Interpretation of subduction initiation in terms of Rayleigh-Taylor instability: implications for the timing of onset of plate tectonics on terrestrial planets

Abstract:

Subduction is thought to be the fundamental process for plate tectonics initiation. It can be approximately described in terms of Rayleigh-Taylor instability. We consider the lithosphere as a cold, dense layer with some characteristic viscosity on top of a low viscosity convecting interior. One major difficulty in subduction initiation is the strength of the cold top layer that prevents it from being unstable to failure. Sublithospheric convection can induce large stresses in the lithosphere and could be sufficient to overcome the strength of the lithosphere and cause it to fail. These stresses are caused by the dipping slope of the base of the lithopshere, and previous analysis on lithospheric stress distribution showed that large aspect ratio cells have higher stresses and thus higher critical yield stress, which means that wide cells are easier to subduct. In time-dependent multi-cell convection systems, we can define sub-cells by a single dipping slope. The sub-cell sizes vary with time, but as the change in the bottom topography of the lithosphere occurs rather slowly, we can study the dynamics in a sub-cell with single-cell steady-state solutions in which the cell size is fixed. We use a yield stress approach to simulate brittle and ductile failure in the lithosphere. The yield stress determines the extent of weakening, and thus controls the stability of the lithosphere. Using simple analytical solutions for Rayleigh-Taylor instability, we develop scaling relations between the yield stress and the timescale of growth of instability. For one of the sub-cells to become sufficiently weakened to initiate subduction, it has to maintain its size for a certain period of time. The scaling relations using this instability model could inform us on the time needed for a wide sub-cell to remain. We use these relations to constrain the time for subduction initiation and the yield stress for terrestrial planets.