We tackle the problem of non-global convergence in seismic velocity model building. We develop a modified approach for tomographic full waveform inversion (TFWI) that allows us to avoid the initially proposed nested-loop scheme and reduce the number of inversion parameters. We use the variable projection method to ensure accurate matching between predicted and observed data. By doing so, we control the cycle-skipping behavior of the data fitting term by letting the regularization term (on which we have better control) guide our objective function. We compare our method to conventional full waveform inversion (FWI) on two examples. We show convergence on a reflection problem in which FWI also converges to the true solution, and global convergence on a transmission test for which FWI cycle-skips. Our proposed algorithm inverts all model scales simultaneously and does not require any frequency-continuation approach.


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