The concept of bed-duplication folding, a process of folding by stacking of duplicate beds above a thrust ramp, was introduced by John L. Rich in 1934, and such folding has been studied mechanically and geometrically during the last few years.
This paper introduces two kinematical models to bridge between geometrical and mechanical analyses, so results of the two methods of determining the deformations and geometry of bedduplication folding can be compared. One kinematical model is required for early stages and the other for late stages of bed-duplication folding, but each involves a simple, domainal, velocity distribution. It is remarkable that such simple kinematical models can produce complex geometrical models. The kinematical models clearly produce the type of bed-duplication fold developed by graphical construction and termed "fault-bend fold". The kinematical models provide new insights into the essence of the type.
The velocity distributions assumed in the kinematical models are similar to those predicted by a first-order, mechanical model for thrust ramps with low slopes (less than about 20 degrees) and zero drag. The fold forms computed from the two sets of models are also similar, so geometrical construction roughly reproduces a simple, low-amplitude bed-duplication fold.
The approximation is poorer for steeper thrust ramps. The upper limit of the kinematical model and geometrical construction is 30 degrees and, at that ramp angle, the dip of the distal limb of the fold is twice the dip of the thrust ramp. Results of the mechanical analysis of relatively steep ramps, carried to second-order accuracy, indicate that the 30-degree limit of the ramp angle is an artifact of the geometrical analysis and that the block being thrusted is subjected to general simple shearing. The simple shear is absent in the kinematical models and the geometrical construction.
Nevertheless, both the kinematical and mechanical models predict asymmetry of fold limbs.