Influence of heterogeneous thermal conductivity on the long-term evolution of the lower-mantle thermochemical structure: implications for primordial reservoirs

Abstract

Abstract. The long-term evolution of the mantle is simulated using 2D spherical annulus geometry to examine the effect of heterogeneous thermal conductivity on the stability of reservoirs of primordial material. Often in numerical models, purely depth-dependent profiles emulate mantle conductivity (taking on values between 3 and 9 Wm-1K-1). This approach synthesizes the mean conductivities of mantle materials at their respective conditions in situ. However, because conductivity also depends on temperature and composition, the effects of these dependencies on mantle conductivity are masked. This issue is significant because dynamically evolving temperature and composition introduce lateral variations in conductivity, especially in the deep mantle. Minimum and maximum variations in conductivity are due to the temperatures of plumes and slabs, respectively, and depth dependence directly controls the amplitude of conductivity (and its variations) across the mantle depth. Our simulations allow assessing the consequences of these variations on mantle dynamics, in combination with the reduction in thermochemical pile conductivity due to its expected high temperatures and enrichment in iron, which has so far not been well examined. The mean conductivity ratio from bottom to top indicates the relative competition between the decreasing effect with increasing temperature and the increasing effect with increasing depth. We find that, when depth dependence is stronger than temperature dependence, a mean conductivity ratio >2 will result in long-lived primordial reservoirs. Specifically, for the mean conductivity profile to be comparable to the conductivity often assumed in numerical models, the depth-dependent ratio must be at least 9. When conductivity is underestimated, the imparted thermal buoyancy (from heat-producing element enrichment) destabilizes the reservoirs and influences core–mantle boundary coverage configuration and the onset of dense material entrainment. The composition dependence of conductivity only plays a minor role that behaves similarly to a small conductivity reduction due to temperature. Nevertheless, this effect may be amplified when depth dependence is increased. For the cases we examine, when the lowermost mantle's mean conductivity is greater than twice the surface conductivity, reservoirs can remain stable for very long periods of time, comparable to the age of the Earth.