Derek Flinn

ON FOLDING DURING THREE-DIMENSIONAL PROGRESSIVE DEFORMATION

This paper is concerned with the geometry of homogeneous strain in rocks. Equations relating rotation of planes and lines to the deformation of the rock containing them are derived with the aid of the deformation ellipsoid. The Fresnel construction is borrowed from optical mineralogy to determine from the deformation ellipsoid the principal axes of compression and extension in any plane, and an expression is derived for determining the lengths of these axes. Further equations are derived which define the surfaces of no infinitesimal strain and no finite strain for all possible ellipsoids, and it is shown that these surfaces may be used for rapidly determining whether the principal axes in any plane have suffered shortening or extension. With these tools the rather complex geometry of three-dimensional homogeneous strain is examined in detail. It is shown, for instance, that during deformation planes and lines develop preferred orientations reflecting the symmetry of the deformation, and pre-existing folds rotate bodily in space and either open or close or both during the deformation. In order to draw further conclusions of general interest the condition of homogeneous strain is relaxed in order to consider the deformation of layered rocks with competence differences between the layers. It is argued that during the deformation of such rocks folds and boudinage form parallel to the principal directions of strain in the layers. The conditions that determine whether folds or boudinage are formed are examined and the subsequent development of the structures after their generation is followed. These methods of analysis are used in the construction of models of superimposed fold-systems which are shown to be similar to some recently described field examples. It is argued that the tectonic axial cross must be replaced by the deformation ellipsoid. The structures treated in the paper are usually derived by shear-plane hypotheses, but it is considered that such hypotheses are superfluous.

On the symmetry principle and the deformation ellipsoid

According to the symmetry principle the fabric of a tectonite reflects the symmetry of the deforming movements. Where the symmetry of the deformation varies from place to place this should be reflected in a similar variation in the fabric. The possible variation in homogeneous strain is best shown by the range of variation possible in the deformation ellipsoid. It is argued in the paper that rocks commonly occur which show a variation in fabric from place to place similar to the whole or part of the possible variation in shape of the deformation ellipsoid. It is concluded that such rocks have deformed by homogeneous strain. This conclusion is supported by the shapes and orientations of pebbles in deformed conglomerates.

On the Deformation of the Funzie Conglomerate, Fetlar, Shetland

The Funzie conglomerate in northeast Shetland is a very large body of deformed metaconglomerate of pre-Middle Old Red Sandstone age. Its elongated and flattened pebbles, which are mostly of quartzite and occasionally of marble, lie in a subgraywacke matrix. A plot based on the measurement of 548 quartzite pebbles shows that the shapes of the pebbles vary systematically over the area. A minimum value for the deformation of the conglomerate at any point is found by comparing the average pebble shape at that point with the average pebble shape in the area of least deformation. Compression in the plane normal to the elongation direction has forced the pebbles to elongate by flow (Einengung). It is shown that the consistency of direction of the pebble axes is related to the elongation of those axes and is due to differential flow of the matrix against the pebbles. During the deformation of the pebbles their constituent quartz grains, the clastic quartz grains in the matrix, and the calcite grains in the marble pebbles developed forms and orientations similar to those of the pebbles. At the same time, the quartz, calcite, and micaceous grains of the pebbles and the micaceous grains of the matrix all developed preferred lattice orientations which give partial girdles of the poles of the c-axes [or of (001) of mica] in the plane perpendicular to the elongation direction, while the clastic quartz grains in the matrix show no preferred lattice orientation. Later ruptural deformation gave rise to fracture cleavage in the quartzite pebbles, tension veins, and calcite twinning.

Construction and computation of three-dimensional progressive deformations

The deformation plot is shown to be ideal for the display of ellipsoid shape, as is its logarithmic transformation for the display of deformation paths of coaxial deformations. Other plots which have been proposed can be derived from the deformation plot by various geometric transformations and by the superposition of other coordinate axes. These variants of the deformation plot are less convenient to use. The deformation plot may also be used for the construction of deformation paths. This use depends on the definition of a number of different types of deformation ellipsoid. In particular, in deformations involving volume change, the shape change arising from the volume change needs to be represented by an ellipsoid. Under these conditions coaxial deformation paths of any imaginable complexity can be easily constructed on the deformation plot. For non-coaxial deformation, matrix representation of the deformation ellipsoids allows deformation paths to be computed, but graphic representation of these results requires both the deformation plot and a stereonet.

The deformation matrix and the deformation ellipsoid

Abstract Homogeneous strain can be computed most easily by the methods of matrix algebra. Lines, planes and ellipsoids represented in matrix form can be homogeneously deformed by simple matrix multiplication by linear transformation matrices, the elements of which are the coefficients of the transformation equations. Deformation matrices or linear transformation matrices which cause geological-type homogeneous strain are divided into four classes based on the presence or absence of symmetry and/or orthogonality. The nature of the homogeneous strain caused by each class of deformation matrix is examined. Orthogonal-symmetrical and orthogonal matrices cause rotation. Symmetrical matrices cause irrotational strain with co-axial strain as a special case. Matrices which are neither orthogonal nor symmetrical cause many different types of rotational strain, some of which are examined.

Transcurrent faults and associated cataclasis in Shetland

A series of transcurrent faults with northerly trend is well exposed in the cliffs of Shetland. The Walls Boundary Fault which cuts through the middle of Shetland has a continuously changing trend so that it forms a very flattened S. Dextral movement along the fault seems to have created further dextral transcurrent faults, including the Nesting Fault, across the eastern concavity in the trend. These main faults lie within broad zones of cataclasis, subsidiary faulting and local folding. The offsets on the subsidiary faults are very much less than on the main faults, and the crushed rocks have isotropic fabrics. The zones probably arose during faulting from varying local stresses caused by the interaction of the unevennesses on the two sides of the non-planar main faults. Gouge in the Walls Boundary Fault contains analcite. Gouge-like laumontite in subsidiary shears was probably formed by mechanochemical reactions. The occurrence of these minerals and of blastomylonitic scapolite veins near the Walls Boundary Fault may indicate up to three phases of movement taking place between Cretaceous and Devonian times under different depths of overburden. Slices of secondarily cataclastic mylonite occurring along the Walls Boundary Fault are probably relics of the Great Glen Fault now partially cut out by the nearly coincident Walls Boundary Fault.

ON THE NAPPE STRUCTURE OF NORTH-EAST SHETLAND

The main serpentine and greenstone block of Unst is traced into Fetlar and shown to be a nappe (the lower nappe) folded into a southerly-trending synform. It lies above a basement of high-grade regional metamorphic and migmatitic rocks and is separated from this basement by the lower schuppen zone. The lower nappe is overlain by an upper nappe (the Vord Hill serpentine in Fetlar and the Clibberswick serpentine in Unst) which forms the core of the synform. It is separated from this nappe by the middle schuppen zone. The upper nappe is overlain in Fetlar by the upper schuppen zone. The three schuppen zones contain slices of migmatite-gneiss and schist from the basement, serpentine and greenstone from the nappes, and Norwick Hornblendie Schist and Phyllite Group rocks which occur only in these zones. Sedimentary structures in the Phyllite Group show that they were formed, in part at least, of the erosion products of the nappes as they were being emplaced. Continued movement of the nappes resulted in the metamorphism and deformation of the rocks in the schuppen zones and of the nappes and basement beside the zones. This, the second metamorphism, was a constructive synkine-matic greenschist facies metamorphism, which completely or partially transformed both metamorphic and sedimentary rocks of the schuppen zones into phyllites. During the metamorphism these rocks were folded and elongated parallel to the fold-axes as a result of constriction in the plane normal to the fold-axes. This deformation was not directly caused by movements on the thrust-planes; it was caused by the flow of the relatively incompetent rocks of the schuppen zones towards the direction of the easiest relief, due to pressure from the relatively rigid masses of the nappes. The direction of movement of the nappes themselves cannot be determined as the roots are not exposed and the thrust-planes lack directional structures.

Grain contacts in crystalline rocks

The distributions of mineral grains in gneisses from Shetland and Siberia are studied. Statistical tests show that the grains, instead of being distributed at random, are specially arranged so that grains of the same phase tend not to occur in contact with each other. It is concluded that this arrangement arises from grain boundary migration leading to the insertion of grains of one phase between pairs of like grains of other phases. This process arises from the fact that the interfacial energies of contacts between like phases are greater than those between unlike phases.

The most recent glaciation of the Orkney-Shetland Channel and adjacent areas

Synopsis During the most recent glaciation Shetland was covered by an ice cap which flowed radially outwards from the islands, but was deflected in the SW so that it flowed in a northwesterly direction across Foula and in a southeasterly direction across Fair Isle. This pattern indicates that a flow to the SW from Shetland was blocked, possibly by a mass of ice lying over Orkney, but that there was no hindrance to flow towards Norway on the E side of Shetland. In the North Sea to the E of the Moray Firth there was an ice free area. Thus there is no evidence for a Scandinavian ice sheet in the area and consequently no reason for the deflection of Scottish ice from the Moray Firth to the NW across Orkney. It is suggested that the Scandinavian ice sheet covered the North Sea and deflected the Scottish ice across Orkney during the previous glaciation, but that in the last glaciation it did not cross the Norwegian Trench.

A revision of the stratigraphic succession of the East Mainland of Shetland.

Synopsis The succession of metamorphic rocks in the eastern part of the Mainland of Shetland is briefly described. Four main divisions are recognised. These rocks are compared in terms of lithology and sedimentary structures with the Moine and Dalradian rocks of Scotland. The westernmost division of the Shetland succession is correlated with the Moine while the other three divisions are considered to be Dalradian.