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Full-waveform inversion is a cutting-edge methodology for recoveringhigh-resolution subsurface models. However, one of the main conventionalfull-waveform optimization problems challenges is cycle-skipping, usuallyleading us to an inaccurate local minimum model. A highly investigated track toalleviate this challenge involves designing a more global measure of misfitbetween the observed and modelled data beyond the sample-to-sample comparison.However, most of these approaches admit relatively smooth inversion results.Here, we introduce a novel misfit function based on the Fourier-based metric.This metric has been successfully applied in molecular physics for solving theBoltzmann equation, and we adapt it to full-waveform inversion. This misfitfunction exploits the power spectrum information between the modelled andobserved data to provide low-wavenumber velocity model updates early, and morehigh resolution updates as we approach the solution. Thus, it also can bereformulated as a weighted $\ell_{2}$-norm in a quadratic case, which can beseen as a simple extension for conventional full-waveform inversion. Thus,despite its robustness to cycle skipping, it is capable of deliveringhigh-resolution models synonymous to conventional FWI. Considering itsfrequency domain utilization, we refer to this inversion method as$\omega$-FWI. Through the synthetic Marmousi model example, this methodsuccessfully recovers an accurate velocity model, starting from a linearlyincreasing model even for the case of noisy observed data and the lack of lowfrequencies below 3 Hz and 5Hz, in which the conventional $\ell_{2}$-normfull-waveform inversion suffers from cycle skipping.

$\omega$-FWI: Robust full-waveform inversion with Fourier-based metric