Until now, modelling of three-dimensional (3-D) velocity variations in the mantle and topography of the transition zone discontinuities have been considered separately. Velocity models were obtained assuming that the radii of the discontinuities are constant. Then, the travel time data sensitive to the topography, such as the SS precursors, were corrected for the effect of 3-D seismic structure and inverted for depth variations of a discontinuity. Such a procedure is unsatisfactory, as it may introduce artefacts that could significantly affect the topographic results; the opposite trade-off is less likely to introduce conceptually important changes in the velocity distribution but should also be considered. In this study we bring together the same set of S -velocity sensitive data as used by Gu et al. and combine it with a large set of differential travel times of SS -S400S , S -S670S , and direct measurements of S400S -S670S . We formulate the inverse problem in terms of the volumetric (3-D) and topographic (2-D) perturbations for both the 400- and 670-km discontinuities. The best-fitting model of the joint inversion significantly improves the variance reduction of SS -S400S and SS -S670S residuals. The velocity distribution in the resulting model, TOPOS362D1, is very similar to that in model S362D1 (with correlation coefficients >0.9 throughout the mantle), which indicates that lateral variations of discontinuity depths have only minor influence on global modelling of velocity. Important changes, however, have been made to the topography of the 400- and 670-km discontinuities with respect to those obtained earlier assuming an existing velocity model. The overall undulation of the 400-km discontinuity is considerably less than that reported by earlier global studies; in TOPOS362D1 its maximum variation does not exceed 12 km. The strong degree-1 component before the joint inversion has decreased, such that the correlation between the velocities above the discontinuity and the shape of the discontinuity itself has substantially diminished. Spatially, this result means a significant diminution in the strength of the earlier reported depression of the 400-km discontinuity under the Pacific. The power spectrum of the topography of the 670-km discontinuity has been enriched in long wavelength component, especially in degree 2. The range of depth variations is +/-18 km and its shape correlates well with the radially averaged velocity perturbations in the transition zone. At wavelengths greater than 1000 km, there is little correlation between the depth perturbations of the 400- and 670-km discontinuities. The topography of the 400-km discontinuity does not appear to be strongly influenced by thermal structures potentially associated with subduction processes and plumes. This implies that thermal influence on the olivine alpha- to beta-phase transformation may not fully account for the observed depth variations; dynamical effects and potential variations in composition may be important near the top of the transition zone.
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