SUMMARY The aim of this study is to quantify the relationship between the kinematics of subduction, deformation in the overriding plate and the evolution of slab geometry. A 2‐D finite element numerical code is used, and a first objective consists in benchmarking previously published analogue models. Far‐field plate velocities are applied, and once the subducting plate reaches the 660 km discontinuity, modelled as a rigid base, we obtain two different forms or styles of subduction that depend on the overriding plate velocity vop: if vop > 0, the slab lies forwards on the 660 km discontinuity (style 1), and if vop≤ 0, the slab lies backwards on the discontinuity (style 2). We also obtain a cyclic pattern with the slab folding on itself repeatedly when vsp > 0 and 2vop+vsp > 0 (where vsp is the subducting plate velocity). These conditions result from the analysis of several simulations in which the subduction velocities and plate viscosities are varied. When the slab periodically folds on the 660 km discontinuity, periods of shallow slab dip and compression in the overriding plate are followed by periods of slab steepening and relative extension in the overriding plate. Folding periodicity is controlled by the slab viscosity and subduction velocity. When a low‐viscosity zone is included in the overriding plate, the trench motion is effectively decoupled from the overriding plate velocity, therefore allowing it to be directly controlled by the deep dynamics of the slab. For the cyclic style 2 corresponding to forward folding of the slab, the low‐viscosity region in the overriding plate increases the stress amplitudes oscillations, the trench motion and the folding periodicity with time. Therefore the strength of the entire overriding plate is shown to directly control the dynamics of subduction. Using the Nazca and South American plate velocities we produce models of cyclic folding with a period of ca. 22 Ma and a minimal dip angle of ca. 10°. Episodic folding of the slab on the 660 km discontinuity would produce the necessary changes in slab dip and overriding plate deformation that explain episodes of volcanic quiescence alternating with greater rates of shortening along the Andes.

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