Geophysical inversion and optimal transport

Sambridge, Malcolm; Jackson, Andrew; Valentine, Andrew P.

Abstract

We propose a new approach to measuring the agreement between two oscillatory time series, such as seismic waveforms, and demonstrate that it can be employed effectively in inverse problems. Our approach is based on Optimal Transport theory and the Wasserstein distance, with a novel transformation of the time series to ensure that necessary normalisation and positivity conditions are met. Our measure is differentiable, and can readily be employed within an optimization framework. We demonstrate performance with a variety of synthetic examples, including seismic source inversion, and observe substantially better convergence properties than achieved with conventional L2 misfits. We also briefly discuss the relationship between Optimal Transport and Bayesian inference.

Citation

Sambridge, M., Jackson, A., & Valentine, A. P. (2022). Geophysical inversion and optimal transport. Geophysical Journal International, 231(1), 172-198. https://doi.org/10.1093/gji/ggac151

• Journal Article Type: Article
• Acceptance Date: Apr 9, 2022
• Online Publication Date: Apr 22, 2022
• Publication Date: 2022-10
• Deposit Date: Apr 29, 2022
• Publicly Available Date: Apr 29, 2022
• Journal: Geophysical Journal International
• Print ISSN: 0956-540X
• Electronic ISSN: 1365-246X
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Volume: 231
• Issue: 1
• Pages: 172-198
• DOI: https://doi.org/10.1093/gji/ggac151
• Public URL: https://durham-repository.worktribe.com/output/1207436