The geometry and topology of natural sheath folds: a new tool for structural analysis

Abstract

Curvilinear sheath folds are classically depicted as displaying symmetrical geometries about two orthogonal mirror planes centred along the (X–Y) axial surface and the (X–Z) medial (culmination/depression) surface which bisects the fold nose. However, 10,000 geometric analyses of minor folds and fabrics formed during ductile thrusting in the Caledonides of northern Scotland reveals that major dome and basin sheath folds can display distinct and predictable asymmetries across both axial and medial surfaces. The strain is typically heterogeneous so that structural fabrics and younging evidence are preserved within sheath folds at varying stages of development. This allows an analysis of the evolution of such structures from ‘tongue’ folds to more extreme ‘tubular’ forms. Geometric relationships between measured orientations of fold hinges, axial planes, extension lineations and foliations are compared on fabric topology plots (FTPs), which provide an effective tool for monitoring planar and linear fabric rotations with increasing progressive non-coaxial deformation. They consistently display systematic variation from regions of lower to higher strain on passing from upper to lower fold limbs across major axial surfaces, and on crossing medial surfaces from short to long hinge-line segments. Axial and medial surfaces effectively therefore divide major sheath folds into quadrants with different amounts, senses and combinations of planar and linear fabric rotation within each domain. Such heterogeneous deformation implies that models of intense non-coaxial deformation uniformly affecting pre-existing folds may overestimate bulk displacement and shear strain. Variable fold hinge-line rotation about medial surfaces also provides an effective mechanism for the closure of major sheaths, which may otherwise project for unfeasible distances in the X direction. Bedding/cleavage intersections are developed at greater angles to the transport direction than fold hinges which they transect in a consistent and predictable sense thereby confirming the direction of fold rotation even in areas which lack information on fold facing. In cross-section, asymmetric tear-drop eyes indicate the sense of fold hinge-line vergence, whilst fold limb and hinge-line asymmetry may be combined on 3-D vergence, ranking and rotation grids, which allow location and relative strain states of minor structures to be accurately predicted within the overall sheath framework. Systematic fabric analysis on FTPs may be applied to the investigation of ductile deformation across a broad range of scenarios.