TRANSITION WAVELENGTH THEORY

A viscoelastic single-layer folding theory is shown to predict a transition from distributed to localized deformation at a specific normalized wavelength - transition wavelength - as a function of the competence contrast at the layer boundaries. This transition is demonstrably independent of stabilizing forces such as gravity and surface energy. The effect of viscoelasticity, compared to the viscous case, is to destabilize folds at wavelengths shorter than the transition wavelength, and stabilize those at longer wavelength. Transition wavelength theory, therefore, not only provides an explanation for the common observation of thrust faults cross-cutting fold hinges in fold-thrust belts, but also the generally short normalized wavelengths of observed natural folds. Fold-wavelength frequency distributions of natural folds, normalized to layer thickness, display marked skewness, with an overall range from about 3 to 35 and modes in the range 4 to 7. Comparison of these data with the theory suggests that competence contrasts attending deformation in fold-thrust belts range from about 10 to 36. This conclusion stands in contrast to those drawn from dominant wavelength theory for both Newtonian and power law viscous rheologies, which suggest competence contrasts in the range of 500 to 1000 or more. Note that the predicted 10 to 36 range is consistent with the classic analysis of Sherwin and Chapple (1968), and well below those values at which Lan and Huddleston (1995) demonstrated the formation of a finite neutral surface in single-layer buckle folds using power law viscous rheology. Observed natural folds generally lack a finite neutral surface. These findings demonstrate the importance of viscoelasticity for fold formation, and raise the often ignored question of extrapolating empirical relationships based on rock mechanics data to deformation at tectonic strain rates.