Profiles of the Bullen parameter from mantle convection modelling

The state of adiabaticity in the mantle can be assessed by using the Bullen parameter profile derived from seismology. We have employed the extended-Boussinesq convection models in a cartesian 2-D domain to extract the Bullen parameter as a function of depth in both base heated and internally heated configurations and for both constant and variable thermal conductivity. We also studied models with depth-dependent thermal expansivity. Our results show that the values of the Bullen parameter for a Rayleigh number of 106 lie close to one, with sometimes excursions out to 0.9 and 1.1. They are sensitive to the mode of heating and the depth dependences of the thermal expansivity and changes of thermal conductivity. We obtained a subadiabatic geotherm above the lower boundary layer in all the models with constant thermal expansivity but a decrease of thermal expansivity with depth can result in a subadiabatic geotherm below the upper boundary layer. Thus the profiles of the Bullen parameter have a definite potential of being useful in constraining the physical parameters and flow structures associated with mantle convection.