[1] The Pacific upper mantle structures revealed from recent seismic studies prompt us to study the dynamics of sublithospheric small-scale convection (SSC) derived from thermal boundary layer instabilities of cooling lithosphere. As oceanic lithosphere cools and thickens, its sublayer may go unstable, thus producing SSC in the asthenosphere. By formulating two-dimensional (2-D) and three-dimensional (3-D) numerical models with realistic mantle rheology, we examine the controls on the onset time of SSC and its dynamic consequences. The onset of SSC is mainly controlled by two parameters: activation energy and asthenospheric viscosity, which can be recast as the FrankKamenetskii parameter q and a Rayleigh number Ra i , respectively. Our models show that the onset time of SSC, t c , scales as Ra i À0.68 q 0.74 , independent of 2-D or 3-D geometry. Our scaling coefficient for q is significantly smaller than that from previous studies, but the weaker dependence on activation energy confirms the result of Korenaga and Jordan [2003]. We found that thermal structure associated with age offset across fracture zones has significant effects on the onset of SSC, and it causes the SSC to occur always first near the fracture zones. Asthenospheric thickness and plate motion may also have significant effects on the onset of SSC. When the thickness of asthenosphere is sufficiently small to be comparable with the wavelength of the SSC, the onset may be delayed significantly. Plate motion also tends to delay the onset of the SSC in our 2-D models. Although at the onset of SSC surface heat flux Q is consistent with the half-space cooling model prediction, Q may eventually deviate from the half-space cooling model prediction as thermal perturbations associated with SSC diffuse through the stable part of lithosphere or stagnant lid to the surface. We found that the time it takes for Q to deviate from the half-space cooling model after the onset of SSC, Át, scales as Ra i À0.65 q 1.52 , while the thickness of the stagnant lid at the onset time, d, scales as Ra i À0.33 q 0.78 , which is consistent with Át $ d 2 for thermal diffusion. At the onset of SSC, Q scales as Ra i 0.34 q À0.37 or t c À0.5 as expected from the half-space cooling model. However, these scaling coefficients change significantly with time. After nine onset times Q scales as Ra i 0.28 q À0.7 , which although showing the trend toward the scaling for steady state convection is still far from the predictions for steady state convection, thus suggesting a fundamentally transient nature of the SSC.

[1] The seafloor topography and heat flux differ significantly from the predictions of the half-space cooling (HSC) model at old ocean basins. Understanding the deviations has important implications for thermal evolution of oceanic lithosphere and large-scale mantle dynamics. A widely used model that explains significant fraction of the deviations is the plate model, but the dynamical feasibility of the plate model has never been demonstrated. In this study, we investigated the effects of sublithospheric small-scale convection (SSC) and of internal heating on seafloor heat flux and topography and mantle thermal structure, and we examined the dynamic feasibility of the plate model by formulating high-resolution two-dimensional numerical models of mantle convection with strongly temperature-and depth-dependent rheology. We found that mantle convection with tectonic plates often leads to formation of a broad thermal anomaly below old lithosphere where the mantle is not cooled by subducted slabs and heat transfer is less efficient because of thick lithosphere, especially when significant internal heating is present. This trapped heat may exist in the middle mantle when the SSC is absent, and it may also be redistributed by the SSC to shallow depths to reheat the lithosphere and to homogenize mantle temperature. When internal heating accounts for >$60% of the total heat output, the trapped heat may provide sufficient heat supply to preferentially reheat old lithosphere via SSC while maintaining uniform mantle temperature. We suggest that the trapped heat and the SSC are responsible for the residual heat flux and topography at old ocean basins relative to the HSC model predictions. Our models also show that for the plate model to be dynamically viable, both the SSC and significant internal heating (>60%) are necessary. This is because only the SSC in a mantle with significant internal heating can erode and reheat the lithosphere while maintaining a nearly constant mantle temperature below lithosphere, which is the basic assumption of the plate model. With the viscosity structure and internal heating rate for the present-day mantle, we think that the plate model is dynamically viable.Citation: Huang, J., and S. Zhong (2005), Sublithospheric small-scale convection and its implications for the residual topography at old ocean basins and the plate model,

[1] Numerical three-dimensional spherical models of stirring of passive tracers in a convective mantle incorporating plate tectonics, taking account of faster mantle overturning in the past and scaling the model to the Earth, show that the mean ages of MORB and OIB samples obtained from the models are $1.7 Ga for a 4.5 Ga Earth, close to the observed apparent lead isotopic age of $1.8 Ga. Only $3% of the mantle remains unprocessed. The processing time, which is the time for a mass equivalent to Earth's mantle to be processed through melting zones, is equal to the value estimated for the Earth (2.9 Ga). These results are consistent with previous results from two-dimensional models. A simple physical processing theory reveals that the degree of processing, the residence time of tracers in the mantle, and their age distribution are mainly controlled by the processing time. Comparison with analogous two-dimensional Cartesian models shows that the geometry, viscosity structure, and vigor of convection have only secondary influence on these results.