Seismological Constraints on Lower-Mantle Convection

Depth profiles of density in modern one-dimensional seismological models of Earth’s interior appear to be inconsistent with the lower mantle convecting, at odds with compelling evidence to the contrary (e.g., estimates of Rayleigh number, and the relative lack of seismologically observed heterogeneity in the mid-mantle). This problem may stem from incorrect a priori constraints used in constructing the seismological models.

Normal-mode frequencies and waveforms for body and surface waves only provide weak constraints on the detailed density profile at depth. Therefore, starting with PEM and including PREM and AK 135-f, models have imposed an initial constraint that Bullen’s inhomogeneity parameter η ≈ 1 (“adiabatic,” consistent with the Adams-Williamson equation) or even < 1 (“super-adiabatic”). Here η ≈ K_S/K_E , the ratio of isentropic bulk modulus K_S to the effective dependence of density on pressure (hence depth), K_E.

Dispersion between normal-mode and body-wave frequencies, a necessary consequence of seismologically observed attenuation, requires K_E < K_S. In addition, internal heating, as expected from radioactive decay, causes the laterally averaged temperature profile to be subadiabatic in the core of the convection cell. Dynamic overshoot further causes a local deviation toward subadiabatic gradients above and below, respectively, bottom and top thermal boundary layers. Altogether, these effects are estimated to yield η ≈ 1.1 (± 0.05) for the bulk of the convecting lower mantle.

In fact, the earlier models 1066A and 1066B match the normal-mode frequencies and show just this pattern, with η ≈ 1.1 (± 0.1) between 1500 and 2500 km depth. Evidently, seismological observations are consistent with a convecting lower mantle, and refined density models should be explored by assuming that the bulk of the lower mantle is suitably “sub-adiabatic.”