Bayesian seismic tomography based on velocity-space Stein variational gradient descent for physics-informed neural network

In this study, we propose a Bayesian seismic tomography inference method using physics-informed neural networks (PINN). PINN represents a recent advance in deep learning, offering the possibility to enhance physics-based simulations and inverse analyses. PINN-based deterministic seismic tomography uses two separate neural networks (NNs) to predict seismic velocity and travel time. Naive Bayesian NN (BNN) approaches are unable to handle the high-dimensional spaces spanned by the weight parameters of these two NNs. Hence, we reformulate the problem to perform the Bayesian estimation exclusively on the NN predicting seismic velocity, while the NN predicting travel time is used only for deterministic travel time calculations, with the help of the adjoint method. Furthermore, we perform BNN by introducing a function-space Stein variational gradient descent (SVGD), which performs particle-based variational inference in the space of the function predicted by the NN (i.e., seismic velocity), instead of in the traditional weight space. The result is a velocity-space SVGD for the PINN-based seismic tomography model (vSVGD-PINN-ST) that decreases the complexity of the problem thus enabling a more accurate and physically consistent Bayesian estimation, as confirmed by synthetic tests in one- and two-dimensional tomographic problem settings. The method allows PINN to be applied to Bayesian seismic tomography practically for the first time. Not only that, it can be a powerful tool not only for geophysical but also for general PINN-based Bayesian estimation problems associated with compatible NNs formulations and similar, or reduced, complexity

Eikonal Tomography With Physics-Informed Neural Networks: Rayleigh Wave Phase Velocity in the Northeastern Margin of the Tibetan Plateau

We present a novel eikonal tomography approach using physics-informed neural networks (PINNs) for Rayleigh wave phase velocities based on the eikonal equation. The PINN eikonal tomography (pinnET) neural network utilizes deep neural networks as universal function approximators and extracts traveltimes and velocities of the medium during the optimization process. Whereas classical eikonal tomography uses a generic non-physics based interpolation and regularization step to reconstruct traveltime surfaces, optimizing the network parameters in pinnET means solving a physics constrained traveltime surface reconstruction inversion tackling measurement noise and satisfying physics. We demonstrate this approach by applying it to 25 s surface wave data from ChinArray II sampling the northeastern Tibetan plateau. We validate our results by comparing them to results from conventional eikonal tomography in the same area and find good agreement