Quantifying the energy dissipation of overriding plate deformation in three-dimensional subduction models

In a subduction system the force and the energy required to deform the overriding plate are generally thought to come from the negative buoyancy of the subducted slab and its potential energy, respectively. Such deformation might involve extension and back-arc basin formation or shortening and mountain building. How much of the slab's potential energy is consumed during overriding plate deformation remains unknown. In this work, we present dynamic three-dimensional laboratory experiments of progressive subduction with an overriding plate to quantify the force (F_OPD) that drives overriding plate deformation and the associated energy dissipation rate (Φ_OPD), and we compare them with the negative buoyancy (F_BU) of the subducted slab and its total potential energy release rate (Φ_BU), respectively. We varied the viscosity ratio between the plates and the sublithospheric upper mantle with η_SP/η_UM = 157-560 and the thickness of the overriding plate with T_OP = 0.5-2.5 cm (scaling to 25-125 km in nature). The results show that F_OPD/F_BU has average values of 0.5-2.0%, with a maximum of 5.3%, and Φ_OPD/Φ_BU has average values of 0.05-0.30%, with a maximum of 0.41%. The results indicate that only a small portion of the negative buoyancy of the slab and its potential energy are used to deform the overriding plate. Our models also suggest that the force required to deform the overriding plate is of comparable magnitude as the ridge push force. Furthermore, we show that in subduction models with an overriding plate bending dissipation at the subduction zone hinge remains low (3-15% during steady state subduction).