A linear perturbation analysis is made on convective instability of the oceanic lithosphere to understand the occurrence of subduction on the Earth. The oceanic lithosphere is modeled by the upper part of top thermal boundary layer in a convecting Newtonian temperature-dependent viscosity fluid. Thickening of oceanic lithosphere with its age due to cooling at the surface is modeled by thickening of the thermal boundary layer with time; its thickening rate L˙ is a measure of the rate with which temperature in the thermal boundary layer decreases with time and hence is a measure of the rate with which viscosity in the thermal boundary layer increases with time. The linear perturbation analysis shows the possible excitation of plural eigenmodes to give rise to an instability in the thermal boundary layer depending on a threshold value Rc of the local Rayleigh number R of the thermal boundary layer. Further, Rc is shown to be a linearly increasing function of L˙, which is treated as a free parameter. From estimates of R and L˙ appropriate for the major oceanic lithosphere (denoted as Robs and L˙obs, respectively), I find that Rc(L˙=0)<Robs<Rc(L˙=L˙obs).

The flow pattern of mantle convection depends strongly on which eigenmodes are excited by the convective instability in thermal boundary layer: (1) When R is lower than Rc, only the fundamental and the first higher modes at most are excited. The resulting mantle convection manifests itself as the secondary convection, (2) When R is higher than Rc, the modes higher than the first higher mode are also excited. The resulting mantle convection involves lithospheric instability, leading to large local deformation in the oceanic lithosphere and finally to subduction of the oceanic lithosphere. This result implies that (1) subduction does not begin newly in the major oceanic lithosphere at present, since lithospheric instability is suppressed by thickening of the major oceanic lithosphere, neither by its high viscosity nor by its buoyancy, (2) subduction will newly begin in the major oceanic lithosphere due to lithospheric instability in future when the oceanic lithosphere becomes so old that its thicknening rate L˙ decreases to sufficiently small value. The latter result suggests that lithospheric instability is an important agent that maintains multiplate tectonics on the Earth. ¿ American Geophysical Union 1990