Seismic tomography using variational inference methods

TL;DR

This paper demonstrates that variational inference methods can efficiently perform seismic tomography, providing accurate uncertainty estimates at a fraction of the computational cost of traditional Monte Carlo methods.

Contribution

It introduces the application of variational inference techniques, specifically ADVI and SVGD, to seismic tomography, offering a scalable alternative to Monte Carlo sampling for uncertainty quantification.

Findings

Variational methods produce accurate results comparable to Monte Carlo sampling.

They significantly reduce computational costs for large datasets.

Gradient computation efficiency is crucial for their success.

Abstract

Seismic 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 datasets 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 probabilistic results. In this study, we applied two variational methods, automatic differential variational inference (ADVI) and Stein variational gradient descent (SVGD), to 2D 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 variational inference methods can produce accurate approximations to the results of Monte Carlo sampling methods 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.