Flexural Mechanics of Subduction

Abstract:

Deformation of subducting lithosphere is controlled by a balance of four forces: the negative buoyancy of the slab, its internal viscous resistance to stretching and bending, and the drag of the ambient mantle. To elucidate the complex dynamics of this system, we study a model in which a 3-D sheet of viscous fluid with thickness $h$ and viscosity $\gamma\eta_1$ subducts in an ambient fluid with viscosity $\eta_1$ and depth $D$. Numerical solutions for the sheet's evolution are obtained using a boundary element method, starting from an initial configuration comprising a short protoslab attached to a longer horizontal plate that is free to move laterally. The dynamics of the sheet are controlled by its dimensionless `stiffness' $S\equiv \gamma (h/\ell_b)^3$, where the `bending length' $\ell_b$ is the sum of the lengths of the slab and of the flexural bulge. The slab's sinking speed is controlled by its own viscosity if $S\gg 1$, and by that of the ambient fluid if $S\leq 1$. Time-dependent solutions with passive tracers demonstrate a partial return flow around the leading edge of a retreating slab and return flow around its sides. A systematic investigation of the slab's interaction with the bottom boundary as a function of $\eta_2/\eta_1$ and $D/h$ delineates a rich regime diagram of subduction modes (trench retreating, slab folding, trench advancing, etc.) that agrees well with laboratory observations. The solutions show that mode selection is controlled by the dip of the slab's leading edge at the time when it first encounters the bottom boundary. We will discuss several geophysical applications of the model, including seismic evidence for slab folding, the radius-of-curvature constraint on the slab/mantle viscosity ratio $\eta_2/\eta_1$, and the distribution of seismic anisotropy around subducting slabs.