Control of folding by gravity and matrix thickness: Implications for large‐scale folding

Abstract

[1] We show that folding of a non-Newtonian layer resting on a homogeneous Newtonian matrix with finite thickness under influence of gravity can occur by three modes: (1) matrix-controlled folding, dependent on the effective viscosity contrast between layer and matrix, (2) gravitycontrolled folding, dependent on the Argand number (the ratio of the stress caused by gravity to the stress caused by shortening), and (3) detachment folding, dependent on the ratio of matrix thickness to layer thickness. We construct a phase diagram that defines the transitions between each of the three folding modes. Our priority is transparency of the analytical derivations (e.g., thin-plate versus thick-plate approximations), which permits complete classification of the folding modes involving a minimum number of dimensionless parameters. Accuracy and sensitivity of the analytical results to model assumptions are investigated. In particular, depth dependence of matrix rheology is only important for folding over a narrow range of material parameters. In contrast, strong depth dependence of the viscosity of the folding layer limits applicability of ductile rheology and leads to a viscoelastic transition. Our theory is applied to estimate the effective thickness of the folded central Asian upper crust using the ratio of topographic wavelength to Moho depth. Phase diagrams based on geometrical parameters show that gravity does not significantly control folding in the Jura and the Zagros Mountains but does control folding in central Asia. Applicability conditions of viscous and thin sheet models for large-scale lithospheric deformation, derived in terms of the Argand number, have implications for the plate-like style of planetary tectonics.

Folding and necking across the scales: a review of theoretical and experimental results and their applications

“…The Argand number Ar N is similar to the one that has been introduced by England and McKenzie (1982) to scale the gravitational stress to the horizontal stress during lithospheric thickening and is similar to the Argand number applicable to lithospheric folding (Schmalholz et al, 2002). Fletcher and Hallet (1983) showed that for a wide range of creep flow laws and an extension rate of the order of 10 −15 s −1 , the necking instability is strong (α d 40) and that the dominant wavelength L d = 30-90 km.…”

“…The dominant wavelength for viscous and power-law viscous layers resting on an inviscid medium under gravity is the same (Schmalholz et al, 2002). Values of n for dislocation creep are usually in the range 3-5.…”

“…Biot (1961) argued that 4η D xx / ρgH >∼ 9 is required for viscous folding under gravity to be significant. The maximum value of the amplification rate for folding of a power-law viscous layer resting on a viscous medium under gravity is (Schmalholz et al, 2002) …”

“…In Eq. (34), Ar F is the Argand number for folding and represents the ratio of gravitational stress acting against folding to compressive stress driving folding (Schmalholz et al, 2002). The Argand number was originally introduced in a slightly different form for thin viscous sheet models (England and McKenzie, 1982).…”

Crustal deformation induced by mantle dynamics: insights from models of gravitational lithosphere removal

“…In some areas, the subsidence events are related to lithosphere extension, thermal subsidence and crustal buckling/folding (e.g. Lambeck 1983;Burg & Podladchikov 1999;Cloetingh et al 2002;Schmalholz et al 2002). In other basins, the subsidence mechanism is less clear, and some intracratonic basins have been linked to processes that originate in the mantle (e.g.…”