We obtained likelihoods in the lower mantle for long-wavelength models of bulk sound and shear wave speed, density, and boundary topography, compatible with gravity constraints, from normal mode splitting functions and surface wave data. Taking into account the large uncertainties in Earth's thermodynamic reference state and the published range of mineral physics data, we converted the tomographic likelihoods into probability density functions for temperature, perovskite, and iron variations. Temperature and composition can be separated, showing that chemical variations contribute to the overall buoyancy and are dominant in the lower 1000 kilometers of the mantle.

Abstract. We present the results of generalized spectral fitting (GSF) regressions which estimate normal mode structure coefficients for the observable spheroidal and toroidal free oscillation multiplets below 3 mHz. The size, accuracy, and precision of our new catalogue of modal constraints make it a powerful new tool for assessing and refining three-dimensional Earth models. The estimates include more than 3100 coefficients for 90 multiplets and 25 pairs of coupled multiplets, including several deep mantle overtones previously obscured by fundamental modes. The coefficients constrain mantle structures of both even and odd spherical harmonic degrees, through degree 12 in some cases. Improvements in accuracy and precision have been achieved with three innovations: the development of GSF, an enhancement of the established spectral fitting technique which incorporates both Coriolis and structural coupling between multiplets; the application of G SF to an edited, high signal-to-noise and geographically diverse data set of more than 4500 seismograms from 33 high moment earthquakes; and the assignment of coefficient uncertainties using a Monte Carlo method to simulate the effects of seismic noise, theoretical errors, and coefficient covariances. The results of G SF are assessed by examining the internal consistency of estimated coefficients and through comparisons with recent mantle models. The new catalogue of structure coefficients and uncertainties is available as an electronic supplement to this paper and through the University of Colorado internet site.

The radial attenuation profile of the Earth is needed to account for dispersion effects when interpreting seismic velocities and can provide important constraints on composition. To date, most radial Q models have been produced using traditional damped inversions of free oscillation and surface wave data. Because such inversions can severely underestimate the model uncertainties that are needed to guide mineralogical and dynamic interpretation, and because the quality of data has continued to improve, we revisit this seismic inverse problem using a model space search approach already proven effective with similar data. We do, indeed, observe model uncertainties at least an order of magnitude greater than earlier estimates. At the same time, we find that Q is determined well enough to confirm that the data favor several important features previously disputed because of questions of consistency. These include shear attenuation that drops significantly in the lower third of the lower mantle and bulk attenuation that is negligible in the inner core but stronger in the outer core and lower mantle than suggested by most models. D

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Abstract.We present inversions for a new three-dimensional mantle v• model, MM2_L12D8, using a recently compiled catalogue of • 2300 normal mode structure coefficients for 90 multipiers below 3 mHz. These inversions demonstrate the capabilities and limitations of existing normal mode data and reveal new images of structures in the midmantle (900-1800 km depth), which is poorly resolved by surface wave and body wave data. Our inversions are distinguished both by efforts to maintain consistency with a variety of seismic models, and hence data sets, and by attempts to characterize the sensitivity of our model to the choice of damping, to unspecified structures, and to data errors. We find that sensitivity to damping is the dominant source of model uncertainty, but MM2_L12D8 proves to be a robust model of v• with amplitude uncertainties less than 35% for most depths and degrees. Other characteristics of MM2_L12D8 include X 2 misfit to normal mode structure coefficients which is 58% smaller than that of the best existing models, greater similarity to existing models than they have to each other, perturbations relative to existing vs models that are largest in the midmantle, and amplitudes that are most consistent with existing models that employ global, rather than local, basis functions. MM2_L12D8 also displays definite images of "slabs" and "plumes" in the midmantle and a spectrum of heterogeneity that is more continuous with depth than in most other models. These characteristics suggest that the midmantle participates in a very long wavelength pattern of circulation that involves at least the whole lower mantle. Inversions for Vp and p heterogeneities decorrelated from v• structure demonstrate that there is a significant signal from such structures in the normal mode data, but Vp and p models are much more sensitive to damping than are v• models. The normal mode catalogue must be expanded before normal mode models of Vp and p approach the reliability of the v• structures in MM2_L12D8. (This model, together with our catalogue of structure coefficients, is available at web site phys-geophys.colorado.edu/geophysics/nm.dir.)