Radial structure of the Earth: (I) Model concepts and data

Abstract

A framework is introduced for developing a radial reference model that incorporates diverse observations and techniques for improving the constraints on bulk Earth structure. This study describes new modeling concepts and reference datasets while features of the reference Earth model REM1D and geological interpretations are discussed in a companion manuscript. Recent measurements from various techniques have improved in precision and are broadly consistent, and are summarized as best estimates with uncertainties. We construct a reference dataset comprising normal-mode eigenfrequencies and quality factors, surface-wave dispersion curves, impedance constraints and travel-time curves from body waves, and astronomic-geodetic observations. Classical radial reference models do not account for the theoretical effects and observational biases resulting from heterogeneity in the crust and mantle. We address three issues that account for lateral variations in the modeling of average elastic, anelastic and density structure. First, current ray coverage of traveling waves is biased towards structure in the northern hemisphere, leading to faster velocities especially in the lower mantle. Second, horizontal wavelength of the heterogeneity that a traveling wave encounters is assumed to be much greater than that of the corresponding normal mode in most ray-theoretical and finite-frequency formulations of wave propagation. Effects of the full volumetric sensitivity on local eigenfrequencies and phase velocities that are ignored with this approximation exceed the data uncertainty for both fundamental spheroidal (Rayleigh waves, T $\ge$ 220 s) and toroidal modes (Love waves, T $\ge$ 120 s); waves at these longer periods cannot be modeled solely in terms of radial variations along the ray path. Third, non-linear effects from the strongly heterogeneous crustal structure are substantial for shorter-period waves (T $\le$ 100 s) and need to be accounted for while deriving radial models. After accounting for these issues on heterogeneity, rapid convergence for average structure is facilitated by utilizing a priori constraints from recent literature, analytical sensitivity kernels that account for physical dispersion, and a flexible parameterization comprising polynomial functions and cubic B-splines. By adopting a higher order polynomial for density than the elastic structure, artifacts that imply strong inhomogeneity and non-adiabaticity are avoided in potentially well-mixed regions like the outer core. Derivative properties like the gradient of bulk modulus with pressure (${\kappa }^{\prime }$ = $\mathrm{d\kappa }/\mathrm{dp}$) and the Bullen's stratification parameter $\left({\eta }_B\right)$ are adjusted in the core to match expectations from mineral physics without deteriorating the fits to reference datasets. A cubic polynomial parameterization in the lower mantle is adequate to capture possible changes in the gradients of the modulus ratio $\left(\mu /\kappa \right)$ associated with spin transitions in iron-bearing minerals. Radial reference models need to account for lateral heterogeneity and prior geological information in their construction to accurately represent the bulk average properties of a heterogeneous Earth.