Seismic Wavefields Modeling With Variable Horizontally Layered Velocity Models via Velocity-Encoded PINN

Seismic modeling is crucial for tackling waveform-based inverse problems in geophysics. Physics-informed neural networks (PINNs) have become a popular tool for simulating seismic waves. Their ability to incorporate partial differential equations (PDEs), initial conditions (ICs), and boundary conditions directly into the loss function allows for physically accurate modeling. The prevalent approach in the current literature treats the wave equation as a parametric PDE. However, the majority of the existing studies simulate wavefields for a specific velocity model, necessitating network retraining for different models, thereby diminishing modeling efficiency. In response, we present a velocity-encoded (VE) PINN (VE-PINN) that introduces feature parameters to represent various layered velocity models, integrating them into the network. Drawing inspiration from supervised learning, our approach employs a VE method to compute initial wavefields for variable layered models. Remarkably, our proposed VE-PINN demonstrates the ability to generalize across different ICs within the dataset. This eliminates the need to retrain the network for each new solution, offering significant efficiency gains. Numerical results show that the VE-PINN significantly enhances efficiency in solving the acoustic wave equation for various layered velocity models compared with finite-difference methods (FDMs). Subsequently, we extend the application of our method to time-domain simulation for variable source locations, demonstrating that the VE-PINN yields the results that are consistent with numerical wavefields.