Soft Dynamic Time Warping Divergence As A Misfit Measure In Full Waveform Inversion

Summary

Full-waveform inversion finds a subsurface model that minimizes the misfit between modelled seismic data and observations. It’s well known that the L2-norm of the waveforms difference is prone to cycle-skipping due to the presence of local minima. We introduce the soft-dynamic time warping divergence distance as a misfit metric in FWI. This formulation contains a hyper-parameter (γ) that renders the functional differentiable, thereby enabling the adjoint state method to compute the FWI gradient. A large value of γ produces a smooth gradient but limits the basin of attraction in the inversion process. Contrary to soft-dynamic time warping, its divergence form is always positive, and its minimum exists only when the modelled trace matches the observed trace. We present its application to a synthetic dataset from the Marmousi model and a marine field dataset from offshore Australia.