SeparationPINN: Physics-Informed Neural Networks for Seismic P- and S-Wave Mode Separation

Accurate separation of P- and S-waves is essential for multicomponent seismic data processing, as it helps eliminate interference between wave modes during imaging or inversion, which leads to high-accuracy results. Traditional methods for separating P- and S-waves rely on the Christoffel equation to compute the polarization direction of the waves in the wavenumber domain, which is computationally expensive. Although machine learning has been employed to improve the computational efficiency of the separation process, most methods still require supervised learning with labeled data, which is often unavailable for field data. To address this limitation, we propose a wavefield separation technique based on physics-informed neural networks (PINNs), which leverage automatic differentiation to compute partial derivatives. We formulate the P- and S-wave separation equations as loss functions to train a neural network (NN) that learns functional solutions to these equations. The network takes spatial coordinates as input and outputs the corresponding separated P- and S-wavefields. Once trained, it enables near-instantaneous evaluation of the separated wavefields at any spatial location. This unsupervised machine learning approach applies to unlabeled data. Numerical tests demonstrate that the proposed PINN-based separation method can accurately separate P- and S-waves in both homogeneous and heterogeneous media.