Global trench migration velocities and slab migration induced upper mantle volume fluxes: Constraints to find an Earth reference frame based on minimizing viscous dissipation

Since the advent of plate tectonics different global reference frames have been used to describe the motion of plates and trenches. The difference in plate motion and trench migration between different reference frames can be substantial (up to 4 cm/yr). This study presents an overview of trench migration velocities for all the mature and incipient subduction zones on Earth as calculated in eight different global reference frames. Calculations show that, irrespective of the reference frame: (1) trench retreat always dominates over trench advance, with 62–78% of the 244 trench segments retreating; (2) the mean and median trench velocity are always positive (retreating) and within the range 1.3–1.5 cm/yr and 0.9–1.3 cm/yr, respectively; (3) rapid trench retreat is only observed close to lateral slab edges (< 1500 km); and (4) trench retreat is always slow far from slab edges (> 2000 km). These calculations are predicted by geodynamic models with a varying slab width, in which plate motion, trench motion and mantle flow result from subduction of dense slabs, suggesting that trench motion is indeed primarily driven by slab buoyancy forces and that proximity to a lateral slab edge exerts a dominant control on the trench migration velocity. Despite these four general conclusions, significant differences in velocities between such reference frames remain. It is therefore important to determine which reference frame most likely describes the true absolute velocities to get an understanding of the forces driving plate tectonics and mantle convection. It is here proposed that, based on fluid dynamic considerations and predictions from geodynamic modelling, the best candidate is the one, which optimises the number of trench segments that retreat, minimizes the trench–perpendicular trench migration velocity (v_T) in the centre of wide (> 4000 km) subduction zones, maximizes the number of retreating trench segments located within 2000 km of the closest lateral slab edge, minimizes the average of the absolute of the trench–perpendicular trench migration velocity (|v_T|) for all subduction zones on Earth, and minimizes the global upper mantle toroidal volume flux (_To) that results from trench migration and associated lateral slab migration (i.e. slab rollback or slab roll-forward). Calculations show that these conditions are best met in one particular Indo-Atlantic hotspot reference frame, where 75% of the subduction zones retreat, v_T in the centre of wide subduction zones ranges between − 3.5 and 1.8 cm/yr, 83% of the trench segments located within 2000 km of the closest lateral slab edge retreat, the average of |v_T| is 2.1 cm/yr, and _To = 456 km³/yr (lower limit) and 539 km³/yr (upper limit). Inclusion of all the incipient subduction zones on Earth results in slightly greater fluxes of 465 km³/yr (lower limit) and 569 km³/yr (upper limit). It is also found that this reference frame is close to minimizing the total sub-lithospheric upper mantle volume flux (_K) associated with motion of continental keels located below the major cratons. It is stressed, however, that _K is an order of magnitude smaller than _To, and thus of subordinate importance. In conclusion, the Indo-Atlantic hotspot reference frame appears preferable for calculating plate velocities and plate boundary velocities.