Differentiable Dynamic Time Warping Divergences In Full Waveform Inversion

Summary

We introduce soft-dynamic-time-warping-divergence and its sharp variant as misfit functionals in full- waveform inversion (FWI). These functionals maintain convexity for large model perturbations, making FWI less vulnerable to cycle-skipping. The sharp variant aims to remove the entropic regularization term from the warping process. Furthermore, both formulations depend on a hyperparameter that makes both functionals differentiable. Unlike soft-dynamic time warping, the proposed functionals attain their minima only when a modelled trace matches its observed counterpart.