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 (⁠ℓ2⁠) is commonly used; however, it is prone to local minima when high-quality initial guess and low-frequency data are unavailable. The Wasserstein-1 (⁠W1⁠) 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 W1 and Fourier metrics. Specifically, in the early stage of inversion, we apply greater weight to the W1 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.

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