Multi-stage deep neural network fusion for hybrid optimization full waveform inversion

Full waveform inversion (FWI) has emerged as a powerful physics-based optimization technique for reconstructing subsurface parameters with high accuracy and resolution. Despite its strong theoretical potential, practical FWI remains challenging due to its sensitivity to the initial velocity model, limited low-frequency data, and strong nonlinearity that often leads to convergence toward local minima. To mitigate these challenges, this study presents a hybrid FWI strategy that focuses on the system integration of existing inversion components within a multi-stage deep learning strategy, combining re-parameterized FWI (indirect optimization component) with conventional FWI (direct parameter optimization component). Specifically, the inversion is performed in two coordinated stages. An indirect optimization stage first re-parameterizes the velocity model using a U-Net with the Mish activation function to recover low-frequency and large-scale structures, providing an improved starting model. This is followed by a direct parameter optimization stage based on conventional FWI to further refine high-frequency details and enhance resolution. The inversion process is driven by a hybrid loss function that combines seismic data misfit and feature misfit through adjustable weights. A loss-based threshold is used to enable multi-stage coordination, in which the first stage is primarily guided by the data-domain misfit to support effective feature extraction, while the second stage is dominated by the feature-domain misfit to stabilize the inversion and reduce redundant data-domain error evaluations, thereby balancing accuracy, efficiency, and stability. Numerical experiments on the Marmousi and Overthrust models demonstrate that the proposed method achieves high-accuracy, robust inversion without reliance on an initial model and offers improved computational efficiency compared with conventional methods. Furthermore, successful applications to land field seismic data validate the engineering feasibility and practical potential of the proposed approach.