Insights Into the D'' Region From Analysis of a Thin Dense Layer Beneath a Convecting Cell

In this study we set up a simple model of the earth's D'' layer as a thin dense layer which is compositionally distinct from the lower mantle. The dominant external mechanism governing the flow within the layer and displacement of its upper boundary is assumed to be tractions acting on the upper surface of D'' resulting from the convecting mantle above. The Navier-Stokes equation is solved analytically and the resulting solutions analysed. Topography on the layer boundaries is predicted by balancing it against dynamic flow stress. A 2D finite element code is used, not only to confirm the results of the analysis but also to allow investigation of solutions with large boundary deflection. The nature of boundary topography depends on the magnitude of the driving tractions and the density variation within the layer. If we impose a variation such that the layer is most dense beneath areas of mantle downwelling and decreases to a minimum beneath areas of mantle upwelling then the upper boundary of D'' builds up into a cusp-like peak beneath the upwelling mantle. The size of this peak can potentially be several times greater than the layer depth. If, however, opposite density variations are imposed we can instead observe solutions where the layer is completely swept away beneath areas of mantle downwelling leaving steep-sided `islands' of dense material. The magnitude of the upper boundary driving tractions compared to the magnitude of density variations within the layer is a crucial parameter in determining the nature of flow in, and consequently boundary topography of, the layer. The deflection of the core-mantle boundary is small compared with that of the top of D'', but a change in sign in the ratio of these deflections is observed as the magnitude of the driving tractions changes relative to the magnitude of density variations. Seismic data of core-mantle boundary topography, D'' topography and lower mantle wave speed are compared to the predictions of the model and used to constrain model parameters.