Foundering of the lithosphere at the onset of subduction

An analytic theory is presented for the foundering of the lithosphere at the onset of subduction. The two‐dimensional cartesian model calculates the instantaneous response of a viscous half‐space to a surface load that corresponds to the negative buoyancy of a semi‐infinite plate. In the early stages of foundering, just after the mantle floods onto the top of the lithosphere, the edge of the slab sinks into the mantle with a downward velocity u z given by (1/6 e ) (Δ ρ/ρ ) 4 ( ρgd²/μ ) ( d/x n )², where ρ is the density of the mantle, Δ ρ is the density of the lithosphere minus the density of the mantle, d is the thickness of the lithosphere, g is the acceleration of gravity, μ is the viscosity of the mantle, and x n is the flexural length scale of the lithosphere. Alternatively, u z is given by (3/ e ) (Δ ρ/ρ )³ ( d/x n )² u z (Stokes), where u z (Stokes) is the Stokes velocity of fall of a sphere of radius d /2 with excess density Δ ρ through a fluid of viscosity μ and density ρ . The initial subsidence velocity of the edge of a lithospheric slab is much slower than the sinking velocity of a similar‐sized and negatively buoyant sphere. For typical values of the above parameters, the edge of the plate sinks into a mantle of viscosity 10 18 P as at a rate of about 7.5 mm yr −1 . Lithospheric foundering is facilitated by low mantle viscosity and old, thick plates.