Bruno Sander has proposed that the fabric symmetry of a deformed rock reflects the kinematic symmetry of its deformation. In order to place this symmetry principle on a firmer basis, the background of the symmetry theory of fabrics is here reviewed. From very general notions of symmetry as a starting point, fabric symmetry is shown to be a statistical space symmetry consisting of a point group of symmetry operations combined with arbitrary translations in all directions. Where likely restrictions are placed upon the point groups to be expected in homogeneously deformed rocks, the usual types of symmetry observed in fabrics of deformed rocks (namely, spherical, axial, orthorhombic, monoclinic, and triclinic) remain as possible types. The general derivation demonstrates that apart from pseudocrystallographic symmetries defined by some crystallographic fabric elements, no other types of fabric symmetry can be expected in homogeneously deformed rocks.
Attention is drawn to the relevance to the views of Sander of Curie's principles governing the symmetries of “cause” and “effect” in physical phenomena. The features of a deformed rock that define its fabric are found to be a three dimensionally ordered array of discontinuities in structure (lattice planes and lines in crystals, grain boundaries, foliations, lineations, folds, and so on) which may be viewed as the “effect” of deformation. These surfaces and lines of discontinuity in structure are generally sites of surfaces and lines of discontinuity in deformation—implicit in Sander's concept of componental movements—which collectively define the “movement picture” (Bewegungsbild) of the deformation. An attempt is made to state more precisely the significance of a movement picture in terms of analysis of local heterogeneities and perturbations in deformation that reflect or are responsible for the development of fabric features in a statistically homogeneously deformed aggregate. The kinds of symmetry observed in tectonite fabrics are found also to be the only kinds possible in movement pictures of homogeneous deformations.
Curie's principles may now be restated in a form directly applicable in the interpretation of tectonite fabrics, thereby amplifying Sander's principle. Without qualification, the most important principle may be restated as follows: whatever the nature of the factors contributing to a deformation may be, the symmetry that is common to them cannot be higher than the symmetry of the deformed fabric, and symmetry elements absent in this fabric must be absent in at least one of the contributing factors.