Earth's Elastic and Density Structure from Diverse Seismological Observations

A large data set comprising normal-mode eigenfrequencies, quality factors and splitting functions, Earth's mass and moment of inertia, surface-wave phase anomalies and dispersion curves, body-wave arrivals and traveltime curves, as well as long-period waveforms is inverted to obtain the distribution of elastic properties, shear attenuation and density in the Earth's interior. We address three fundamental aspects of global seismology by reconciling and modeling data sets with several methodological improvements, such as accounting for radial and azimuthal anisotropy, development of better methods for crustal corrections, and devising novel regularization and parameterization schemes. In the first contribution, we incorporate normal-mode splitting functions with other seismological data sets to examine the variation of anisotropic shear-wave velocity in the Earth's mantle. Our preferred anisotropic model, S362ANI+M, has strong isotropic velocity anomalies in the transition zone while the anisotropy is restricted to the upper 300~km in the mantle. When radial anisotropy is allowed throughout the mantle, large-scale anisotropic patterns are observed in the lowermost mantle with v_SV > v_SH beneath Africa and South Pacific and v_SH > v_SV beneath several circum-Pacific regions. However, small improvements in fits to the data on adding anisotropy at depth leave the question open on whether large-scale radial anisotropy is required in the transition zone and in the lower mantle. We demonstrate the utility of mode-splitting data in reducing the tradeoffs between even-degree variations of isotropic velocity and anisotropy in the lowermost mantle. We then devise a methodology to detect seismological signatures of chemical heterogeneity using scaling relationships between shear velocity, density and compressional velocity in the Earth's mantle. Several features reported in earlier tomographic studies persist with 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 velocity scaling (nu=dlnv_S/dlnv_P) with depth in the lower mantle are found to be robust. Many spheroidal and toroidal modes are largely incompatible with perfect correlations between density and shear-velocity variations in the lowermost mantle. A way to fit concurrently the 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 this study disfavors a purely thermal contribution to heterogeneity in the lowermost mantle. In the third contribution, we introduce an approach to construct a 1-D reference model that is consistent with crustal heterogeneities and various asphericities in the Earth's mantle. We demonstrate that the crust contributes substantially to fundamental-mode dispersion curves when the nonlinear effects of its thickness and velocity variations are taken into consideration. We apply appropriate crustal corrections and perform several iterations to converge to our preferred radial model NREM1D, which is anisotropic in the upper mantle and smooth across the 220-km discontinuity for all physical parameters. Radial anisotropy in the shallowest mantle, with a maximum at ~150~km depth, is required to fit global averages of fundamental-mode Rayleigh and Love wave dispersion (25--250s). NREM1D also predicts arrival times of major mantle and core phases in agreement (+/- 0.5s) with a recent isotropic velocity model that was optimized for earthquake location. The new reference Earth model NREM1D introduced here is easily extendable due to its modular construction as a linear combination of radial basis functions and can be used for earthquake location, spherical-earth normal mode calculations, and as a starting model in studies of lateral heterogeneity.