Quasi‐Global Search Behaviour of Large‐Step Gradient‐Based Optimization in Full Waveform Inversion

ABSTRACT

Full waveform inversion (FWI) iteratively updates the velocity model by minimizing the difference between observed and simulated data. However, because FWI typically relies on gradient‐based local optimizers, it is prone to cycle skipping when the initial velocity model is inaccurate and low‐frequency data are absent. In such cases, the mismatch between simulated and observed data can exceed half a wavelength, causing the optimization to converge to local minima. Inspired by optimization strategies in machine learning, we employ gradient‐based optimizers with relatively large step lengths, beyond the traditional local optimization limit, to promote a quasi‐global search behaviour. This strategy allows the inversion to first approach the global minimum in the shallow subsurface, where the problem is more linear and convex, while deeper updates behave more like a global search. As iterations proceed, the improved shallow model gradually facilitates convergence at greater depths. Synthetic and field data experiments demonstrate that this approach can still produce accurate velocity models even in the presence of significant cycle skipping, highlighting an important property of the FWI loss topology related to the propagation of information from shallow to deep.