Modeling the shortening history of a fault-tip fold using structural and geomorphic records of deformation

We present a methodology to derive the growth history of a fault-tip fold above a basal detachment. Our approach is based on modeling of the stratigraphic and geomorphic records of deformation, as well as the finite structure of the fold constrained from seismic profiles. We parametrize the spatial deformation pattern using a simple formulation of the displacement field derived from sandbox experiments [Bernard et al., 2006]. Assuming a stationary spatial pattern of deformation, we simulate the gradual warping and uplift of stratigraphic and geomorphic markers, which provides bounds on the cumulative amount of shortening they have recorded. This approach allows modeling of isolated terraces or growth strata. We apply this method to the study of two fault-tip folds in the Tien Shan, the Yakeng and Anjihai anticlines, documenting their deformation history over the past 6-7Myr. We show that the modern shortening rates can be estimated from the width of the fold topography provided that the sedimentation rate is known, yielding respective rates of 2.15mm/yr and 1.12mm/yr across Yakeng and Anjihai, consistent with the deformation recorded by fluvial and alluvial terraces. This study demonstrates that the shortening rates of both folds accelerated significantly since the onset of folding. It also illustrates the usefulness of a simple geometric folding model, and highlights the importance of considering local interactions between tectonic deformation, sedimentation and erosion.