FWI-WF: Robust full waveform inversion using hybrid Wasserstein-1 and Fourier metrics

The performance of full-waveform inversion (FWI) in constructing high-resolution subsurface models is closely related to the design of mismatch functions. The least-squares norm ([Formula: see text]) is commonly used; however, it is prone to local minima when high-quality initial guess and low-frequency data are unavailable. The Wasserstein-1 ([Formula: see text]) metric captures time shifts more effectively, but it may be plagued by imprecise deep structures. The Fourier metric leverages power spectra from simulated and observed data, offering higher-resolution updates near solutions. We develop a progressive waveform inversion method called FWI-WF using [Formula: see text] and Fourier metrics. Specifically, in the early stage of inversion, we apply greater weight to the [Formula: see text] metric for constructing a good background model and avoiding falling into local minima. Then, the Fourier metric gradually dominates to refine edges and deep structures, providing high-resolution inversion results. During the optimization process, we use automatic differentiation to improve inversion efficiency. Experimental results on three baseline geologic models indicate that FWI-WF outperforms three state-of-the-art methods.