Scale invariant sheath folds in salt, sediments and shear zones

Sheath folds are developed in a broad spectrum of geological environments in which material flow occurs, including gravity-driven surficial deformation in ignimbrites, unconsolidated sediments and salt, together with deeper level ductile shear zones in metamorphic rocks. This study represents the first geometric comparison of sheath folds in these different settings across a wide range of scales. Elliptical closures defining eye-folds represent (y–z) cross sections through highly-curvilinear sheath folds. Our analysis of the published literature, coupled with field observations, reveals remarkably similar ellipticities (Ryz) for sheath folds in metamorphic shear zones (Ryz 4.23), salt (Ryz 4.29), sediment slumps (Ryz 4.34), glaciotectonites (Ryz 4.48), and ignimbrites (Ryz 4.34). Nested eye-folds across this range of materials (N = 1800) reveal distinct and consistent differences in ellipticity from the outer- (Ryz) to the inner-most (Ry′z′) elliptical “rings” of individual sheath folds. The variation in ratios from outer to inner rings (R′ = Ryz/Ry′z′) in gravity-driven surficial flows typically displays a relative increase in ellipticity to define cats-eye-folds (R′ < 1) similar to those observed during simple and general shear in metamorphic rocks. We show that sheath folds develop across a range of scales within these different environments, and display elliptical ratios (Ryz) that are remarkably constant (R2 > 0.99) across 9 orders of magnitude (sheath y axes range from ∼0.1 mm to >75 km). Our findings lead us to conclude that the geometric properties of sheath folds are scale invariant and primarily controlled by the type and amount of strain, with R′ also reflecting the rheological significance of layering associated with original buckle fold mechanisms. The scaling pattern of sheath folds reflects the length scales of the precursor buckle folds (and width of deformation zones) across a broad range of materials and environments. With continued deformation, the layering marking the original folds may become increasingly passive to define sheath folds. These empirical relationships suggest sheath folding is a fundamental mode of viscous response across a broad spectrum of materials, strain rates and scales encompassing a variety of deformation settings.