WNW and have a variable degree of overturning in that direction. Axial planes thus have a range of inclinations to the ESE. The common limbs of most folds in the lower nappes are non-mylonitic. If the observed D1-structures (Fig. 2a) indicate a deformation sequence arrested at progressively later stages from west to east (foreland to orogen), the sequence led from layer-parallel shortening to buckling then, by the imposition of rotational strain, through increasing asymmetry of the folds to mylonitisation of their common limbs: The plane of shear was thus likely to have been congruous with the pre-mylonite bedding geometry, the overall symmetry being monoclinic (Fig. 2b). It is also probable that the shear
147
WNW foreland
-
Fig. 2. (a) Schematic diagram showing Dl-structure of the Moine Thrust Belt. (b) Idealised geometry of shear plane and bedding surface.
direction was approximately normal to the fold axes and thus in the symmetry plane. It is possible to identify the symmetry plane in the deformed rock. During rotational strain the bedding (colour banding) undergoes passive rotation towards the XY-plane of the finite ellipsoid and the XY-plane rotates towards the shear plane. At the very high strains involved in mylonite formation (q.v.) all three approach coplanarity. The plane of monoclinic symmetry can be identified as a plane normal to the colour banding which contains the axis of the deformed pipes (or, in practical terms, the longer axis of the elliptical pipe section on the colour banding, Fig. 4). It may be noted that at the Stat of Glencoul the symmetry plane so defined is vertical and strikes ESE, approximately normal to the thrust front, thus lending support to the above argument. Having defined the symmetry plane it is then necessary to consider only relationslnps in this plane, and the problem reduces to one of two dimensions. Figs. 3 and 5 are drawn so that the plane of the paper is the symmetry plane; in simple-shear dimensions normal to it remain unchanged. The important unknown parameter is the orientation of bedding and pipes prior to the mylonitisation. This can be expressed as the angle (S) between bedding and potential shear plane, measured in the symmetry plane. In the case of a mylonite belt superimposed on the already inverted limb of a D,-fold pair the bedding in the ‘undeformed’ (pre-mylonitisation) state was inclined
-\ d
148
bedding
a
a shear
plane
field
A
\--7
= S
O”<
S
shear
plane
-
/I
P
<45”
S
E
450<
s
<90”
1’
b
\
beddmg
\
,/I
PlPe
field
C
90”<
S
<135’
D 135”<
S
<180c
F!!!f P
S
/
C
0
PlPe
beddmg
Fig. 3. (a) Angular relationships between bedding and shear plane. (b) Inverted (c) Right-way-up situation showing angular conventions adopted.
situation.
more steeply to the ESE than the shear plane (0” < S < 90” in the convention adopted in Fig. 3). To cover the possiblity of mylonitisation affecting fold limbs not already inverted the field 90” < S < 180” must also be considered. Measured
parameters
The two independent parameters which can be measured mylonitised Pipe Rock are (Fig. 4):
in samples of
a=C b
?I
E
Z
z
2 k
colour banding (bedding1
Skol:thos pipe
Fig. 4. Block
diagram
of mylonitised
Pipe Rock
showing
measured
parameters
0’ and L’.
149
8’ = angle between pipe axis metry plane (initial angle = 8); L’ = ratio of elliptical section ratio = L). Measurement techniques are It is now necessary to derive yandS to 0’ and L’. MATHEMATICAL
Simplifying
and colour banding, measured
in the sym-
of pipes on the colour banding (initial described subsequently. expressions relating the unknown
parameters
MODEL
assumptions
In addition to the choice of a particular deformation mechanism, the geological basis for which has been outlined above, it is necessary to make further simplifying assumptions in order to render the problem tractable. (1) Skolithos pipes in the unstrained state were statistically circular, cylindrical and oriented normal to the bedding (L = 1 and 8 = 90”, Fig. 5a) see Hallam and Swett, 1966. (2) Volume change during the mylonitisation was sufficiently small to be neglected; this is reasonable in the case of previously lithified orthoquartzite. (3) There was no significant ductility contrast between the pipes and enclosing sediment. This is supported by the very small degree of contact strain discernible around the pipes in sections of mylonite cut normal to the pipe axis. (4) Strain prior to the mylonitisation (so that L # 1 and 0 # 90”) is neglected for the purpose of developing a mathematical model. So too are the effects
a
Unstrained
bs
state
trained
state
c-g-
L taken
Fig.
as
5. Geometrical
unity
relationships
of pipe,
bedding
and shear
plane before
and after
strain
of post-D, deformation episodes. These deformations validity of the results and are discussed subsequently. Mathematical
profoundly
affect the
development
In Fig. 5a, ABCD represents a unit square which under simple shear deforms into the parallelogram ABC’D’ in Fig. 5b in which AB is the direction of shear. AX is the bedding trace lying at an angle S to the shear plane AB. During simple shear the bedding rotates to AX’ at a new angle S’ to AB. Similarly, the pipe AE lies at an initial angle P = 90” + S to AB and rotates to AE’ at a new angle P’ to AB. The angle between pipe and bedding, initially 8 = 90” becomes 0’. Before strain the section of a pipe on the bedding is circular; the diameter in the plane of the diagram (L) may be taken as unit. During simple shear the cross-sectional dimension normal to the diagram remains unchanged but that in the plane ABC’D’ changes and can be measured as the ratio L’ (see Fig. 4). The cross-sectional dimension of the pipe on the shear plane (d) remains unchanged. Two independent simultaneous equations are required, relating 8’ and L’ to the unknowns y and S. From Fig. 5b: p’
0’ =
therefore:
tan 0’ =
-S’
tan P’ - tan S’ 1 + tan P’ - tan S’
Now: tan S’ = X’ Y/A Y and: X’ Y = XB = tan S (under conditions
of simple shear)
AY=AB+BY =l+BY
but: BY = y tan S (similar triangles, BX’ Y, BC’Z and BZ = y) Hence:AY=l+ytanS Substituting
P’ = 90 -
Also : therefore
tan S in (3): tan S’ = (1+ ___y tan s)
(4)
@’
tan P’ = cot $’ = l/DE’ tan P’ =
Substituting
y -
1 tan S
(4) and (5) in (2):
(5)
151
1 + tan2S
tan 19’= -__---
(6)
y(1- tan2S + y tan S) or: cot 0, = y(cot Y) __-- S - tan S +__ tan S + cot S For computing y = i[tan
(64
convenience,
eq. 6a may be rearranged
as:
S - cot S + {(cot S f tan S)(cot S + tan S + 4 cot 0’) - 4}*j2]
(6b)
From Fig. 5c: L’ set S -__ = sin 0’ sin [180 - (S’ + e’)]
(sine rule)
L’ = sin (S’ + 0’) therefore:
L’ =
secS*sin(S’+8’) sin 8’
or: L’ = set S - sin S’(cot
(7)
8’ + cot S’)
Now: cot S’ = cot S + y (Ramsay
(8)
1967, eq. 3.71)
1 _____
from which: sin S’ =
(94
[(r + cot s)s + 1]“2 Substituting L’ = set S
(9)
(6a), (9) and (9a) in (8) we find: y(cot S - tan S + y) ------+ tanS+cotS II
which simplifies
cots
1
+ y /[(y + cot s)a + 11 li2
to:
L’ = sin S[(y + cot S)2 + 11 1’2 For computing
convenience,
this rearranges
y = k(Lr2 cosec2S - 1)lj2 - cot S
(10) to: (lOa)
We now have two equations (6a and 10) linking y and S to the measured variables 8’ and L’. It proves difficult to solve directly for y and S. Fig. 6 shows a graphical solution for all values of S and a wide range of y computed from eqs. 6b and 10a. The intervals for L’ and 8’, have been chosen to fill the field evenly and have no other significance. Fig. 6 may be divided into four fields: Field A: 0” < S < 45”. According to the angular convention adopted (Fig.
152
3) the bedding is inverted and inclined more steeply than the shear plane. With increasing shear strain 7, L’ increases and 19’decreases progressively. Field B: 45” < S < 90”. Most values of S in this field also relate to inverted bedding. As y increases, L’ increases progressively while 0’ first increases (> 90”) then decreases. Field C: 90” < S < 135”. Right way up bedding dips in the opposite direction to the shear plane. As y increases, 8’ increases progressively while L’ first decreases (< 1.0) then increases. Field D: 135” < S < 180”. Most values of S relate to right way up bedding. As y increases both L’ and 8’ initially decrease. Subsequently both increase from a minimum value. The change of 8’ with y is related to variation in the relative rates of passive rotation of pipe and bedding. The velocity of rotation of a planar element (e.g. bedding) in simple shear is given by:
ds’ G=-
1 1 + (cots
+ r)2
which is at a maximum as it passes through the direction of no infinitesimal longitudinal strain at 90” to the shear direction, that is when: y =&tan
S - cot S)
Thus in field A the bedding initially lies in the extensional field of infinitesimal strain and with constant rate of change of y rotates more slowly than the pipe, which is in the compressional field and accelerates as it approaches the n.i.1.s. position; 8’ therefore decreases progressively from 8 = 90” with increasing strain. In field B the bedding initially rotates faster than the pipe so that 0’ first becomes obtuse. The bedding rotates more slowly as it moves away from the n.i.1.s. position while the pipe rotates more quickly as it approaches that position. 0’ therefore begins to decrease and at sufficiently high shear values becomes less than 90”. The behaviour of 8’ with increasing y in fields C and D may be similarly interpreted. The value of L’ is controlled by the orientation of the pipe section on the bedding in relation to the fields of finite compression and extension. The L’ = 1.0 curves on Fig. 6 thus record the positions where the bedding passes through a direction of no finite longitudinal strain. One corresponds to S = 0” or 180” for all values of y, that is when the bedding and therefore the pipe section on it lies in the shear plane and remains in that orientation. The other locus of L’ = 1.0 corresponds to positions where the bedding passes through the second position of n.f.1.s. during passive rotation. This starts at 90” to the shear direction and under increasing y rotates towards the principal extension direction and thus towards the shear plane. Hence only fields C and D contain values of L’ < 1.0.
3NVld
dllS
313NV
pamseaur
N33M138
1 sqdures
5INKXl39
‘z pm ONV
S
Zh.r!~oys ~01 pue qg xba WIIINI
JO uoqnlos
pqyde.rf)
‘g ‘%!d
154 RESULTS
Measurement
techniques
The small angle 19’proved surprisingly easy to measure. Samples (about 20 X 15 X 5 cm) were cut parallel to the symmetry plane (Fig. 4), so that twenty slices a few mm in thickness were obtained, leaving about half the sample for measurement of L’. After polishing, the white pipes could easily be distinguished against the grey and green colour banding. An enlarged image was projected onto tracing paper, the angle between pipe axis and colour banding defined as intersecting lines and the angle of intersection determined by completing a right angled triangle. The measurement of L’ presented greater difficulties. The remaining half of each sample was placed on a surface grinder and progressively ground parallel to the colour banding. As each pipe appeared on the ground surface its elliptical section was measured directly on the sample. The terminations of the longer axes were often difficult to locate with precision. A further source of inaccuracy lay in the difficulty of grinding samples precisely parallel to the colour banding, which is not always perfectly planar. Of the samples available, only two were judged suitable in this respect. Results Results of measurement on two samples are shown in Table I. The two derived values for the initial angle between bedding and the direction of shear, S, are acceptably close and are consistent with the geological model proposed. Since the values lie in Field A of Fig. 6 and pipes dip more steeply than bedding, it is concluded that the mylonite belt was developed in the inverted limb of a major fold. The values for y are also acceptably close, and large, but not unrealistically so (see the results of Ramsay and Graham, 1970). The errors, as indicated by the standard deviations of the measurements, are also large and no great weight should be placed on their exact numerical value. However, it is important to note that the minimum likely value of y, at the 5% significance level, cannot be less than 7. TABLE
I
Measured statistical
--
Sample Sample
1 2
(mean) and derived notation)
parameters
from field samples,
Stat
of Glencoul
(standard
-, 0
Se’
-, L
SL’
n
s
Y
lO.11 lO.45
0.33 0.34
4.63 5.36
1.88 0.95
15 17
17O.8 29O.8
12.0 9.0
155 DISCUSSION
Neglected
fat tars
The principal sources of error in the results arise from inaccuracy of measurement and the effects of other strains to which the rocks have been subjected. The former could be overcome by further determinations and statistical analysis of the results, but this seems scarcely worthwhile in view of the difficulties presented by the second factor. The effect of pre- and post-mylonititsation strains can only be assessed qualitatively. The ‘pre-mylonitisation’ strain comprises the effects of several processes to which the rocks were subjected early in the Dr-episode; layer-parallel shortening, buckling and cleavage formation. As a result of these strains, pipe sections on the bedding in the lower nappes are elongated parallel to the D,fold traces, so that L < 1, and the pipe axes are rotated towards the cleavage, so that 8 > 90” (McLeish, 1971). Thus, after mylonitisation, observed values of L’ are too small and of 0’ too large. In field A (Fig. 6) too small a value of Z;’ for a given 8’ leads to too small a value of S but too large a shear strain. Too large a value of 8’ for a given L’ produces the opposite effect: too large a value of S but too small a strain. A powerful linear fabric produced during Da in the Sutherland Moines suggests that the Da-strain lies in the constriction-extension field. The strain determination made by Wood (1973) on the conglomerate at Ben Hutig (Fig. 1) is compatible with this interpret,ation, but the extremely prolate pebble shapes probably indicate the combined effects of both D,- and Da-strains. In the Stat mylonites the La-extension lineation is weak and lies within 5” of the longer axis of the elliptical pipe sections on the colour banding. The effect of the D2-strain was thus to extend pipe sections in the direction of shearing, to produce an erroneously large value for L’, but to rotate the pipe sections towards the principal extension direction for Da, thus producing too small a value for 0’. The result of the former is to give too large a value for S and too small a shear strain, while too small a value for 0’ has the opposite effect. Thus the influence of both the pre- and post-mylonitisation strains on the results are to some degree self-compensating and in addition tend to compensate for each other. In the absence of reliable quantitative data for either strain it is impossible to judge whether their residual effect is important. A very weak La-microcrenulation is visible in the measured samples; its effect is negligible. D,-structures are non-penetrative and not present in the samples chosen. Conclusions We have shown that, providing our choice of deformation mechanism is correct, it is possible to make strain determinations in rocks which have undergone mylonitisation. The value of these particular results is limited because
156
of the effects of other strains which have not been quantified. We have, however, shown that these are to some extent self-compensating, so that a value for the shear strain of y = 10 may not be grossly inaccurate. This is an extremely large strain: X1/h, > 10,000. Some implications may be discussed. Dislocation zones on the margins of erogenic belts are commonly oriented so that the shear belts dip gently inwards towards the orogen. If cover rocks are involved, their gross pre-deformation attitude is likely to have been subhorizontal and right way up. Very high shear strains in this geometrical situation tend always to produce inverted mylonite ‘stratigraphies’ within the shear belts. A useful principle for the interpretation of field relationships in mylonite zones might thus emerge: inversions, for example basement-derived mylonites overlying cover mylonites, could be interpreted as passively rotated unconformities, while right-way-up relationships could imply dislocation. Thus at the sampled locality at the Stat of Glencoul there is an upward transition from mylonitised Pipe Rock through quartz-mylonite without pipes (presumably Basal Quartzite) to Lewisian mylonite: clearly an inverted sequence. This is interpreted as rotated and tectonically thinned, but not disrupted. Above, the Lewisian mylonite is overlain by arkosic Moine mylonite; this junction could be a D,-slide. The second point is of relevance to the problem of distinguishing rotational from irrotational strains. Johnson (1967), while favouring an irrotational mechanism for mylonitisation, recognised that . . . “in progressive simple shear, planes of ‘flattening’ may be rotated into near-parallelism with shear planes”. The present results allow this statement to be quantified in relation to the Stat mylonites. At y = 10 the dihedral angle between the shear plane and the XY-plane of the strain ellipsoid is only 5.7”. In addition, for S = 25” the colour banding after strain lies at 4.7” to the shear plane. Thus in the Stat mylonites the colour banding lies at about 1” to the XY-plane of an immensely elongated finite ellipsoid. It is evident that the visible layering in mylonites must have suffered a very large degree of thinning and ‘flattening’ but that this does not consitute evidence in favour of irrotational strain. No firm conclusions concerning displacments in the Moine Thrust Belt can be made, in view of the uncertainty of the strain measurement. If the average shear strain is about 10, the westward displacement during D,-mylonitisation at Loch Eriboll, where the mylonites attain a thickness of 800 m, is about 8 km. Pre-mylonite buckling might add a further few kilometres. But it is clear that this displacement is small compared to that attributable to movement on the Moine and other discrete thrust planes which developed subsequently to the mylonitisation. ACKNOWLEDGEMENTS
We wish to thank Professor J.G. Ramsay for reading the manuscript and for making helpful comments. Thanks are also due to G. Mulhearn for technical assistance and to M.G. Cooper for draughting the diagrams.
157 REFERENCES Barber, A.J., 1965. The history of the Moine Thrust zone, Lochcarron and Lochalsh, Scotland. Proc. Geol. Assoc., 76: 215-242. Christie, J.M., 1963. The Moine Thrust zone in the Assynt region, northwest Scotland. IJniv. Calif. Publ. Geol. Sci., 40: 345-440. Hallam, A. and Swett, K., 1966. Trace fossils from the Lower Cambrian Pipe Rock of the north-west Highlands. Scott. J. Geol., 2: 101-106. Johnson, M.R.W., 1957. The structural geology of the Moine thrust zone in the Coulin Forest, Wester Ross. Q.J. Geol. Sot. Lond., 113: 241-270. Johnson, M.R.W., 1960. The structural history of the Moine thrust zone at Lochcarron, Wester Ross. Trans. R. Sot. Edinb., 64: 139-l 68. Johnson, M.R.W., 1967. Mylonite zones and mylonite banding. Nature, 213: 246-247. Knopf, E.B. and Ingerson, E., 1938. Structural Petrology. Geol. Sot. Am. Mem., 6. McLeish, A.J., 1971. Strain analysis of deformed Pipe Rock in the Moine Thrust zone, northwest Scotland. Tectonophysics, 12: 469--503. Peach, B.N., Horne, J., Gunn, W., Glough, C.T. and Hinxman, L.W., 1907. The geological structure of the north-west Highlands of Scotland. Mem. Geol. Surv. U.K. Ramsay, J.G., 1967. Folding and fracturing in rocks. McGraw-Hill, New York, 568 pp. Ramsay, J.G. and Graham, R.H., 1970. Strain variation in shear belts. Can. J. Earth Sci., 7: 786-813. Soper, N.J. and Wilkinson, P., 1975. The Moine Thrust and Moine Nappe at Loch Eriboll, Sutherland. Scott. J. Geol. (in press). Wood, D.S., 1973. Patterns Sot. Land., Ser. A, 274:
and magnitudes 373-382.
of natural
strain
in rocks.
Philos.
Trans.
R.
SKOLITHOS
PIPES AS STRAIN
MARKERS
IN MYLONITES
P. WILKINSON, N.J. SOPER and A.M. BELL ~e~~rtrnen~ osteology,
Un~uers~tyof Sheffield, Sheffield (Great ~ritai~~
(Submitted February 6, 1975; revised version accepted ApriI 28, 1975)
ABSTRACT Wilkinson, P., Soper, N.J. and Bell, A.M., 1975. S~o~~~~ospipes as strain markers in mylonites. Tectonophysics, 28: 143-157. It is argued that mylonite zones result from translatory movements between rock masses and that the deformation mechanism is one of simple shear. Evidence is adduced to show that the mylonite zones in the Moine Thrust Belt of northwestern Scotland were developed in association with the inverted limbs of early Caledonian folds which trend parallel to the thrust front. On this basis a method is developed for the determination of shear strain from parameters which can be measured in mylonites which contain deformed Skolithos worm burrows. Very large strains are indicated (y 2 10). Some general implications are discussed.
INTRODUCTION
Many erogenic belts are hounded by thrust dislocations, which may be accompanied by mylonite zones. It is usually inferred that major displacements have occurred in these zones and their interpretation requires an estimate of the states of strain within them. Strain measurements in mylonites present considerable problems. Cataclastic flow tends to destroy such strain markers as may have been originally present in the rock. Very large strains lead to small angular discordances which are difficult both to interpret and measure. Reformation episodes earlier and later than the mylonitisation are a complicating factor. This paper presents an approach to the problem utilising S~~~~~~os worm burrows (‘pipes’) as strain markers in mylonitised Cambrian quartzite from the Moine Thrust Belt on the western margin of the British Caledonides in the Northwest Highlands of Scotland. It represents a development of the valuable pioneer work of McLeish (1971) on the same rocks. Mytonites
in the northern
part
of the Moine Thrust Belt
The Moine Thrust Belt comprises a number of nappe units which bave been displaced northwestwards relative to the Caledonian foreland on thrust planes
144
inclined gently to the southeast. The structurally highest (and most easterly) of these, the Moine Thrust, underlies the major Moine Nappe, which forms part of the interior of the orogen. On the northern coast of Scotland, at Loch Eriboll (Fig. l), the western part of this nappe, immediately overlying the Moine Thrust, is composed of 600-800 m of mylonite of greenschist facies, derived from both the Lewisian basement and Cambrian cover rocks as developed on the foreland to the west. The mylonites are overlain by Moine metasediments (Soper and Wilkinson, 1975). Four major Caledonian deformation episodes are recognized, of which the development of the mylonitic foliation is the earliest (D1) and displacement on the Moine Thrust the latest (D4). The deformation sequence is comparable with that recognised in more southerly parts of the thrust belt by Johnson (1957, 1960) and Barber (1965), although there the major development of mylonite is in the sub-Moine nappes.
THE
NORTHERN PART OF THE MOINE THRUST BELT
Forelond
SubMaine
Maine
thrust
Lew~uon. Torridoniar 8 Combro -0rdowic
napper
I
nappe
planer
0
5
Moinion mylonite
&
Lewirian
belt
-
Mo,ne
---------
Assynt -Amaboll Sole
IO
1.5 I
20
Kmr
Fig. 1. Sketch map of the Moine Thrust mentioned in the text.
Belt in northern
Scotland,
showing
localities
i45
The mylonite belt at the base of the Moine Nappe diminishes in thickness southwards from Loch Eriboll. At the Stat of Glencoul (Fig. 1) it is less than 100 m thick, rests on the Moine Thrust plane and is overlain by Moine psammites (see Christie, 1963, fig. 4). The lowest few metres of mylonite exposed on the northwest side of the Stat are very platy quartz-blastomylonites banded in grey and green. These were derived from the Pipe Rock Member of the Cambrian Eriboll Quartzite: highly deformed but still recognisable white Skolithos burrows are present (as originally noted by Clough in Peach et al., 1907, p. 504). The preservation of these trace fossils indicates that the colour banding represents bedding (Johnson, 1967). A strain study utilising the pipes has been made by McLeish (1971) on both mylonitised and non-mylonitised quartzites in the thrust belt. His evaluations of the states of strain in the Stat mylonites are based on the view (following Christie, 1963) that the deformed pipes lie parallel to the mylonitic foliation. The foliation comprises a penetrative planar microfabric plus an effectively coplanar colour banding (Johnson, 1967; Soper and Wilkinson, 1975). Since the colour banding represents bedding, to which the pipes were originally at right angles, this would imply infinite strain. The pipes in fact lie at a very small angle to the colour banding, and this is one of the key observations which rendered the present study possible. A complete strain solution is independent of assumptions regarding such factors as deformation mechanism, volume change or special types of strain. Unfortunately so few independent parameters can be measured in the mylonitised Pipe Rock that a complete finite-strain solution cannot even be approached. The problem can only be overcome by using geological evidence to select the most probable deformation mechanism and then making further simplifying assumptions. Deformation.
mechanism
of the mylonites
The origin of mylonite zones in the Moine Thrust Belt is controversal. The early view was that the mylonitic foliation represented closely spaced slip surfaces which developed in association with major thrust dislocations. This interpretation was modified by Barber (1965) who regarded the mylonite zones as shear belts located on the common limbs of northwesterly overturned primary (D1) folds, along which basement blocks or slices had been displaced upwards to the northwest relative to the foreland. Johnson (1967) adduced evidence to show that the mylonitic foliation had developed parallel to the XY-plane of the finite-strain ellipsoid, analogously to slaty cleavage, and proposed an irrotational ‘flattening’ rather than a rotational ‘movement zone’ mechanism for its generation. While accepting Johnson’s interpretation of the mylonite fabric in terms of strain, we favour a rotational mechanism for its development. Firstly, the mylonites of the thrust belt were produced in an environment in which large translatory movements demonstrably took place. Certain of the thrust planes
146
which predate the Moine Thrust (e.g. Glencoul, Arnaboll) are spatially associated with narrow mylonite zones, a metre or so in thickness. The morphology of these thin mylonite zones indicates that the strain in them was rotational and increased in intensity towards the failure plane. Although the main mylonite belt in the Moine Nappe was probably not developed synchronously with these lower thrusts and mylonite zones, it is reasonable to make a similar interpretation in terms of rotational strain. The principal difference is that in the main mylonite belt shear strain was distributed through a considerable thickness of rock (see Knopf and Ingerson, 1938) rather than confined to the vicinity of a discrete plane of failure. Secondly, the main mylonite belt is bounded above and below (where original relationships are not obscured by subsequent thrust faulting) by much less deformed rocks. It is difficult to envisage how irrotational strain could produce this degree of inhomogeneity. Thirdly, the mylonite belt is gently inclined and there is no evidence to indicate that it was not developed in approximately this attitude. Irrotational shortening would have been a response to subvertical compressive stress, presumably gravitational loading, which is unlikely to produce high strain zones of this type. We therefore consider that the mylonite belt results from large, northwesterly directed translatory movements. It is a shear belt in the sense of Ramsay and Graham (1970) the mechanism being essentially that of simple shear. The finite-strain state can be expressed as shear strain (y), together with the orientation of the shear plane and shear direction on that plane. The latter can be deduced from the geometry of the deformed rock; the sense of rotation is clockwise as viewed from the northeast. Orientation
of bedding and shear plane
The orientation of the shear plane cannot be deduced directly from the rock fabric. Geological considerations again allow certain simplifying assumptions to be made. The overall geometry of the Moine Thrust Belt and mylonite zones within it indicates that regionally the plane of simple shear was inclined gently to the ESE. Barber’s interpretation (1965, fig. 8) envisaged the mylonite belts to be associated with the common limbs of early folds and oriented so as to lie within the interlimb angle (Fig. 2a). Early fold pairs in the lower nappes trend NNE, face upwards to the WNW and have a variable degree of overturning in that direction. Axial planes thus have a range of inclinations to the ESE. The common limbs of most folds in the lower nappes are non-mylonitic. If the observed D1-structures (Fig. 2a) indicate a deformation sequence arrested at progressively later stages from west to east (foreland to orogen), the sequence led from layer-parallel shortening to buckling then, by the imposition of rotational strain, through increasing asymmetry of the folds to mylonitisation of their common limbs: The plane of shear was thus likely to have been congruous with the pre-mylonite bedding geometry, the overall symmetry being monoclinic (Fig. 2b). It is also probable that the shear
147
WNW foreland
-
Fig. 2. (a) Schematic diagram showing Dl-structure of the Moine Thrust Belt. (b) Idealised geometry of shear plane and bedding surface.
direction was approximately normal to the fold axes and thus in the symmetry plane. It is possible to identify the symmetry plane in the deformed rock. During rotational strain the bedding (colour banding) undergoes passive rotation towards the XY-plane of the finite ellipsoid and the XY-plane rotates towards the shear plane. At the very high strains involved in mylonite formation (q.v.) all three approach coplanarity. The plane of monoclinic symmetry can be identified as a plane normal to the colour banding which contains the axis of the deformed pipes (or, in practical terms, the longer axis of the elliptical pipe section on the colour banding, Fig. 4). It may be noted that at the Stat of Glencoul the symmetry plane so defined is vertical and strikes ESE, approximately normal to the thrust front, thus lending support to the above argument. Having defined the symmetry plane it is then necessary to consider only relationslnps in this plane, and the problem reduces to one of two dimensions. Figs. 3 and 5 are drawn so that the plane of the paper is the symmetry plane; in simple-shear dimensions normal to it remain unchanged. The important unknown parameter is the orientation of bedding and pipes prior to the mylonitisation. This can be expressed as the angle (S) between bedding and potential shear plane, measured in the symmetry plane. In the case of a mylonite belt superimposed on the already inverted limb of a D,-fold pair the bedding in the ‘undeformed’ (pre-mylonitisation) state was inclined
-\ d
148
bedding
a
a shear
plane
field
A
\--7
= S
O”<
S
shear
plane
-
/I
P
<45”
S
E
450<
s
<90”
1’
b
\
beddmg
\
,/I
PlPe
field
C
90”<
S
<135’
D 135”<
S
<180c
F!!!f P
S
/
C
0
PlPe
beddmg
Fig. 3. (a) Angular relationships between bedding and shear plane. (b) Inverted (c) Right-way-up situation showing angular conventions adopted.
situation.
more steeply to the ESE than the shear plane (0” < S < 90” in the convention adopted in Fig. 3). To cover the possiblity of mylonitisation affecting fold limbs not already inverted the field 90” < S < 180” must also be considered. Measured
parameters
The two independent parameters which can be measured mylonitised Pipe Rock are (Fig. 4):
in samples of
a=C b
?I
E
Z
z
2 k
colour banding (bedding1
Skol:thos pipe
Fig. 4. Block
diagram
of mylonitised
Pipe Rock
showing
measured
parameters
0’ and L’.
149
8’ = angle between pipe axis metry plane (initial angle = 8); L’ = ratio of elliptical section ratio = L). Measurement techniques are It is now necessary to derive yandS to 0’ and L’. MATHEMATICAL
Simplifying
and colour banding, measured
in the sym-
of pipes on the colour banding (initial described subsequently. expressions relating the unknown
parameters
MODEL
assumptions
In addition to the choice of a particular deformation mechanism, the geological basis for which has been outlined above, it is necessary to make further simplifying assumptions in order to render the problem tractable. (1) Skolithos pipes in the unstrained state were statistically circular, cylindrical and oriented normal to the bedding (L = 1 and 8 = 90”, Fig. 5a) see Hallam and Swett, 1966. (2) Volume change during the mylonitisation was sufficiently small to be neglected; this is reasonable in the case of previously lithified orthoquartzite. (3) There was no significant ductility contrast between the pipes and enclosing sediment. This is supported by the very small degree of contact strain discernible around the pipes in sections of mylonite cut normal to the pipe axis. (4) Strain prior to the mylonitisation (so that L # 1 and 0 # 90”) is neglected for the purpose of developing a mathematical model. So too are the effects
a
Unstrained
bs
state
trained
state
c-g-
L taken
Fig.
as
5. Geometrical
unity
relationships
of pipe,
bedding
and shear
plane before
and after
strain
of post-D, deformation episodes. These deformations validity of the results and are discussed subsequently. Mathematical
profoundly
affect the
development
In Fig. 5a, ABCD represents a unit square which under simple shear deforms into the parallelogram ABC’D’ in Fig. 5b in which AB is the direction of shear. AX is the bedding trace lying at an angle S to the shear plane AB. During simple shear the bedding rotates to AX’ at a new angle S’ to AB. Similarly, the pipe AE lies at an initial angle P = 90” + S to AB and rotates to AE’ at a new angle P’ to AB. The angle between pipe and bedding, initially 8 = 90” becomes 0’. Before strain the section of a pipe on the bedding is circular; the diameter in the plane of the diagram (L) may be taken as unit. During simple shear the cross-sectional dimension normal to the diagram remains unchanged but that in the plane ABC’D’ changes and can be measured as the ratio L’ (see Fig. 4). The cross-sectional dimension of the pipe on the shear plane (d) remains unchanged. Two independent simultaneous equations are required, relating 8’ and L’ to the unknowns y and S. From Fig. 5b: p’
0’ =
therefore:
tan 0’ =
-S’
tan P’ - tan S’ 1 + tan P’ - tan S’
Now: tan S’ = X’ Y/A Y and: X’ Y = XB = tan S (under conditions
of simple shear)
AY=AB+BY =l+BY
but: BY = y tan S (similar triangles, BX’ Y, BC’Z and BZ = y) Hence:AY=l+ytanS Substituting
P’ = 90 -
Also : therefore
tan S in (3): tan S’ = (1+ ___y tan s)
(4)
@’
tan P’ = cot $’ = l/DE’ tan P’ =
Substituting
y -
1 tan S
(4) and (5) in (2):
(5)
151
1 + tan2S
tan 19’= -__---
(6)
y(1- tan2S + y tan S) or: cot 0, = y(cot Y) __-- S - tan S +__ tan S + cot S For computing y = i[tan
(64
convenience,
eq. 6a may be rearranged
as:
S - cot S + {(cot S f tan S)(cot S + tan S + 4 cot 0’) - 4}*j2]
(6b)
From Fig. 5c: L’ set S -__ = sin 0’ sin [180 - (S’ + e’)]
(sine rule)
L’ = sin (S’ + 0’) therefore:
L’ =
secS*sin(S’+8’) sin 8’
or: L’ = set S - sin S’(cot
(7)
8’ + cot S’)
Now: cot S’ = cot S + y (Ramsay
(8)
1967, eq. 3.71)
1 _____
from which: sin S’ =
(94
[(r + cot s)s + 1]“2 Substituting L’ = set S
(9)
(6a), (9) and (9a) in (8) we find: y(cot S - tan S + y) ------+ tanS+cotS II
which simplifies
cots
1
+ y /[(y + cot s)a + 11 li2
to:
L’ = sin S[(y + cot S)2 + 11 1’2 For computing
convenience,
this rearranges
y = k(Lr2 cosec2S - 1)lj2 - cot S
(10) to: (lOa)
We now have two equations (6a and 10) linking y and S to the measured variables 8’ and L’. It proves difficult to solve directly for y and S. Fig. 6 shows a graphical solution for all values of S and a wide range of y computed from eqs. 6b and 10a. The intervals for L’ and 8’, have been chosen to fill the field evenly and have no other significance. Fig. 6 may be divided into four fields: Field A: 0” < S < 45”. According to the angular convention adopted (Fig.
152
3) the bedding is inverted and inclined more steeply than the shear plane. With increasing shear strain 7, L’ increases and 19’decreases progressively. Field B: 45” < S < 90”. Most values of S in this field also relate to inverted bedding. As y increases, L’ increases progressively while 0’ first increases (> 90”) then decreases. Field C: 90” < S < 135”. Right way up bedding dips in the opposite direction to the shear plane. As y increases, 8’ increases progressively while L’ first decreases (< 1.0) then increases. Field D: 135” < S < 180”. Most values of S relate to right way up bedding. As y increases both L’ and 8’ initially decrease. Subsequently both increase from a minimum value. The change of 8’ with y is related to variation in the relative rates of passive rotation of pipe and bedding. The velocity of rotation of a planar element (e.g. bedding) in simple shear is given by:
ds’ G=-
1 1 + (cots
+ r)2
which is at a maximum as it passes through the direction of no infinitesimal longitudinal strain at 90” to the shear direction, that is when: y =&tan
S - cot S)
Thus in field A the bedding initially lies in the extensional field of infinitesimal strain and with constant rate of change of y rotates more slowly than the pipe, which is in the compressional field and accelerates as it approaches the n.i.1.s. position; 8’ therefore decreases progressively from 8 = 90” with increasing strain. In field B the bedding initially rotates faster than the pipe so that 0’ first becomes obtuse. The bedding rotates more slowly as it moves away from the n.i.1.s. position while the pipe rotates more quickly as it approaches that position. 0’ therefore begins to decrease and at sufficiently high shear values becomes less than 90”. The behaviour of 8’ with increasing y in fields C and D may be similarly interpreted. The value of L’ is controlled by the orientation of the pipe section on the bedding in relation to the fields of finite compression and extension. The L’ = 1.0 curves on Fig. 6 thus record the positions where the bedding passes through a direction of no finite longitudinal strain. One corresponds to S = 0” or 180” for all values of y, that is when the bedding and therefore the pipe section on it lies in the shear plane and remains in that orientation. The other locus of L’ = 1.0 corresponds to positions where the bedding passes through the second position of n.f.1.s. during passive rotation. This starts at 90” to the shear direction and under increasing y rotates towards the principal extension direction and thus towards the shear plane. Hence only fields C and D contain values of L’ < 1.0.
3NVld
dllS
313NV
pamseaur
N33M138
1 sqdures
5INKXl39
‘z pm ONV
S
Zh.r!~oys ~01 pue qg xba WIIINI
JO uoqnlos
pqyde.rf)
‘g ‘%!d
154 RESULTS
Measurement
techniques
The small angle 19’proved surprisingly easy to measure. Samples (about 20 X 15 X 5 cm) were cut parallel to the symmetry plane (Fig. 4), so that twenty slices a few mm in thickness were obtained, leaving about half the sample for measurement of L’. After polishing, the white pipes could easily be distinguished against the grey and green colour banding. An enlarged image was projected onto tracing paper, the angle between pipe axis and colour banding defined as intersecting lines and the angle of intersection determined by completing a right angled triangle. The measurement of L’ presented greater difficulties. The remaining half of each sample was placed on a surface grinder and progressively ground parallel to the colour banding. As each pipe appeared on the ground surface its elliptical section was measured directly on the sample. The terminations of the longer axes were often difficult to locate with precision. A further source of inaccuracy lay in the difficulty of grinding samples precisely parallel to the colour banding, which is not always perfectly planar. Of the samples available, only two were judged suitable in this respect. Results Results of measurement on two samples are shown in Table I. The two derived values for the initial angle between bedding and the direction of shear, S, are acceptably close and are consistent with the geological model proposed. Since the values lie in Field A of Fig. 6 and pipes dip more steeply than bedding, it is concluded that the mylonite belt was developed in the inverted limb of a major fold. The values for y are also acceptably close, and large, but not unrealistically so (see the results of Ramsay and Graham, 1970). The errors, as indicated by the standard deviations of the measurements, are also large and no great weight should be placed on their exact numerical value. However, it is important to note that the minimum likely value of y, at the 5% significance level, cannot be less than 7. TABLE
I
Measured statistical
--
Sample Sample
1 2
(mean) and derived notation)
parameters
from field samples,
Stat
of Glencoul
(standard
-, 0
Se’
-, L
SL’
n
s
Y
lO.11 lO.45
0.33 0.34
4.63 5.36
1.88 0.95
15 17
17O.8 29O.8
12.0 9.0
155 DISCUSSION
Neglected
fat tars
The principal sources of error in the results arise from inaccuracy of measurement and the effects of other strains to which the rocks have been subjected. The former could be overcome by further determinations and statistical analysis of the results, but this seems scarcely worthwhile in view of the difficulties presented by the second factor. The effect of pre- and post-mylonititsation strains can only be assessed qualitatively. The ‘pre-mylonitisation’ strain comprises the effects of several processes to which the rocks were subjected early in the Dr-episode; layer-parallel shortening, buckling and cleavage formation. As a result of these strains, pipe sections on the bedding in the lower nappes are elongated parallel to the D,fold traces, so that L < 1, and the pipe axes are rotated towards the cleavage, so that 8 > 90” (McLeish, 1971). Thus, after mylonitisation, observed values of L’ are too small and of 0’ too large. In field A (Fig. 6) too small a value of Z;’ for a given 8’ leads to too small a value of S but too large a shear strain. Too large a value of 8’ for a given L’ produces the opposite effect: too large a value of S but too small a strain. A powerful linear fabric produced during Da in the Sutherland Moines suggests that the Da-strain lies in the constriction-extension field. The strain determination made by Wood (1973) on the conglomerate at Ben Hutig (Fig. 1) is compatible with this interpret,ation, but the extremely prolate pebble shapes probably indicate the combined effects of both D,- and Da-strains. In the Stat mylonites the La-extension lineation is weak and lies within 5” of the longer axis of the elliptical pipe sections on the colour banding. The effect of the D2-strain was thus to extend pipe sections in the direction of shearing, to produce an erroneously large value for L’, but to rotate the pipe sections towards the principal extension direction for Da, thus producing too small a value for 0’. The result of the former is to give too large a value for S and too small a shear strain, while too small a value for 0’ has the opposite effect. Thus the influence of both the pre- and post-mylonitisation strains on the results are to some degree self-compensating and in addition tend to compensate for each other. In the absence of reliable quantitative data for either strain it is impossible to judge whether their residual effect is important. A very weak La-microcrenulation is visible in the measured samples; its effect is negligible. D,-structures are non-penetrative and not present in the samples chosen. Conclusions We have shown that, providing our choice of deformation mechanism is correct, it is possible to make strain determinations in rocks which have undergone mylonitisation. The value of these particular results is limited because
156
of the effects of other strains which have not been quantified. We have, however, shown that these are to some extent self-compensating, so that a value for the shear strain of y = 10 may not be grossly inaccurate. This is an extremely large strain: X1/h, > 10,000. Some implications may be discussed. Dislocation zones on the margins of erogenic belts are commonly oriented so that the shear belts dip gently inwards towards the orogen. If cover rocks are involved, their gross pre-deformation attitude is likely to have been subhorizontal and right way up. Very high shear strains in this geometrical situation tend always to produce inverted mylonite ‘stratigraphies’ within the shear belts. A useful principle for the interpretation of field relationships in mylonite zones might thus emerge: inversions, for example basement-derived mylonites overlying cover mylonites, could be interpreted as passively rotated unconformities, while right-way-up relationships could imply dislocation. Thus at the sampled locality at the Stat of Glencoul there is an upward transition from mylonitised Pipe Rock through quartz-mylonite without pipes (presumably Basal Quartzite) to Lewisian mylonite: clearly an inverted sequence. This is interpreted as rotated and tectonically thinned, but not disrupted. Above, the Lewisian mylonite is overlain by arkosic Moine mylonite; this junction could be a D,-slide. The second point is of relevance to the problem of distinguishing rotational from irrotational strains. Johnson (1967), while favouring an irrotational mechanism for mylonitisation, recognised that . . . “in progressive simple shear, planes of ‘flattening’ may be rotated into near-parallelism with shear planes”. The present results allow this statement to be quantified in relation to the Stat mylonites. At y = 10 the dihedral angle between the shear plane and the XY-plane of the strain ellipsoid is only 5.7”. In addition, for S = 25” the colour banding after strain lies at 4.7” to the shear plane. Thus in the Stat mylonites the colour banding lies at about 1” to the XY-plane of an immensely elongated finite ellipsoid. It is evident that the visible layering in mylonites must have suffered a very large degree of thinning and ‘flattening’ but that this does not consitute evidence in favour of irrotational strain. No firm conclusions concerning displacments in the Moine Thrust Belt can be made, in view of the uncertainty of the strain measurement. If the average shear strain is about 10, the westward displacement during D,-mylonitisation at Loch Eriboll, where the mylonites attain a thickness of 800 m, is about 8 km. Pre-mylonite buckling might add a further few kilometres. But it is clear that this displacement is small compared to that attributable to movement on the Moine and other discrete thrust planes which developed subsequently to the mylonitisation. ACKNOWLEDGEMENTS
We wish to thank Professor J.G. Ramsay for reading the manuscript and for making helpful comments. Thanks are also due to G. Mulhearn for technical assistance and to M.G. Cooper for draughting the diagrams.
157 REFERENCES Barber, A.J., 1965. The history of the Moine Thrust zone, Lochcarron and Lochalsh, Scotland. Proc. Geol. Assoc., 76: 215-242. Christie, J.M., 1963. The Moine Thrust zone in the Assynt region, northwest Scotland. IJniv. Calif. Publ. Geol. Sci., 40: 345-440. Hallam, A. and Swett, K., 1966. Trace fossils from the Lower Cambrian Pipe Rock of the north-west Highlands. Scott. J. Geol., 2: 101-106. Johnson, M.R.W., 1957. The structural geology of the Moine thrust zone in the Coulin Forest, Wester Ross. Q.J. Geol. Sot. Lond., 113: 241-270. Johnson, M.R.W., 1960. The structural history of the Moine thrust zone at Lochcarron, Wester Ross. Trans. R. Sot. Edinb., 64: 139-l 68. Johnson, M.R.W., 1967. Mylonite zones and mylonite banding. Nature, 213: 246-247. Knopf, E.B. and Ingerson, E., 1938. Structural Petrology. Geol. Sot. Am. Mem., 6. McLeish, A.J., 1971. Strain analysis of deformed Pipe Rock in the Moine Thrust zone, northwest Scotland. Tectonophysics, 12: 469--503. Peach, B.N., Horne, J., Gunn, W., Glough, C.T. and Hinxman, L.W., 1907. The geological structure of the north-west Highlands of Scotland. Mem. Geol. Surv. U.K. Ramsay, J.G., 1967. Folding and fracturing in rocks. McGraw-Hill, New York, 568 pp. Ramsay, J.G. and Graham, R.H., 1970. Strain variation in shear belts. Can. J. Earth Sci., 7: 786-813. Soper, N.J. and Wilkinson, P., 1975. The Moine Thrust and Moine Nappe at Loch Eriboll, Sutherland. Scott. J. Geol. (in press). Wood, D.S., 1973. Patterns Sot. Land., Ser. A, 274:
and magnitudes 373-382.
of natural
strain
in rocks.
Philos.
Trans.
R.