A large data set of surface-wave phase anomalies, body-wave travel times, normal-mode splitting functions and long-period waveforms is used to investigate the scaling between shear velocity, density and compressional velocity in the Earth's mantle. We introduce a methodology that allows construction of joint models with various levels of scaling complexity ( , ), in order to detect seismological signatures of chemical heterogeneity. We demonstrate that the datasets considered cannot be fit concurrently with a uniform ν or a positive and uniform ϱ throughout the mantle. The variance reductions to P-wave travel times and v P -sensitive modes are up to 40 percent higher with our preferred model of anisotropic shear and compressional velocity than the recent anisotropic shear-velocity model S362ANI+M, which was constructed assuming a uniform ν throughout the mantle. Several features reported in earlier tomographic studies persist after the inclusion of new and larger data sets; anti-correlation between bulk-sound and shear velocities in the lowermost mantle as well as an increase in ν with depth in the lower mantle are largely independent of the regularization scheme. When correlations between density and shear-velocity variations are imposed in the lowermost mantle, variance reductions of several spheroidal and toroidal modes deteriorate by as much as 40 percent. Recent measurements of the splitting of 0 S 2 , in particular, are largely incompatible with perfectly correlated shear-velocity and density heterogeneity throughout the mantle. A way to significantly improve the fits to various data sets is by allowing independent density perturbations in the lowermost mantle. Our preferred joint model consists of denser-than-average anomalies (∼1 % peak-to-peak) at the base of the mantle roughly coincident with the low-velocity superplumes. The relative variation of shear velocity, density and compressional velocity in our study disfavors a purely thermal contribution to heterogeneity in the lowermost mantle, with implications for the long-term stability and evolution of superplumes.