A model for low amplitude detachment folding and syntectonic stratigraphy based on the conservation of mass equation

This paper presents a model for the structural evolution of low strain detachment folds in which rock is treated as an incompressible deformable material and its kinematics is governed by the continuity equation. The model also considers the following boundary conditions: (i) the vertical flux across the core of the fold is described by a cosine function, (ii) the horizontal flux due to transport along a basal detachment remains constant with depth, and (iii) the depth of the detachment remains fixed. Upon finding analytical expressions for the velocity field of this deformation process, a model for the accumulation of growth strata and the degradation of the topography created by folding is then derived. These processes are approximated by means of the transport-diffusion equation. ons of these two models are in excellent agreement with geometric, and stratigraphic relations documented in fold-and-thrust belts, and analog experiments. Moreover, the model indicates that fold growth in this class of structures is a self-affine process. A compilation of detachment folds around the world indicates that these structures share a common profile. Moreover, fold amplitude and wavelength of these folds are scaled by different amounts, confirming this result. The stratigraphy obtained with the growth strata model exhibits the typical thinning, and truncation of timelines toward the core of the anticline, cross-cutting relations often observed in seismic cross-sections and field data.