Physics-Informed Neural Networks (PINNs) for Wave Propagation and Full Waveform Inversions

We propose a new approach to the solution of the wave propagation and full waveform inversions (FWIs) based on a recent advance in deep learning called physics-informed neural networks (PINNs). In this study, we present an algorithm for PINNs applied to the acoustic wave equation and test the method with both forward models and FWI case studies. These synthetic case studies are designed to explore the ability of PINNs to handle varying degrees of structural complexity using both teleseismic plane waves and seismic point sources. PINNs' meshless formalism allows for a flexible implementation of the wave equation and different types of boundary conditions. For instance, our models demonstrate that PINN automatically satisfies absorbing boundary conditions, a serious computational challenge for common wave propagation solvers. Furthermore, a priori knowledge of the subsurface structure can be seamlessly encoded in PINNs' formulation. We find that the current state-of-the-art PINNs provide good results for the forward model, even though spectral element or finite difference methods are more efficient and accurate. More importantly, our results demonstrate that PINNs yield excellent results for inversions on all cases considered and with limited computational complexity. We discuss the current limitations of the method with complex velocity models as well as strategies to overcome these challenges. Using PINNs as a geophysical inversion solver offers exciting perspectives, not only for the full waveform seismic inversions, but also when dealing with other geophysical datasets (e.g., MT, gravity) as well as joint inversions because of its robust framework and simple implementation.

Automated summary

We propose a new approach based on physics-informed neural networks (PINNs) to solve wave propagation and full waveform inversions (FWIs). PINNs are tested with forward models and FWI case studies, demonstrating their ability to handle various degrees of structural complexity and automatically satisfy absorbing boundary conditions. The formulation of PINNs allows for the seamless encoding of a priori knowledge of subsurface structures. Results show that PINNs provide good results for both forward models and inversions, with limited computational complexity. PINNs offer exciting perspectives for geophysical inversion problems and can easily be extended to other geophysical datasets and joint inversions.