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SUMMARY We report finite-frequency imaging of the global 410- and 660-km discontinuities using boundary sensitivity kernels for traveltime measurements made on SS precursors. The application of finite-frequency sensitivity kernels overcomes resolution limits in previous studies associated with large Fresnel zones of SS precursors and their interferences with other seismic phases. In this study, we calculate the finite-frequency sensitivities of SS waves and their precursors based on a single-scattering (Born) approximation in the framework of travelling-wave mode summation. The global discontinuity surface is parametrized using a set of triangular gridpoints with a lateral spacing of about 4°, and we solve the linear finite-frequency inverse problem (2-D tomography) based on singular value decomposition (SVD). The new global models start to show a number of features that were absent (or weak) in ray-theoretical back-projection models at spherical harmonic degree l > 6. The thickness of the mantle transition zone correlates well with wave speed perturbations at a global scale, suggesting dominantly thermal origins for the lateral variations in the mantle transition zone. However, an anticorrelation between the topography of the 410-km discontinuity and wave speed variations is not observed at a global scale. Overall, the mantle transition zone is about 2–3 km thicker beneath the continents than in oceanic regions. The new models of the 410- and 660-km discontinuities show better agreement with the finite-frequency study by Lawrence & Shearer than other global models obtained using SS precursors. However, significant discrepancies between the two models exist in the Pacific Ocean and major subduction zones at spherical harmonic degree >6. This indicates the importance of accounting for wave interactions in the calculations of sensitivity kernels as well as the use of finite-frequency sensitivities in data quality control. 

Abstract In geophysical applications, solutions to ill‐posed inverse problems Ax=b are often obtained by analyzing the trade‐off between data residue ‖Ax−b‖2 and model norm ‖x‖2. In this study, we show that the traditional L‐curve analysis does not lead to solutions closest to the true models because the maximum curvature (or the corner of the L‐curve) depends on the relative scaling between data residue and model norm. A Bayes approach based on empirical risk function minimization using training datasets may be designed to find a statistically optimal solution, but its success depends on the true realization of the model. To overcome this limitation, we construct training models using eigenvectors of matrix ATA as well as spectral coefficients calculated from the correlation between observations and eigenvector projected data. This approach accounts for data noise level but does not require it as a priori knowledge. Using global tomography as an example, we show that the solutions are closest to true models.