Sheath folds as discriminators of bulk strain type

Abstract

Nested elliptical closures defining “eye-folds” represent classic ( y– z) cross sections through highly curvilinear sheath folds generated during intense ductile deformation in metamorphic rocks. Systematic analysis of 1425 such eye-folds based on our own field observations and examples from the published literature reveals distinct and consistent differences in ellipticites measured from the outer- ( R yz ) to the inner-most ( R y′ z′ ) elliptical “rings” of individual sheaths. The variation in overall aspect ratios from outer to inner rings is defined as R′ (where R′ = R yz / R y′ z′ ) and may display a relative increase or decrease in ellipticity to define ‘ cats-eye’ ( R′ < 1) or ‘ bulls-eye’ ( R′ > 1) fold patterns respectively. Layer thicknesses may also be measured along the y axis (parallel to the axial surface) ( t y ) and at 90° to this along the z axis ( t z ) to define the ratio of T yz . Sheath folds generated during broadly simple shear deformation ( k ≅ 1) display (mean) R yz 4.61, T yz 3.31 and cats-eye-folds ( R′ 0.69). Sheath folds generated during general shear also display cats-eye-folds with identical mean R′ 0.69 values, but greater thickness variations and elliptical ratios ( T yz 4.35, R yz 5.76). Thus, within both simple- and general shear-dominated deformations, the overall variation in layer thickness ( T yz ) and ellipticity of eye-folds ( R yz ) increases with increasing deformation and a greater component of pure shear, whilst the R′ value remains constant and reflects original fold patterns. Sheath folds formed during constrictional ( k > 1) deformation display markedly lower aspect ratios ( R yz 2.42) and thickness variations ( T yz 2.94), together with distinctive bulls-eye-folds ( R′ 1.23). These empirical relationships suggest fundamental and universal constraints on curvilinear fold generation across this broad spectrum of deformation types, and allow sheath folds to act as both effective (>95% consistent) and robust discriminators of bulk strain type.