High-resolution velocity model estimation with neural operator and the time-shift imaging condition

Extracting subsurface velocity information from seismic data is mainly an undetermined problem that requires injecting a priori information to constrain the inversion process. Machine learning has offered a platform to do so through the training process, as we formulate our training dataset to inject as much prior knowledge as possible in the trained ML model. Here, we use a neural-operator-based framework for high-resolution seismic velocity model building, which integrates Neural Operators with time-lag reverse time migration imaging. Unlike conventional full waveform inversion (FWI) methods that rely on iterative forward and adjoint-state computations, our approach learns a direct mapping from initial velocity models and extended seismic images to high-resolution velocity estimates through supervised learning. The network architecture enables mesh-independent generalization by learning mappings in infinite-dimensional function spaces, while synthetic velocity models and time-lag reverse time migration (RTM) images provide complementary high-frequency information critical for recovering mid- and high-wavenumber velocity components. Synthetic experiments demonstrate that the proposed method accurately reconstructs fine-scale structures and complex geologies, including out-of-distribution features such as salt bodies. Applications to real seismic field data acquired offshore Australia further validate the method's robustness and resolution capability. The predicted models show enhanced structural details and improved consistency with well-log data, outperforming traditional multi-scale FWI in both accuracy and computational efficiency. The entire prediction process is completed within seconds, making the proposed approach highly suitable for rapid and scalable velocity model building in practical exploration scenarios.