Uncertainty quantification in time-lapse full waveform inversion with Stein Variational Gradient Descent

Jinji Li, Kristopher A. Innanen

Seismic full-waveform inversion (FWI) is a critical technique for constructing high-resolution images of the Earth's subsurface, offering insights into geological structures and resource monitoring. However, the nonlinear characteristics of full-waveform modeling present substantial challenges in accurately assessing uncertainties in the resulting images. Variational Bayesian FWI offers a computationally efficient strategy to tackle these challenges by minimizing the Kullback–Leibler (KL) divergence between desired and current distributions. In this study, we conduct a feasibility analysis on a 2D time-lapse FWI problem, applying the Stein variational steepest descent (SVGD) method to approximate the posterior distribution of parameters using finite particles. Our analysis evaluates the method's performance across different scenarios, demonstrating better results with more extensive data acquisitions during monitor surveys. Additionally, utilizing the baseline posterior matrix in monitor inversions enhances convergence. Additionally, our study underscores the importance of using an optimal number of particles for distribution approximation to balance the computational efficiency with the estimation accuracy. This approach allows us to estimate posterior distributions effectively within manageable computational limits, facilitating potential extensions to larger datasets and broader 3D geological applications. However, the deterministic nature of this method introduces inherent limitations that warrant further investigation efforts.