The viscosity of the mantle affects every aspect of the thermal and
compositional evolution of Earth's interior. Radial variations in
viscosity can affect the sinking of slabs, the morphology of plumes, and
the rate of convective heat transport and thermal evolution. Below the
mantle transition zone, we detect changes in the long-wavelength pattern
of lateral heterogeneity in global tomographic models, a peak in the the
depth-distribution of seismic scatterers, and changes in the dynamics
plumes and slabs, which may be associated with a change in viscosity. We
analyze the long-wavelength structures, radial correlation functions,
and spectra of four recent global tomographic models and a suite of
geodynamic models. We find that the depth-variations of the spectral
slope in tomographic models are most consistent with a geodynamic model
that contains both a dynamically significant phase transition and a
reduced-viscosity region at the top of the lower mantle. We present new
inferences of the mantle radial viscosity profile that are consistent
with the presence of such a feature.