Controls on sublithospheric small-scale convection

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 Frank-Kamenetskii parameter theta and a Rayleigh number Ra-i, respectively. Our models show that the onset time of SSC, tau(c), scales as Ra(i)(-0.68)theta(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, Deltatau, scales as Ra(i)(-0.65)theta(1.52), while the thickness of the stagnant lid at the onset time, delta, scales as Ra(i)(-0.33)theta(0.78), which is consistent with Deltatau similar to delta(2) for thermal diffusion. At the onset of SSC, Q scales as Ra(i)(0.34)theta(-0.37) or tau(c)(-0.5) 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)theta(-0.7), 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.