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A formalism is developed for the tomographic inversion of seismic travel time residuals. The travel time equations are solved both simultaneously, for velocity model terms and corrections to the source locations, and progressively, for each set of terms in succession. The methods differ primarily in their treatment of source mislocation terms. Additionally, the system of equations is solved directly, neglecting source terms. The efficacy of the algorithms is explored with synthetic data as we perform simulations of the general procedure used to produce tomographic images of Earth`s mantle from global earthquake data. The patterns of seismic heterogeneity in the mantle that would be returned reliably by a tomographic inversion are investigated. We construct synthetic data sets based on real ray sampling of the mantle by introducing spherical harmonic patterns of velocity heterogeneity and perform inversions of the synthetic data.

Imaging earth`s interior: Tomographic inversions for mantle P-wave velocity structure