Bullen’s parameter η: a link between seismology and geodynamical modelling

Valuable information concerning the style of mantle density stratification can be gleaned from the spatial distribution of Bullen’s parameter. By means of numerical modelling of 2-D cartesian convection and by monitoring this with the 2-D field of the local Bullen’s parameter values, which were obtained by post-processing the convection results, we show that the local adiabaticity is seriously influenced by the presence of an endothermic phase transition at 670 km depth. In this situation the upper mantle suffers much more from non-adiabatic effects than the lower mantle. We have also employed the 3-D distributions of density and seismic velocities from the model of Ishii and Tromp based on free oscillation observations and constructed 3-D local Bullen’s parameter for a spherical Earth. In the lower mantle we find that there is a striking similarity in the range of magnitudes of the local Bullen’s parameter calculated from convection and those inferred from the splitting of seismic free oscillations. The morphologies of subadiabatic regions in the deep mantle under Africa and the central Pacific would suggest a thermal–chemical nature of the superplumes. Their vertical extent is limited to around 400 km above the core–mantle boundary (CMB). Underneath the Icelandic area in the North Atlantic such an subadiabatic region in the deep mantle above the CMB cannot be discerned. We conclude that the mantle is not as adiabatic as has commonly been held.