A kinematic model for the formation of duplex systems with a perfectly planar roof thrust

We present a cross-sectional kinematic forward model for the formation of duplexes with a perfectly planar roof thrust. The major assumptions are a constant dip and constant spacing of the ramps in the undeformed state and sequential deformation in the direction of tectonic transport, with equal displacement along each ramp. The model is based on a coordinate transformation that simulates flexural slip parallel to the active fault surface. This causes angular parallel folds and keeps the layer thickness constant, except in the forelimbs of the horses. Attempts by previous workers to simulate the formation of duplexes with a perfectly planar roof thrust, on the other hand, were based on the assumptions of constant bed thickness and bed length, or a different topology of the axial planes delimiting the forelimbs of the horses, and resulted in corrugated roof thrusts. We show that it is not possible to form a flat roof duplex type and preserve the forelimb thickness of the horses under flexural slip parallel to the active fault. We describe duplexes by three parameters which are the separation s between ramps, the ramp length l, and the displacement u along the ramps. In a us vs ls diagram, duplexes with a perfectly planar roof thrust, resulting from numerical experiments with our kinematic algorithm, occupy specific families of straight lines. Our results are independent of the dip or internal geometry of the thrust ramps.