Gravity, topography, and melt generation rates from simple 3D models of mantle convection

Abstract: Convection in fluid layers at high Rayleigh number (Ra $\sim 10^6$) have a spoke pattern planform. Instabilities in the bottom thermal boundary layer develop into hot rising sheets of fluid, with a component of radial flow towards a central upwelling plume. The sheets form the "spokes" of the pattern, and the plumes the "hubs". Such a pattern of flow is expected to occur beneath plate interiors on Earth, but it remains a challenge to use observations to place constraints on the convective planform of the mantle. Here we present predictions of key surface observables (gravity, topography, and rates of melt generation) from simple 3D numerical models of convection in a fluid layer. These models demonstrate that gravity and topography have only limited sensitivity to the spokes, and mostly reflect the hubs (the rising and sinking plumes). By contrast, patterns of melt generation are more sensitive to short wavelength features in the flow. There is the potential to have melt generation along the spokes, but at a rate which is relatively small compared with that at the hubs. Such melting of spokes can only occur when the lithosphere is sufficiently thin ($\lesssim 80$ km) and mantle water contents are sufficiently high ($\gtrsim 100$ ppm). The distribution of volcanism across the Middle East, Arabia and Africa north of equator suggests that it results from such spoke pattern convection.