Mantle flow induces dynamic topography at the core-mantle boundary (CMB), with distribution and amplitude that depend on details of the flow. To assess whether observations of CMB topography can give constraints on deep mantle structure, we determine CMB dynamic topography associated with different models of mantle convection, including thermochemical and purely thermal models. We investigate the influence of key controlling parameters, specifically the thermal viscosity ratio (Δη_T) and, for thermochemical models, the density contrast (Δρ_C) and viscosity ratio (Δη_C) between primordial and regular materials. In purely thermal models, plume clusters induce positive topography with an amplitude that decreases with increasing Δη_T. In thermochemical models with moderate density contrasts, around 100-200 kg m^-3, reservoirs of dense material induce depressions in CMB topography, surrounded by a ridge of positive topography. The average depression depth and ridge height increase with increasing Δρ_C and Δη_C, but decrease with increasing Δη_T. We find that for purely thermal models or thermochemical models with Δρ_C ∼ 90 kg m^-3 and less, the long-wavelength (spherical harmonic degrees up to l = 4) dynamic topography and shear wave velocity anomalies predicted by thermochemical distributions anticorrelate. By contrast, for models with Δρ_C ≥ 100 kg m^-3 and Δη_C > 1, long-wavelength dynamic topography and shear wave velocity anomalies correlate well. This potentially provides a test to infer the nature, that is, either purely or mostly thermal (Δρ_C ≤ 100 kg m^-3 m^-3) or strongly thermochemical (Δρ_C ≥ 100 kg m^-3), of the low shear wave velocity provinces observed by global tomographic images. The presence of post-perovskite, provided that its viscosity is similar to that of bridgmanite, does not alter these conclusions.