Minimal upper mantle temperature variations consistent with observed heat flow and plate velocities

Abstract

The momentum equations applied to 5° block means are integrated from the observed surface plate velocities downward to a depth of 280 km, assuming no lateral heterogeneities in density or viscosity. It is assumed that 85% of the global heat production QG = 0.85 × 4.0 ×1013 W comes from below 280 km and that at this level the transfer is fully convective. A temperature field 7 is inferred at depth 280 km by minimizing the quantity∫|T− T0|n dS + nλ{QG−pC∫(T−T0)υrdS}, where the integrals are over the sphere, ρ is density, C is heat capacity, υr is radial velocity, T0 is a prescribed mean, and λ is a Lagrangian multiplier. Norms n, ranging from 1.5 to 2.5, are tried. The intervening temperature fields are then inferred, integrating the energy equation downward by using the previously calculated velocity field. This integration is subject to the limitations that the derivative of the temperature with respect to depth is everywhere sufficient to attain the fully convecting temperature, but never less than adiabatic. A surface heat flow based on observations plus age and tectonic setting is used. The principal inferences are: (1) the greatest lateral variations in temperature, ∼1000°C, occur with the top 20 km; (2) the greatest advection, ∼200°C/m.y., occurs within the top 20 km; (3) below 50 km, the greatest departures of temperature from the mean are negative “tongues,” reaching an extreme of about −800°C at depth 100 km; (4) below 50 km, heat transfer becomes more convective than conductive; (5) at the fully convecting level, 280 km, temperature variations are at least ±180°C about the mean. The principal defect in the entire calculation is unrealistically low temperatures arising from unrepresentatively low surface heat flows. The principal defect of the model probably arises from the assumption that all heat transfer at a depth of 280 km is representable by 5° means in velocity and temperature.