Upwind, No More: Flexible Traveltime Solutions Using Physics-Informed Neural Networks

Abstract

Summary There have been numerous attempts to solve the eikonal equation, which can be broadly categorized as finite-difference and physics informed neural network (PINN) based approaches. While the former has been developed and optimized over the years, it still inherits some numerical inaccuracies and also scales exponentially with the velocity model size. More importantly, it requires upwind calculations to satisfy the viscosity solution. PINNs, on the other hand, has shown great promise due to several features allowing for higher accuracy and scalability than conventional approaches. We demonstrate a unique feature of PINNs solutions, specifically its flexibility resulting from the global nature of the neural networks functional optimization, allowing for functional gradients referred to as automatic differentiation. We highlight an important aspect of using our modelling scheme: overcoming the inability of conventional methods to handle large areas of missing information (gap) in the velocity model. We find empirically that the PINNs interpolation-extrapolation capability enables us to circumvent a scenario when traveltime modelling is performed on velocity models containing gaps. Such a capability is crucial when performing traveltime modelling using the global tomographic Earth velocity model.