Seismic Tomography Using Variational Inference Methods

Abstract

AbstractSeismic tomography is a methodology to image the interior of solid or fluid media and is often used to map properties in the subsurface of the Earth. In order to better interpret the resulting images, it is important to assess imaging uncertainties. Since tomography is significantly nonlinear, Monte Carlo sampling methods are often used for this purpose, but they are generally computationally intractable for large data sets and high‐dimensional parameter spaces. To extend uncertainty analysis to larger systems, we use variational inference methods to conduct seismic tomography. In contrast to Monte Carlo sampling, variational methods solve the Bayesian inference problem as an optimization problem yet still provide fully nonlinear, probabilistic results. In this study, we applied two variational methods, automatic differential variational inference and Stein variational gradient descent, to 2‐D seismic tomography problems using both synthetic and real data, and we compare the results to those from two different Monte Carlo sampling methods. The results show that automatic differential variational inference provides a biased approximation because of its implicit transformed‐Gaussian approximation, and it cannot be used to find generally multimodal posteriors; Stein variational gradient descent produces more accurate approximations to the results of Monte Carlo sampling methods. Both methods estimate the posterior distribution at significantly lower computational cost, provided that gradients of parameters with respect to data can be calculated efficiently. We expect that the methods can be applied fruitfully to many other types of geophysical inverse problems.