Robust Surface‐Wave Full‐Waveform Inversion Using a Sigmoid‐Modulated Instantaneous‐Phase Coherency Misfit

ABSTRACT Surface‐wave full‐waveform inversion (FWI) has emerged as a powerful technique for resolving high‐resolution S‐wave velocity ( V s ) structures in shallow seismic investigations. However, strong surface‐wave dispersion often exacerbates the cycle‐skipping problem, and field‐recorded wavefields are frequently affected by amplitude errors. To mitigate these challenges, we propose a misfit function that integrates an amplitude‐unbiased instantaneous‐phase coherency (IPC) measure with sigmoid modulation. The sigmoid function reshapes the objective function landscape by suppressing spurious local minima while preserving the robustness of phase‐based metrics against amplitude variations. Notably, this approach is straightforward to implement, as it directly builds upon the existing IPC framework and can be readily adapted to other misfit functions. Synthetic tests demonstrate that the proposed sigmoid‐modulated IPC misfit function significantly improves inversion convergence and enhances the recovery of deeper subsurface anomalies. Compared with conventional IPC‐based FWI, the modulated approach yields sharper anomaly boundaries and exhibits greater resilience to random noise, achieving lower relative percentage error (RPE) in noisy data scenarios. Application to a published field dataset from an archaeological site in Southern Germany further validates the method's robustness. Inversions with and without sigmoid modulation produce broadly consistent V s structures that align well with features independently confirmed by archaeological excavations. Although the high quality of the initial model limits the observable advantage of the modulated objective in this specific case, the sigmoid‐modulated IPC approach demonstrates faster convergence, reaching a lower misfit value within fewer iterations due to its improved objective function landscape. These findings confirm that the proposed method is a practical and reliable alternative for field‐scale surface‐wave FWI applications, particularly in environments prone to amplitude errors and cycle skipping.