Uncertainty-aware Frequency-domain Acoustic Full Waveform Inversion Using Gaussian Random Fields and Ensemble Kalman Inversion

Summary In recent years, full waveform inversion (FWI) research has increasingly focused on providing informative uncertainty estimates alongside inversion results. Bayesian inference methods-particularly Monte Carlo-based approaches-have been widely employed to quantify uncertainty. However, these techniques often require extensive posterior sampling, resulting in high computational costs. To address this challenge and enable efficient uncertainty quantification in FWI, we introduce an uncertainty-aware FWI framework-EKI-GRFs-FWI-that integrates Gaussian random fields (GRFs) with the ensemble Kalman inversion (EKI) algorithm. This approach jointly infers subsurface velocity fields and provides reliable uncertainty estimates in a computationally efficient manner. Specifically, we leverage the highly parallelizable nature and derivative-free nature of the EKI algorithm with an effective stopping criterion, making it suitable for large-scale inverse problems. Meanwhile, we incorporate prior knowledge of the spatial correlation via GRFs, enabling the generation of physically feasible initial ensembles for EKI. Numerical results demonstrate that EKI-GRFs-FWI yields reasonably accurate velocity reconstructions while delivering informative uncertainty estimates.