Robust thermo-chemical inferences require self-consistent descriptions of bulk physical properties in terms of radial reference Earth models and lateral heterogeneity in terms of three-dimensional tomographic models. These complementary aspects of seismic imaging are typically considered in isolation since radial and tomographic models often employ divergent modeling approximations, discrepant observations and starting models. We introduce a new approach based on full-spectrum tomography that permits global tomographic models whose average structure is constrained using the sensitivity afforded by normal-mode eigenfrequencies, Earth's mass and moment of inertia. Additional constraints on both radial and lateral variations are afforded by a large and diverse set of observations comprising free-air gravity anomalies, surface-wave phase anomalies, body-wave travel times, normal-mode splitting functions and long-period waveforms.