Efficient Bayesian physics-informed neural networks for surface tomography via ensemble Kalman inversion

Abstract

Surface traveltime tomography is a widely used method to characterize the structure of the underground. However, conventional seismic tomography techniques often require a high-fidelity numerical forward model, which leads to significant computational burden and time consumption. In addition, the inverse problem in traveltime tomography is prone to ill-posedness and lacks uncertainty quantification for the inferred results. To tackle these challenges, we use an efficient approach that combines ensemble Kalman inversion (EKI) with Bayesian physics-informed neural networks (NNs). This method represents the traveltime field using an NN as a surrogate solution, effectively replacing the forward solver and enhancing inversion efficiency. The NNs' weights and biases are iteratively inferred using the EKI algorithm, leveraging its derivative-free and fast convergence property for efficient inference. Furthermore, the ensemble nature of the method enables informative uncertainty quantification of the inversion results. Experimental results demonstrate that our method can efficiently infer a relatively accurate velocity model, which can potentially serve as a good initial model for full-waveform inversion when dealing with complex models.