Acoustic Wave Equation Full Waveform Inversion Based on Optimal Transport and L₂ Norm Hybrid Weighting

Full waveform inversion (FWI) holds substantial potential for finely characterizing the velocity models of complex underground structures. However, conventional L₂-norm-based FWI is prone to cycle-skipping issues owing to local minima during the iterative process. The FWI algorithm, based on the 2-Wasserstein (W₂) distance from optimal transport (OT) theory, treats waveform data as probability distributions and calculates the OT cost between these distributions to measure differences, thereby enabling global matching and mitigating the impact of the local minima. Despite its advantages, this method suffers from low convergence efficiency in the later stages of inversion. To address this issue, this paper proposes a hybrid weighted FWI method based on the W₂ distance and L₂ norm. By introducing an adaptive weighting factor, this method leverages the global matching capability of the OT theory in the early stages of inversion, thereby reducing dependence on the initial model and addressing the issue of local extrema that arise with the L₂ norm when the initial model is inaccurate. In the later stages of inversion, this method minimizes the discrepancy between simulated and observed seismic records using the L₂ norm, overcoming the limitations of the OT theory, which tends to produce blurred structural delineations and poor convergence owing to its global matching nature. Model data experiments and actual data processing results demonstrate that the hybrid weighted objective function effectively combines the global constraint capability of the OT function on background velocity with the high convergence efficiency of the L₂ norm. This method is less dependent on the initial velocity model and achieves high-efficiency and high-precision inversion, making it suitable for complex structural models and actual seismic data processing.