Our primary tool for deciphering the inner workings of Earth and other rocky planets is through images derived from seismology. The primary objective of seismic imaging or tomography is to determine the elastic, anelastic, and density structure of the Earth from observations recorded at seismic stations. The problem can be described as a system of equations, or an inverse problem, to find models of seismic sources and Earth structure that reproduce most accurately the measured data. In global seismology, three classical concepts are typically used in the interpretation of recorded seismograms. The broadband body-wave arrivals (T 1–10 s) in the first few tens of minutes of a seismogram can be analyzed using ray-theoretical methods akin to geometrical optics. The large-amplitude, dispersed surface waves (T 25–250 s) arriving in the first few minutes to hours of a seismogram are analyzed using characteristics that describe a wave packet such as group and phase velocity. The third concept is that of free oscillations of the whole Earth that manifest as resonance peaks in the spectra of very long seismograms. The spectral peaks at the longest periods (T ≥ 250 s) are fingerprints of various types of standing waves in the whole Earth caused by a major earthquake. Recently, we pioneered full-spectrum tomography that employs all aforementioned data types along with complete seismic waveforms, while accounting for various theoretical complexities like anisotropy and attenuation.

Robust inferences about the interior 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. Full-spectrum tomography 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. Below are a growing set of models derived using this modeling philosophy.