A permutation that optimizes correspondence between the seismic data and the simulated data is computed using a graph space optimal transport formulation-based misfit. The seismic data or simulated data are transformed into auxiliary data by applying a portion of time shifts computed from the optimal permutation before updating the structural model of the explored underground formation. The full-waveform inversion minimization of the distance between auxiliary data and the seismic data or simulated data to which partial time shifts have not been applied, may be embedded in a Kantorovich-Rubinstein norm.