Seismic Velocity Inversion Based on Physically Constrained Neural Networks

The propagation velocity of seismic waves is a crucial parameter in seismic exploration, encompassing the entire process of seismic data acquisition, processing, and interpretation. Traditional model-driven full-waveform inversion (FWI) methods, which rely on an initial velocity, suffer from low computational efficiency. Conversely, data-driven deep-learning (DL) approaches heavily rely on extensive training data and lack interpretability due to overreliance on training data for generalization. To address these challenges, we present a seismic velocity inversion network model that incorporates prior knowledge and constraints based on physical laws. The proposed approach involves constructing a data-driven inversion network with dual encoders and single decoder structure, enabling the learning of nonlinear mappings from seismic data to velocity models. By incorporating prior well-logging data and attention mechanisms, the inversion process is improved. In addition, a seismic forward modeling network based on recurrent neural networks (RNNs) is developed to solve the acoustic wave equation. Leveraging the advantages of parallel computing, the forward modeling process achieves fast calculations. The automatic differentiation algorithm in DL facilitates gradient calculations, specifically back propagation of the residuals to incorporate the physical constraints. Ultimately, the proposed seismic velocity inversion network combines the two network structures while incorporating the constraint of wave field extrapolation law. Numerical experiments demonstrate that this network exhibits advantages in terms of result accuracy and model generalization.