Can we resolve 3D density heterogeneity in the lower mantle?

We reexamine the possibility of resolving 3D density structure in the mantl e, by performing test inversions using a dataset of well constrained degree 2 splitting coefficients. We show that degree 2 in V-s and V-p can be reso lved, and confirm that dlnV(s)/dlnV(p) >2.5 at depths > 2000km, indicating a chemical component to large scale heterogeneity. Models with rho positive ly correlated with V-s in the deepest mantle fit the data at least as well as those in which density and velocities are anti-correlated. However, some rough bounds on dln rho /dlnV(s) can be inferred. Models obtained from geo dynamic considerations are acceptable, in contrast to models with large neg ative (< -0.3) or positive (> 0.6) dln rho /dlnV(s) throughout the lower ma ntle. The most robust feature is a marked increase in dln rho /dlnV(s) at t he top of the lower mantle reaching a maximum around 1500 km.