Slab stiffness control of trench motion: Insights from numerical models

Subduction zones are not static features, but trenches retreat (roll back) or advance. Here, we investigate the dominant dynamic controls on trench migration by means of two- and three-dimensional numerical modeling of subduction. This investigation has been carried out by systematically varying the geometrical and rheological model parameters. Our viscoplastic models illustrate that advancing style subduction is promoted by a thick plate, a large viscosity ratio between plate and mantle, and a small density contrast between plate and mantle or an intermediate width (w 1300 km). Advancing slabs dissipate 45% to 50% of the energy in the system. Thin plates with relatively low viscosity or relatively high density, or wide slabs (w 2300 km), on the other hand, promote subduction in the retreating style (i.e., slab roll-back). The energy dissipated by a retreating slab is 35% to 40% of the total dissipated energy. Most of the energy dissipation occurs in the mantle to accommodate the slab motion, whereas the lithosphere dissipates the remaining part to bend and ‘‘unbend.’’ With a simple scaling law we illustrate that this complex combination of model parameters influencing trench migration can be reduced to a single one: plate stiffness. Stiffer slabs cause the trench to advance, whereas more flexible slabs lead to trench retreat. The reason for this is that all slabs will bend into the subduction zone because of their low plastic strength near the surface, but stiff slabs have more difficulty ‘‘unbending’’ at depth, when arriving at the 660-km discontinuity. Those bent slabs tend to cause the trench to advance. In a similar way, variation of the viscoplasticity parameters in the plate may change the style of subduction: a low value of friction coefficient weakens the plate and results in a retreating style, while higher values strengthen the plate and promote the advancing subduction style. Given the fact that also on Earth the oldest (and therefore probably stiffest) plates have the fastest advancing trenches, we hypothesize that the ability of slabs to unbend after subduction forms the dominant control on trench migratio