Trench motion, slab geometry and viscous stresses in subduction systems

SUMMARY A semi-analytic, 3-D model for subduction within a Newtonian viscous upper mantle provides a dynamically consistent means of computing viscous stress, trench motion and slab geometry in subduction systems. Although negative slab buoyancy provides the basic driving force for subduction, slabs that extend from the surface to the base of the upper mantle are oversupported by viscous stresses in the shallow (<100‐150 km) mantle and undersupported by viscous stresses at greater depth in the upper mantle. These deeper parts of the subduction system act as an ‘engine’ for subduction while shallower parts act as a ‘brake’ on trench motion; trench migration rates and slab geometry reflect a competition between these two effects. During steady-state subduction, trench migration rates vary approximately linearly with slab buoyancy and model rates of trench motion are in good agreement with the range of observed rates for a two layer upper mantle viscosity of ∼2 × 10 20 Pa s above 300 km and ∼5 × 10 20 Pa s below. Steady-state slab dip increases as slab density decreases, especially for very low-density slabs, which dip significantly more steeply than high-density slabs. The horizontal velocity at the top of the lower mantle, measured relative to the foreland, has a very large effect on trench migration rates, rivalling or even exceeding that of slab buoyancy. Slab width, parallel to the trench, also has a significant effect on trench migration rates due to the viscous pressure of toroidal flow around the slab. The stiffness of the subducting lithosphere does not exert a significant effect on trench migration rates or slab geometries for rigidities compatible with oceanic lithosphere. Very stiff slabs, with elastic plate thicknesses more that ∼40 km or viscosities in the range of 10 25 ‐10 26 Pa s, subduct significantly more slowly than weak slabs, with trench migration rates in the range of half to a third that of weak slabs. Large, unexpected effects on trench migration rates and slab geometry are exerted by the structure and density of the frontal prism and overriding plate, indicating that local geology can exert important constraints on slab dynamics. During non-steady-state subduction, rates of trench migration respond rapidly as variably buoyant lithosphere penetrates into the asthenosphere. In the absence of other driving forces for convergence, trench migration rates can change by a factor of two or more in as little as 2‐3 Myr, for example, from 35 to 70 mm yr −1 when an oceanic piece of slab follows a continental one into the subduction system. Subduction of variable-buoyancy lithosphere is accompanied by changes in slab dip with depth and through time.